text:
\section{Introduction}

Let $\mathbf{F}\in\mathbb{K}[x]^{n\times n}$ be a square, nonsingular polynomial matrix with
$\mathbb{K}$ a field. In this paper we give a deterministic algorithm for finding the determinant of $\mathbf{F}$. The complexity of the algorithm is ${O\tilde{\phantom{\imath}}}\left(n^{\omega}s\right)$ field operations from $\mathbb{K}$ where $s$ is the average column degree or the average row degree of $\mathbf{F}$. Here ${O\tilde{\phantom{\imath}}}$ denotes $O$ with $\log^c (nd)$ factors suppressed for some positive real constant $c$ and $\omega$ is the exponent of matrix multiplication.
The fact that the complexity of determinant computation is related to the complexity of matrix multiplication is well-known. In the case of matrices over a field, for example, Bunch and Hopcroft \cite{BunchHopcroft1974} showed that if there exists a fast algorithm for matrix multiplication then there also exists an algorithm for determinant computation with the same exponent.

In the case of square matrices of polynomials of degree at most $d$, Storjohann \cite{storjohann:phd2000} gives a recursive deterministic algorithm to compute a determinant making use of fraction-free Gaussian elimination with a cost of ${O\tilde{\phantom{\imath}}}(n^{\omega + 1} d)$ operations. A $O(n^3 d^2)$ deterministic algorithm was later given by Mulders and Storjohann \cite{mulders-storjohann:2003}, modifying their weak Popov form computation. Using low rank perturbations, Eberly, et al  \cite{EberlyGiesbrechtVillard} gave a determinant algorithm requiring  ${O\tilde{\phantom{\imath}}}(n^{2 + \omega/2} d)$ field operations, while Storjohann \cite{storjohann:2003} used higher order lifting to give an algorithm which reduces the complexity to $(n^\omega ( \log n)^2 d^{1 + \epsilon})$ field operations. Finally, we mention the algorithm of Giorgi et al  \citep{Giorgi2003} which computes the determinant with complexity $O^{\sim}\left(n^{\omega}d\right)$. However the algorithms in both  \cite{EberlyGiesbrechtVillard} and \cite{storjohann:2003} are both probabilistic, while the algorithm from  \cite{Giorgi2003} only works efficiently on a class of generic input matrices, matrices that are well behaved in the computation.
Deterministic algorithms for general polynomial matrices with complexity similar to that of fast matrix multiplication have not appeared previously.

In the case of an arbitrary commutative ring (with multiplicative unit) or integers other fast determinant algorithms have been given by  Kaltofen \cite{kaltofen92},
Abbott et al \cite{abbott}, Eberly et al  \cite{EberlyGiesbrechtVillard} and Kaltofen and Villard \cite{KaltofenVillard}. We refer the reader to the last named  paper and the references therein for more details on efficient determinant computation of such matrices.

Our algorithm takes advantage of a fast algorithm  \cite{za2012} for computing a shifted minimal kernel basis to efficiently eliminate blocks of a polynomial matrix. More specifically, we use kernel bases to partition our input $\mathbf{F}$ as
$$
\mathbf{F} \cdot \mathbf{U}=\begin{bmatrix}\mathbf{G}_{1} & 0\\
* & \mathbf{G}_{2}
\end{bmatrix}
$$
with $\mathbf{U}$ unimodular.  Such a unimodular transformation almost preserves the determinant of  $\mathbf{F}$, but results in  an extra factor coming from the determinant of the unimodular matrix $\mathbf{U}$, a nonzero field element in $\mathbb{K}$. The computation of the determinant of $\mathbf{F}$ can therefore be reduced to the computations of the determinants of $\mathbf{U}$,  $\mathbf{G}_{1}$ and $\det \mathbf{G}_{2}$. The computations of $\det \mathbf{G}_{1}$ and $\det \mathbf{G}_{2}$ are similar to the original problem of computing $\det \mathbf{F}$, but with input matrices of lower dimension and possibly higher degrees.  To achieve the desired efficiency, however, these computations need to be done without actually determining the unimodular matrix $\mathbf{U}$, since its potential large degree size may
prevent it from being efficiently computed.  We show how the determinant of $\mathbf{U}$ can be computed without actually computing the entire unimodular multiplier $\mathbf{U}$. In addition, for fast, recursive computation, the degrees of each of the diagonal blocks need to be controlled in order to ensure that these are also not too large.
We accomplish this by making use of the concepts of {\em shifted} minimal kernel bases and column bases of polynomial matrices. Shifts basically allow us to control the computations using column degrees rather than the degree of the polynomial matrix. This becomes an issue when the degrees of the input columns vary considerably from column to column (and hence to the degree of the input). The shifted kernel and column bases computations can be done efficiently using algorithms from \cite{za2012}  and \cite{za2013}.
We remark that the use of shifted minimal kernel bases and column bases, used in the context of fast block elimination, have also been used for deterministic algorithms for inversion \cite{zls2014} and unimodular completion
\cite{zl2014} of polynomial matrices.

The remainder of this paper is organized as follows. In the next section we give preliminary information for shifted degrees, kernel and column bases of polynomial matrices. Section 3 then contains the algorithm for recursively computing the diagonal elements of a triangular form and a method to compute the determinants of the unimodular matrices.
The paper ends with a conclusion and topics for future research.

\section{Preliminaries}

In this section we
give the basic definitions and properties of {\em shifted
degree}, {\em minimal kernel basis} and {\em column basis} for a matrix
of polynomials. These will be the building blocks used in our algorithm.

