text:
\section{Introduction}
The dynamics of many complex applications are described by a PDE model $F(u, k) = 0$,
with solution or state variables $u$ and parameters or control variables $k$.
Examples include all forms of wave scattering problems \cite{abdoulaev2005, bruckner2017},
various financial models \cite{kaebe2009, inthout2010}, etc. The forward problem,
i.e. solving the PDE for $u$ given the parameters $k$, is often well understood
and is in many cases solved fast and accurately by a numerical method. The inverse
problem, i.e. finding the parameters $k$ such that the solution $u$ matches a
set of observations $\wt{u}$ as best as possible, is, however, much more complicated
because these problems are typically ill-posed.

Let $H(k)\in\mbbC^{m\times n}$, $u\in\mbbC^n$, $f(k)\in\mbbC^m$ and $k\in\mbbC^l$
be such that
\begin{equation}\label{eq:discretePDE}
		H(k)u = f(k),
\end{equation}
is the discretized version of the PDE with the appropriate initial and boundary
conditions. If $\wt{u}\in\mbbC^p$ are the observations of the solution of the PDE
and assuming that $u$ is an implicit function of $k$, we consider the following
constrained optimization problem:
\begin{equation}\label{eq:constropt}
		\left\{\begin{aligned}
				\min_{k\in\mbbC^l}\mc{J}(k) &= \min_{k\in\mbbC^l}\underbrace{\left\|Lu - \wt{u}
						\right\|^2}_{\mc{D}(k):=} + \alpha\underbrace{\left\|k - k_0
						\right\|^2}_{\mc{R}(k):=}\\
				H(k)u &= f(k).
		\end{aligned}\right.
\end{equation}
Here, $\left\|\cdot\right\|$ denotes the standard Euclidian norm, $L\in\mbbR^{p
\times n}$ is a linear operator that maps the full solution $u$ of the PDE to
the observed output $\wt{u}$, $\mc{D}(k)$ is a discrepancy or residual term
measuring the mismatch between the model predictions $u$ and the observations
$\wt{u}$ and $\mc{R}(k)$ is the regularization term added in order to  place
certain constraints on the parameters, incorporate prior knowledge, suppress
numerical errors or guarantee that the problem is well-posed.

There are now two difficulties, the first of which is calculating the gradient
of $\mc{J}(k)$. This is necessary because many nonlinear optimization algorithms
use some form of gradient information, e.g. Newton's method, steepest descent, nonlinear
CG, etc \cite{nocedal2006}. However, approximating $\nabla \mc{J}(k)$ using finite
difference methods is inefficient when, for example, $k$ is very high dimensional
\cite{tortorelli1994}. In order to avoid this, the adjoint method can be used in
order to calculate the gradient at the cost of only one PDE solve \cite{tortorelli1994,
plessix2006, jadamba2017}. The second difficulty is choosing the regularization
parameter $\alpha\in\mbbR^+$. Since this parameter models the balance between
model fidelity ($\alpha\rightarrow 0$) and the regularity of $k$ ($\alpha\rightarrow+\infty$),
its value greatly influences the reconstruction. While many papers describe how
the adjoint method can be used to solve nonlinear inverse problems, often the
regularization parameter is chosen by trial-and-error or using the L-curve
\cite{calvetti1999, calvetti2004, hansen2010, vogel2002}. Recent examples of
this include \cite{bruckner2017, jadamba2017}. These approaches, however, require
the solution of the inverse problem for many different values of the regularization
parameter, which is inefficient, computationally expensive and may take a long
time for large scale problems.

In this paper we derive two methods that simultaneously solve the inverse
problem and determine a suitable value for the regularization parameter. The
first method we call ``generalized Newton-Tikhonov'' (GNT) and is a direct
generalization of the Generalized Arnoldi Tikhonov method (GAT) for linear inverse
problems \cite{gazzola2014_2, gazzola2014, gazzola2015}. However, as we will
demonstrate, GNT requires a number of redundant computations which were not
needed in the original GAT method. The second method we call ``regula falsi
generalized Newton-Tikhonov'' (RFGNT) and is a novel method based on
similar ideas, but with a number of advantages which make it more efficient
for nonlinear problems.

The outline of the paper is as follows. In \hypref{section}{sec:lip} we give
an overview of how the regularization parameter can be chosen and how this is
automatically done by the generalized Arnoldi-Tikhonv method. This method will then
be used as a basis for the GNT and RFGNT algorithms we derive in \hypref{section}
{sec:nlip}. We then apply our methods to an inverse scattering problem in \hypref{section}
{sec:numexp}, where we use the adjoint method for the gradient computations, and
compare our results with other known regularization approaches.

\section{Automatic regularization for linear problems}\label{sec:lip}

\subsection{Choosing the regularization parameter}
It is well known that when dealing with inverse problems and measured data some
form of regularization is necessary in order to find a good solution \cite{hansen2010,
vogel2002}. However, the regularization parameter $\alpha$ can greatly influence
the outcome since it determines the balance between fitting the model to the noisy
data and the regularization. If, on the one hand, $\alpha$ is too small, the
regularization will have little to no effect and the noise in the data will corrupt
the outcome of the algorithm. If, on the other hand, $\alpha$ is too large, this
will lead to a solution that no longer fits the data very well. It may also
have lost many small details and be what is referred to as ``oversmoothed''.

\begin{figure}[h]
		\centering
		\input{TikZ/LcurveDP}
		\caption{Sketch of the L-curve: the curve $(\mc{D}(k_\alpha),
				\mc{R}(k_\alpha))$ typically has a rough L-shape. The L-curve
				method proposes to use the regularization parameter which
				corresponds to the corner of the L. The discrepancy principle on the
				other hand uses the value that corresponds to the intersection of the
				curve and the vertical line at $\eta\varepsilon$. This value is typically
				slightly bigger \cite{hansen1992}}
		\label{fig:LcurveDP}
\end{figure}

Let $k_\alpha$ be the solution of \eqref{eq:constropt} for a fixed regularization
parameter $\alpha$ and $u(k_\alpha)$ the corresponding solution to the PDE
\eqref{eq:discretePDE}. One way of determining a good value for $\alpha$ -- and
illustrating its effect on $k$ -- is the L-curve, see \hypref{figure}{fig:LcurveDP}.
By solving the inverse problem \eqref{eq:constropt} for a whole range of values
for $\alpha$ and looking at the the curve
\[
		(\mc{D}(k_\alpha), \mc{R}(k_\alpha)) = \left(\left\|Lu(k_\alpha) - \wt{u}
				\right\|^2, \left\|k_\alpha - k_0\right\|^2\right),
\]
it can be observed that it is roughly L-shaped. Heuristically, a ``good''
regularization parameter is the one that corresponds to the corner of the L,
since this will balance model fidelity and regularization \cite{hansen2010, vogel2002}.

Another way of choosing the regularization parameter $\alpha$ is the discrepancy
principle \cite{vogel2002, gazzola2014_2, morozov1984}, i.e. choose the regularization
parameter such that
\[
		\mc{D}(\alpha) := \mc{D}(k_\alpha) = \eta\underbrace{
				\left\|Lu - \wt{u}\right\|^2}_{\varepsilon:=}.
\]
Here, $\varepsilon$ is called the error norm and $1\leq\eta$ is a
tolerance value. The motivation behind this choice is that decreasing the
discrepancy $\mc{D}(\alpha)$ below the error norm will not necessarily
improve the reconstruction and can lead to overfitting. The downside of the
discrepancy principle is that (an estimate of) $\varepsilon$ must be available.

\subsection{Generalized Arnoldi-Tikhonov}
The generalized Arnoldi-Tikhonov method was introduced in \cite{gazzola2014_2,
gazzola2014, gazzola2015} as a method to solve the classical Tikhonov problem for
linear problems of the form
\begin{equation}\label{eq:clasTik}
		\argmin_{x\in\mbbR^n}\left\|Ax - b\right\|^2 +
				\alpha\left\|x\right\|^2,
\end{equation}
with $x, b\in\mbbR^n$ and $A\in\mbbR^{n\times n}$. It is an iterative algorithm that
generates a sequence of approximations $x_0, x_1, x_2, \ldots$ that converge towards
the solution of \eqref{eq:clasTik}, while also updating the regularization parameter
in each iteration. This is done based on the discrepancy principle and the
current approximation of the solution. The method can best be understood by looking at the
discrepancy curve $(\alpha, \mc{D}(\alpha))$, see \hypref{figure}{fig:LcurveDPadj},
which can be seen as the analogue of the L-curve for the discrepancy principle.

\begin{figure}
		\centering
		\input{TikZ/Dcurve}
		\caption{Plot of the discrepancy as a function of the regularization parameter.
				When $\alpha$ is small the model fidelity will be very high, but due to the
				noise in the data can exhibit overfitting. By increasing $\alpha$ more
				emphasis is put on the regularization term and overfitting is reduced.
				The discrepancy will start to increase however.}
		\label{fig:LcurveDPadj}
\end{figure}

The idea behind GAT is to use the secant method in order to approximate the value of
$\alpha$ for which $\mc{D}(\alpha) = \eta\varepsilon$. The method is also a Krylov
subspace method based on the Arnoldi decomposition of the matrix $A$ \cite{saad2003,
vandervorst2003}. This means that the iterates for the solution of \eqref{eq:clasTik}
are given by
\[
		x_{\alpha, i} := \argmin_{x\in\mc{K}_i}\left\|Ax - b\right\|^2 + \alpha\left\|x\right\|^2,
\]
with
\[
		\mc{K}_i = \mc{K}_i(A, b) = \spn\left\{b, Ab, A^2b, \ldots, A^{i - 1}b\right\}
\]
the associated Krylov subspace of dimension $i$. In each iteration, a new basis vector
is added to the Krylov subspace and the iterates are updated in order to account for
this new basis vector. It is important to note that the constructed Krylov basis is independent
of the regularization parameter. This means that it can be stored and reused in the next
iteration when the regularization parameter is updated. In order to update the
current best estimate for the regularization parameter $\alpha_{i - 1}$, GAT assumes that
\eqref{eq:clasTik} is simultaneously solved without regularization, i.e. for $\alpha = 0$.
This means that the points $(0, \mc{D}(0))$ and $(\alpha_{i - 1}, \mc{D}(\alpha_{i - 1}))$
on the discrepancy curve are known and
the regularization parameter can be updated using one step of the secant method:
\[
		\alpha_i = \frac{\eta\varepsilon - \mc{D}(0)}{\mc{D}(\alpha_{i - 1}) - \mc{D}(0)}\alpha_{i - 1}
\]
Furthermore, instead of solving \eqref{eq:clasTik} to convergence each time the regularization
parameter is updated and calculate the value $\mc{D}(\alpha_{i - 1})$ exactly,
the inverse problem is solved in the currently constructed Krylov subspace. This means
that if
\[
		\mc{D}_i(\alpha) := \mc{D}(x_{\alpha, i}) = \left\|Ax_{\alpha, i} - b\right\|^2
\]
is the discrepancy after $i$ iterations -- or equivalently the discrepancy in the Krylov subspace $\mc{K}_i$
of dimension $i$ -- then the GAT update for the regularization
parameter is given by:
\begin{equation}\label{eq:alphaupdate}
		\alpha_i = \left|\frac{\eta\varepsilon - \mc{D}_i(0)}{\mc{D}_i(\alpha_{i - 1}) - \mc{D}_i(0)}\right|\alpha_{i - 1}.
\end{equation}
Then, once the discrepancy principle is satisfied, i.e. $\mc{D}_i(\alpha_{i - 1}) \leq\eta\varepsilon$,
the algorithm is stopped.

