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text:
\section{Introduction}

{The asymptotics of the determinant of large Toeplitz matrices is often given by limit theorems \cite{BS}. Yet, subtleties can sometimes prevent one from applying known theorems in particular cases. This note is motivated by a difficulty encountered by three of us in applying the Szeg\"o-Widom theorem for block Toeplitz matrices \cite{Widom1} in a statistical physics problem connected to critical Casimir forces in a confined Ising model \cite{DSE1,DSE2}.

Let us start by recalling the theorem. Let $\mathbb{T} = \{ z \in \mathbb{C}; \, |z|=1 \}$ be the unit circle, and $\phi : \mathbb{T} \rightarrow \mathbb{C}^{N\times N}$ an $N \times N$ matrix valued function, called the {\it symbol}. Usually, one asks that the symbol $\phi$ satisfies certain technical assumptions regarding its regularity, but for the purposes of this note it is sufficient to work with smooth symbols, such that those assumptions hold automatically. The finite block-Toeplitz matrix $T_n(\phi)$ is defined as the matrix of total size $N n\times N n$, with an $N\times N$ block at position $i$, $j$ ($1\leq i,j \leq n$), that is the $(i-j)^{\rm th}$ Fourier coefficient of the symbol,
\begin{equation}
\phi_{i-j} = \frac{1}{2\pi i} \oint_{|z|=1} z^{i-j-1} \phi(z) dz \, .
\end{equation}
Similarly, one defines the semi-infinite block-Toeplitz matrix $T(\phi)$ with $i,j$ entry $\phi_{i-j}$ for $ 0 \leq i,j < \infty$. Then we have the

\paragraph{Szeg\"o-Widom theorem \cite{Widom1}:} {\it Let $\phi$ be a matrix-valued symbol (assumed to be smooth in this note) such that $\det \phi$ does not vanish and has winding number zero. Then
$$
\det T_n (\phi)  \, \sim \, G(\phi)^n E(\phi) , \qquad {\rm as} \; n \rightarrow \infty,
$$
where}
\begin{equation}
\label{eq:GofPhi}
G(\phi)  =  \exp \left(  \frac{1}{2\pi} \int_0^{2\pi} \log \det \phi (e^{i \theta}) d \theta  \right)
\end{equation}
{\it and $E(\phi)$ is a constant that can be expressed as $E(\phi)  =  \det T(\phi) T(\phi^{-1})$ where $T(\phi)$ and $T(\phi^{-1})$ are semi-infinite Toeplitz matrices.
}
\vspace{0.5cm}

The theorem has a long history whose development was often motivated by a problem in mathematical physics. The first version, in the scalar case (i.e. $N=1$), was based on a question of Onsager that arose from for the 2-dimensional Ising Model \cite{McCoyWu}. It was proved by Szeg\"o \cite{Sz} in the case of positive symbols. He showed that the constant $E(\phi)$ was $$\exp \sum_{k=1}^{\infty} k s_{k}s_{-k} $$ where $s_{k}$ is the $k^{\rm th}$ Fourier coefficient of $\log \phi.$ Notice {that} in this scalar case the constant can never be zero.  Later, the theorem was generalized to more general scalar symbols, and then extended by Widom to the block case. For scalar symbols, the theorem was generalized (with a different asymptotic formula) for symbols that had jump discontinuities or vanished on the circle. For results of this type, please see \cite{Bot} where much of the history of the subject can be found.

It should also be noted that an exact identity, even in the block case, exists for the determinants for smooth symbols under certain conditions. This expression, called the Borodin-Okounkov-Geronimo-Case identity, was discovered after the original theorem was proved, but does imply the asymptotic expression. The identity is not relevant for the purposes of this paper, but for the interested reader, we refer to \cite{Bot, BW}.  \vspace{0.4cm}

Another way to state the result of the Szeg\"{o}-Widom theorem is
$$
\det T_n (\phi) / G(\phi)^n  \, \rightarrow \, E(\phi ) \qquad {\rm as} \; n \rightarrow \infty,
$$
which implies, when $E(\phi)$ is non-zero,
$$
\frac{1}{n}  \log \det T_n (\phi) \, \rightarrow \, \frac{1}{2\pi} \int_0^{2\pi} \log \det \phi (e^{i \theta}) d \theta   \qquad {\rm as} \; n \rightarrow \infty .
$$
In practice, in the block case, as opposed to the scalar case, the expression of $E(\phi)$ in terms of semi-infinite matrices does not allow an explicit calculation, and, in fact, it does not even allow one to decide whether or not $E(\phi)$ is zero. This can be problematic, because, if $E(\phi)$ is zero, then the Szeg\"o-Widom theorem loses its predictive value about the asymptotics of $\det T_n (\phi)$. \vspace{0.4cm}

This can be illustrated by the following examples: \vspace{0.3cm}

\noindent {\bf Example 1}. For $u \in \mathbb{R}$, consider the $2\times 2$ matrix-valued symbol
\begin{equation}
	\label{eq:symbol_C_1}
	\phi(e^{i \theta}) \, = \, \left( \begin{array}{cc}
		0  &  1 - u e^{-i \theta} \\
		-1 + u e^{i \theta} & 0
	\end{array} \right)  ,
\end{equation}
and the associated finite block Toeplitz matrix of $n \times n$ total blocks of size $2\times 2$,
\begin{equation*}
	T_n(\phi) \, = \, \left(
                  \vphantom{\begin{array}{c}1\\1\\1\\1\\1\\1\\1\\1\\1\\1\\1\\1\end{array}}
                      \begin{array}{c|c|c|c|c|c}
		\begin{array}{cc} 0 & 1 \\ -1 & 0 \end{array} & \begin{array}{cc} 0 & 0 \\ u & 0 \end{array} & 0 &   & \dots & 0 \\ \hline
		 \begin{array}{cc} 0 & -u \\ 0 & 0 \end{array}  & \begin{array}{cc} 0 & 1 \\ -1 & 0 \end{array} & \begin{array}{cc} 0 & 0 \\ u & 0 \end{array} & 0 & \dots &  \\ \hline
		 0 & \begin{array}{cc} 0 & -u \\ 0 & 0 \end{array}  & \begin{array}{cc} 0 & 1 \\ -1 & 0 \end{array} & \begin{array}{cc} 0 & 0 \\ u & 0 \end{array} & 0 & \vdots \\ \hline
		  & 0 & \begin{array}{cc} 0 & -u \\ 0 & 0 \end{array}  & \ddots  & \ddots & \vdots \\ \hline
		 \vdots & \vdots & 0 & \ddots  & \ddots &  \begin{array}{cc} 0 & 0 \\ u & 0 \end{array} \\ \hline
		0 &  &  & \dots  & \begin{array}{cc} 0 & -u \\ 0 & 0 \end{array} & \begin{array}{cc} 0 & 1 \\ -1 & 0 \end{array}
	\end{array}
              \right)
              \vspace{0.7cm}
\end{equation*}
which is real antisymmetric. It is easy to check (for instance, with an expansion by minors) that $\det T_n(\phi) = 1$, for any $n$. On the other hand, the outcome of the Szeg\"o-Widom theorem is the following. For $u \notin \{-1,1 \}$, $\det \phi (e^{i \theta}) = 1+u^2 - 2 u \cos(\theta) > 0$, so the determinant of the symbol does not vanish and has winding number zero, and the Szeg\"o-Widom theorem applies. Evaluating $G(\phi)$, one finds
\begin{equation*}
	G(\phi ) \, =\, \exp \left( \oint_{|z|=1} \frac{dz}{2 \pi i} \frac{1}{z} \log \left[(1 - u z)(1- u z^{-1})\right]  \right) \, = \,  {\rm max} (1, u^2) .
\end{equation*}
Thus, for $-1<u < 1$, the Szeg\"o-Widom theorem predicts the correct asymptotic behavior of $\det T_n(\phi)$.  However, for $|u| > 1$, although the theorem applies, its outcome is essentially useless, because $E(\phi)$ is, in fact, zero. Then the asymptotic behavior of $\det T_n (\phi)$ is {\it not} obtained by evaluating $G(\phi)$. \vspace{0.5cm}