\subsection{Shifted Degrees}

Our methods makes use of the concept of {\em shifted} degrees of
polynomial matrices \citep{BLV:1999}, basically shifting the importance
of the degrees in some of the rows of a basis. For a column vector
$\mathbf{p}=\left[p_{1},\dots,p_{n}\right]^{T}$ of univariate polynomials
over a field $\mathbb{K}$, its column degree, denoted by ${\rm cdeg}\,\mathbf{p}$,
is the maximum of the degrees of the entries of $\mathbf{p}$, that
is,
\[
{\rm cdeg}\,~\mathbf{p}=\max_{1\le i\le n}\deg p_{i}.
\]
 The \emph{shifted column degree} generalizes this standard column
degree by taking the maximum after shifting the degrees by a given
integer vector that is known as a \emph{shift}. More specifically,
the shifted column degree of $\mathbf{p}$ with respect to a shift
$\vec{s}=\left[s_{1},\dots,s_{n}\right]\in\mathbb{Z}^{n}$, or the
\emph{$\vec{s}$-column degree} of $\mathbf{p}$ is
\[
{\rm cdeg}\,_{\vec{s}}~\mathbf{p}=\max_{1\le i\le n}[\deg p_{i}+s_{i}]=\deg(x^{\vec{s}}\cdot\mathbf{p}),
\]
 where
\[
x^{\vec{s}}={\rm diag}\,\left(x^{s_{1}},x^{s_{2}},\dots,x^{s_{n}}\right)~.
\]
 For a matrix $\mathbf{P}$, we use ${\rm cdeg}\,\mathbf{P}$ and ${\rm cdeg}\,_{\vec{s}}\mathbf{P}$
to denote respectively the list of its column degrees and the list
of its shifted $\vec{s}$-column degrees. When $\vec{s}=\left[0,\dots,0\right]$,
the shifted column degree specializes to the standard column degree.

 Shifted degrees have been used previously in polynomial matrix computations
and in generalizations of some matrix normal forms \citep{BLV:jsc06}.
The shifted column degree is equivalent to the notion of \emph{defect}
commonly used in the literature.

Along with shifted degrees we also make use of the notion of a matrix
polynomial being column (or row) reduced. A polynomial matrix $\mathbf{F}$
is column reduced if the leading column coefficient matrix, that is
the matrix
\[
[\mbox{coeff}(f_{ },x,d_{j})]_{1\leq i,j\leq n},\mbox{ with }\vec{d}=\mbox{cdeg }\mathbf{F},
\]
 has full rank. A polynomial matrix $\mathbf{F}$ is $\vec{s}$-column
reduced if $x^{\vec{s}}\mathbf{F}$ is column reduced.

The usefulness of the shifted degrees can be seen from their applications
in polynomial matrix computation problems \citep{ZL2012,zl2014,za2012,zls2014}.
One of its uses is illustrated by the following
lemma, which follows directly from the definition of shifted degree.
\begin{lem}
\label{lem:predictableDegree} Let $\vec{s}$ be a shift whose entries
bound the corresponding column degrees of $\mathbf{A} \in
\mathbb{K}^{\ast \times m}$. Then for any polynomial matrix
$\mathbf{B}\in\mathbb{K}\left[x\right]^{m\times \ast}$, the column
degrees of $\mathbf{A}\cdot \mathbf{B}$ are bounded by the corresponding
$\vec{s}$-column degrees of $\mathbf{B}$.
\end{lem}
\begin{comment}
One of its uses is illustrated by the following lemma from \citep[Chapter 2]{zhou:phd2012},
which can be viewed as a stronger version of the predictable-degree
property \citep[page 387]{kailath:1980}. For completeness we also
include the proof.
\begin{lem}
\label{lem:predictableDegree} Let $\mathbf{A}\in\mathbb{K}\left[x\right]^{m\times n}$
be a $\vec{u}$-column reduced matrix with no zero columns and with
${\rm cdeg}\,_{\vec{u}}\mathbf{A}=\vec{v}$. Then a matrix $\mathbf{B}\in\mathbb{K}\left[x\right]^{n\times k}$
has $\vec{v}$-column degrees ${\rm cdeg}\,_{\vec{v}}\mathbf{B}=\vec{w}$
if and only if ${\rm cdeg}\,_{\vec{u}}\left(\mathbf{A}\mathbf{B}\right)=\vec{w}$. \end{lem}
\begin{proof}
Being $\vec{u}$-column reduced with ${\rm cdeg}\,_{\vec{u}}\mathbf{A}=\vec{v}$
is equivalent to the leading coefficient matrix of $x^{\vec{u}}\cdot\mathbf{A}\cdot x^{-\vec{v}}$
having linearly independent columns. The leading coefficient matrix
of $x^{\vec{v}}\cdot\mathbf{B}\cdot x^{-\vec{w}}$ has no zero column
if and only if the leading coefficient matrix of
\[
x^{\vec{u}}\cdot\mathbf{AB}\cdot x^{-\vec{w}}=x^{\vec{u}}\cdot\mathbf{A}\cdot x^{-\vec{v}}x^{\vec{v}}\cdot\mathbf{B}\cdot x^{-\vec{w}}.
\]
 That is, $x^{\vec{v}}\cdot\mathbf{B}\cdot x^{-\vec{w}}$ has column
degree $\vec{0}$ if and only if $x^{\vec{u}}\cdot\mathbf{AB}\cdot x^{-\vec{w}}$
has column degree $\vec{0}$.
\end{proof}
\end{comment}
An essential subroutine needed in our algorithm, also based on the
use of the shifted degrees, is the efficient multiplication of a
pair of matrices $\mathbf{A} \cdot \mathbf{B}$ with unbalanced
degrees.  The following result follows as a special case of~\citep[Theorem
5.6]{zhou:phd2012}.  The notation $\sum\vec{s}$, for any list
$\vec{s}$, denotes the sum of all entries in $\vec{s}$.