Note that the absolute value is added because now it is possible for both $\mc{D}_i(0)$
and $\mc{D}_i(\alpha_{i - 1})$ to be bigger than $\eta\varepsilon$, which can otherwise
result in negative values for the regularization parameter. This only happens in
the first few iterations when the constructed Krylov subspace is to small to contain
a good approximation for the solution. Since the constructed Krylov basis is
independent of $\alpha$, the fact that the regularization parameter is estimated
incorrectly in the first few iterations does not matter. It is typically
only when $\mc{D}_i(0)$ becomes smaller than $\eta\varepsilon$ that the estimates
start to improve. Finally, we remark that the value $\alpha = 0$ is chosen and fixed
for the secant updates because in this case the linear system that needs to be solved
is smaller and the method becomes equivalent to the GMRES algorithm \cite{saad1986}.
However, since the algorithm is stopped once the discrepancy principle is satisfied,
this may result in an underestimation of the regularization parameter.

\section{Automatic regularization for nonlinear problems}\label{sec:nlip}

\subsection{Generalized Newton-Tikhonov}
Although GAT is a Krylov subspace method for linear the linear Tikhonov problem,
the same idea can be used for nonlinear problems. The update for the regularization
parameter \eqref{eq:alphaupdate} can even be applied directly if we change the notation
back to our nonlinear problem. The only difference is how the iterates are calculated.
If we use Newton's method to solve \eqref{eq:constropt}
and $k_{\alpha, i}$ is the $i$th Newton iteration using a fixed regularization parameter
and $u(k_{\alpha, i})$ the corresponding solution to the PDE \eqref{eq:discretePDE}, then
the discrepancy after $i$ iterations is now given by
\begin{equation}\label{eq:nldiscrp}
		\mc{D}_i(\alpha) := \mc{D}(k_{\alpha, i}) = \left\|Lu(k_{\alpha, i}) - \wt{u}\right\|^2.
\end{equation}
An overview of this method, which we will call generalized Newton-Tikhonov (GNT),
is given in \hypref{algorithm}{alg:gnt}. This method should be seen as a direct
generalization of the GAT algorithm for nonlinear problems. As we will demonstrate
with our numerical experiments, the method can be used to solve our nonlinear inverse problem,
but it has a number of drawbacks that were not present in the original GAT method
for linear inverse problems.

\begin{algorithm}
		\caption{generalized Newton-Tikhonov (GNT)}\label{alg:gnt}
		\begin{algorithmic}[1]
				\State Choose initial $\alpha_0$, $k_0$
				\For{$i = 1, \ldots,$ maxIter}
						\State Calculate $k_{0, i}$ based on $k_{0, i - 1}$.
								\Comment{This requires 1 Newton step.$\:$}\label{alg:gnt:3}
						\State Calculate $k_{\alpha_{i - 1}, i}$ based on $k_0$.
								\Comment{This requires i Newton steps.}\label{alg:gnt:4}
						\State Calculate $\mc{D}_i(0)$ and $\mc{D}_i(\alpha_{i - 1})$ using \eqref{eq:nldiscrp}.
						\If{$\mc{D}_i(\alpha_{i - 1})\leq\eta\varepsilon$}
								\Break
						\Else
								\State Calculate $\alpha_i$ using \eqref{eq:alphaupdate}.\label{alg:gnt:9}
						\EndIf
				\EndFor
		\end{algorithmic}
\end{algorithm}

A first thing to note is that both GAT and GNT update the regularization parameter
based on the regularized and the non-regularized solution after a certain number of
iterations. For the non-regularized iterations, this means that in each GNT iteration
we need to perform one Newton step, see \hypref{algorithm}{alg:gnt} \hypref{line}{alg:gnt:3}.
However, when we wish to determine $k_{\alpha_{i - 1}, i}$, we cannot use previous
best approximation $k_{\alpha_{i - 2}, i - 1}$. This is
because the Newton iterations depend on $\alpha$, so we have to restart them from
$k_0$ and perform $i$ new Newton steps, see \hypref{algorithm}{alg:gnt} \hypref{line}{alg:gnt:4}. In the original GAT method for linear
problems this is not an issue, since the Krylov basis is independent from
the regularization parameter. Therefore, in each iteration only one new Krylov
basis vector has to be determined and added to the current basis. For GNT on the
other hand, in each iteration the regularized Newton iterations have to be restarted
and the number of Newton steps that needs to be computed increases each time. In order to
to perform $i$ GNT iterations, the number of Newton iterations needed is:
\[
		\underbrace{(1 + 1 + \ldots + 1)}_{i\text{ times \hypref{line}{alg:gnt:3}}} +
				\underbrace{(1 + 2 + \ldots + i)}_{i\text{ times \hypref{line}{alg:gnt:4}}}
				= \frac{i(i + 3)}{2}.
\]

Another thing to remark is that in the original GAT method the reason
for using $\alpha = 0$ as the second point for the secant step and not updating it,
is because for this choice of $\alpha$ the linear system that needs to be solved
is smaller and hence, easier to solve. To draw the parallel with the original method
we also use this value for GNT. However, for nonlinear problems there is no direct
benefit for using this value and if a better initial estimate for the regularization
parameter is available or if $\alpha$ must be larger than $0$ in order for the
inverse problem to be well posed, another value can be used. This might also improve
the quality of the estimate for the regularization parameter.

\subsection{Regula falsi generalized Newton-Tikhonov}
Two drawbacks of GNT are the increasing number of Newton iterations and the
fact that the value for the regularization parameter only slowly converges to
the value satisfying the discrepancy principle, which we will refer to as $\alpha^*$.
This can be seen in our numerical experiments, see \hypref{figure}{fig:details}, and
is explained by the fact that the secant update step for the regularization parameter
is done with a fixed point at $\alpha = 0$ and the discrepancy is only calculated
up to a limited number of Newton iterations, see \hypref{algorithm}{alg:gnt}
\hypref{line}{alg:gnt:9}. Therefore, in order to limit the total number of Newton iterations
and better approximate $\alpha^*$, we propose an alternative approach based on the
regula falsi method.

Assuming we have values $\alpha_0, \alpha_1\in\mbbR^+$ such that $\alpha_0\leq\alpha^*\leq\alpha_1$,
we determine the line between $(\alpha_0, \mc{D}(\alpha_0)$ and $(\alpha_1, \mc{D}(\alpha_1))$
and take $\alpha_2$ as the value for which this equals the discrepancy:
\begin{equation}\label{eq:alphaupdate2}
		\alpha_2 = \frac{\eta\varepsilon - \mc{D}(\alpha_0)}{
				\mc{D}(\alpha_1) -	\mc{D}(\alpha_0)}\left(\alpha_1 -
				\alpha_0\right) + \alpha_0
\end{equation}
We then solve \eqref{eq:constropt} with $\alpha_2$ to determine
$\mc{D}(\alpha_2)$ and replace either $\alpha_0$ or $\alpha_1$ with $\alpha_2$,
such that the interval $[\alpha_0, \alpha_1]$ will always contain $\alpha^*$.
Furthermore, in contrast to GNT, we will calculate $\mc{D}(\alpha)$ and
$k_\alpha$ exactly and not up to a limited number of iterations. This is justified
in the GAT algorithm, where due to the presence of a basis of the Krylov subspace
the discrepancy after $i$ iterations could be acquired at a low cost. However, as
we saw with GNT, this is no longer the case for nonlinear problems. In order to
limit the total number of required Newton iterations we will instead update the initial
guess for the Newton iterations every time $\alpha_2$ is updated. Similarly to the
regula falsi step for the regularization parameter, we take a weighted
linear approximation based on the solutions in $\alpha_0$ and $\alpha_1$, i.e.
$k_{\alpha_0}$ and $k_{\alpha_1}$, which were already calculated:
\begin{equation}\label{eq:k0update}
		k_{\alpha_2, 0} = \frac{\alpha_2 - \alpha_0}{\alpha_1 - \alpha_0}\left(
				k_{\alpha_1} - k_{\alpha_0}\right) + k_{\alpha_0}
\end{equation}
Then, once the value for $\alpha_2$ starts to converge, we terminate the algorithm,
see \hypref{algorithm}{alg:rfgnt} \hypref{line}{alg:rfgnt:9}.

An overview of this algorithm, which we call regula falsi generalized Newton-Tikhonov
(RFGNT), is given in \hypref{algorithm}{alg:rfgnt}. It should be noted that the only
difference between the updates for the regularization parameter in GNT and in RFGNT
is that in RFGNT $\alpha_0$ does not have the fixed value $0$. This also means that
when the initial interval $[\alpha_0, \alpha_1]$ does not contain $\alpha^*$, we
can update the interval based on the secant method until it does, i.e. $\alpha_0\leftarrow\alpha_1$
and $\alpha_1\leftarrow\alpha_2$ (or vise versa if $\alpha_2 < \alpha_1$).

\begin{algorithm}
		\caption{Regula falsi generalized Newton-Tikhonov (RFGNT)}\label{alg:rfgnt}
		\begin{algorithmic}[1]
				\State Choose initial $k_0$.
				\State Choose initial $\alpha_0$ and $\alpha_1$ such that $\alpha_0\leq
						\alpha^*\leq\alpha_1$.
				\State Calculate $k_{\alpha_0}$ and $\mc{D}(\alpha_0)$ by
						solving \eqref{eq:constropt} (starting with initial $k_0$).\label{alg:rfgnt:1}
				\State Calculate $k_{\alpha_1}$ and $\mc{D}(\alpha_1)$ by
						solving \eqref{eq:constropt} (starting with initial $k_0$).\label{alg:rfgnt:2}
				\For{$i = 1, \ldots,$ maxIter}
						\State Calculate $\alpha_2$ using \eqref{eq:alphaupdate2}.
						\State Calculate $k_{\alpha_2, 0}$ using \eqref{eq:k0update}.
						\State Calculate $k_{\alpha_2}$ and $\mc{D}(\alpha_2)$ by
								solving \eqref{eq:constropt} (starting with initial $k_{\alpha_2, 0}$).\label{alg:rfgnt:8}
						\If{$\left|\alpha_2 - \alpha_2^{old}\right|/\alpha_2^{old} < 10^{-3}$}\label{alg:rfgnt:9}
								\Break
						\Else
								\State $\alpha_2^{old}\leftarrow\alpha_2$
								\State Replace $\alpha_0$ or $\alpha_1$ with $\alpha_2$
										based on $\mc{D}(\alpha_2)$.
						\EndIf
				\EndFor
		\end{algorithmic}
\end{algorithm}