\noindent {\bf Example 2.} Let $u,v$ be positive real numbers with $u v <1$, and consider the symbol
\begin{equation}
	\label{eq:exact_symbol_D2}
	\phi(e^{i \theta}) \, = \,  \frac{1}{\cos \theta - \frac{uv + u^{-1}v^{-1}}{2}} \left( \begin{array}{cc}
		i \sin \theta  &   \frac{v+v^{-1}}{2}  - e^{-i \theta } \frac{u+u^{-1}}{2} \\
		-\frac{v+v^{-1}}{2}  + e^{i \theta } \frac{u+u^{-1}}{2} 	& i \sin \theta
	\end{array} \right) ,
\end{equation}
that gives the real anti-symmetric block Toeplitz matrix of size $2n \times 2n$
\begin{equation*}
	 T_n(\phi) =
	  {\tiny
	 \left( \begin{array}{cc|cc|c|cc}
		0 & u  & u v  & u^2 v & \dots & u^{n-1} v^{n-1} &   u^{n} v^{n-1}   \\
		-u & 0 & v  & u v & \dots &  u^{n-1} v^n &  u^{n-1} v^{n-1}  \\ \hline
		- uv & - v & 0 & u  &   \dots & u^{n-2} v^{n-2} &   u^{n-1} v^{n-2}   \\
		-u^2 v &  - uv &  -u & 0 &  \dots  & u^{n-2} v^{n-1} &  u^{n-2} v^{n-2}    \\ \hline
		- u^2 v^2 & - u v^2 & - u v  & -v &  \dots & u^{n-3} v^{n-3} &   u^{n-2} v^{n-3}    \\
		-u^3 v^2 &  - u^2v^2 &  -u^2 v & -u v &   \dots  &  u^{n-3} v^{n-2} &  u^{n-3} v^{n-3}    \\ \hline
		\vdots & \vdots    & \vdots & \vdots &   \ddots    &  \vdots & \vdots   \\ \hline
		-u^{n-1} v^{n-1} & - u^{n-1} v^n  &  -u^{n-2} v^{n-2} & - u^{n-2} v^{n-1}  &  \dots &  0 & u  \\
		-u^n v^{n-1}  &  -u^{n-1} v^{n-1}  & -u^{n-1} v^{n-2}  &  -u^{n-2} v^{n-2}   & \dots & -u & 0
	\end{array} \right)  }
\end{equation*}
Like in the previous example, this determinant can be evaluated exactly. For any $n\geq 1$, $\det T_n (\phi)\,= \, u^{2n} $. If we assume that $u \neq v$, such that
\begin{equation*}
\det \phi(e^{i \theta}) \, = \,  \frac{(uv^{-1} + u^{-1}v)/2 - \cos \theta}{(uv + u^{-1}v^{-1})/2- \cos \theta }  >0 \, ,
\end{equation*}
then the Szeg\"o-Widom theorem applies. One finds
\begin{equation*}
	G(\phi) \,=\, \exp \left(  \oint_{|z|=1} \frac{dz}{2 \pi i}  \frac{1}{z} \log \left[ \frac{(z-u^{-1}v )(z-u v^{-1})}{(z-u v)(z-u^{-1}v^{-1})} \right] \right)  \, = \, {\rm max}(u^2,v^2)  .
\end{equation*}
Thus, the constant $E(\phi)$ in the Szeg\"o-Widom theorem is non-zero only if $u>v$. If $u<v$, the theorem does not predict the correct asymptotic behavior, because $E(\phi)=0$. \vspace{0.5cm}

These two examples show that, in general, it would be useful to have
\begin{enumerate}
	\item[(P1)] a criterion that would allow to determine whether or not, for a given matrix valued symbol $\phi$, $E(\phi)$ is zero,
	\item[(P2)] a modification of the Szeg\"o-Widom theorem for the cases with $E(\phi)=0$ that would give the correct asymptotics of $\det T_n(\phi)$.
\end{enumerate}
We shall refer to these two problems as (P1) and (P2) in the following.

The rest of this note is organized as follows. In the next section, we discuss {\bf Examples 1 and 2} from a mathematics point of view, and summarize the current knowledge about (P1) and (P2).
In section 3, we give a very brief introduction to 1d topological superconductors following Kitaev \cite{kitaev_wire}, and we explain the connection to real antisymmetric block Toeplitz matrices. In section 4, we provide precise answers to (P1) and (P2) for the class of matrices which have exactly one pair of zero modes (which includes the matrices of the so-called ``class D'' of topological superconductors in the physics literature \cite{kitaev_wire, kitaev_periodic, ryu2010topological, zirnbauer}). In the appendix we provide more examples of block Toeplitz matrices with $E(\phi) = 0$, all obtained from ``topologically non-trivial band structures''.

\section{Overview: What is known}

We start by reviewing partial answers to (P1) and (P2) from the mathematics perspective.

There is a partial answer to (P1) for certain symbols that is at times helpful. Here is what is true. If we assume the conditions of the Szeg\"o-Widom theorem and, in addition, assume that $\phi_k=0$ for all $k> a$ or that $\psi_{-k}=0$ for all $k> a$ {for some positive integer $a$}, then \[
  E(\phi)=G(\phi)^a \det T_a(\phi^{-1}).
\]

This result was originally due to Widom \cite{Widom1}, but also follows from the Borodin-Okounkov-Geronimo-Case identity mentioned above.  Notice that $\det T_a(\phi^{-1})$ is a fixed finite size matrix, so that if $a$ is not too large, it can be computed directly. Using this, one could show that for {\bf Example 1}, $E(\phi)$ vanishes for $|u| >1.$ This amounts to computing by hand a four-by-four determinant. However, this result is much less useful in {\bf Example 2}.   \\

While it is not readily clear, some insight into (P2) is gained by returning to the scalar case when we have non-zero winding. It takes only a bit of linear algebra to see that, because of the anti-diagonal structure of the symbol, the determinant of the block Toeplitz matrix in {\bf Example 1} is $(-1)^{n}$ times the product of two scalar Toeplitz determinants with symbols,

\[ \lambda(e^{i\theta}) = 1 - ue^{-i\theta},\,\,\,   \psi(e^{i\theta} )= -1 +ue^{i\theta}  . \]

{When $|u|>1$, }the first function has winding number $-1$ and the second $1$. Since both these Toeplitz determinants are triangular, their determinants are straightforward to compute. One is $(-1)^{n}$ and the other is one. Here is an alternative way to do this.

Again using some basic linear algebra it is easy to show that, if we define
\[ \xi(e^{i \theta})  = e^{-i \theta} \psi (e^{i \theta}) , \]
then
\[ \det T_{n-1}(\psi) = \det T_{n}(\xi) \, (-1)^{n}\,(T_{n}(\xi)^{-1}(v))_{0} \]
where in the last term $v = (0,0,\dots,0, 1)$ and the subscript indicates the first component of the vector. In this case $T_{n}(\xi)^{-1} = T_{n}(\xi^{-1}).$ If we compute these terms asymptotically, we have
\[ G(\xi)^{n} E(\xi) (-1)^{n} u^{-n} = u^{n} \times 1 \times (-1)^{n}\times u^{-n} = (-1)^{n}\]
as we know to be the case. Now, using the standard basis notation, another way to write the above is
\[ G(\xi)^{n} E(\xi) (-1)^{n} \times \int _{0}^{2\pi}\frac{d \theta}{2\pi} e^{i n \theta}\psi^{-1}(e^{i\theta})  .\]
A similar computation can be done for $\det T_{n-1} (\lambda)$ to arrive at the asymptotic expression
\[ G(\zeta)^{n} E(\zeta) (-1)^{n} \times \int _{0}^{2\pi}\frac{d \theta}{2\pi} e^{-i n \theta}\lambda^{-1}(e^{i\theta}) \]
where $\zeta (e^{i\theta})=  e^{i \theta}\lambda(e^{i\theta}) $.

So the final answer for the original determinant in {\bf Example 1} is
\[ (-1)^{n}\,G(\xi)^{n} E(\xi) G(\zeta)^{n} E(\zeta) \times \int _{0}^{2\pi}\frac{d \theta}{2\pi} e^{i n \theta}\psi^{-1}(e^{i\theta})   \times \int _{0}^{2\pi}\frac{d \theta}{2\pi} e^{-i n \theta}\lambda^{-1}(e^{i\theta})  .\]

{We see that one way to look at this example} is to understand that, while the determinant of the symbol has no winding, there is some hidden winding. We also can see from this example that, in general, the inverse elements of $T_{n}(\xi)^{-1}$ can provide the extra factor to arrive at the correct asymptotics. In fact, whenever one can show that the leading term of  $T_{n}(\xi)^{-1}$ comes as above from the inverse of the symbol, the above formula holds in general.

The general result for scalar functions with non-zero winding is the following.
Suppose that $\psi = e^{-im\theta} \phi,$ where the winding number of $\phi$ is zero.
Then
\begin{equation}
\det T_{n}(e^{-im\theta} \phi) \sim (-1)^{nm} \det(T_{n+m}(\phi)) F_{n,m}(\phi)
\label{th:winding_number}
\end{equation}
where this last term is $\det (T_{m}( e^{-in \theta} \alpha))$ where $\alpha$ is determined by the Wiener-Hopf factorization of $\phi$. For the interested reader, more about the theorem (\ref{th:winding_number}) and its applications can be found in \cite{BS}, Chapter 10.

The {Wiener-Hopf} factorization is of the form $\phi = \phi_{-}\phi_{+}$ where $\phi_{+}$ is a function whose Fourier coefficients vanish for negative index, $\phi_{-}$ is a function whose Fourier coefficients vanish for positive index, and  this is also true of their algebraic inverses. Another way to say this is that the `plus' function and its inverse are {in} the Hardy space, and that the `minus' function and its inverse are in the conjugate Hardy space. From the factors we define $\alpha = \phi_{-}\phi_{+}^{-1}$.
There is an analogous statement for functions with positive winding.

Before we had derived this formula in the case of  $m = \pm1$ when we decomposed {\bf Example 1} into two scalar determinants, but it can be used for similar cases such as Examples 1b and 3 in the Appendix. In general, the same analysis based on theorem (\ref{th:winding_number}) holds  in the block case when the matrix valued symbol can be factorized in the form $\phi = \phi_{-}\phi_{+}$\cite{BS}. \vspace{0.5cm}

We now turn to the more difficult and more interesting {\bf Example 2}. There, the factorization of the symbol helps to explain why things do not work exactly as we like. } Using the power decreasing method found in \cite{BB} or a direct matrix ansatz, and assuming that $uv <1$ and $u < v,$ one can show that the symbol $\phi$ of {\bf Example 2} can be factorized in the Wiener-Hopf form
\[ \phi = \phi_{+} D \phi_{-} \]
where $D$ is the diagonal matrix with $e^{-i\theta}$ and $e^{i\theta}$ on the diagonal, and the matrix valued functions are defined by
\begin{align}
\phi_+ & = \frac{-2vu}{1 - uve^{i\theta}} \twotwo{\frac{e^{2i\theta } - 1} {2} }{\frac{1}{2uv}}{\frac{e^{2i \theta } }{2}(\frac{1}{u }+ u ) - \frac{e^{i \theta }}{2} (\frac{1}{v} + v )}{\frac{1}{2u^{2}v}}
\nonumber \\
\phi_- & = \frac{1}{1 - uve^{-i\theta}}\twotwo{1}{\frac{1 }{u}}{0 } {(1-uve^{-i\theta})(ue^{-i\theta} - v)}
\, .\nonumber
\end{align}
The elements of $\phi_+$ have vanishing Fourier coefficients for negative index, and the elements of $\phi_-$ have vanishing Fourier coefficients for positive index, guaranteeing their analyticity inside and outside the unit disk in the complex plane of $z=e^{i \theta}$, respectively. This is also true, respectively, for their algebraic inverses.
If the powers of $z=e^{i \theta}$ on the diagonal of $D$ had the same winding, then a similar result to the one given above for scalar functions exists \cite{BS} (Chapter 10). But if they are different, as in this case, then it is difficult to say anything in general. We shall come back to {\bf Example 2} in Section 4 and show how the correct determinant can be computed in the asymptotic limit. \\