\begin{thm}
\label{thm:multiplyUnbalancedMatrices} Let
$\mathbf{A}\in\mathbb{K}[x]^{n \times m}$ and
$\mathbf{B}\in\mathbb{K}[x]^{m\times n}$ be given, $m\le n$.
Suppose
$\vec{s} \in \mathbb{Z}_{\geq 0}^n$ is a shift that bounds the
corresponding column degrees of $\mathbf{A}$, and $\sum \vec{s} \ge \sum {\rm cdeg}\,_{\vec{s}} \mathbf{B}$. Then the
product $\mathbf{A}\cdot \mathbf{B}$ can be computed in $O^{\sim}\left(n^{\omega}s\right)$ field operations from $\mathbb{K}$, where $s=\sum\vec{s}/n$ is the average of the entries of $\vec{s}$.
\end{thm}

\subsection{Kernel and Column Bases}

The kernel of $\mathbf{F}\in\mathbb{K}\left[x\right]^{m\times n}$
is the $\mathbb{F}\left[x\right]$-module
\[
\left\{ \mathbf{p}\in\mathbb{K}\left[x\right]^{n}~|~\mathbf{F}\mathbf{p}=0\right\}
\]
 with a kernel basis of $\mathbf{F}$ being a basis of this module.
Formally, we have:
\begin{defn}
\label{def:kernelBasis}Given $\mathbf{F}\in\mathbb{K}\left[x\right]^{m\times n}$,
a polynomial matrix $\mathbf{N}\in\mathbb{K}\left[x\right]^{n\times k}$
is a (right) kernel basis of $\mathbf{F}$ if the following properties
hold:
\begin{enumerate}
\item $\mathbf{N}$ is full-rank.
\item $\mathbf{N}$ satisfies $\mathbf{F}\cdot\mathbf{N}=0$.
\item Any $\mathbf{q}\in\mathbb{K}\left[x\right]^{n}$ satisfying $\mathbf{F}\mathbf{q}=0$
can be expressed as a linear combination of the columns of $\mathbf{N}$,
that is, there exists some polynomial vector $\mathbf{p}$ such that
$\mathbf{q}=\mathbf{N}\mathbf{p}$.
\end{enumerate}
\end{defn}
It is not difficult to show that any pair of kernel bases $\mathbf{N}$
and $\mathbf{M}$ of $\mathbf{F}$
are unimodularly equivalent, that is, $\mathbf{N} = \mathbf{M} \cdot \mathbf{V}$ for some unimodular matrix $\mathbf{V}$.

A $\vec{s}$-minimal kernel basis of $\mathbf{F}$ is just a kernel
basis that is $\vec{s}$-column reduced.
\begin{defn}
Given $\mathbf{F}\in\mathbb{K}\left[x\right]^{m\times n}$, a polynomial
matrix $\mathbf{N}\in\mathbb{K}\left[x\right]^{n\times k}$ is a $\vec{s}$-minimal
(right) kernel basis of $\mathbf{F}$ if\textbf{ $\mathbf{N}$} is
a kernel basis of $\mathbf{F}$ and $\mathbf{N}$ is $\vec{s}$-column
reduced. We also call a $\vec{s}$-minimal (right) kernel basis of
$\mathbf{F}$ a $\left(\mathbf{F},\vec{s}\right)$-kernel basis.

\end{defn}

We will need the following result from \citep{za2012} to bound the
sizes of kernel bases.
\begin{thm}
\label{thm:boundOfSumOfShiftedDegreesOfKernelBasis}Suppose $\mathbf{F}\in\mathbb{K}\left[x\right]^{m\times n}$
and $\vec{s}\in\mathbb{Z}_{\ge0}^{n}$ is a shift with entries bounding
the corresponding column degrees of $\mathbf{F}$. Then the sum of
the $\vec{s}$-column degrees of any $\vec{s}$-minimal kernel basis
of $\mathbf{F}$ is bounded by $\sum\vec{s}$.
\end{thm}
A column basis of $\mathbf{F}$ is a basis for the $\mathbb{K}\left[x\right]$-module
\[
\left\{ \mathbf{F}\mathbf{p}~|~\mathbf{p}\in\mathbb{K}\left[x\right]^{n}~\right\} ~.
\]
 Such a basis can be represented as a full rank matrix $\mathbf{T}\in\mathbb{K}\left[x\right]^{m\times r}$
whose columns are the basis elements. A column basis is not unique
and indeed any column basis right multiplied by a unimodular polynomial
matrix gives another column basis.