\section{Numerical experiments}\label{sec:numexp}

\subsection{Inverse scattering}
Consider the homogeneous Helmholtz equation
\[
		\left(\Delta + k^2\right)u_{tot} = 0.
\]
on a square domain $\Omega\subseteq\mbbR^2$ with exterior complex scaling (ECS) boundary
conditions and a spatially varying wave number $k:\Omega\longrightarrow\mbbR$.
We will assume that the total wave $u_{tot}:\Omega\longrightarrow\mbbC$ can be written
as the sum of an incoming wave and the resulting scattered wave:
\[
		u_{tot} = u_{in} + u_{sc}.
\]
If for multiple incoming waves of the form
\[
		u_{in}^\theta(x, y) = \euler^{ik_0(\cos\theta x + \sin\theta y)},
\]
the resulting scattered waves are given by $u_{sc}^\theta$, then this can be written
as one big system of equations:
\[
		\underbrace{\begin{pmatrix}\left(\Delta + k^2\right)\\&\left(\Delta + k^2\right)
				\\&&\ddots\\&&&\left(\Delta + k^2\right)\end{pmatrix}}_{\mc{H}:=}\begin{pmatrix}
				u_{in}^{\theta_1} + u_{sc}^{\theta_1}\\u_{in}^{\theta_2} + u_{sc}^{\theta_2}\\
				\vdots\\u_{in}^{\theta_t} + u_{sc}^{\theta_t}\end{pmatrix} =
				\begin{pmatrix}0\\0\\\vdots\\0\end{pmatrix}
\]
If we denote $u_{in} = \left(u_{in}^{\theta_1}, \ldots, u_{in}^{\theta_t}\right)^T$
and $u_{sc} = \left(u_{sc}^{\theta_1}, \ldots, u_{sc}^{\theta_t}\right)^T$, then
this is equivalent to
\begin{equation}\label{eq:constr}
		\mc{H}u_{sc} = \underbrace{\left(k_0^2 - k^2\right)u_{in}}_{\mc{F}:=}.
\end{equation}
For our numerical experiment, we will try to reconstruct the wave number $k$ based
on measurements of the scattered wave at the boundary $\delta\Omega$. If $Hu = f$
is the discrete version of \eqref{eq:constr}, $\wt{u}$ the measured values at $\delta\Omega$ and $L$
the restriction operator that maps the full solution $u$ on the discretized domain
to its values on boundary of the domain, then we get the following constrained minimization
problem:
\begin{equation}
		\left\{\begin{aligned}
				\min_{k\in\mbbR^n}\mc{J}(k) &= \min_{k\in\mbbR^n}\left\|Lu - \wt{u}
						\right\|_2^2 + \alpha\left\|k - k_0\right\|_2^2\\
				Hu &= f
		\end{aligned}\right.
\end{equation}

\subsection{The adjoint method}\label{sec:adj}
Because we will use Newton's method for the optimization in GNT and RFGNT, we
calculate the gradient of $\mc{J}(k)$ using the adjoint method. Let $\left<x\mid y\right>
= x^*y$ denote the complex inner product for $x, y\in\mbbC^n$ and $x^*$ the conjugate
transpose of $x$, then we can write the cost function as
\[
		\mc{J}(k) = \left<Lu - \wt{u}\left|Lu - \wt{u}\right.\right>
				+ \alpha\left<k - k_0\left|k - k_0\right.\right>.
\]
It follows that:
\begin{align*}
		\frac{\df\mc{J}}{\df k}\ =&\ \left<Lu - \wt{u}\left| L\frac{\df u}{\df k}
				\right.\right> + \left<\left.L\frac{\df u}{\df k}\right|Lu - \wt{u}\right>\\
		& +\alpha\left<1\left|k - k_0\right.\right> + \alpha\left<\left.k - k_0\right|1\right>\\
		=&\ 2\real\left(\left<L^*(Lu - \wt{u})\left|\frac{\df u}{\df k}\right.
				\right> + \alpha\left<\left.k - k_0\right|1\right>\right).
\end{align*}
The difficulty is now the derivative of the state variables with respect to the control
variables, i.e. $\df u/\df k$. In order to avoid needing to calculate this term, the
adjoint method introduces an adjoint variable $\lambda\in\mbbC^m$ as the solution of
\begin{equation}\label{eq:adjeq}
		H^*(k)\lambda = L^*\left(Lu - \wt{u}\right),
\end{equation}
where $H$ was the matrix representing the discretized PDE, see \eqref{eq:discretePDE}.
From \eqref{eq:discretePDE} it also follows that
\[
		\frac{\df H}{\df k}u + H\frac{\df u}{\df k} =	\frac{\df f}{\df k}.
\]
Substituting this into the derivative of $\mc{J}$, we can eliminate the term
$\df u/\df k$:
\begin{align*}
		\frac{\df\mc{J}}{\df k} &= 2\real\left(\left<H^*\lambda\left|\frac{\df u}
				{\df k}\right.\right> + \alpha\left<\left.k - k_0\right|1\right>\right)\\
		&= 2\real\left(\left<\lambda\left|H\frac{\df u}{\df k}\right.\right>
				+ \alpha\left<\left.k - k_0\right|1\right>\right)\\
		&= 2\real\left(\left<\lambda\left|\frac{\df f}{\df k} - \frac{\df H}{\df k}u
				\right.\right> + \alpha\left<\left.k + k_0\right|1\right>\right).
				\numberthis\label{eq:djdk}
\end{align*}
This means that the gradient of the cost function can now be evaluated in three steps:
\begin{enumerate}[i)]
		\item Given $k$, solve the original PDE, see \eqref{eq:discretePDE}, for $u$.
		\item Use $u$ to solve the adjoint PDE, see \eqref{eq:adjeq}, for $\lambda$.
		\item Evaluate the gradient $\df\mc{J}/\df k$ using \eqref{eq:djdk}.
\end{enumerate}
Note that solving the adjoint equation \eqref{eq:adjeq} is closely related to the
original PDE \eqref{eq:discretePDE} and that the cost of solving it will be similar.
This also means that we can evaluate the gradient of $\mc{J}(k)$ at the cost of
only one extra PDE solve per iteration. For more information on the adjoint method
we refer to \cite{tortorelli1994, plessix2006}.

\subsection{Newton-Krylov}
In order to solve the inverse problem \eqref{eq:constropt}, we will use an algorithm
based on the line search Newton-CG method described in \cite{nocedal2006}. This is
a Newton-Krylov method, where the parameters $k$ are updated using Newton's method, i.e.
\[
		k_{\alpha, i + 1} = k_{\alpha, i} + \gamma\Delta k,
\]
and the Hessian system for the Newton search direction $\Delta k$ is solved using a Krylov
subspace method, CG in this case \cite{nocedal2006, shewchuk1994}:
\[
		\nabla^2\mc{J}(k_{\alpha, i})\Delta k= -\nabla\mc{J}(k_{\alpha, i}).
\]
The CG iterations are stopped once the residual is smaller than
\[
		\min\left(0.5, \sqrt{\left\|\nabla\mc{J}(k_{\alpha, i})\right\|}\right)\nabla\mc{J}(k_{\alpha, i})
\]
or $\left\|\Delta k\right\| < 10^{-3}$. The line search will be a simple backtracking algorithm
starting from $\gamma = 1$ and halving this value until
\[
		\mc{J}(k_{\alpha, i} + \gamma\Delta k) < \mc{J}(k_{\alpha, i}).
\]
We terminate the Newton iterations once they start to stagnate, i.e.
\[
		\left|\frac{J(k_{\alpha, i + 1}) - J(k_{\alpha, i})}{J(k_{\alpha, i})}\right| < 10^{-3}
\]

It should be noted that each function evaluation comes at the cost of one PDE solve. Furthermore,
each CG iteration requires one matrix vector product with the Hessian. In order to
avoid this, a finite difference approximation can be used. Using a central difference
scheme the approximation is given by:
\begin{equation}\label{eq:hessapprox}
		\nabla^2\mc{J}(k)v\approx\frac{\nabla\mc{J}(k + hv) - \nabla\mc{J}(k - hv)}{2h}.
\end{equation}
This implies that each Newton iterations requires three gradient calculations.
Using the adjoint method, this is equivalent to three solves of the original PDE and three
solves of the adjoint PDE.  By replacing the central difference approximation of the Hessian matrix-vector product
 \eqref{eq:hessapprox} with a forward or backward difference approximation, this can
be reduced to two. It should be noted that the Hessian matrix-vector product can also be determined using the
second order adjoint method, see \cite{tortorelli1994, jadamba2017, wang1992}. For
simplicity we chose not to do so.

\subsection{Discretization}
The discretization of the Helmholtz systems in $\mc{H}$ is independent with respect
to the angle of the incoming wave. $H$ will therefore be a block diagonal matrix
with each block being a discrete version of the operator $(\Delta + k^2)$. For our
numerical experiment we take $\Omega = [-5, 5]^2$ and discretize it using a regular
$200\times 200$ grid with grid spacing $h$. We add a small buffer zone of 10 grid points
before the points where the measurements are taken and then add another 10 grid
points before the start of the complex tails for the exterior complex scaling.

\begin{figure}
		\centering
		\input{./TikZ/ECS}
		\caption{Exterior complex scaling in 1D: by adding complex tails to the domain
				and Dirichlet boundary conditions at the end of these tails, outgoing waves
				at the boundary $\partial\Omega$ can be simulated. The angle with respect
				to the real axis and how far the complex tails extend into the complex plain
				can be chosen.}
		\label{fig:ECS}
\end{figure}

The idea behind exterior complex scaling \cite{mccurdy2004} is to extend the domain
into the complex plane. By imposing Dirichlet boundary conditions at the end of
these complex ``tails'', outgoing waves at the boundary $\delta\Omega$ can be simulated.
Numerically we do this by adding points to the real domain (with the same spacing $h$)
and rotating them into the complex plane under a chosen angle, see \hypref{figure}{fig:ECS}.
We use 80 grid points for the complex tails -- one third of the real domain --
in each direction with an angle $\alpha = \pi/6$. This means that the full grid has size
$400\times 400$.