More will be said about the block determinants {in the next sections}, where a very similar result to the above is found, motivated by different reasoning that comes from physics. Indeed, in physics, {there exist many examples of block Toeplitz matrices for which $E(\phi) = 0$.} Those cases are inspired by 1d tight-binding models of topological insulators and superconductors, that have been studied in great detail in the physics literature since Kitaev \cite{kitaev_wire}. In addition to being physically relevant examples of block Toeplitz symbols $\phi$ with $E(\phi) = 0$, we believe that the connection with 1d topological band structures, and their classification \cite{kitaev_periodic, ryu2010topological,zirnbauer}, can shed some light on the two points above. Indeed, deciding whether $E(\phi)$ vanishes or not for a given symbol $\phi$ is, in physics, very similar to the question whether a 1d tight-binding Hamiltonian possesses zero modes, and there exist precise criteria for that in the physics literature. The question of how the Szeg\"o-Widom theorem should be modified in order to yield the correct asymptotics of $\det T_n (\phi)$ when $E(\phi)=0$ also possesses a nice reformulation in physics language: it translates to the question ``{\it How fast do the low-lying energies of a system of length $n$ go to zero as} $n \rightarrow \infty$?'', which has a precise answer, at least in simpler cases.

\section{A physics perspective: real anti-symmetric block-Toeplitz matrices and 1d topological superconductors}
\label{Szego_var}

In the { {\bf Examples 1 and 2} given in the introduction}, the block Toeplitz matrix $T_n(\phi)$ is real and antisymmetric. To some physicists, this may suggest a connection with translation invariant tight-binding models of superconductors and insulators in 1d \cite{kitaev_wire, kitaev_periodic}. We elaborate on this connection in this section.

Translation-invariant tight-binding models of fermions can be defined as follows. The degrees of freedom are self-adjoint fermions $\eta_{a,i}$, $a=1,\dots, N$, $j=0,\dots, n-1$ (also called {\it Majorana fermions}), that satisfy the canonical anti-commutation relations
\begin{equation*}
	 \{ \eta_{a,i} , \eta_{b,j} \} = 2 \delta_{a,b} \delta_{i,j} ,\qquad \quad \eta_{a,i} = \eta_{a,i}^\dagger .
\end{equation*}
Here one thinks of $j$ as a site index along a 1d lattice, and of $a$ as an internal index on each site. The Hamiltonian of the model is of the form
\begin{equation}
	H \, = \, \frac{i}{4}   \sum_{i,j} \sum_{a,b} \eta_{a,i}   \, A_{iN + a, jN+b}  \, \eta_{b,j}
\end{equation}
where $A$ is an $nN \times n N$ real anti-symmetric matrix that has the following block structure. There is a smooth symbol $\phi : \mathbb{T} \rightarrow \mathbb{C}^{N\times N}$ such that $A$ is of the form
\begin{equation}
	\label{eq:choices}
	A \, =\, \left\{   \begin{array}{l} T_n (\phi) \qquad ({\rm open \; boundary \; conditions})  \\
	 C_n (\phi) \qquad  ({\rm periodic \; boundary \; conditions})  \end{array} \right.
\end{equation}
where $T_n(\phi)$ is the finite block Toeplitz matrix with symbol $\phi$, and $C_n (\phi)$ is the finite {\it block circulant} matrix with the $N \times N$ block at entry $i,j$ given by the Fourier coefficients
$$
 \left\{ \begin{array}{lll}
	\phi_{i-j+n}  & {\rm if} &   i - j < -n/2 \\
	 \phi_{i-j}  & {\rm if} &   -n/2 \leq   i-j   < n/2 \\
	 \phi_{i-j-n}  & {\rm if} &   i - j \geq n/2 .
\end{array}  \right.
$$
The two choices of $A$ in Eq.~(\ref{eq:choices}) describe the same physical system in the bulk, but with different boundary conditions. \\

First, we focus on periodic boundary conditions. Because $C_n(\phi)$ is a circulant matrix, the problem of calculating its spectrum reduces to the computation of the spectrum of the $N \times N$ matrix $\sum_{p = -n/2}^{n/2-1} e^{-i p \theta} \phi_p$ which, when $n \rightarrow \infty$, is equivalent to the spectrum of the symbol $\phi (e^{i \theta})$. In particular, it is clear that, for the {\it block circulant} matrix, $\det (C_n(\phi)) \sim G(\phi)^n$ as $n \rightarrow \infty$. \\

{
Next, we turn to open boundary conditions (b.c.), and ask the question: How does the spectrum of that system (with open b.c.) differ from the previous one (periodic b.c.)?

If the two spectra are sufficiently close, that is if they are the same up to small corrections that vanish exponentially with $n$, then the asymptotics given by the Szeg\"o-Widom theorem should hold, with $E(\phi)$ non-zero. On the other hand, the case $E(\phi) = 0$ should correspond to a rather substantial change in the energy spectrum of the tight-binding model when one cuts it open.

This question is precisely the one that is at the heart of 1d topological band structures \cite{kitaev_wire, kitaev_periodic}. A Hamiltonian $H$ that has an energy gap for periodic boundary conditions can have one or more pairs of ``zero modes'' with open boundary conditions. We borrow the terminology ``zero modes" from the topological condensed matter literature, where it refers either to exact zero-energy modes or to  exponentially small tunneling modes (the case we are facing here).
 The ``zero modes'' are the eigenvalues of $T_n(\phi)$ that behave as $\lambda \sim \alpha^n$, $|\alpha| < 1$, when $n \rightarrow \infty$, that are absent from the spectrum of the circulant matrix $C_n (\phi)$. If the system has $p$ zero modes $\lambda_1  \sim \alpha_1^n$, \dots, $\lambda_p \sim \alpha_p^n $, then the Toeplitz determinant $\det T_n(\phi)$ cannot have the same asymptotics as the circulant determinant $\det C_n(\phi)$.} Instead, its behavior will be of the form
$$
\det  T_n(\phi)  \, \sim  \, \alpha_1^n \, \dots \alpha_p^n \, \det C_n(\phi) \; \times \; {\rm const.} \qquad \quad {\rm as} \quad n \rightarrow \infty .
$$
Notice that this is automatically a case where $E(\phi) = 0$ is zero in the Szeg\"o-Widom theorem.  \\

The connection with available results on 1d topological superconductors allows to go further, and to shed some light on (P1) and (P2) raised in the introduction. {\ In fact, Kitaev \cite{kitaev_wire} described all the necessary ingredients for a particular class of symbols called ``class D'' in the periodic classification of topological insulators and superconductors \cite{kitaev_periodic, ryu2010topological, zirnbauer}. For that particular class of symbols, he exhibited a precise criterion that determines whether a Hamiltonian has zero modes, solving (P1), and provided a method to evaluate the corresponding decay rates $\alpha_j$, solving (P2).

That particular class of symbols is the one of real anti-symmetric matrices with {\it no additional symmetries}. Roughly speaking, this corresponds to the case where the symbol satisfies
\begin{equation}
	\phi(e^{i \theta}) \, = \, \phi^*(e^{-i \theta}) \, = \, -\phi^\dagger(e^{i \theta}) ,
\end{equation}
and has {\it no additional block structure}. In particular, it must be neither block diagonal nor block anti-diagonal. Because the matrix $T_n(\phi)$ is antisymmetric, its eigenvalues come in complex-conjugated pairs. Kitaev argued that, for such symbols, there is either no zero mode, or exactly one pair of complex-conjugated zero modes.

While both our examples in the introduction have exactly one pair of zero modes, only {\bf Example 2} belongs to this ``class D''. Indeed, the symbol in {\bf Example 1} is anti-diagonal and thus belongs to another symmetry class.} In this ``class D'', the existence/non-existence of a pair of zero modes is decided by the value of Kitaev's $\mathbb{Z}_2$ index \cite{kitaev_wire},
\begin{equation}
	\mathcal{I}_{\rm D} \, = \, {\rm sgn} [ {\rm Pf} \, \phi(1) \,   {\rm Pf} \, \phi(-1) ] ,
\end{equation}
where ${\rm Pf} \, M$ is the Pfaffian of the real anti-symmetric matrix $M$.
When $\mathcal{I}_{\rm D} = +1$, there are no zero modes. When $\mathcal{I}_{\rm D} = -1$, there is exactly one pair of zero modes with eigenvalues $\lambda = \pm i \varepsilon$ for $\varepsilon \in \mathbb{R}_{>0}$. { This is the answer to (P1) provided by Kitaev \cite{kitaev_wire} for ``class D'' symbols.

He also sketched an answer to (P2), by answering the physics question: How fast do the zero modes go to zero? Indeed, he argued that, for finite $n$, the reason why the energies $\pm \varepsilon$ are not exactly zero is the non-zero overlap between the two wavefunctions of the zero modes, which induces tunneling between them, and therefore energy splitting. This energy splitting is proportional to the tunneling rate, which itself is proportional to the overlap between the left and right zero modes. Therefore, the energy splitting must scale as $\varepsilon \sim e^{-n/\ell}$, where $\ell$ is the decay rate of the components of the wavefunction of each of the two zero mode.