The cost of kernel basis computation is given in \citep{za2012} while
the cost of column basis computation is given in \citep{za2013}.
In both cases they make heavy use of fast methods for order bases
(also sometimes referred to as sigma bases or minimal approximant bases) \citep{BeLa94,Giorgi2003,ZL2012}.
\begin{thm}
\label{thm:costGeneral} Let $\mathbf{F}\in\mathbb{K}\left[x\right]^{m\times n}$
with $\vec{s}={\rm cdeg}\,\mathbf{F}$. Then a $\left(\mathbf{F},\vec{s}\right)$-kernel
basis can be computed with a cost of ${O\tilde{\phantom{\imath}}}\left(n^{\omega}s\right)$ field
operations where $s=\sum\vec{s}/n$ is the average column degree of
$\mathbf{F}$.
\end{thm}
~
\begin{thm}
\label{thm:fastcolbasis}
The algorithm from \citep{za2013} can compute a column basis of a polynomial matrix $\mathbf{F}$ deterministically with
${O\tilde{\phantom{\imath}}}\left(nm^{\omega-1}s\right)$ field operations
in $\mathbb{K}$, where $s$ is the average average column degree
of $\mathbf{F}$. In addition, if $r$ is the rank of $\mathbf{F}$, then
the column basis computed has column
degrees bounded by the $r$ largest column degrees of $\mathbf{F}$,
\end{thm}

\begin{example}
\label{ex:example1} Let
\[
\mathbf{F}=\left[\begin{array}{rcrcr}
x & -{x}^{3} & -2\,{x}^{4} & 2x & -{x}^{2}\\
\noalign{\medskip}1 & -1 & -2\, x & 2 & -x\\
\noalign{\medskip}-3 & 3\,{x}^{2}+x & 2\,{x}^{2} & -\,{x}^{4}+1 & 3\, x
\end{array}\right]
\]
 be a $3\times5$ matrix over $\mathbb{Z}_{7}[x]$ having column degree
$\vec{s}=(1,3,4,4,2)$. Then a column space $\mathbf{G}$ and a
kernel basis $\mathbf{N}$ of $\mathbf{F}$ are given by
\[
\mathbf{G}=\left[\begin{array}{rcr}
x & -{x}^{3} & -2\,{x}^{4}\\
\noalign{\medskip}1 & -1 & -2\, x\\
\noalign{\medskip}-3 & 3\,{x}^{2}+x & 2\,{x}^{2}
\end{array}\right]~~\mbox{ and }~~\mathbf{N}:=\left[\begin{array}{rc}
-1 & x\\
\noalign{\medskip}-{x}^{2} & 0\\
\noalign{\medskip}-3\, x & 0\\
\noalign{\medskip}-3 & 0\\
\noalign{\medskip}0 & 1
\end{array}\right]~.
\]
 For example, if $\{\mathbf{g}_{i}\}_{i=1,...,5}$ denote the columns
of $\mathbf{G}$ then column $4$ of $\mathbf{F}$ - denoted by $\mathbf{f}_{4}$
- is given by
\[
\mathbf{f}_{4}=-2~\mathbf{g}_{1}-2x^{2}~\mathbf{g}_{2}+x~\mathbf{g}_{3}+2~\mathbf{g}_{4}.
\]
 Here ${\rm cdeg}\,_{\vec{s}}\mathbf{N}=(5,2)$ with shifted leading coefficient
matrix
\[
\mbox{lcoeff}_{\vec{s}}(\mathbf{N})=\left[\begin{array}{rc}
0 & 1\\
-1 & 0\\
-3 & 0\\
0 & 0\\
0 & 1
\end{array}\right].
\]
The kernel basis  $\mathbf{N}$  satisfies  $\mathbf{F} \cdot \mathbf{N} = \mathbf{0}$.
 Since $\mbox{ lcoeff}_{\vec{s}}(\mathbf{N})$ has full rank, it is $\vec{s}$-column reduced, and we have
that $\mathbf{N}$ is a $\vec{s}$-minimal kernel basis. \qed
\end{example}
Column bases and kernel bases are closely related, as shown by the
following result from \cite{zhou:phd2012,za2013}.
\begin{lem}
\label{lem:unimodular_kernel_columnBasis} Let $\mathbf{F}\in\mathbb{K}\left[x\right]^{m\times n}$
and suppose $\mathbf{U}\in\mathbb{K}\left[x\right]^{n\times n}$ is
a unimodular matrix such that $\mathbf{F} \cdot \mathbf{U}=\left[0,\mathbf{T}\right]$
with $\mathbf{T}$ of full column rank. Partition $\mathbf{U}=\left[\mathbf{U}_{L},\mathbf{U}_{R}\right]$
such that $\mathbf{F}\cdot\mathbf{U}_{L}=0$ and $\mathbf{F} \cdot \mathbf{U}_{R}=\mathbf{T}$.
Then
\begin{enumerate}
\item $\mathbf{U}_{L}$ is a kernel basis of $\mathbf{F}$ and $\mathbf{T}$
is a column basis of~$\mathbf{F}$.
\item If $\mathbf{N}$ is any other kernel basis of $\mathbf{F}$, then
$\mathbf{U}^{*}=\left[\mathbf{N},~\mathbf{U}_{R}\right]$ is
unimodular and also unimodularly transforms $\mathbf{F}$ to $\left[0,\mathbf{T}\right]$.
\end{enumerate}
\end{lem}

\section{\label{sec:diagonals}Recursive Computation}

In this section we show how to recursively compute the determinant
of a nonsingular input matrix $\mathbf{F}\in\mathbb{K}\left[x\right]^{n\times n}$
having column degrees $\vec{s}$.
The computation makes use of fast kernel basis and column basis computation.