To discretize the Laplace operator we use second order finite differences, which on a
regular grid with spacing $h$, is given by the formula:
\begin{equation}\label{eq:discretelap}
		\begin{aligned}
				\Delta u(x, y)\approx&\phantom{+}\frac{u(x - h, y) - 2u(x, y) +	u(x + h, y)}{h^2}\\
																		&+\frac{u(x, y - h) - 2u(x, y) +  u(x, y + h)}{h^2}
		\end{aligned}
\end{equation}
However, because of the way the complex tails are constructed, the full grid is no
longer regular. Therefore, the general form for irregular grids has to be used.
Furthermore, we will assume that the wave number $k\in\mbbR^n$ with $n = 200^2$
is equal to a base value $k_0 = 1$ outside of $\Omega$. Inside the region of interest
itself we add an offset based on the sum of three Gaussian functions placed symmetrically
on a circle with radius $r = 2.5$:
\[
		k = k_0\sqrt{1 + \chi},
\]
with
\begin{align*}
		\chi(x, y) =&\ \euler^{-(x - r)^2 - y^2} + \euler^{-\left(x - r\cos\left(\frac{2\pi}{3}
				\right)\right)^2 - \left(y - r\sin\left(\frac{2\pi}{3}\right)\right)^2}\\
		&+\ \euler^{-\left(x - r\cos\left(\frac{4\pi}{3}\right)\right)^2 - \left(y -
				r\sin\left(\frac{4\pi}{3}\right)\right)^2}.
\end{align*}

In order to simulate the measurements, we generate incoming waves of the form
\[
		u_{in}^\theta(x, y) = \euler^{ik_0(\cos\theta x + \sin\theta y)}
\]
for $50$ different value of $\theta\in[0, 2\pi[$ and calculate the corresponding
scattered waves $u_{exact}\in\mbbC^{50\cdot 400^2}$. Taking into account the $10$ buffer
points we added, we have $876$ observations for every angle $\theta$, which we
select using the matrix $L\in\mbbR^{50\cdot 876\times 50\cdot 400^2}$, see \hypref{figure}{fig:scatwave}.
We then add random Gaussian white noise to generate the measurements
\[
		\wt{u} = Lu_{exact} + \sigma\left(e_1 + \im e_2\right)
\]
with $e_1$ and $e_2\sim\mc{N}(0, I_{50\cdot 876})$ and choose $\sigma$ such that the noise level
is approximately $10\%$:
\[
		\frac{\left\|Lu_{exact} - \wt{u}\right\|^2}
				{\left\|Lu_{exact}\right\|^2}\approx 0.10
\]
This resulted in a value $\sigma = 0.075$ and $\varepsilon = 492.7031$,
which we use for the discrepancy principle combined with $\eta = 1$. Because of the
diagonal structure of \eqref{eq:constr} we also do not construct the matrix $H$ explicitly,
but rather solve the $50$ Helmholtz systems for the different angles in parallel,
where each discrete version of the Helmholtz system $(\Delta + k^2)$ has size
$160000\times 160000$.

\begin{figure}
		\centering
		\includegraphics[width = 0.33\linewidth]{./Images/u_sc_real}\hspace{2.5pt}
		\includegraphics[width = 0.33\linewidth]{./Images/u_sc_imag}\hspace{2.5pt}
		\includegraphics[height = 0.33\linewidth]{./Images/colorbar}\\[2.5pt]
		\includegraphics[width = 0.49\linewidth]{./Images/u_sc_border_real}\hspace{2.5pt}
		\includegraphics[width = 0.49\linewidth]{./Images/u_sc_border_imag}
		\caption{Top: real and complex part of the scattered wave for
				$\theta = 86.4^\circ$ (left and right) on $\Omega$, including the 10 buffer points to
				where the measurements are taken. Bottom: real and complex values of
				the same scattered wave (left and right) at the measurement points.
				The measurements are ordered counter clockwise starting from
				the top left corner of the domain and the dashed lines correspond to the
				corners.}
		\label{fig:scatwave}
\end{figure}

\subsection{Results}
In order to test the GNT and RFGNT algorithms, we consider two other reconstruction
methods. The first is Newton's method without a regularization term, but with the
discrepancy as an early stopping criterion. The second is the L-curve approach.
We calculated 26 points on the L-curve for $\alpha\in[0, 0.5]$ and selected the one
with the smallest error with respect to the exact wave number. Since the D-curve is
another way of looking at the L-curve, we can also use these points to see whether
or not the regularization parameter found by GNT and RFGNT is correct. Also, for GNT
and RFGNT we solved the problem using a backward (B), a central (C) and a forward (F)
finite difference approximation for the Hessian matrix vector product in the CG
iterations. However, since there was little difference in the quality of the
reconstructions, the early stopping solution and L-curve solution were calculated only
for the forward finite difference approximation. The details of all the reconstructions
are listed in \hypref{table}{tab:results} and \hypref{figures}{fig:recs}
and \ref{fig:details} illustrate some of these results for the forward finite
difference scheme.

When comparing the different reconstructions, we see that there is little difference
between the finite difference schemes, except in the number of gradient evaluations
(and hence the number of PDE, adjoint PDE and Helmholtz solves). We also see that while
GNT finds a good solution for the inverse problem, it requires a lot more Newton iterations
to do so. This can also be seen when looking at the relative error and regularization
parameter in \hypref{figure}{fig:details}. Each time the Newton method is
restarted, progress is lost. While this approach was natural for linear problems
combined with a Krylov subspace method, it is inefficient for nonlinear problems.
The adaptations we made in order to derive the RFGNT method on the other hand seem to
be very effective. The method first needs to solve the problem for our initial choices
for $\alpha_0 = 0$ and $\alpha_1 = 1$, but due to the update of the initial estimate
for the Newton iterations, only 1 or 2 Newton iterations are needed afterwards for
\hypref{line}{alg:rfgnt:8} of \hypref{algorithm}{alg:rfgnt}. The convergence of the
regularization parameter is also drastically increased and by looking at the
discrepancy curve in \hypref{figure}{fig:details}, we see that the method
does indeed converge to the desired value for the regularization parameter.

When we compare GNT and RFGNT with early stopping, we see that the latter needs
less iterations before satisfying its stopping criterion. Then again, the early
stopping reconstruction has a much larger relative error than the other the
reconstructions. Using the L-curve approach, on the other hand, we find a
reconstruction that has the same quality as the GNT and RFGNT reconstructions.
However, while calculating a single point on the L-curve is cheaper than solving
the inverse problem with GNT or RFGNT, calculating all points the L-curve (26 in this case)
is much less efficient. This clearly illustrates the effectiveness off the automatic
regularization approach of RFGNT.

\begin{figure}
		\centering
		\includegraphics[width = 0.49\linewidth]{./Images/k_exact}\\[2.5pt]
		\includegraphics[width = 0.49\linewidth]{./Images/k_gnt}\hspace{2.5pt}
		\includegraphics[width = 0.49\linewidth]{./Images/k_rfgnt}
		\includegraphics[width = 0.49\linewidth]{./Images/k_es}\hspace{2.5pt}
		\includegraphics[width = 0.49\linewidth]{./Images/k_lcurve}
		\caption{Top: the exact wave number $k$. Middle left: GNT reconstruction.
				Middle right: RFGNT reconstruction. Bottom left: early stopping reconstruction.
				Bottom right: L-curve reconstruction.}
		\label{fig:recs}
\end{figure}

\begin{figure}
		\centering
		\includegraphics[width = 0.49\linewidth]{./Images/error}\hspace{2.5pt}
		\includegraphics[width = 0.49\linewidth]{./Images/alpha}\\[2.5pt]
		\includegraphics[width = 0.49\linewidth]{./Images/dcurve}\hspace{2.5pt}
		\includegraphics[width = 0.49\linewidth]{./Images/lcurve}
		\caption{Top left: the relative error of GNT and RFGNT in each Newton iteration.
				We can clearly see at which point GNT restarts its Newton iterations.
				Top right: The regularization parameter used in each Newton iteration.
				Bottom: D-curve and L-curve. The red line corresponds to the discrepancy
				value $\eta\varepsilon$ and the point with the lowest error w.r.t. the exact
				solution is marked with a red circle.}
		\label{fig:details}
\end{figure}

\begin{table}
		\centering
		\scalebox{0.89}{
				\begin{tabular}{l|l||c|c|c|c|c|c|c|c|c}
						\multicolumn{2}{l||}{} & \rot{Newton iterations}& \rot{CG iterations} & \rot{$\mc{J}$ evaluations} & \rot{$\nabla\mc{J}$ evaluations}
								& \rot{PDE solves} & \rot{Adjoint solves} & \rot{$(\Delta + k^2)$  solves} & \rot{Relative error} & \rot{$\alpha$} \\ \hline\hline
						\multirow[c]{2}{*}{B} & GNT           & 54  & 175 & 101 & 108 & 209  & 108 & 15850 & 0.0803  & 0.3431  \\ \cline{2-11}
																	& RFGNT 				& 21  & 73  & 44  & 42  & 86   & 42  & 6400  & 0.0746  & 0.3613  \\ \hline\hline
						\multirow[c]{2}{*}{C} & GNT           & 65  & 225 & 118 & 195 & 313  & 195 & 25400 & 0.0702  & 0.3398  \\ \cline{2-11}
																	& RFGNT 				& 21  & 72  & 44  & 63  & 107  & 63  & 8500  & 0.0746  & 0.3613  \\ \hline\hline
						\multirow[c]{4}{*}{F} & GNT           & 54  & 175 & 101 & 108 & 209  & 108 & 15850 & 0.0804  & 0.3429  \\ \cline{2-11}
																	& RFGNT         & 21  & 81  & 44  & 42  & 86   & 42  & 6400  & 0.0747  & 0.3613  \\ \cline{2-11}
																	& Early stopping & 3   & 7   & 8   & 6   & 14   & 6   & 1000  & 0.2089  & $\cdot$ \\ \cline{2-11}
																	& L-curve       & 9   & 37  & 20  & 18  & 38   & 18  & 2800  & 0.0871  & 0.1400  \\ \cline{2-11}
																	& L-curve (all) & 267 & 983 & 633 & 534 & 1167 & 534 & 85050 & $\cdot$ & $\cdot$
				\end{tabular}
		}
		\caption{Details from the different reconstructions for the different reconstruction
				methods and finite difference approximations for the Hessian matrix vector
				product in the CG iterations. The number of gradient evaluations is 2 or 3
				times the number of Newton iterations (depending on the finite difference
				scheme) which is equal to the number of solves of the adjoint PDE. The
				number of PDE solves is sum of the number of cost function evaluations
				and the number of gradient evaluations. The number of Helmholtz system solves
				is 50 times, i.e. the number of projection angles, the number of
				PDE and Adjoint solves.}
		\label{tab:results}
\end{table}

\section{Conclusion and remarks}
In this paper we describe two methods to solve a nonlinear inverse problem that
iteratively determine the solution and the regularization parameter. The first method,
generalized Newton-Tikhonov (GNT), is a direct generalization of the generalized
Arnoldi-Tikhonov method to nonlinear problems. However, this method turns out to
have a number of drawbacks that were not present in the original algorithm for linear
problems. In order to improve the method, we proposed the regula falsi generalized
Newton-Tikhonov method (RFGNT). We replace the secant update step from GNT with a
regula falsi approach and updating the initial guess for the Newton iterations with
every update of the regularization parameter. This decreases the number of Newton
iterations needed and finds a better value for the regularization parameter. Our
numerical experiments also show that this is computationally much more efficient than,
for example, calculating the L-curve or other grid based approaches to determine
the regularization parameter.