In the next section we revisit this physics argument in more detail and discuss the modification of the Szeg\"o-Widom theorem that is needed in the presence of a pair of zero modes.}

\section{Modified Szeg\"o-Widom asymptotics for Toeplitz matrices with one pair of zero modes}

{To correct the asymptotics given by the Szeg\"o-Widom theorem in the presence of a pair of zero modes, we need to evaluate the decay rate $\alpha_1$. To do this, we make the following observation.} When $n \rightarrow \infty$, the matrix $T_n(\phi)^{-1}$ has one pair of eigenvalues that diverge, corresponding to the pair of zero modes, and all other eigenvalues are bounded. This allows us to use the {\it power iteration method} to construct the eigenvector that corresponds to the zero modes. For $n$ large, the eigenvalue is so large that a single application of $T_n (\phi)^{-1}$ is sufficient. {In other words,} for any vector $v_0 \in \mathbb{C}^{N n}$ that has non-zero overlap with the zero mode, the new vector
$$
v_1 \, = \,  T_n(\phi)^{-1} v_0
$$
is the eigenstate we are looking for, when $n \rightarrow \infty$. For $v_0$, one can generically chose one of the basis vectors $e_{iN+a}$ ($i = 1, \dots , n$, $a=1,\dots,N$) of $\mathbb{C}^{N n}$. While in general calculating the inverse of $T_n(\phi)$ is difficult, the crucial point is that the decay rate of the components of $T_n(\phi)^{-1} e_{i N+a}$ is generically the same as the one of the components of $C_n(\phi)^{-1} e_{i N+a}$. This is because one can imagine starting form a position $i$ somewhere in the bulk, so that it does not ``feel'' the boundary. Thus, the problem reduces to evaluating how fast the matrix element $[C_n (\phi)^{-1}]_{iN+a,  jN+b} =  e_{iN+a} C_n (\phi)^{-1} e_{jN+b}$ tends to zero as the distance $|i-j|$ increases. This matrix element is obtained from the Fourier transform of the inverse of the symbol, thus
$$
\int_0^{2\pi} \frac{d\theta}{2\pi} e^{i (i-j) \theta} [\phi^{-1} (e^{i \theta})]_{a b}  \; \sim \; e^{-(i-j) /\ell} \times {\rm const.}
$$
and the decay rate $\ell$ is expected to be generically the same for all matrix elements $(a,b)$. Thus, if there is exactly one pair of zero modes we have
$$
\varepsilon^2 \, \propto \,  e^{- 2 n /\ell}  \, \propto \,  \det \left( \int_0^{2\pi} \frac{d\theta}{2\pi} e^{i n \theta} [\phi^{-1} (e^{i \theta})]_{a b} \right) \;  \; $$
as $n \rightarrow \infty$.

In summary, these arguments lead us to the following modification of the Szeg\"o-Widom theorem for the asymptotics of the determinant of $T_n(\phi)$ (which was used by three of us in the context of Refs.~\cite{DSE1,DSE2}): \\

{\bf Modified Szeg\"o-Widom asymptotics.} {\it For a Toeplitz matrix with exactly one pair of zero modes the Szeg\"o-Widom theorem is not sufficient to determine the asymptotics of $\det T_n(\phi)$, because $E(\phi) = 0$. The correct asymptotics is then given by
\begin{equation}
	\label{eq:Szego_as2}
	 \det T_n(\phi) \sim   G(\phi)^n   \; \det \left[ \int_0^{2\pi} \frac{d\theta}{2\pi}  e^{i n \theta}  \phi^{-1} (e^{i \theta}) \right] \,  \tilde E(\phi) \qquad {\rm as} \quad n \rightarrow \infty,
\end{equation}
where the constant $\tilde E(\phi)$ is not zero. Here $G(\phi)$ is given by Eq.~\eqref{eq:GofPhi}.} \\

We emphasize that all $T_n(\phi)$ in ``class D'' with index $\mathcal{I}_{\rm D} = -1$ have exactly one pair of zero modes. But in general, the class of matrices with exactly one pair of zero modes is larger, {and this modification solves the problem in these cases as well. Notice that (\ref{eq:Szego_as2}) solves the problem of both examples in the introduction.

Indeed, for {\bf Example 2}, one finds that $\mathcal{I}_{\rm D} \, = \, {\rm sign } \left[ u-v\right] $, so the Kitaev $\mathbb{Z}_2$ index correctly predicts that $E(\phi)=0$ when $v>u$, and the asymptotics is correctly predicted by Eq.~(\ref{eq:Szego_as2}). The matrix elements of the Fourier transform of $\phi^{-1}(\theta)$ all decay as $(u v^{-1})^n$, because the decay rate is set by the complex zero of $\det \phi (\theta)$ that is closest to the real axis. As a consequence, $\det \left[ \int \frac{d\theta}{2\pi} e^{i  n \theta} \phi^{-1}(\theta) \right]  \, \sim \, (u v^{-1})^{2 n}$ up to a non-zero multiplicative constant. Hence, Eq.~(\ref{eq:Szego_as2}) correctly predicts $\det T_n(\phi) \sim  G(\phi)^n (u/v)^{2n}$, in agreement with the exact finite-size result $\det T_n (\phi) = u^{2n}$.

Although {\bf Example 1} is not in ``class D'' because it has an additional block-structure, it possesses exactly one pair of zero modes, and the correct asymptotics is also given by Eq.~(\ref{eq:Szego_as2}). }

\section{Conclusion}

Motivated by a problem encountered by three of us in applying the Szeg\"o-Widom theorem \cite{Widom1} to a statistical physics problem \cite{DSE1, DSE2}, we have pointed out an interesting phenomenon that is specific to the block Toeplitz case, and has no analog in the scalar case: Even when $\det \phi$ has no winding, $E(\phi)$ can vanish and can lead to modified versions of the Szeg\"o-Widom theorem. As an example for such a modification, we have given an explicit expression for the asymptotic determinant in the case of block Toeplitz matrices with one pair of zero modes. We also pointed out an interesting connection with 1d topological insulators and superconductors.

\paragraph{Acknowledgements.} We would like to thank E. Ardonne, K. Kozlowski, J.-M. St\'ephan and D. Vodola for inspiring discussions. This work was partly supported by the A*MIDEX Project ANR-11-IDEX-0001-02 cofunded by the French program Investissements d'Avenir, managed by the French National Research Agency.