Consider unimodularly transforming $\mathbf{F}$ to
\begin{equation}
\mathbf{F} \cdot \mathbf{U}=\mathbf{G}=\begin{bmatrix}\mathbf{G}_{1} & 0\\
* & \mathbf{G}_{2}
\end{bmatrix},\label{eq:step1HermiteDiagonal}
\end{equation}
which eliminates a top right block and gives two square diagonal blocks
$\mathbf{G}_{1}$ and\textbf{ $\mathbf{G}_{2}$} in $\mathbf{G}$.
Then the determinant of $\mathbf{F}$ can be computed as
\begin{equation}
\det\mathbf{F}=\frac{\det\mathbf{G}}{\det\mathbf{U}}=\frac{\det\mathbf{G}_{1}\cdot\det\mathbf{G}_{2}}{\det\mathbf{U}},\label{eq:determinantFromDiagonalBlocks}
\end{equation}
which requires us to first compute $\det\mathbf{G}_{1}$, $\det\mathbf{G}_{2}$,
and $\det\mathbf{U}$. The same procedure can then be applied
to compute the determinant of $\mathbf{G}_{1}$ and the determinant
of $\mathbf{G}_{2}$. This can be repeated recursively until the dimension
becomes $1$.

One major obstacle of this approach, however, is that the degrees
of the unimodular matrix $\mathbf{U}$ and the matrix $\mathbf{G}$
can be too large for efficient computation. %
\begin{comment}
To construct such an example, just use a random $k\times\left(k+1\right)$
matrix $\mathbf{A}$, and set $\mathbf{F}=\begin{bmatrix}\mathbf{A} & 0\\
* & *
\end{bmatrix}$, and compute $\mathbf{G}_{1}$ as a column basis of $\mathbf{A}$.
Then the degrees of $\mathbf{U}$ and $\mathbf{G}$ are often $\Theta(nd)$.
\end{comment}
{}
To sidestep this issue, we will show that the matrices $\mathbf{G}_{1}$,
$\mathbf{G}_{2}$, and the scalar $\det\mathbf{U}$ can in fact be computed
without computing the entire matrices $\mathbf{G}$ and $\mathbf{U}$.

\subsection{Computing the diagonal blocks}

Suppose we want $\mathbf{G}_{1}$ to have dimension $k$. We can partition\textbf{
$\mathbf{F}$ }as $\mathbf{F}=\begin{bmatrix}\mathbf{F}_{U}\\
\mathbf{F}_{D}
\end{bmatrix}$ with $k$ rows in $\mathbf{F}_{U}$, and note that both $\mathbf{F}_{U}$
and $\mathbf{F}_{D}$ are of full-rank since $\mathbf{F}$ is assumed
to be nonsingular. By partitioning $\mathbf{U}=\begin{bmatrix}\mathbf{U}_{L}~~, & \mathbf{U}_{R}\end{bmatrix}$,
with $k$ columns in $\mathbf{U}_{L}$, then
\begin{equation}
\mathbf{F} \cdot \mathbf{U}=\begin{bmatrix}\mathbf{F}_{U}\\
\mathbf{F}_{D}
\end{bmatrix}\begin{bmatrix}\mathbf{U}_{L} & \mathbf{U}_{R}\end{bmatrix}=\begin{bmatrix}\mathbf{G}_{1} & 0\\
* & \mathbf{G}_{2}
\end{bmatrix}=\mathbf{G}.\label{eq:UPartitioned}
\end{equation}
Notice that the matrix $\mathbf{G}_{1}$ is nonsingular and is therefore
a column basis of $\mathbf{F}_{U}$. As such this can be efficiently
computed
as mentioned in Theorem \ref{thm:fastcolbasis}. In addition, the
column basis algorithm makes the resulting column degrees of $\mathbf{G}_{1}$
small enough for $\mathbf{G}_{1}$ to be efficiently used again as
the input matrix of a new subproblem in the recursive procedure.
\begin{lem}
\label{lem:firstDiagonalBlock}The first diagonal block $\mathbf{G}_{1}$
in $\mathbf{G}$ can be computed with a cost of ${O\tilde{\phantom{\imath}}}\left(n^{\omega}s\right)$
and with column degrees bounded by the $k$ largest column degrees
of $\mathbf{F}$.
\end{lem}
For computing the second diagonal block $\mathbf{G}_{2}$, notice
that we do not need a complete unimodular matrix $\mathbf{U}$, as only
$\mathbf{U}_{R}$ is needed to compute $\mathbf{G}_{2}=\mathbf{F}_{D}\mathbf{U}_{R}$.
In fact, \prettyref{lem:unimodular_kernel_columnBasis} tells us much
more. It tells us that the matrix $\mathbf{U}_{R}$ is a right kernel
basis of $\mathbf{F}$, which makes the top right block of $\mathbf{G}$
zero. In addition the kernel basis $\mathbf{U}_{R}$ can be replaced by any
other kernel basis of $\mathbf{F}$ to give another unimodular matrix
that also transforms $\mathbf{F}_{U}$ to a column basis and also
eliminates the top right block of $\mathbf{G}$.
\begin{lem}
\label{lem:oneStepHermiteDiagonal} Partition $\mathbf{F}=\begin{bmatrix}\mathbf{F}_{U}\\
\mathbf{F}_{D}
\end{bmatrix}$ and suppose $\mathbf{G}_{1}$ is a column basis of $\mathbf{F}_{U}$
and $\mathbf{N}$ a kernel basis of $\mathbf{F}_{U}$. Then there
is a unimodular matrix $\mathbf{U}=\left[~*~,~\mathbf{N}\right]$
such that
\[
\mathbf{F} \cdot \mathbf{U}=\begin{bmatrix}\mathbf{G}_{1} & 0\\
* & \mathbf{G}_{2}
\end{bmatrix},
\]
 where $\mathbf{G}_{2}=\mathbf{F}_{D} \cdot \mathbf{N}$. If $\mathbf{F}$
is square nonsingular, then $\mathbf{G}_{1}$ and $\mathbf{G}_{2}$
are also square nonsingular.
\end{lem}
Note that the blocks represented by the symbol $*$ are not needed in
our computation. These blocks may have very large degrees and cannot
be computed efficiently.