It should also be noted that in this paper we solve the PDE and the adjoint PDE
sequentially. By contrast, it is also possible to solve both simultaneously by
considering the Karush-Kuhn-Tucker conditions and using Newton's method combined
with a suitable preconditioner to find the optimum, see for example \cite{biros2005,
haber2000, haber2001, mardal2017}. The difficulty with this approach is finding a
suitable preconditioner for the problem, but it can easily be combined with the
proposed RFGNT method. This is because using this approach to solve the problem
for a fixed value of the regularization parameter $\alpha$ corresponds to
calculating $k_\alpha$ and $\mc{D}(\alpha)$, i.e. \hypref{lines}{alg:rfgnt:1},
\ref{alg:rfgnt:2} and \ref{alg:rfgnt:8} of \hypref{algorithm}{alg:rfgnt}.

Furthermore, although we used an inverse scattering problem as a test problem to
demonstrate the methods, no specific properties of this problem were used to derive
the methods and they are likely to be effective in many other inverse problems.
Future work therefore includes more in-depth analysis of the robustness of the methods
and its use in other application. We did, for example, not use any preconditioner
for the solution of the Helmholtz problem or the inner CG iterations. However,
there has been done many interesting work concerning preconditioners for the
Helmholtz equations using multigrid methods \cite{cools2013, erlangga2006}. Including
these in the optimization procedure could reduce the number of required solves
of the Helmholtz equation and CG iterations. Another possible issue is the fact
that since Newton can only be used for local minimization a proper initial
estimate needs to be determined.

\section*{Acknowledgement}
The authors wish to thank the Department of Mathematics and Computer Science,
University of Antwerp, for financial support.

\section*{References}
\bibliographystyle{elsarticle-num}

redpajama_set_name: RedPajamaArXiv


text:
Nitocris puede referirse a:

 Nitocris, última reina de la dinastía VI de Egipto.
 Nitocris I, Divina Adoratriz de Amón.
 Nitocris de Babilonia, reina de Babilonia, hija de Nabucodonosor II.

redpajama_set_name: RedPajamaWikipedia


The property BK-26625 is a 44 square meter resale condo with 1 bedroom and 1 bathroom that is available for sale. It is part of the Noble BE33 project in Watthana, Bangkok and is scheduled for completion in 2019 Jan. You can buy this condo for a base price of ฿11,900,000 (฿272,187/Sq.M).
I am interested in unit BK-26625 at Noble BE33. Please send me more details.
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The information being provided by The Nation about this 1 bed condo in Watthana (BK-26625) that is available for sale is for the visitor's personal, non-commercial use and may not be used for any purpose other than to identify prospective condo visitor may be interested in buying 1 bed condos. Any information relating to this sales condo referenced on this web site comes from the Internet Data Exchange program defined by The Nation. This web site may reference condo listing(s) that are for sale and held by a brokerage firm other than the broker and/or agent who owns this web site. Any information relating to a condo that is for sale, regardless of source, including but not limited to square footages, lot sizes and sales price, is deemed reliable but not guaranteed and should be personally verified through personal inspection by and/or with the appropriate professionals. The data contained herein is copyrighted by The Nation and is protected by all applicable copyright laws. Any dissemination of this information is in violation of copyright laws and is strictly prohibited.


At sixteen, Tommy MacNeill and Beth Renshaw fell in love, the kind of love that was innocent and filled with promise. It felt hopeful and hope was something Tommy and Beth desperately wanted to hold on to in a place like St. Jude's Home for Court Placed Juveniles, more appropriately called St. Joke's. But then one fateful night stole all that hope away, sending the two of them and their friends scattering in very different directions, with everyone owing a debt to someone you wish you owed nothing to...it's a debt that won't be called in until seven years later.
When Tommy and Beth see each other again, it's under very different circumstances than the ones they were forced to live with as teenagers. He bears physical scars while hers are hidden but manifest in ways that make it clear just how damaged she is. She's a famous singer and he's a mason...turned kidnapper. The last thing that they need is to reconnect, especially since being together brings back memories--both good and bad. Theirs is a connection that's never been easy to ignore, but so is someone who's come back to demand payment on all debts.
Lost Without You is the first full-length novel in bestselling author M. O'Keefe's The Debt duet. This book also contains the free prologue, The Debt, which was released a couple of weeks ago, so feel free to skip forward to the rest of Tommy and Beth's story if you've already read the novella, which is what I did. My first M. O'Keefe read was the first in a romantic suspense series of hers, one that had her switching from "Molly O'Keefe" to just having her first initial with the rest of her name. I was impressed with her writing then and I've remained hooked ever since.
There's nothing easy about Tommy and Beth's love story, especially since it was so innocent once upon a time, only to be tarnished by what happened to them in St. Joke's. Seven years later, they lead very different lives, but the shadow of their time in the home that felt anything but is still there, although neither one acknowledges that dark part of their lives. Their reunion is awkward, and their feelings for one another are a jumble of confusing thoughts and emotions, although Tommy seems to be far more attached to what they once shared since Beth buried it away.
Purchase Lost Without You on Amazon | B&N | iBooks | Kobo.


On 3 March 2017 in Sydney (and streamed live to Melbourne), AUSTRAC hosted the launch of Fintel Alliance - a world-first private-public partnership to combat money laundering and terrorism financing. It was formally launched by the Minister for Justice, the Hon Michael Keenan MP.
Launch attendees included senior executives of the banking and financial sector, law enforcement agencies, academia, and members of the media. The MC was Alex Malley, Chief Executive of CPA Australia and host of the Nine Network's 'In Conversation'.
Established by AUSTRAC, Fintel Alliance is a historic milestone involving industry and government agencies co-designing solutions that will transform the fight against terrorism financing and organised crime. It will also focus on developing 'smarter regulation', including streamlining the anti-money laundering and counter-terrorism financing (AML/CTF) regulatory framework for industry.
Below are the Fintel Alliance media kit and video 'A day in the life of Fintel Alliance'.


text:
La Santa Maria di Merino è un'antica statua lignea di Maria che è conservata a Vieste; la città pugliese è affidata al suo patronato, insieme a quello di San Giorgio.

La tradizione narra che la statua (anche se diverse fonti ci dicono che la statua è risalente alla fine del '500) della Beata Vergine venne rinvenuta sulla spiaggia della frazione viestana di Merino da alcuni pescatori, intenti in una battuta di pesca. Essendo la località di Merino, esattamente a metà strada tra Vieste e Peschici, si decise di mettere la statua su un carro di buoi, questi presero la direzione di Vieste, cosicché i pescatori viestani se ne impossessarono.  In quel luogo venne costruito il Santuario di Santa Maria di Merino, una chiesa tuttora esistente il cui nucleo più antico risale al secolo XI-XII, scomparso in seguito ad un maremoto. A questo santuario è legato anche un episodio di papa Celestino V, che qui avrebbe trovato rifugio prima di essere riconosciuto a riportato ad Anagni il 10 maggio o 16 maggio 1295.

Successivamente, quando la popolazione si trasferì in gran numero a Vieste, anche la statua di Maria venne portata all'interno della città, nella Cattedrale dell'Assunta. Della statua non si ha alcuna notizia, è molto probabile che facesse parte di un carico che da Bisanzio fosse diretto a Venezia. La statua è ancora esistente, ha resistito a moti, saccheggi, terremoti ed incendi, ed è custodita nella Cattedrale di Vieste. Recentemente è stata portata nell'Istituto di Belle Arti di Bari per essere restaurata.

Il luogo del santuario coinciderebbe con il sito della antica città di Merinum. Gli scavi iniziati nel 1938 non sono stati mai conclusi e quanto era stato scoperto i contadini dell'epoca lo hanno riseppellito, tuttavia i resti di una villa Romana visibili ancora oggi confermano la presenza di insediamenti umani di epoca paleocristiana. La supposizione dell'esistenza di una vera e propria "città di Merinum" è  da attribuirsi ad una controversa citazione dell'opera " Naturalis Historia" di Plinio il Vecchio,  in cui si fa riferimento del popoli Merinate del gargano "Merinates ex Gargano",  dalla città di Merinum, (anche se alcune versioni riportano l'iscrizione "Metinates").

La festa patronale ricorre il 9 maggio: in quel giorno si forma una processione di fedeli che portano a spalla la venerata immagine fino all'antico santuario, luogo del ritrovamento.

Note

Maria di Merlino
Vieste


text:
Buyandship, an affordable way for online shoppers to ship parcels from the world, just launched in Australia
Customers can choose Buyandship for international shipping and deals, products, and exclusives from overseas merchants
Buyandship
SYDNEY, Nov. 14, 2019 /PRNewswire/ -- Buyandship, a cross-border e-commerce shipping services company based in Hong Kong, recently launched in Australia to offer worry-free international mail forwarding services to Australian online shoppers.
Founded in 2014, Buyandship provides global shipping services for e-commerce customers. They can choose the firm for international shipping and deals, products, and exclusives from overseas merchants. Customers can pay AU$22 for the first 2 pounds, and AU$9 per pound after the first 2 pounds in shipping fees, and receive parcels at home. Using the service, the parcels are fully tracked from end to end with an average delivery time of 7-12 working days from the arrival to the warehouse.
It currently operates collection and export warehouses in the US, the UK, Italy, Australia, Japan, South Korea, Thailand, Mainland China, Taiwan and Hong Kong. Scheduled flights from these warehouses back to Hong Kong are arranged on a weekly basis, while the delivery fee will be based on the parcel's actual weight (not parcel size).
Back in June this year, Buyandship has secured US$2.2 million in pre-Series B funding round led by existing investor Infinity Venture Partners. Other investors include Asia-focussed VC firm SQ Capital and unnamed strategic angel investors, besides Buyandship's key management. The money will be used to improve operational efficiencies and for market expansion.
After closing its Series A funding in mid-2017, it has expanded into Mainland China, Macau, Taiwan, Japan, India, Malaysia, Singapore, and the UAE. It boasts of more than 430,000 users.
Buyandship has already signed agreements with eBay, StockX, GLADD, Drop, and other merchants to support their Asia expansions.
As per a 2018 Australia Country Commercial Guide by Export.gov, 21% of Australians purchased products from international sellers in 2017, while 40% of goods were purchased from America, 32% came from Mainland China, and 22% from the U.K., mainly due to the increased product offerings from overseas merchants and cheaper prices. A recent industry report released by Australia Post, indicates that a quarter of Australia's cross-border purchases were Fashion related, followed by Consumer Electronics (17%) and Healthy & Beauty (15%).
Wilson Chan, Co-founder, and CEO of Buyandship, says that the majority of its users are primarily motivated by the enormous difference in prices: "Buying a Dyson cleaner on Australian online store costs around AU$800, but less than AU$450 from an overseas online store. At a discount rate of nearly 45 percent, customers naturally prefer to shop from overseas stores."
"Our goal is to build a borderless, international e-commerce network for our users, so they can easily and comfortably enjoy the best bargains from around the world through our service. When they need a cutting-edge, forward-thinking e-commerce logistics service, they think of Buyandship," he added.
Source: Buyandship
https://au.buynship.com
Keywords: Computer/Electronics Electronic Commerce Maritime/Shipbuilding Transportation
Cross-border e-commerce shipping startup Buyandship raises US$2.2M
Sino-Global Sign JV Agreement with Shanming Liang
Elbit Systems Successfully Demonstrates High-Altitude High-Precision Aerial Firefighting Solution
Beezy secures a $16M senior secured credit facility from Goldman Sachs Merchant Banking Division to transform Employee Experience in the Enterprise