redpajama_set_name: RedPajamaArXiv


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A rosier view for pensions.
Posted on July 28, 2018 by henry tapper
I've promised the guys (and it's almost exclusively men) who've been involved in a week long debate on twitter, this article. I have asked been asked for positive arguments for measuring pension liabilities against the cost of meeting them (rather than their present value).
I'm happy to do that , but not "peer-reviewed", these thoughts are mine and mine only!
That will be a start, but please tell us the foundations of the non-FE approach, or at least point us to works that do, preferably peer-reviewed by respected actuaries and economists.
— John Kiff (@Kiffmeister) July 27, 2018
To meet this request would mean that I take the conversation away from ordinary people who are interested in this subject because it effects their retirements. Academics – whether economists or actuaries – need to understand how their ideas play with non-academics. Beside which I have two boat loads of people looking to have me skipper Lady Lucy on the Thames this weekend!
Proof of the pudding – we still have 6000 private DB plans
The proof of the value of the system of pension valuations that prevailed before the arrival of financial economics is still visible in the PPF 6000, there are 6000 private pension schemes in the UK that provide or will pensions to millions of people promised a wage for life. Some of the benefits will be paid from the PPF at lower rates than promised, but the vast majority will be paid in full.
The system that is in place, exists because it was relatively easy between 1960 and 2000 to set up a defined benefit plan for staff. If the liabilities of those schemes had been valued at mark to market from day one, it is extremely unlikely that any but a handful of those schemes would have ever been set up.
These schemes have collectively been called "Britain's economic miracle" by Frank Field and their existence sets the standard of pension provision in the UK. We may moan about the dumbing down of pensions in the last fifteen years, but that is because we started from a very good place.
The proof of the value of using the system of smoothing future returns which made pensions affordable to employers, is all around us.
Where investment is not stymied, schemes prosper
The last ten years have been characterised in terms of the market, by consistent real returns for equities. The assets of schemes that have continued to invest for the future have prospered. As my recent report on the First Actuarial Best Estimates Index (FABI), shows, British DB pensions are doing very well thank you, and its the ones that have continued to invest for growth that are in best shape.
Of course there will be market crashes in years to come and growth orientated schemes will not be immune from their impact, but we believe that over time schemes prosper from being invested in real assets.
It is also easy to see the social benefits of pension schemes investing long-term capital in infrastructure, in companies and in commercial property.
Where schemes have a long term strategy, people stay with them
We've found that transfers from our schemes are much lower than from schemes that adopt a mark to market approach and set about de-risking. This- in financial terms – is because transfer values are lower (the discount rates being higher). But I think it's more than that. Where a scheme is properly promoted to its staff as wanting to pay pensions (rather than striving to be bought out by an insurer), members are reluctant to leave it.
There are exceptions (BSPS being the obvious one); but by and large where employers express a confidence in their ability and wish to retain the pension scheme, members are more likely to stay in the scheme.
Schemes which have an open strategy are more affordable to employers.
The more a scheme moves to de-risk , the more expensive the scheme becomes in terms of cash flow. An obvious example is Royal Mail's recently closed DB Scheme who's funding rate – had it been kept open would have been more than 50% of payroll.
We can see how the cost of USS has rocketed as it moves towards a more conservative asset allocation. The ongoing cost of USS is estimated to be 38% of payroll. I'm grateful to this insight from Mike Otsuka correcting my original statement that the ongoing cost of USS would be 41% of payroll.
" You're right that this is on account of movement "towards a more conservative asset allocation" — namely a 20 year shift towards bonds, which will result in expected returns on the portfolio being almost 1.5% lower in 20 year's time than if they held onto their current growth-asset-weighted portfolio. Without the shift towards bonds, the contribution rate would be about 28% of payroll."
These costs are based on the low discount rates caused by using gilts + valuation methodologies. Schemes which employ a discount rate that reflects the expected returns of the assets invested in use higher discount rates and don't have to pay so much.
This may sound like munchkin economics to those in financial economics, but cash flow matters to small and medium sized businesses and it matters to members.
Simply driving up the cash contributions on DB schemes is not necessarily good. In extreme cases it can force employers into insolvency and schemes into the PPF. The Pensions Regulator has statutory duties to both employers and the PPF to stop this happening. We argue that by staying open and adopting a long-term strategy to scheme funding, the risk of ruin is reduced leaving employers to invest in more than pensions!
The opportunity to keep pension promises still exists and it is evolving.
We have in the past months , seen the revival of interest in new open collective pension schemes. Not of the guaranteed variety – we now call DB – but of the non-guaranteed variety we call CDC.
The impact of closing DB has been to drive people into individual DC schemes which only offer an annuity for those who want to draw a "wage for life". We think that most people, when they think of a DC pension pot, still want it to provide them with a wage that lasts as long as they do.
By adopting the principles that underpinned the original conception of DB all those years ago, we believe that we can offer many people who have DC pots , but problems spending them, a wage for life solution. Whether this be an employer sponsored scheme like that proposed for Royal Mail or a general purpose scheme (perhaps run by a master trust), the old methods of running pensions as open collective and pooled investment schemes, looks like returning.
So the old way of doing things may have a future as well as a past!
I could have written this piece another way, pointing to the ruination of our defined benefit schemes by the over-zealous adoption of the principles of financial economics.
Alternatively, I could have made arguments based on economic theory.
There are others much better placed to argue the economics. I'm arguing from what I see going on around me at First Actuarial, in the Friends of CDC and in my conversations with Government.
I am confident that "pensions" can break free from the pernicious embrace of financial economics and that we can return to a world where a "pension" meant a wage for life and not a pot of money.
For this to happen, we need to champion the advantages of open collective pensions and put to one side the argument that pension schemes cannot take "risk".
We all live with risk in everything we do, it is by identifying the good risks which we should take, that we get stuff out of life. There are many bad risks which we should avoid, some of which I've talked about in this article.
But overall, the future for pensions looks bright and lets hope they look brighter still when we move back to being positive about their future.
About henry tapper
Founder of the Pension PlayPen,, partner of Stella, father of Olly . I am the Pension Plowman
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6 Responses to A rosier view for pensions.
Michael Otsuka says:
July 28, 2018 at 7.32
Re "The ongoing cost of USS is estimated to be 41% of payroll."
That should be 37%. You're right that this is on account of movement "towards a more conservative asset allocation" — namely a 20 year shift towards bonds, which will result in expected returns on the portfolio being almost 1.5% lower in 20 year's time than if they held onto their current growth-asset-weighted portfolio. Without the shift towards bonds, the contribution rate would be about 28% of payroll.
Stuart Fowler says:
'I am confident that "pensions" can break free from the pernicious embrace of financial economics and that we can return to a world where a "pension" meant a wage for life and not a pot of money.'
I think you're conflating a number of different pension-related issues Henry. When the new theory of DB schemes emerged in the 90s it was a reaction to the uncertainty of value of the 'pot' or fund and an interpretation of wage for life that was legally closer to contractual pay than an aspiration. The direction of travel did not depend on company finance theory. We could have got to the same outcome of hedging liabilities simply as a consequence of both a tougher replacement regime for MFR and international accounting standards.
What finance theory does usefully add is the logic that made a distinction between a sponsoring company balance sheet on the one hand and both its shareholders and its pension scheme members. It therefore did not seek to impose a universal investment approach or imply nobody should engage in the harvesting of risk premiums. What was right for the company members or for scheme members was not necessarily right for the company.
This is an important insight for your thinking about transfers. The theory makes it entirely logical that the risk should be transferred to those scheme members better able and willing to bear it. The only stipulation is that the terms are fair for those choosing to remain.
The idea that members choosing to transfer from derisked schemes are motivated to any extent by some form of weakening of the scheme is both speculative and counter intuitive. The logic of company finance makes this plain. It is because of the difference in risk tolerance that has crystallised between the sponsor and members. This is the only insight you need to understand why transfers are occurring, are inevitable and (properly managed) improve individual welfare.
henry tapper says:
The phrase "The theory makes it entirely logical that the risk should be transferred to those scheme members better able and willing to bear it" – evinces a hollow laugh.
Yes, this is perhaps somewhat arresting, Henry. But what might the objections to such an attitude be? Do we believe it's unlikely, or even self-evident, that there are no individuals who happens to members of a pension scheme who, given a sum of money calculated to provide a risk free income for life, would entirely rationally take the same sum and take risk with it? Obviously they wouldn't if the sum in question was calculated based on the same risk approach, because the risk-return trade-off per pound invested would then be identical (except for costs and longevity cover). But if the sum was the 'extravagant' amount that either the scheme or the member would have to come up with to invest entirely in hedging assets then the trade off is different. This is what I think you may be overlooking in your comments on pension transfers.
What's changed is the utility definition of the scheme (loosely: how you define and measure success and how you make trade offs). It has changed because international accounting rules changed (and I would argue that would have happened without any overlay of corporate finance theories and indeed did so in other countries) so that avoiding an accounting mismatch (even if it is only a convention) became more important than the traditional trade off made between path variance and the range of probable outcomes at the point the money is consumed. Private individuals, nor being affected by accounting consequences, are free to think about risk in exactly the same terms as sponsors used to (and which you clearly favour). For me that has always been the penny-drop moment. But the difference in the way utility is defined, and success measured, is not alone a condition to justify transfers. It also requires the sum transferred to be as great as the same a private individual would need to avoid all risk and this is what the CETV rules ensure whenever a scheme has already derisked. Hence my firm's preference in the past for outsourcing transfer advice: it rarely increased utility and then only for non-investment reasons, so it wasn't worth it – even though we had that as a permitted business.
This perspective on transfers makes it a kind of arbitrage opportunity created when market participants show different utility functions. But it is either a matter of contextual differences (e.g. steel workers versus bank employees) or random whether many or few, if presented with a certain amount, would in fact trade it for an uncertain amount based on the distribution of the latter relative to the former.
The MPT acronym you pretended (?) on Twitter not to recognise refers inter alia to the choices portfolio investors make every day between accepting a bet and paying the price of avoiding the bet (i.e. between risky and risk free, or return-seeking and hedged). A transfer is only a logical extension of this practical exercise. Indeed the FCA rules make it explicit (although the probability distribution is not itself entirely prescribed – return models, including stochastic models, can within limits compete). The new rules even recognise that it would not be enough to identify a difference in the asset allocation of the scheme and that of the member's own capital (assuming any is at risk in markets), because the outcomes or utility could in theory be increased by retaining the former and adjusting the riskiness of the latter. How logical and complete is that!
Financial economics can also be seen to provide a conceptual justification for transfers, as I pointed out in my comment above (without need of a theory), by validating (without the need of a particular accounting convention) the distinction between the utility of the sponsor (particular if a company with shareholders) and the utility of its shareholders or its pension scheme members – both being individuals not corporates.
So why a 'hollow laugh'? Is it the logical argument itself we should reject? Is it the assumption that there will be individuals who will knowingly and rationally prefer to make the trade off themselves that companies used to make? Is it, in other words, because most members as unwilling or unsuited to such freedom? Alternatively, we might feel the vulnerabilities of some members should outweigh the freedom given to all. These are perfectly respectable and defensible points of view (indeed that are the vital focus of regulators and public policy makers) but we ought to be able to see them for what they represent: a view of human nature, not of finance. Our resistance to the logic may say more about us than about the logic!
Excuse my Trumpian double negative, Henry: the question is whether we believe there are no individuals who would rartionally take the bet.
I don't understand a lot of this Stuart, but get the gist. i don't think we need financial economics so much as common sense, international accounting standards have corroded the core of UK pensions, our DB system, to the point where it is in terminal decline. We have no replacement – unless CDC becomes common. People are driven towards DC pots and these seem attractive right now, but we are giving people minimal help in managing their pots and there are too few financial advisers to go round.
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This year represented our best ever points haul at varsity, taking home 4.5/6 avaliable points. The Men's 2's recorded a landmark victory over a team placed in the division above, and the first varsity win for the team since varsity's inauguration, through a thrilling 3-2 victory. The Women's 1's also deservingly beat Hallam in a game tinged with controversy, but full of quality from our girls. The Womens 2's won their game through a disqualification from Hallam after fielding ineligble players and our Men's 3's also recorded a brilliant victory at Goodwin. The women's 2's were unlucky to end up drawing but still gave a great spectacle to all who were in attendance.
Varsity 2016


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Collins Advanced Dermatology Institute is delighted to introduce another facet to the products we carry in-office, qilib™.
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pnBlawg | Section 61 relief: is Santander v RA Legal  EWCA Civ 183 the high-water mark for claimants?
and obtained an advance from Abbey of £150,000. He instructed RA. The seller instructed Sovereign Law LLP.
The completion monies were transferred to Sovereign Law and the transaction apparently completed.
In fact it did not complete. Although the seller did want to sell the property, she had not contracted with V and had not instructed Sovereign Law to act for her.
Abbey sued RA on the basis that completion never took place and RA paid away the advance in breach of trust. At first instance the judge relieved RA under section 61.
Court of Appeal: RA had Abbey's implied authority to transfer the money to the client account of the solicitor acting for the vendor. They did not have authority to transfer it to the client account of a solicitor who was not acting for the vendor. RA acted in breach of trust.
RA did not obtain relief under section 61.
One question that arises from this decision is, when can departure from standard practice in a conveyancing transaction be reasonable and therefore engage section 61? The CML Handbook (last revised 12.7.13) 1.4 states that the standard of care is that of a reasonably competent solicitor or licensed conveyancer acting on behalf of a mortgagee. The retainer does not require strict adherence to standard pratice, although I accept departure would need to be justified.
An application for permission to appeal was filed with the Supreme Court in March 2014. Perhaps this question will be answered.