We have just seen how $\mathbf{G}_{1}$
and $\mathbf{G}_{2}$ can be determined without computing the unimodular matrix $\mathbf{U}$. We still need to make sure that
$\mathbf{G}_{2}$ can be computed efficiently, which can be done by using the existing
algorithms for kernel basis computation and the multiplication of
matrices with unbalanced degrees. We also require that the column
degrees of $\mathbf{G}_{2}$ be small enough for $\mathbf{G}_{2}$
to be efficiently used again as the input matrix of a new subproblem
in the recursive procedure.
\begin{lem}
\label{lem:secondDiagonalBlock}
The second diagonal
block $\mathbf{G}_{2}$ can be computed with a cost of ${O\tilde{\phantom{\imath}}}\left(n^{\omega}s\right)$
field operations. Furthermore $\sum{\rm cdeg}\,\mathbf{G}_{2}\le\sum\vec{s}$.
\end{lem}
\begin{proof}
From \prettyref{lem:oneStepHermiteDiagonal} we have that $\mathbf{G}_{2}=\mathbf{F}_{D} \cdot \mathbf{N}$
with $\mathbf{N}$ a kernel basis  of $\mathbf{F}_{U}$. In fact, this
kernel basis can be made $\vec{s}$-minimal using the algorithm from
\cite{za2012}, and computing such a $\vec{s}$-minimal kernel basis
of $\mathbf{F}_{U}$ costs ${O\tilde{\phantom{\imath}}}\left(n^{\omega}s\right)$ field
operations by \prettyref{thm:costGeneral}.
In addition, from \prettyref{thm:boundOfSumOfShiftedDegreesOfKernelBasis} the sum of
the $\vec{s}$-column degrees of such a $\vec{s}$-minimal $\mathbf{N}$
is bounded by $\sum\vec{s}$.

For the matrix multiplication $\mathbf{F}_{D} \cdot \mathbf{N}$, the sum
of the column degrees of $\mathbf{F}_{D}$ and the sum of the $\vec{s}$-column
degrees of $\mathbf{N}$ are both bounded by $\sum\vec{s}$.
Therefore
we can
apply \prettyref{thm:multiplyUnbalancedMatrices}
directly to multiply $\mathbf{F}_{D}$ and $\mathbf{N}$ with a cost
of ${O\tilde{\phantom{\imath}}}\left(n^{\omega}s\right)$ field operations.

The second statement follows from \prettyref{lem:predictableDegree}.
\end{proof}

The computation of a kernel basis $\mathbf{N}$ of $\mathbf{F}_{U}$ is actually also used as an intermediate step by the column basis algorithm for computing the column basis $\mathbf{G}_{1}$  \citep{za2013}. In other words, we can get this kernel basis from the computation of $\mathbf{G}_{1}$ with no additional work.

\subsection{Determinant of the unimodular matrix}

\prettyref{lem:firstDiagonalBlock} and \prettyref{lem:secondDiagonalBlock}
show that the two diagonal blocks in \prettyref{eq:step1HermiteDiagonal}
can be computed efficiently. In order to compute the determinant of $\mathbf{F}$
using \prettyref{eq:determinantFromDiagonalBlocks}, we still need
to know the determinant of the unimodular matrix $\mathbf{U}$
satisfying \prettyref{eq:UPartitioned}, or equivalently, we can also
find out the determinant of $\mathbf{V}=\mathbf{U}^{-1}$. The column basis computation from  \cite{za2013} for computing the diagonal block $\mathbf{G}_{1}$  also gives $\mathbf{U}_{R}$,
the matrix consisting of the right $(n-k)$ columns of $\mathbf{U}$, which is also a right kernel
basis of $\mathbf{F}_{U}$. In fact, this column basis computation also gives
 a right factor multiplied with the column basis $\mathbf{G}_{1}$ to give  $\mathbf{F}_{U}$.  The following lemma shows that this right factor coincides with the the matrix $\mathbf{V}_{U}$ consisting of the top $k$ rows of $\mathbf{V}$.  The column basis computation therefore gives both $\mathbf{U}_{R}$ and $\mathbf{V}_{U}$ with no additional work.
\begin{lem}
Let $k$ be the dimension of $\mathbf{G}_{1}$. The matrix $\mathbf{V}_{U}\in\mathbb{K}\left[x\right]^{k\times n}$
satisfies $\mathbf{G}_{1} \cdot \mathbf{V}_{U}=\mathbf{F}_{U}$ if and only
if $\mathbf{V}_{U}$ is the submatrix of $\mathbf{V}=\mathbf{U}^{-1}$
consisting of the top $k$ rows of $\mathbf{V}$. \end{lem}
\begin{proof}
The proof follows directly from
\[
\mathbf{G} \cdot \mathbf{V}=\begin{bmatrix}\mathbf{G}_{1} & 0\\
* & \mathbf{G}_{2}
\end{bmatrix}\begin{bmatrix}\mathbf{V}_{U}\\
\mathbf{V}_{D}
\end{bmatrix}=\begin{bmatrix}\mathbf{F}_{U}\\
\mathbf{F}_{D}
\end{bmatrix}=\mathbf{F}.
\]