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UK, Covid-19 passports not ruled out for clothing stores after June 21
Vaccination certificates will not be needed for clothing stores.
The British government has not ruled out the possibility that Covid-19 passports will be needed in clothing stores after June 21.
Prime Minister on Covid-19 passports
The government is considering Covid certificates, which indicate whether someone has been vaccinated, recently been tested, or developed immunity through a recent infection, but Prime Minister Boris Johnson said a decision had yet to be made and that would not come into effect during the next two stages of easing the lockdown in England.
However, when asked if they might be needed in clothing stores after the final easing stage, a Downing Street spokesperson decided not to rule it out.
Speaking to The Independent, they said: "We have been clear that we will not require them as businesses reopen in stages two and three of the roadmap.
But again, the Prime Minister was clear that longer term there will some essential services such as essential retail and public transport where they will not be required."
The government said such certificates could "provide reassurance", but such a move would be controversial as the Labor Party's shadow health secretary Jonathan Ashworth called them "discriminatory".
He said: 'I'm not going to support a policy that, here in my Leicester constituency, if someone wants to go into Next or H&M, they have to produce a vaccination certificate on their phone, on an app."
England's road to a new normality
England is scheduled to begin Step Two of the lockdown relaxation next Monday (April 12), which will see open-air hospitality, gyms, libraries, all retail stores and outdoor attractions reopen.
If all goes well, Step Three will kick off on May 17 and allow groups of up to 30 people to gather outdoors, hospitality to reopen indoors, cinemas to reopen, and organized indoor sport to restart.
International travel will also be allowed, although there will be numerous restrictions and procedures in place.
Step Four will begin no earlier than June 21, at which time there will be no legal limits on social contact, allowing nightclubs to reopen and large events to take place.
Progressing each step as scheduled depends on the following four steps being met:
the vaccine implementation program continues successfully;
evidence shows that vaccines are effective enough to reduce hospitalizations and deaths in vaccinated people;
infection rates are not at risk of an increase in hospitalizations that would put unsustainable pressure on the NHS;
the risk assessment is not fundamentally modified by new variants;
Tom Ironside of the British Retail Consortium told The Independent: "Having consulted with our retail members, we have concluded that neither voluntary nor compulsory vaccine certificates would be appropriate or useful in the retail setting.
"Vaccination does not guarantee that an individual cannot pass on the virus, and we do not want to create false expectation for costumers.
"Instead, we believe that following strict safety protocols, including regular cleaning, a legal requirement for face coverings and regular hand-washing are the best course of action to protect staff and customers in stores."
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You are here: NUHA Foundation > Country Resource Pages > Education in Bolivia
Education in Bolivia
Key Country Statistics
Structure of the Educational System
Major Government and International Actors within the Educational System
NGO Projects Supporting the Educational System
Accurate as of March 2013; unless stated otherwise, the websites are all in English. Acknowledgement: Linda Schayman Pino.
Key statistics for Bolivia relevant to education are as follows:
Age structure: 0-14 years = 34.2% of the total population; 15-24 years = 20.1% of the total population
Median age: 22.8 years (average men and women)
Urbanisation: 67%
Education expenditure: 6.3% of GDP (2006)
Literacy (understood as age 15 and over can read): 86.7% (breakdown: male 93.1% and female 80.7% according to 2001 census)
School life expectancy total = 14 years (primary to tertiary education)
GDP growth forecast: 5% (2012)
Official national languages: Spanish, Quechua and Aymara
Sources: country census, Bolivia.gov.bo [Spanish] and CIA World Factbook.
For complementary data…
World Data on Education [Spanish]: Country profile on education made available through the database of the International Bureau of Education. This is the seventh and most recent edition of the profile, which provides a national report on the development of education as of April 2010.
Index Mundi: Information on literacy rates and charts for Bolivia, which has data as of 26 July 2012.
UNESCO Institute for Statistics: For comparisons of Bolivia's profile on education, literacy and science and technology with other country and regional profiles – as of December 2010.
Similar to other education systems, Bolivia's National Education System is composed of a formal and a non-formal sector. Formal education is organized in four cycles: initial or pre-primary, primary, secondary, and higher education.
The initial cycle is divided in two sub-cycles: the first cycle refers to pre-school education up to children of 4 years of age, is non-formal and not mandatory. It refers to childcare institutions as crèches and communitarian care facilities. The second cycle is for children of 4 to 6 years of age and compulsory by law.
Primary education in Bolivia is compulsory and starts at the age of 6 and lasts eight years. It has two cycles: the basic vocational cycle lasting five years, and advanced vocational cycle lasting three years.
Secondary education is offered to students of 14 to 18 years of age. Divided in two sub-cycles, students can either follow the basic technical degree, preparing apprenticeship for technical work (Bachillerato de técnico básico); or the general education degree (Bachillerato en Humanidades), preparing students for the entrance to university according to the subject of choice: Science, Literature or Biology.
Higher education in Bolivia allows students having approved the Aptitude Entrance Exam (Prueba de Suficiencia Académica) to freely enroll at any state public university and in any subject they wish. In general, there are three types of higher education in Bolivia: Higher technician (Técnico superior o avanzado), Undergraduate studies leading to a Bachelor's degree (Licenciatura), and Post-graduate studies (Maestría y Doctorado)
Of note, for the period 2010-2014, Bolivia's Ministry of Education and Cultures (see below) intended to reflect the adoption of the "Bolivia moves forward" (Bolivia Avanza) principles on education: broader access to public education in rural Bolivia, the development of a new regional targeted learning strategies, and the promotion of a "new revolutionary, productive, communitarian, decolonized" vision of education in Bolivia.
Sources: World Data for Education [Spanish]; Organizacion de Estados Iberoamericanos [Spanish]; World Bank; Bolivian Ministry of Education and Cultures [Spanish], The Education Information System [Spanish].
These are the Ministry of Education and Cultures [Spanish] (Ministerio de Educación y Culturas), whose website provides information on the programmes, policies, institutions, activities, and projects created by or functioning under the umbrella of the Bolivian Ministry of Education. The Vice Ministry of Science and Technology [Spanish] (Viceministerio de Ciencia y Tecnología de Bolivia) has as mission to promote research and studies on science and technology in Bolivia. In addition, the Vice Ministry has a website which contains updated information on the organization of national and international competition projects for students and teachers (Olimpiadas estudiantiles científicas y tecnológicas); partnerships and agreements between the Ministry and similar organs of foreign States; and interestingly, bases and lines of participation and qualifications for Bolivian entrepreneurs in national and international science and technological contests. The Bolivian University Executive Committee [Spanish] (Comité Ejecutivo de la Universidad Boliviana) plans and programmes legislation, information to students and professors. This website also contains a list of Bolivian universities (state and private institutions) with the respective links to their websites.
Government and NGO Projects Supporting the Educational System
Yo si puedo (Yes, I can) [Spanish]: is a national literacy programme created to eradicate illiteracy and as a tool related to adult education in Bolivia, and implemented by the Government. For further explanation of the programme's stages and functioning, please click here.
The National Project of Access and Continuity in Rural Education for Young Girls (Proyecto de acceso y permanencia de las niñas a la Educación Rural) [Spanish]: this project has as objective the creation of an action plan for the accessibility and continuity of young girls in rural schools.
Project of Transformation of Secondary Education (Proyecto de Transformación de la Educación Secundaria) [Spanish]: the project was presented by the Bolivian Ministry of Education to the World Bank in 2007. The project has as objective the strategic support of the municipal governments' educative structure. An important component of the project is its institutional strength. To read more about the project's implementation status and results report, click here [Spanish and English].
The National Programme for New Information and Communication Technologies in the Educative Sector (Programa Nacional de Nuevas Tecnologías de Información y Comunicación en la Educación) [Spanish]: this programme was approved to encourage the supply the educative system with the technological tools required to improve the learning process. This policy accentuates the importance of access to up-to-date information for students.
The Community Educative Telecenter Project (Telecentro Educativo Comunitario) [Spanish]: this project creates common spaces where students, teachers and the community in general have access to computers, internet and new technologies that increase the accessibility to information and facilitate communication for community development.
Agencia Adventista para el Desarrollo y Recursos Asistenciales [Spanish], for work on literacy, school abandonment
Fundación Ayuda en Acción [Spanish], for work on literacy, formal education, non-formal education, alternative education, school abandonment
Asociación ANAWIN, for work on literacy, formal education, non-formal education, alternative education, school abandonment
Asociación Ecunémica para el Desarrollo, for work on literacy
AYNISUYU "Territorio de Reciprocidad" [Spanish], for work on literacy, alternative education
Christian Children's Fund, for work on literacy, formal education, non-formal education
Centro para el Desarrollo Regional, for work on literacy, non-formal education, school abandonment, breakfast and/or lunch at school
Caritas Boliviana – CEPAS CARITAS [Spanish], for work on literacy, alternative education
Coordinamento Delle Organizzazione per ill Servizio Volontario [English and Italian], for work on literacy
Centro Regional de Estudios Multidisciplinarios "CRIAR", for work on literacy, alternative education
Instituto de Investigación y Capacitación Campesina, for work on literacy
Instituto de Investigación Cultural para Educación Popular, for work on literacy
Kinder Not Hilfe [Spanish, English and German], for work on literacy, formal education, non-formal education, school abandonment, breakfast and/or lunch at school
Promotores Agropecuarios – PROAGRO [Spanish, English, French, German, Portuguese], for work on literacy, formal education, non-formal education, alternative education
Proceso – Servicios Educativos, for work on literacy, formal education, non-formal education, alternative education, school abandonment, breakfast and/or lunch at school
Sociedad Católica San José, for work on literacy, alternative education, school abandonment, breakfast and/or lunch at school
Servicios Múltiples de Tecnologías Apropriadas, for work on literacy, school abandonment, breakfast and/or lunch at school
Visión Mundial Internacional en Bolivia [Spanish], for work on literacy, alternative education, school abandonment
Care International, for work on formal education, non-formal education, alternative education, school abandonment
Centro Boliviano de Investigación y Acciones Educativas [Spanish], for work on formal education, alternative education, school abandonment
Centro de Desarrollo Agropecuario, for work on formal education, non-formal education
Centro de Multiservicios Educativos [Spanish], for work on formal education, non-formal education, school abandonment
Centro de Educación y Desarrollo de la Mujer "AYNI", for work on formal education, alternative education, school abandonment
Centro de Promoción Agropecuaria Campesina [Spanish], for work on formal education, alternative education
Centro de Estudios Regionales para el Desarrollo de Tarija, for work on formal education, non-formal education
Conservación Internacional en Bolivia [Spanish], for work on formal education
Fomento al Desarrollo Infantial, for work on formal education, alternative education
Fundación para la Producción [Spanish], for work on formal education
Fundación Etnica – Agroforestal – Ecológica, Educativa y Previsional, for work on formal education, alternative education
INTERVIDA [Spanish, English, French, Catalan], for work on formal education, alternative education, breakfast and/or lunch at school
Map Internacional Sección Bolivia, for work on formal education, non-formal education, alternative education
Fundación Participación y Sostenibilidad – PASOS, for work on formal education, alternative education
Proyecto de Desarrollo de Area Arani, for work on literacy, formal education, school abandonment
Proyecto de Desarrollo de Area Azirumarca, for work on formal education, alternative education, school abandonment
Proyecto de Desarrollo de Area Santivañez, for work on formal education, school abandonment
Proyecto de Desarrollo de Area Tiraque, for work on formal education, school abandonment
Proyecto de Desarrollo de Area Viloma, for work on formal education, school abandonment
Asociación Cristiana Benéfica de Rehabilitación y Reinserción de Marginados, for work on formal education
Servicio de Asesoría a Cooperativas Agrarias, for work on formal education, alternative education
Save the Children USA, for work on formal education, non-formal education, school abandonment
Save the Children Canada [Spanish and English], for work on formal education, non-formal education, school abandonment, breakfast and/or lunch at school
Servicios Múltiples de Tecnologías Apropriadas, for work on formal education, non-formal education, alternative education
Servicio, Capacitación e Investigación, for work on formal education, non-formal education
Asociación Boliviana para la Conservación – TROPICO [Spanish and English], for work on formal education
Agencia Internacional Esperanza Bolivia, for work on non-formal education
Asociación de Promotores de Salud de Area Rural [Spanish], for work on non-formal education
Audiovisuales Educativos, for work on non-formal education
Centro de Asesoramiento Legal y Desarrollo Social, for work on non-formal education
Centro de Desarrollo y Fomento a la Autoayuda, for work on non-formal education, alternative education
Centro de Documentación e Información Bolivia [Spanish], for work on non-formal education, alternative education
Centro de Servicios y Asistencia a la Producción Triguera, for work on non-formal education, alternative education
Centro de Investigación y Promoción del Campesinado [Spanish], for work on non-formal education, alternative education
Centro de Investigación Social y Trabajo en Equipos Multidisciplinarios, for non-formal education, alternative education
Crédito con Educación Rural [Spanish], for work on non-formal education
Fundación Bartolomé de las Casas, for work on non-formal education
Fundación Cultural Quipus, for work non-formal education, alternative education
Instituto de Investigación Cultural para Educación Popular, for work on non-formal education, alternative education
Promoción Integral de la Mujer y la Infancia – INFANTE, for work on literacy, non-formal education, alternative education, school abandonment
Project Concern International [Spanish], for work on non-formal education, school abandonment, breakfast and/or lunch at school
Trabajo con Mujeres, Niños, Niñas y Adolescentes, for work on non-formal education, alternative education
World Concern Bolivia [Spanish], for work on non-formal education, alternative education
Centro de Promoción y Educación Yunta, for work on non-formal education
Asociación de Cooperación Rural en Africa y América Latina, for work on alternative education
AIS, for work on alternative education
Audiovisuales Educativos, for work on alternative education, school abandonment
Centro de Estudios para el Desarrollo, for work on alternative education
Centro de Educación y Desarrollo Integral del Campesino, for work on alternative education
Centro de Investigación y Documentación Santa Cruz – CIDCRUZ [Spanish], for work on alternative education, breakfast and/or lunch at school
Centro de Investigación de Energía y Población, for work on alternative education
Centro de Investigación, Promoción y Desarrollo de la Ciudad – CIPRODEC, for work on alternative education, breakfast and/or lunch at school
Centro Juana Azurduy, for work on alternative education
Centro de Promoción de la Mujer Gregoria Apaza [Spanish], for work on alternative education
Fundación Bartolomé de las Casas, for work on alternative education, school abandonment
Fundación Cuerpo de Cristo [Spanish], for work on alternative education
Instituto Politécnico Tomas Katari [Spanish], for work on alternative education
Medicus Mundi España – Delegación Bolivia, for work on alternative education
Programas para la Mujer – PRO MUJER, for work on alternative education
Centro de Servicios Múltiples de Apoyo a Desarrollo – SEMILLA, for work on alternative education
This Year's Blogging Entries
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Past Time
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The offered products and services of COMPACT are either developed by the company itself or in cooperation with renowned international companies that constitute the group of strategic partners.
COMPACT utilizing the expertise of more than 20 years already, since 2011 extends its portfolio with software solutions Enterprise Social Media. Our objective is to offer our customers the opportunity of sharing tacit knowledge and improve communication among their employees in order to increase their efficiency and competitiveness.
Our philosophy is to create long-lasting and substancial partnerships with our customers based on mutual respect and trust.
To become a strategic partner for each Organization and Business that recognize the important contribution of the Human Factor in business development and invest systematically in the development of Human Capital.
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Final rinse
Humboldt Dump cleanup commences amid neighbor concerns, heavy monitoring
MOUND BUILDERS Bulldozers level a pad of ground where a water tank will sit at the old Humboldt Road Burn Dump in east Chico. After 20 years of debate, cleanup of the site began this week. Hank Marsh Junior High sits in the backgroound.
Land deal: The contaminated soil at the old Humboldt Road Burn Dump will be collected into a containment cell on a 10-acre parcel west of Bruce Road. The city purchased the land from John Scott for about $200,000. Toxic soil from land east of Bruce Road will be scooped up and trucked across the road to the same cell for containment.
Two yellow bulldozers, accompanied by two water trucks, prepared to plow tons of contaminated soil into a mound this week as work began on the city-owned property known as the old Humboldt Road Burn Dump.
Located just west of the site of one of Chico's largest-ever proposed housing developments, the project is being carried out by Performance Excavators out of San Rafael. The idea is to consolidate thousands of cubic yards of toxic soil into a single cell and cover it with an impermeable material, clean soil and vegetation.
After nearly 20 years of debate on how best to clean up the hazardous waste, the City Council finally settled on a plan two years ago. The property was once the site of the county and then city burn dump, where locals went to unload their junk, including appliances, batteries, unused paint cans and other potentially toxic material. The stuff was pushed into a pile and burned, leaving a toxic legacy discovered in the late 1980s, 20 years after dump operations had ceased.
Builder Tom Fogarty pushed the contaminated soil on his and Edmund Johnson's properties into a containment seal last winter. He is now moving forward with his 1,300-unit Oak Valley project just east of the dump site.
A worker for Performance Excavators, who asked not to be identified, said he's done hazardous excavation work before and he expected this job to last until mid-October, although a deadline of mid-August has been set, so the potentially dust-stirring work ends before classes resume at Hank Marsh Junior High, which sits about a mile upwind from the site.
Robert McLaughlin works for the Butte County Air Quality Management District, whose task is to monitor the work for high levels of lead-laden dust kicked up while soil is moved for containment. The water from the tank will be used to try to control the dust.
Robert McLaughlin, assistant air pollution control officer of the Butte County Air Quality Management District, said his office is overseeing the project and that its charge is to "make sure the public health is protected."
To that end the district has hired an independent contractor to be on the site every workday to monitor the levels of lead exposed. Ron Vernesoni of ELTERRA Environmental Consulting Services is out of Sedona, Arizona, but is here for the summer, McLaughlin said. Vernesoni's phone number is 624-0122, and people with concerns and questions can contact him.
Neighbors, including those who live in nearby Stilson Canyon and those across Highway 32 in California Park, the direction the prevailing winds blow, have expressed deep concerns to the city about the dangers of the cleanup work.
The Stilson Canyon folks asked that an alternate route be built to their neighborhood so they would not have to drive past the work site when leaving or coming home. The city denied the request, saying it was unnecessary.
McLaughlin said there are 14 lead-monitoring devices in place, including one mounted on the roof of the junior high gymnasium. He said the results from samples collected by the devices will be posted on a Web site, www.bcaqmd.org, but there will be a five-day delay from when the sample is taken and the results are posted.
"We get the results back as fast as we can get them," he said. "We encourage the public to call us with any questions."
For 20 years the issue of what to do with the old burn site was pushed around by a variety of Chico City Councils. In 2003, just when it looked like the city would foot the entire bill, Councilman Dan Nguyen-Tan learned that there had actually been a number of private dumps operating close to the city/county dump that had taken in refuge from the early 1900s to the mid-1960s. Landowners were told if they could prove the city had polluted their acres, the city would pay. None did.
Last month the Pleasant Valley Assembly of God church tried to bill the city for its share, $70,000, but was turned down.
KRCR, KCVU to split
Local FOX news killed.
LaMalfa offended by raise
LaMalfa vows to give raise to northstate causes.
CUSD hopes for smooth supe search
The last one was a doozy.
Parking garage foes launch campaign
Foes of the parking structure start their campaign.
CARD to finalize MLK honor
CARD board set to detail MLK honor in Community Park.