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The man kept on and travelled a long distance. At last, after many days, he came to a lodge--a strange lodge, for it was made of stone. Just like any other lodge it looked, only it was made of stone. This was the home of the Raven chief. The man entered.
"Are you brave enough to enter the lodge of that dreadful person?" asked the Raven. "He lives near here. His lodge is of stone like this one, and hanging in it are eyes--the eyes of those he has killed or taken away. He has taken out their eyes and hung them in his lodge. Now, then! Dare you enter there?"
"Can you tell how many days you have traveled?"


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Jail for knifeman apprehended thanks to Humberside Police dog Ben
Humberside Police dog Ben helped apprehend knife-wielding Louis Ryan who had called at his ex-partner's home in Inchmery Road and damaged her car
Police dog Ben, left, helped apprehend a man in Inchmery Road
A man apprehended with the help of a police dog as he wielded a knife in a Grimsby street has been jailed.
Police Dog Ben was part of the team called to an address on Inchmery Road on Sunday, December 8.
PD Ben and his handler ran to Louis Ryan, 28, when he had called at his ex-partner's home in breach of a non-molestation order.
Ryan, of Millom Way, Grimsby admitted five offences including possession of a knife, criminal damage to a car and three offences of breaching of the court order not to contact his former partner.
Prosecuting at Grimsby Magistrates' Court, Joanne Markham said Humberside Police officers were called at around 3am on that Sunday morning after the woman's car was vandalised by Ryan.
He had also been to her home, in breach of an order imposed in September last year not to contact her, and was seen brandishing a kitchen knife.
Humberside Police PC Emma Coulten with PD Ben when he won awards at trials in Nottinghamshire (Image: Humberside Police)
Officers were called to Inchmery Road at around 9am in the morning to a report that man was causing criminal damage to a car and had a knife.
The prosecutor said PD Ben was called to detain Ryan.
The knife was dropped before the dog got to him but not before Ryan had cut one of his own arms.
The prosecutor said the victim felt scared for her safety when he appeared at her home.
Man accused of 11 offences in December crime spree will spend new year behind bars
Brutal and sadistic murderers, a violent husband, killer drivers and depraved child sex offenders - the worst criminals of 2019
In a victim impact statement, she said it was lucky none of her children were at home at the time of the attack.
She said: "If he had got to me he would have stabbed me. I am more worried about the damage to my car because I need it to take my daughter to hospital in Sheffield each week for the treatment she needs."
For Ryan, Saleem Khan said his client had stayed out of trouble since 2013.
"He has proved he can keep out of trouble. What underpinned all this is his relationship between him and his ex-partner, with whom he has a young daughter.
Inchmery Road, Grimsby, where Louis Ryan was apprehended thanks to PD Ben (Image: Google Street Maps)
"After the non-molestation order there was contact between him and his ex-partner in which both were willing."
Mr Khan said Ryan had gone into a downward spiral with his mental health and had been drinking alcohol.
"He has not helped himself by drinking heavily. He accepts the offences and he is full of remorse," he said.
December in the courts
Thief snatched purse with just £1
Man jailed for brutal murder
Dealer sold drugs to pay massive debt
Man 'died twice' after street stabbing
Presiding magistrate Robert Munday told Ryan: "Knives in public are not to be tolerated in any way.
"This was a nasty incident. You need to break the chain (of offending)."
Magistrates imposed a prison sentence of 24 weeks for possession of the knife and an additional six weeks for breach of the non-molestation order, adding up to a total of 30 weeks. Ryan had already served three weeks in custody
A £120 victim surcharge was ordered and a two-year restraining order was imposed not to contact the ex-partner.
For more top stories and breaking news see Grimsby Live
Contact us : Email the reporter who wrote this story.


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Turbo( Hangul : 터보) was a popular South Korean duo in the mid to late '90s.
Turbo was formed in October 1994 to compete against the then popular dance group, Deux . Leader and former DJ Kim Jung Nam was responsible for the rap and choreography while Kim Jong Kook , former vocalist for a high school band, took care of the vocals. This combo proved to be well matched, as Turbo's name soon became synonymous with dance music.
They launched their first album in August 1995, titled "280 km/h speed". Living up to their group name and album title, Turbo took the dance world by storm debuting with the song "나 어릴적 꿈"(My Childhood Dream). The untimely death of Deux member Kim Sung Jae just one month after Turbo's debut, made Turbo the heir apparent to become the kings of the Korean dance scene. Following up with songs "검은 고양이" (Black Cat) and "선택" (Decision), Turbo was labeled as "dance music's scary kids" for rising in popularity so fast.
Just a year after their debut, Turbo returned with their second album, "New Sensation". Reaffirming their popularity, the album sold 800,000 copies within the first two months and their title track "Twist King" swept all the charts. After "Twist King" Turbo performed "Love Is...(3+3=0)" and "어느 재즈 바... (At the Jazz Bar...)". By the end of their second album promotion, Turbo was firmly entrenched as a premier dance group.
This status was short lived however, as Turbo broke up just months later. Citing problems with their management, Turbo went into seclusion. Their hiding was so effective that police were brought in to investigate their whereabouts. Eventually, due to public demand for Turbo's return, half of Turbo returned. Kim Jung Nam, unable to reconcile his differences with the management, left the group. He later joined the 5 member group SNAP in 1999. This left Kim Jong Kook looking for a new partner.
That partner was found in California resident Mikey. Immigrating to America at the age of 6, he had his dreams set on becoming a singer ever since watching videos of the popular group Seo Taiji and Boys . In May 1997, with the goal of becoming a singer, Mikey returned to South Korea alone. Just two months later he auditioned for Turbo among 3500 other hopefuls. Mikey shined both in his rapping skills and also his ability to speak English, gaining him the spot.
Resurrected with the addition of Mikey, Turbo returned to the gayo world October 1997 with their aptly titled 3rd album "Born Again...". Performing "회상" (Remembrance/December), "금지된 장난 (Forbidden Games)" and "Goodbye Yesterday", they took back the dance music title. During this time, Turbo was offered to sing a duet with American singer and movie star Will Smith . Smith, who had just launched his fourth single "Just the Two of Us" (Bill Withers song) said he wanted to make an Asian version of the song. After reviewing singers from Asia he picked Turbo for their music abilities and unique style. Also of interest, singer Choi Chang Min served as a back dancer for Turbo from 97-98 before launching his own solo career.
While preparing for their 4th album Kim Jong Kook injured his hip, hampering their album release. Eventually released October 1998, entitled "Perfect Love" Turbo ventured into different types of music, including Latin, Techno, R&B, Hip Hop and Ballad. Turbo's title track "애인이 생겼어요" (I Got a Girlfriend) was described as a fresh and comical change for Turbo. Following up with a more traditional Turbo style song "X: The Greatest Love", Turbo showed they were still going strong, getting voted as one of the best artists of 98.
But once again Turbo faced breakup. Turbo was invited to participate in the Asia Superconcert on the 30th of December 1998 to represent South Korea with names like H.O.T. , S.E.S. , Fin.K.L , Clon and Sechs Kies . This concert featured singers from all over Asia including Japan, Hong Kong, Malaysia and Taiwan and was broadcast live to South Korea, China and Japan. Due to arguments with management before the concert, Kim Jong Kook protested his role in the concert by not performing his section of the concert and leaving without bowing. This rude behavior was heavily criticized by many who watched the live KBS 1TV broadcast, including top politicians. Due to this incident Kim Jong Kook and Turbo were banned from appearing on TV.
With the ban reluctantly lifted October 1999, Turbo returned in full force just 4 months later with their 5th album "Email my heart". Wanting to raise their level of music, Turbo requested the help of Korea's top musicians and composers including Yoon Il Sang, Yoo Jung Yun, Joo Young Hoon, and Ahn Jung Hoon. Labeled "Cyber Lover", Turbo's title track was not only an exciting song but provided an entertaining look at today's Internet based society. Also to celebrate the millennium Turbo included a special ticket in 2000 of their albums, with the winners guaranteed a copy of Turbo's new albums henceforth.
Not only was their 5th album a success, the music video for their follow up song "Tonight" garnered much popularity and was regarded as one of the years best music videos. Starring talent Kim Min and Turbo's own Kim Jong Kook, the video was directed by Kim Sae Hoon who also did the videos "To Heaven" Jo Sung Mo and "Youngone" [sky]. Set in LA's Harlem, Tonight dramatizes gang violence in typical Korean style. But this dramatization was deemed too violent for tv and Turbo was forced to take it off the air. Having their video banned was nothing new, since their title video, "Cyber Lover" was also banned for inappropriate chat dialog within the video.
Although their 5th album was a huge success, lead singer Kim Jong Kook took an opportunity to go solo leaving Mikey and many disappointed Turbo fans. Kim Jong Kook was offered a 700 million won (more than half million USD) contract for 2 albums by I Star media. Mikey, with his visa expiring, also took leave to New York City to study music under Paul Bay. To end their long career, Turbo released one last album titled "History" revisiting all their hit songs from previous albums and including 3 new songs. A music video for "History" was also released, featuring for the first time transsexual model and singer Harisu .
Amid all the ups and downs Turbo faced in their career and their premature breakup, they have always remained hugely popular. Attributing to this popularity is the fact that every Turbo album has been a million seller. Kim Jong Kook has gone on to have major solo success, releasing 7 albums and winning many accolades, including 3 of out of the 4 best artist awards in 2005, a feat which hasn't been matched since. Mikey was a part of the K-pop group M3.


text:
Луганск (, ) град је у Украјини, у Луганској области. Према процени из 2012. у граду је живело 427.187 становника. Луганск је 11. по величини град у Украјини, а такође је и најисточнији административни центар неке од области.