\end{proof}
While the determinant of $\mathbf{V}$ or the determinant of $\mathbf{U}$
is needed to compute the determinant of $\mathbf{F}$, a major problem
is that we do not know $\mathbf{U}_{L}$ or $\mathbf{V}_{D}$, which
may not be efficiently computed due to their large degrees. This means
we need to compute the determinant of $\mathbf{V}$ or $\mathbf{U}$
without knowing the complete matrix $\mathbf{V}$ or $\mathbf{U}$.
The following lemma shows how this can be done using just $\mathbf{U}_{R}$
and $\mathbf{V}_{U}$, which are obtained from the computation of the column basis $\mathbf{G}_{1}$.
\begin{lem}
\label{lem:scalingToDeterminant} Let $\mathbf{U}=\left[\mathbf{U}_{L},\mathbf{U}_{R}\right]$
and $\mathbf{F}$ be as before, that is, they satisfy
\[
\mathbf{F} \cdot \mathbf{U}=\begin{bmatrix}\mathbf{F}_{U}\\
\mathbf{F}_{D}
\end{bmatrix}\begin{bmatrix}\mathbf{U}_{L} & \mathbf{U}_{R}\end{bmatrix}=\begin{bmatrix}\mathbf{G}_{1} & 0\\
* & \mathbf{G}_{2}
\end{bmatrix}=\mathbf{G},
\]
 where the row dimension of $\mathbf{F}_{U}$, the column dimension
of $\mathbf{U}_{L}$, and the dimension of $\mathbf{G}_{1}$ are $k$.
Let $\mathbf{V}=\begin{bmatrix}\mathbf{V}_{U}\\
\mathbf{V}_{D}
\end{bmatrix}$ be the inverse of $\mathbf{U}$ with $k$ rows in $\mathbf{V}_{U}$.
If $\mathbf{U}_{L}^{*}\in\mathbb{K}\left[x\right]^{n\times k}$ is
a matrix such that $\mathbf{U}^{*}=\left[\mathbf{U}_{L}^{*},\mathbf{U}_{R}\right]$
is unimodular, then
\[
\det\mathbf{F}~=~\frac{\det\mathbf{G}\cdot\det\left(\mathbf{V}_{U}\mathbf{U}_{L}^{*}\right)}{\det\left(\mathbf{U}^{*}\right)}.
\]
\end{lem}
\begin{proof}
Since $\det\mathbf{F}~=~\det\mathbf{G}\cdot\det\mathbf{V}$, we just
need to show that $\det\mathbf{V}=\det\left(\mathbf{V}_{U}\mathbf{U}_{L}^{*}\right)/\det\left(\mathbf{U}^{*}\right)$.
This follows from
\begin{eqnarray*}
\det\mathbf{V}\cdot\det\mathbf{U}^{*} & = & \det\left(\mathbf{V}\cdot\mathbf{U}^{*}\right)\\
 & = & \det\left(\begin{bmatrix}\mathbf{V}_{U}\\
\mathbf{V}_{D}
\end{bmatrix}\begin{bmatrix}\mathbf{U}_{L}^{*} & \mathbf{U}_{R}\end{bmatrix}\right)\\
 & = & \det\left(\begin{bmatrix}\mathbf{V}_{U}\mathbf{U}_{L}^{*} & 0\\
* & I
\end{bmatrix}\right)\\
 & = & \det\left(\mathbf{V}_{U}\mathbf{U}_{L}^{*}\right).
\end{eqnarray*}

\end{proof}
\prettyref{lem:scalingToDeterminant} shows that the determinant of
$\mathbf{V}$ can be computed using $\mathbf{V}_{U}$, $\mathbf{U}_{R}$, and
a unimodular completion $\mathbf{U}^*$ of $\mathbf{U}_{R}$.
In fact, this can be made more efficient still by noticing that the
higher degree parts do not affect the computation.
\begin{lem}
\label{lem:determinantOfUnimodular}If $\mathbf{U}\in\mathbb{K}\left[x\right]^{n\times n}$
is unimodular, then $\det\mathbf{U}=\det\left(\mathbf{U}\mod x\right)=\det\left(\mathbf{U}\left(0\right)\right)$.\end{lem}
\begin{proof}
Note that $\det\left(\mathbf{U}\left(\alpha\right)\right)=\left(\det\mathbf{U}\right)\left(\alpha\right)$
for any $\alpha\in\mathbb{K}$, that is, the result is the same whether
we do evaluation before or after computing the determinant. Taking
$\alpha=0$, we have
\[
\det\left(\mathbf{U}\mod x\right)=\det\left(\mathbf{U}\left(0\right)\right)=\left(\det\mathbf{U}\right)\left(0\right)=\det\left(\mathbf{U}\right)\mod x=\det\mathbf{U}.
\]