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Rent includes maid service, wireless internet and all taxes & charges except outgoing international telephone calls.
Monthly rentals (30 days plus) receive a 20% discount.


WASHINGTON – James Harden had to scurry off to the Houston Rockets' team bus after another spectacular statistical performance, made even more remarkable because he made it look so routine. Security guard leading the way, Harden made his way down a hallway, where a misplaced mirror leaned up against a wall. Harden walked by, caught his reflection in the periphery and paused. Harden then stepped back to briefly gaze and admire, rubbing his patented beard to make sure he looked OK, and strolled toward the exit.
The swag champ has returned.
If it hasn't been apparent by a recent run of brilliance that hasn't been seen since Michael Jordan more than a quarter-century ago, or an early season eruption that harkens back to the pre-merger magic of Nate "Tiny" Archibald and Oscar Robertson, Harden's bravado is back.
D'Antoni already twice unlocked the MVP in Steve Nash and the early returns on his partnership with Harden have yielded the kind of mind-blowing production to rival an unburdened LeBron James and an unleashed Russell Westbrook this season. Harden, the bobbing, weaving and probing scorer who has turned drawing fouls into fine art, and D'Antoni, the architect of the innovative offense in Phoenix that served as the precursor to the current high-scoring, pace-and-space NBA, have teamed up to make stat sheets great again, and it shouldn't be all that surprising considering the track records of the parties involved.
Harden was mostly overlooked after dropping a career-best statistical performance last season. But that effort didn't make a sound, muted by the malaise of disappointment and dissension. When the Rockets followed up a trip to the Western Conference finals by barely reaching the playoffs with a 41-41 record and he failed to make any of the three All-NBA teams – despite being the fourth player to ever finish with averages of at least 29 points, 7.5 assists and six rebounds – Harden learned that nothing he does individually can remove the stench of team failings.
So, while he would join Archibald and Robertson as the only players in NBA history to average at least 30 points and 10 assists in the same season – and could become the first player since Archibald in 1972-73 to lead the league in scoring and assists – if he is somehow able keep up this insane pace for an entire season, Harden said he isn't making it his priority to become a unique footnote in history.
But in order to be considered the best, Harden can't make his presence felt on one side of the ball. His indifference toward defense has inspired its fair share of hilarious memes, Vines and YouTube videos. Combined with D'Antoni's reputation for fielding teams that view defense as the necessary break between offensive possessions, the potential is there for Harden to become even more of a sieve – but teammate Trevor Ariza refuses to allow that to happen under his watch.