Положај
Луганск се налази на ушћу река Лугањ и Олховаја. Удаљеност до Кијева износи 811 километара.

Историја
Луганск је два пута мењао име у Ворошиловград, и два пута му је враћан назив Луганск, који потиче од старог назива Лугански Завод.

Луганск се развио из села Камени Брод, некадашњег седишта Треће чете (роте) српског пука у оквиру Славеносрбије под командом Ивана Шевића.

Камени Брод је постојао 1740-1750. године као разбацани поседи неколико породица. Од 1755. године ту се насело 100 српских граничарских породица, и насеље улази у састав Српског насељеничког пука. Православна црква посвећена Св. апостолима Петру и Павлу подигнута је од дрвета 1761. године. У њему је 1782. године било 171 дом са 563 душе. Нову саборну православну цркву сада од камена изградили су мештани 1793. године.

Сјединили су се у другој половини 19. века суседна насеља Камени Брод и Лугански завод у јединствено место. Град Луганск постоји као такав од 9. новембра 1882. године.

Данас је Луганск град у којем се већински говори руски језик те је усвојено јединствено решење исписивања званичних табли са именима улица, оне су практично исписане на руском језику, али да би се испоштовао званични државни језик коришћена је азбука украјинског језика.

Луганск је током 2014. и 2015. поприште рата на истоку Украјине као центар самопроглашене Луганске Народне Републике.

Географија

Становништво
Према процени, у граду је 2012. живело 427.187 становника.

Градови побратими
Градови побратими Луганска су Кардиф, Секешфехервар, Сент Етјен, Лублин и Перник.

Извори

Партнерски градови
  Ростов на Дону
  Лублин
  Кардиф
  Сент Етјен
  Дачинг
  Столни Београд
  Перник
  Општина Вансбро
  Белгород
  Вороњеж

Спољашње везе

 Град Луганск
 Уличне камере Луганска

Луганск
Википројект географија/Насеља у Украјини
Луганск

redpajama_set_name: RedPajamaWikipedia


A small bunch of asparagus spears , tough ends removed, then cut lengthwise into 3/4-inch pieces (store the tough ends for vegetable stock).
Bring a large pot of water to boil. Dunk in the kale leaves. Bring the water back to a boil and let the kale leaves cook for five minutes. Then, using a pair of tongs, fish out the kale leaves and set them aside. Bring the water to a boil again and add your pasta.
About five minutes before the pasta is cooked, add the chopped asparagus.
Meanwhile, assemble the pesto. Place the cooked kale, 1/2 cup of toasted walnuts, nutritional yeast, miso, garlic and olive oil in a food processor or blender.
Process into a paste. I processed mine pretty smooth this time, but you can leave it coarse if you like your pesto that way. The jewel-green color of this sauce has to be seen to be believed-- it's just gorgeous.
Mix the pesto, cooked pasta and asparagus, lemon juice, and remaining walnuts in a large bowl. Add salt and pepper to taste, if desired.


Hamsa Al-Jundi, a doctoral student in the College of Technology, demonstrates the technology available in EMU's new Virtual Reality Accelerated Prototyping (VRAP) lab.
Imagine designing the interior of a van, then entering the vehicle to check out the space. You open and close compartments, turn on an overhead light, and get a feel for your ability to move comfortably inside.
Now, imagine doing this without having to build a physical van prototype.
This isn't science fiction. It's happening today in Eastern Michigan University's Virtual Reality (VR) Lab.
The School of Engineering Technology completed the lab during the Winter 2018 semester as a tool for students in electrical engineering, mechanical engineering technology, and product design and development. In addition to computers and video controllers, the lab includes a 160-square-foot viewing area with rigid acrylic screens making up three walls and a floor.
Advanced VR enabling software and a photorealistic rendering engine make it possible to transform a two-dimensional computer-aided design (of, say, a passenger van) into a highly realistic, three-dimensional virtual image. Special liquid crystal shutter glasses allow the viewer to step inside the screened space, enter the virtual van and move about inside. Special high-tech gloves add to the lifelike experience, providing the sensation of touch and allowing the viewer to open and close compartments or handle light switches. A hand-held 3-D interactive device allows the viewer to rotate and manipulate the images.
Tanbour built the lab with community service in mind. Its initial project involves redesigning the patient compartment of ambulances used by Huron Valley Ambulance, a division of Emergent Health Partners. Huron Valley has a fleet of about 135 ambulances serving seven counties surrounding Ypsilanti and Ann Arbor.
Last fall, EMU senior mechanical engineering technology students used a computer-aided design program to reconfigure the patient compartment of a Huron Valley ambulance. Then they transformed it into a VR image.
Representatives from Emergent Health Partners visited the lab in May to see a virtual ambulance demonstration. To enhance the viewing experience, students placed the ambulance within a virtual accident scene, including a highway, freeway overpass, passing vehicles and an overturned car.
"It was as if we were standing on a highway with an ambulance near an accident site," says Shaun Pochik, education manager for Emergent Health Partners. "We entered the ambulance patient compartment and had a 180-degree view of the interior. We could reach up into virtual space and simulate the opening of cabinets. It was very realistic and really neat—not at all like a video game.
The VR project is timely. Several national companies design and build ambulance interiors. Within the next five to 10 years, Pochik expects to see those companies introduce major redesigns.
VR also provides an opportunity for paramedic training, Pochik says.
Huron Valley will bring a real ambulance to campus this fall so EMU students can compare the vehicle to their VR version.
Eastern completed the $174,000 lab with the help of a $50,000 grant from the Ford Motor Company Fund. Drawing on his extensive experience with VR applications, Tanbour built the lab and designed its software at a fraction of the retail cost.
The lab's capabilities appear limitless. Besides engine and vehicle component design, other uses could include prosthetics or personalized medical applications.


Recently I got into a fight with my dentist's office.
It started innocently. I received a bill I didn't agree with, and I left a message asking for a $30 charge to be removed from my account. But when it took several rounds of phone tag to get a reply, I got irritated.
Then when the reply was not only a "no," but a fairly unkind one, I got downright grumpy. I spent an hour drafting a strongly worded, self-righteous letter about the injustice of the fee, the shortcomings of their customer service, and the disrespectful way the receptionist had spoken to me.
As I was about to hit "print," I stopped myself.
What are you doing? I thought. People are starving. Families are being separated by violence. The ice caps are melting. This is how you've spent an hour of your time?
Stuck on ourselves in a self-righteous,inward-focused spiral. You know you've been there too. You're stuck in traffic when you have somewhere to be. Or your friend was supposed to meet you but hasn't bothered to call. Or maybe you read something in a magazine that you didn't agree with.
As Bev Stratton points out (p. 28), acknowledging the errors of our ways is only the first of many steps along the road to repentance. True repentance must compel action. "Confident in God's grace, we dare to feel good guilt—the kind of guilt that invites us to be accountable to serve our neighbor…free to name our wrongdoings at the individual and societal levels, free to repent and free to change our behaviors," Stratton says.
When I realized I had given far too much of my time to being angry about nonsense, I closed my laptop. I paid the bill. I thanked God that I had $30 in my bank account. And I gave another $100 to a nonprofit organization that would do much better things with the money than I would.
I'd much rather overflow with mercy than anger; with grace and peace instead of self-righteousness and rage. Repentance may not be as easy as giving in to frustrations and irritations, but our world could certainly be better for it. I hope this issue makes us all a little kinder; a little more eager to care for one another; a little quicker to turn, to change, to repent.
Sarah Carson is associate editor of Gather.
This article is from the October 2018 issue of Gather magazine. To read more like it, subscribe to Gather.
Sarah I love your story about the dentist office bill — been there, done that, spent/wasted/killed my time and my spirit that way. Thanks for sharing YOUR repentance and bringing a smile and a breeze of grace to my day.


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White, Charles (44)
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Kuhn, Walt (9)
Otis Art Institute (9)
Smithsonian Institution. Bureau of American Ethnology (7)
Pollock, Jackson (6)
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Archives of American Art (183)
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Finding aids (253) Images (194) Electronic resource (13) Sound recordings (11)
Query: Otis Art Institute
New York: The Last Ten Years (1979: Otis Art Institute of Parsons Design School, Los Angeles, California)
Oversize Otis Art Institute, Printed Materials, Newspaper Clippings
Otis Art Institute, Otis Art Associates Fundraising Material
Otis Art Institute, Otis Art Associates Board of Directors List
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Oversize Otis Art Institute, "A Series of Visual Letters to the Councilpersons of Los Angeles in Support of the Arts" Photocopies
Otis Art Institute, Tutor/Art Program
Otis Art Institute, Exhibition and Event Catalogs
Otis Art Institute, Goals Conference (1969)
Otis Art Institute, Transfer of Charter to Parsons School of Design
Otis Art Institute, Student Appraisals of Teaching
Otis Art Institute, Printed Material, Newsletters
341 records — Page 1 of 29


text:
Aviation Industry: IATA Harps On Security Of Passengers
The International Air Transport Association (IATA) has reiterated that the security of passengers and employers is a top priority for the aviation industry.
As a result, IATA has urged the United States Department of Homeland Security (DHS) and its Transportation Security Administration (TSA) to partner with the industry to identify the most effective and efficient ways to address the evolving security challenge in light of the foiled terrorist plot to down a Detroit – bound aircraft.
In a letter to the Homeland Security Secretary Napolrtano in Geneva recently, the Director General and Chief Executive Officer, Giovanni Besignam has expressed his appreciation to the swift reaction of DHS to maintain the confidence of the flying public and airline employees.
He maintained the need for short-term temporary and extra-ordinary security measures until the immediate threat has abated.
But he cautioned Secretary Napolatano that long-term solutions must include improved technology and effective risk assessment techniques.
According to Borynani, the air transport system cannot support 100 per cent pat-down searches over the long-term.
He noted that each year airlines and their passengers invest $ 5.9 billion in security measures.
He said that IATA is recommending a smaller percentage of intensive pat downs accompanied by technology or proportionate screening procedure as a means to achieve near-term security requirement with reduced delays.
While explaining that security is a government responsibility, and shared priority with the industry, Bisignani, however, urged DHS to allow the current short-term measure to be urgently followed-up by a comprehensive Dots/Industry review of security system to address existing and evolving security threats.
The IATA boss said that the failed Detroit terror plot has emphasised two key realities, such as the global nature of the threat and the need for effective cooperation and information sharing among and within intelligence organisations.
His words, "Effective security needs a system that is built on global harmonisation, effective information exchange, industry/government cooperation, risk assessment and efficient technology.
This is how we made flying the safest way to travel. We must take the same approach with security".
IATA revealed that in the 12 months to September 2009, air transport connected 2.2 billion passenger safely and securely.
This includes 820 million international travellers of which 140 million were international travellers on US routes.
Another component is the US domestic market which accounts for 620 million travellers.
Oil Ends 2009 With $79 Per Barrel
Spring Bank Records 65% Income Rise


A warning has been handed out by police to women to watch out for pickpockets who have been stealing purses from handbags in Windsor.
The force said last week thieves stole several purses from the handbags of women who were out shopping in the town centre.
Jeffrey Pick, police, neighbourhood watch and community messaging co-ordinator for Windsor and Maidenhead LPA said: "Please be aware if you become surrounded be people who are within your private space, or if you get nudged.
"Purses should not be easily accessible in your handbag."
He warned women with large handbags not to make them accessible for pick pockets to unzip and access.


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We understand the fundamentals of hosting an event and are here to work with you to make yours memorable — and delicious. With our mobile Roccbox oven, we can tailor our services to suit your needs.
Our portable ovens ensure that we have a small-sized setup: we can fit into almost any back/front yard, driveway, etc. We also have an indoor pizza oven for intimate events in any weather. Throw a fun, personal event without the worry of prepping food: we've got you covered with our buffet-style service.
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text:
Steve Knightley
Venue: The Atkinson
Town: Southport
Website: http://www.steveknightley.co.uk
"No Secrets- Songs and Stories" - the title of this new show by the esteemed songwriter Steve Knightley says it all. It's a candid trip through Steve's life in music, from his formative years in Exmouth through to his considerable success ,including playing at the Royal Albert Hall [twice] , with Show of Hands.
The show begins with Steve, off stage, singing Bob Dylan's "It Ain't Me Babe" .Steve recounts how he started playing the guitar and his first ,tentative attempts at writing songs. He plays us his first , heavily Dylan-influenced song ,and invites the audience to predict the last word in each line.
If Dylan was his first inspiration , another revelatory moment came when he saw Martin Carthy [with Dave Swarbrick] at the Sidmouth Festival. Steve was in awe of Martin's guitar playing and use of the DADGAD tuning.
To illustrate the profound effect that this had on his teenage self, Steve plays us superb renditions of "Polly On The Shore" and "Banks Of Newfoundland".
After Dylan and Carthy , the next major influence on Steve is meeting the poet Ted Hughes on a poetry course. Steve tells how the poet changed the way he thought about words and he plays one of his most poetic songs "The Hook Of Love".
Steve then recounts how he left "small town" Exmouth for the bright lights of ,ahem, Coventry , describing his need to escape in the song "Undertow" ["No way we'll stay trapped in the undertow"].
Steve's first set ends with the particularly poignant "Sit You Down", his Mum's favourite song ,which tells of leaving one's loved ones [ "You left an empty space and it still remains"].
The second set begins with Steve relocating to London ,trying to make it as a rock musician on the Pub-Rock Circuit ,where you have to be cruel "if you would be king".
1987 sees Steve returning to the West Country ,playing the pubs and bars along the South Coast with Phil Beer. To illustrate a typical set list, Steve gives us "Seven Yellow Gypsies" with a bit of Radiohead and Prince ["Purple Rain"] thrown in to keep the punters happy.
We then move on to success with Show Of Hands ,beginning with the wonderful "Santiago"[one of my favourite SOH songs] ,which tells of Britain's relationship with Chile.
Steve then tells us about his fourth great influence after Dylan ,Carthy and Hughes , namely , Bruce Springsteen and his "Working Man" songs. To illustrate this, Steve gives a powerful rendition of The Boss's "One Step Up and Two Steps Back".
To bring things more or less up to date, Steve sings a medley of three of his greatest songs , "Country Life", "AIG" [Arrogance, Ignorance and Greed] and "Cousin Jack". As a nod to Bob and Bruce , Steve does an excellent impersonation of each of them on a couple of verses. The medley ends with a return to "Country Life" and a lament for all of the rural pubs ,post offices and shops that have closed down.
To conclude a wonderfully entertaining evening, Steve encapsulates the whole story in the autobiographical song "Hard Shoulder" ,for which he receives rapturous applause from the packed auditorium.
Steve described his show as him "rambling on and on". It was much more than that , it was a fascinating and humorous insight into the musical life of one of our foremost songwriters and musicians and it was a privilege to share it with him. Two hours passed in a flash.
Peter Cowley


text:
Q: Set mileage destination displaying I have some experience with excel but its very limited. I have a list of regular To & From destinations setup as historical data along with the mileage between.
What I have is basically cell A1 WIGAN + cell B1 LUTTERWORTH in Sheet 2 and I want a formula to match both of these from Sheet 1 and display the mileage. If the journey has no history then to display a NIL value.
It sounds simple but as yet I've not located anything that works or been able to work it out myself.

A: Try this:
=INDEX('Sheet1'!C:C,MATCH("NEWHOUSE",IF('Sheet1'!A:A = "WIGAN",'Sheet1'!B:B),0))

It is an array formula and must be confirmed with Ctrl-Shift-Enter.
Change the Column references to the actual reference; change C:C to $C$2:$C$1000.  It will speed it up.

A: You could minimize the cross-reference table of mileage values by adding a reversed lookup if the first fails.

In Sheet5!C2 as,
=INDEX(Mileage!C:C, IFERROR(AGGREGATE(15, 6, ROW($1:$99)/((Mileage!$A$1:$A$99=A2)*(Mileage!$B$1:$B$99=B2)), 1), AGGREGATE(15, 6, ROW($1:$99)/((Mileage!$A$1:$A$99=B2)*(Mileage!$B$1:$B$99=A2)), 1)))

redpajama_set_name: RedPajamaStackExchange


Working directly with Intensives to provide care to a specific patient population within the guidelines of written protocols. Will be performing critical care procedures such as, but not limited to, intubation, arterial lines/central line insertion, chest tube placement and therapeutic bronchoscopy.
Master's Degree - Nursing; Nurse Practitioner Degree Emphasis or Program Certificate equivalent.
3 years- Previous nursing experience in a critical care area such as ICU, CCU required. Some NP experience preferred but physicians will provide additional training.


text:
Q: How do I add these arguments to netbeans run.xml file for a project? I am going from this batch file
@echo off
"C:\Program Files\Java\jdk-11.0.3\bin\java.exe" -cp bin;lib/clientlibs.jar client 0 live english game0
pause

to run.xml in netbeans and I keep getting this error:

Bad argument count, Usage: worldid, <live/rc/wip>, <english/german>, <game0/game1>
C:\Users\aaron\AppData\Local\NetBeans\Cache\8.2\executor-snippets\run.xml:53: Java returned: 1

I've tried resolving the arguments but I can't figure out how this run.xml file works. Really trying to get this one figured out.

I expect the project to load the client but it won't because of "bad arguments"


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HomeNewsVivo V3, V3 Max launching in India today
Vivo V3, V3 Max launching in India today
By Meenu Rana
Vivo has been teasing the phones with a tagline "FASTER THAN FASTER"
Chinese Smartphone maker, Vivo is all set to launch its two new smartphones, Vivo V3 and Vivo V3 Max in India today.
Vivo has been teasing the smartphones through social media platforms for quite some time now with tagline "FASTER THAN FASTER". Vivo has posted several features of the phones on social media too. However it has not revealed the detailed specification of the devices.
As per the teasers, Vivo V3 Max features 4 GB of RAM and 32 GB of internal storage. Its camera has Phase Detection AutoFocus (PDAF). The camera, as per the company, can start in just 0.7 seconds, and focusing will take 0.2 seconds. The phone also features fast charging technology which allows 2 hours of (Hi-Fi) music playback after only 5 minutes of plugging in.
Both the phones will come with full metal body. The devices will feature Vivo's super fast fingerprint scanner. As per the company, it will come with 360 degree recognition fingerprint sensor.
Vivo has not provided much information on Vivo V3 and V3 Max. We have to wait till tomorrow for the detailed information on both the smartphones.
Vivo recently launched Y31L in India at Rs 9,450. The Vivo Y31L feature a 4.7 inches (540×960 pixels) display. It is powered by a 1.2 GHz quad-core Qualcomm Snapdragon 410 processor, which is paired with 1GB of RAM and 16GB of internal storage. Using its expandable storage slot, you can increase its memory by another 128GB via a micro SD card. The smartphone runs on Android 5.1 Lollipop operating system with Funtouch OS 2.1 on top of it and is backed up by a 2200 mAh battery.
The smartphone sports an 8-megapixel rear camera with LED flash and a 5-megapixel front camera. Further, the smartphone offers 4G LTE, Bluetooth 4.0, WiFi, GPS, and a micro USB 2.0 port that offers OTG support as well. Besides, it has Accelerometer, Light sensor, Proximity sensor, and Electronic compass.The handset measures 137.24×68.76×8.39mm and weighs 133 grams.
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