Join Slow Food Phoenix and Changing Hands Bookstore (clever name) for a celebration of seasonal fruit on Saturday, May 22 from 8:30 to 10 a.m.
Visiting cookbook author Deborah Madison and Phoenix urban farmer Greg Peterson will lead guests through an orchard walk and a peach and apricot tasting followed by a book signing for Deborah's new book, Seasonal Fruit Desserts.
Advance tickets required. RSVP and check out the event details for location and price.
Sponsored by Slow Food Phoenix and Changing Hands Bookstore.
Many years ago, I spent a week at the Santa Fe School of Cooking and one day we met Deborah Madison at the Santa Fe farmers market. She led us through the market, buying this and that. Then we went back to the School and she prepared a lovely vegetarian lunch with the purchases.


Spektrum is a collective effort by Liverpool students, from two of the universities, to bring more drum and bass to the city.
The general aim of Spektrum is to explore and present all areas of drum and bass. Though run by students, the party is open to all drum and bass heads. The genre itself has built a strong reputation and history, which this show looks to highlight; no egos, with an open mind and quality DJs.
This month Josie, Suspekt and the Shadows Residents split things down the middle for an hour each of DnB, liquid and smatterings of jungle. Lock in!


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Apple iPhone Rocks Cell Phone Industry*
The latest ChangeWave consumer cell phone survey shows the startling impact the Apple (AAPL) iPhone continues to have on the cellular industry. The survey of the ChangeWave Alliance reveals the huge ripple effect created by the upcoming June release of the iPhone. The survey also uncovered an additional surge in demand for the iPhone if the proposed price point of the device is lowered.
As more and more consumers switch to the iPhone, we are going to see a huge migration from cell phone manufacturers like Motorola to the hipper, cooler iPhone
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Rockville, MD (PRWEB) April 24, 2007
The latest ChangeWave consumer cell phone survey shows the startling impact the Apple (AAPL) iPhone continues to have on the cellular industry. The survey of 3,489 members of the ChangeWave Alliance - conducted April 4-10 - reveals the huge ripple effect created by the upcoming June release of the iPhone.
Nearly one-in-ten respondents (9%) say they are 'Very' or 'Somewhat Likely' to buy the new iPhone once it becomes available in June. Another 7% of respondents say they are likely to buy the iPhone as a gift for someone else.
These results are nearly identical to ChangeWave's previous consumer cell phone survey conducted in January, and provide strong evidence that Apple should exceed its iPhone sales goals for 2008 - provided the device lives up to consumer expectations.
The survey also uncovered an additional surge in demand for the iPhone if the proposed price point of the device is lowered.
How far would the price have to drop to turn those who are not considering the iPhone into potential buyers? Another 10% say they'd consider buying a 4GB iPhone if the price falls to the $200-$299 range, while 20% said they'd consider the 8GB model in this price range.
The iPhone's looming impact on cell phone manufacturers becomes clear when you compare current market share with planned purchases for the next six months.
Currently, Motorola (33%) is the leading manufacturer among the cell phone owners surveyed - with LG (15%) second and Nokia (14%) third. However, when we focus on planned future buying, the startling impact of the iPhone becomes apparent:
For the second consecutive survey, Motorola's future share among consumers has registered a dramatic decline - falling from 33% in October 2006 to just 17% currently.
"As more and more consumers switch to the iPhone, we are going to see a huge migration from cell phone manufacturers like Motorola to the hipper, cooler iPhone," said Tobin Smith, founder of ChangeWave Research and editor of ChangeWave Investing. "And, because of Apple's deal with AT&T's Cingular as their exclusive service provider for the iPhone, we are also going to see a big migration away from Verizon and other cellular providers."
Speaking of service providers, the current survey shows Verizon (30%) holding the market share lead among respondents. Second place Cingular (27%) - Apple's exclusive service provider for the United States - has gained 1-point on Verizon since the previous survey in January, while Sprint/Nextel (12%) has dropped 1-point to a new low.
But in terms of momentum going forward we find a dramatic turn of events. Cingular (28%; up 6-points) has surged ahead of Verizon in terms of future planned buying, and is now the top choice among those likely to switch service providers.
For a summary of the 'Apple iPhone Rocks Cell Phone Industry' report, simply click the following link: http://alliance.changewave.com/iphone2.htm
The ChangeWave Alliance is a network of over 10,000 highly qualified business, technology, and medical professionals in leading companies of select industries--credentialed experts who spend their everyday lives working on the frontline of technological change. ChangeWave surveys its Alliance members on a range of business and investment research and intelligence topics, collects feedback from them electronically, and converts the information into proprietary quantitative and qualitative reports.
DARLENE MARCH
ChangeWave Research


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Watercress Wildlife Association
Local nature reserve in St Albans
The best way to get in touch is to send an email to the chairman (info@watercresslnr.org.uk).
You can send post to:
WWA
47 Cornwall Road
AL1 1SQ
The site itself is located down a short track from the corner of Cornwall and Riverside Road in St Albans, as per the Google map below. Note that there is no parking at the site so visitors are encouraged to arrive on foot or by bicycle. There is a small amount of cycle parking on the site itself.
Sadly, your browser doesn't support iframes, otherwise you would see an embedded Google map here.
About the WWA
Nature resources
Map of the reserve
Flickr group
GDPR Statement and Policy
Original WWA Website
Archived here
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© 2022 Watercress Wildlife Association. All photos are copyright their respective owners


Hypertext Transfer Protocol (HTTP), main communication port with legacy players (e.g. XMP-3250/3350/3450).
HTTP alternate, main communication port with all players.
For cloud update service through Google drive.
Microsoft Simple Service Discovery Protocol (SSDP), to discover IAdea players on the network.


IPStar subsidiary SEMiLLA Sanitation Hubs exhibits at the Hannover Messe 2017 to present progress regarding the mobile sanitation units. These units are desigend to provide clean water, sanitation and nutrients everywhere. The units will come with advanced space technology from the MELiSSA program for urine, grey and black water treatment. We expect to accelerate the development and deployment of the technology in remote places and disaster areas.
The technology provides cost-efficient solutions with no or low environmental impacts to process human urine and feces and produce water and nutrients.The sanitation-unit with toilets en washing facilities convert the yellow, grey and black water into clean water to drink and water and nutrients to use for growing plants and making food.
For more information please visit our dedicated webpage.


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APGA only party authorised to use Ojukwu's image – son
By Orientdaily	 Last updated Dec 3, 2020
By Praise Necherem
Emeka Ojukwu junior, the son of the late Igbo leader, Chukwuemeka Odumegwu-Ojukwu, has warned politicians in Anambra state against the use of his father's image for political reasons. He described the ugly trend as an abuse of what his late father stood for while alive.
Ojukwu (jnr) who is a member of the Board of Trustees of the All Progressives Grand Alliance (APGA), said APGA remained the only party authorised to use his late father's image.
He said, "my father stood for fair-play and justice. His belief in selflessness was legendary, while he also believed in the empowerment of the Igbo nation. Ironically, some of these politicians now attempting to lay claim to Ikemba's endorsement with his photographs and images don't even understand or reflect his ideals.
"We will no longer tolerate indiscriminate use of my late father's iconic images on social media, political posters and fabrics by politicians. APGA remains the only party that could use my father's images for their activities because of his role as the patron saint of the party.
"Ezeigbo Gburugburu (late Ojukwu) is only meant for APGA and that position remains sacrosanct even in death.
"Let's respect our late hero, Ikemba Nnewi, by showing respect to his blessed memory. By showing respect to our heroes, those who have sacrificed for us, we would be respecting ourselves as respect is reciprocal."
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Prev Article 8. - REGISTRATION OF VETERINARIANS Next
47-819. State board of veterinary examiners; meetings; quorum; officers, election and duties; compensation and expenses. (a) The board shall meet each year at such times and places as specified by the board.
(b) Except as otherwise provided in this act, a majority of the board shall constitute a quorum.
(c) At its first meeting following April 1 of each year, the board shall organize by electing a president and a vice-president. Each officer so elected shall serve for a term of one year or until a successor is elected and qualifies. A special election shall be held whenever a vacancy occurs in an office of the board.
(d) In general, but not by way of limitation, the officers and the executive director of the board shall have and exercise the following powers and duties:
(1) The president's duties shall include the calling of and presiding at meetings of the board.
(2) The vice-president's duties shall include serving as presiding officer at meetings of the board in the absence of the president or upon the president's inability or refusal to act and overseeing budgetary and financial aspects of the operation of the board.
(3) The executive director shall perform duties which shall include carrying on the correspondence of the board, keeping permanent accounts and records of all receipts and disbursements by the board and of all board proceedings, including the disposition of all applications for license, keeping a register of all persons currently licensed by the board, and furnishing a copy of the Kansas veterinary practice act to each newly licensed veterinarian. All board records, except as otherwise provided by law, shall be open to the public during regular office hours.
(4) The executive director shall be bonded as required by the state surety bond committee pursuant to K.S.A. 75-4103 to 75-4106, and amendments thereto.
(e) Each member of the board shall be paid compensation, subsistence allowances, mileage and other expenses as provided in K.S.A. 75-3223, and amendments thereto, when engaged in the performance of the member's official duties or other board business or board activities away from the member's place of residence.
History: L. 1969, ch. 261, § 6; L. 1974, ch. 348, § 19; L. 1980, ch. 155, § 5; L. 1993, ch. 129, § 6; L. 1999, ch. 25, § 4; July 1.


The 11th Annual World Wine Tour is presented by Coldwell Banker. Wine lovers will travel the world, tasting over 20 outstanding domestic and international wines, hand selected by Cru's Executive Chef Bob Boye, all while taking in tunes by New Beginnings Events and indulging in light bites from participating Bell Tower Shops Restaurants. Big thanks to our partners, Bell Tower Shops and Cru, for helping us put on this awesome event! We also thank our Presenting Sponsor, Coldwell Banker and our Gold sponsor, Aubuchon Team of Companies!