\end{proof}
Lemma \ref{lem:determinantOfUnimodular} allows us to use just the degree zero coefficient matrices in the computation. Hence \prettyref{lem:scalingToDeterminant} can be improved as follows.
\begin{lem}
\label{lem:scalingToDeterminantSimplified} Let $\mathbf{F}$, $\mathbf{U}=\left[\mathbf{U}_{L},\mathbf{U}_{R}\right]$,
and $\mathbf{V}=\begin{bmatrix}\mathbf{V}_{U}\\
\mathbf{V}_{D}
\end{bmatrix}$ be as before. Let $U_{R}=\mathbf{U}_{R}\mod x$ and $V_{U}=\mathbf{V}_{U}\mod x$
be the constant matrices of $\mathbf{U}_{R}$ and $\mathbf{V}_{U}$,
respectively. If $U_{L}^{*}\in\mathbb{K}^{n\times*}$ is a matrix
such that $U^{*}=\left[U_{L}^{*},U_{R}\right]$ is unimodular, then
\[
\det\mathbf{F}~=~\frac{\det\mathbf{G}\cdot\det\left(V_{U}U_{L}^{*}\right)}{\det\left(U^{*}\right)}.
\]
 \end{lem}
\begin{proof}
\prettyref{lem:determinantOfUnimodular} implies that $\det\mathbf{V}=\det V$
and $\det\mathbf{U}^{*}=\det U^{*}$. These can then be substituted
in the proof of \prettyref{lem:scalingToDeterminant} to obtain the
result.\end{proof}
\begin{rem}
\prettyref{lem:scalingToDeterminantSimplified} requires us to compute
$U_{L}^{*}\in\mathbb{K}^{n\times *}$ a matrix such that $U^{*}=\left[U_{L}^{*},U_{R}\right]$
is unimodular. This can be obtained from the unimodular matrix
that transforms $V_{U}$ to its reduced column echelon form computed
using the Gauss Jordan transform algorithm from \citep{storjohann:phd2000}
with a cost of $O\left(nm^{\omega-1}\right)$ where $m$ is the column dimension of $U_{L}^{*}$.
\end{rem}
We now have all the ingredients needed for computing the determinant
of $\mathbf{F}$. A recursive algorithm is given in Algorithm \prettyref{alg:determinant},
which computes the determinant of $\mathbf{F}$ as the product of
the determinant of $\mathbf{V}$ and the determinant of $\mathbf{G}$.
The determinant of $\mathbf{G}$ is computed by recursively computing
the determinants of its diagonal blocks $\mathbf{G}_{1}$ and $\mathbf{G}_{2}$.

\begin{algorithm}[t]
\caption{$\determinant(\mathbf{F})$}
\label{alg:determinant}

\begin{algorithmic}[1]
\REQUIRE{$\mathbf{F}\in\mathbb{K}\left[x\right]^{n\times n}$,  nonsingular.
}

\ENSURE{the determinant of $\mathbf{F}$.}

\STATE{$\begin{bmatrix}\mathbf{F}_{U}\\
\mathbf{F}_{D}
\end{bmatrix}:=\mathbf{F}$, with $\mathbf{F}_{U}$ consists of the top $\left\lceil n/2\right\rceil $
rows of $\mathbf{F}$;}

\STATE{\textbf{if }$n=1$ \textbf{then} \textbf{return} $\mathbf{F}$; \textbf{endif};}

\STATE{$\mathbf{G}_{1},\mathbf{U}_{R},\mathbf{V}_{U}:=\colBasis(\mathbf{F}_{U})$;
\\ \hspace{0.15in} {\bf Note:} Here $\colBasis()$ also returns the kernel basis $\mathbf{U}_{R}$ and
the
right factor $\mathbf{V}_{U}$
\\ \hspace{0.3in}
 it computed in addition to the column basis $\mathbf{G}_{1}$.}

\STATE{$\mathbf{G}_{2}:=\mathbf{F}_{D}\mathbf{U}_{R}$;}

\STATE{$U_{R}:=\mathbf{U}_{R}\mod x$; $V_{U}:=\mathbf{V}_{U}\mod x$;}

\STATE
Compute $U_{L}^{*}\in\mathbb{K}^{n\times k}$ , a matrix that makes
 $U^{*}=\left[U_{L}^{*},U_{R}\right]$ unimodular;
}

\STATE{$d_{V}:=\det\left(V_{U}U_{L}^{*}\right)/\det(U^{*};$}

\STATE{$\mathbf{d}_{G}:=\determinant(\mathbf{G}_{1})\cdot\determinant(\mathbf{G}_{2});$}

\STATE{\textbf{return} $d_{V}\cdot\mathbf{d}_{G}$;}
\end{algorithmic}
\end{algorithm}

\begin{example}
In order to see correctness of the algorithm, let
\[
\mathbf{F}=\left[\begin{array}{rcccc}
x & -{x}^{3} & -2\,{x}^{4} & 2x & -{x}^{2}\\
\noalign{\medskip}1 & -1 & -2\, x & 2 & -x\\
\noalign{\medskip}-3 & 3\,{x}^{2}+x & 2\,{x}^{2} & -\,{x}^{4}+1 & 3\, x\\
\noalign{\medskip}0 & 1 & {x}^{2}+2\, x-2 & \,{x}^{3}+2x-2 & 0\\
\noalign{\medskip}1 & -{x}^{2}+2 & -2\,{x}^{3}-3\, x+3 & 2x+2 & 0
\end{array}\right]
\]
 working over $\mathbb{Z}_{7}[x]$. If $\mathbf{F}_{U}$ denotes the
top three rows of $\mathbf{F}$ then a column basis
\[
\mathbf{G}_{1}=\left[\begin{array}{rcr}
x & -{x}^{3} & -2\,{x}^{4}\\
\noalign{\medskip}1 & -1 & -2\, x\\
\noalign{\medskip}-3 & 3\,{x}^{2}+x & 2\,{x}^{2}
\end{array}\right]
\]
 and minimal kernel basis
\[
\mathbf{U}_{R}=\left[\begin{array}{rc}
-1 & x\\
-x^{2} & 0\\
-3x & 0\\
-3 & 0\\
0 & 1
\end{array}\right]
\]
for $\mathbf{F}_{U}$ were given in Example \ref{ex:example1}. The computation of the
column basis also gives the right factor
\[
\mathbf{V}_{U}=\left[\begin{array}{cccrr}
1 & 0 & 0 & 2 & -x\\
0 & 1 & 0 & 2x^{2} & 0\\
0 & 0 & 1 & -x & 0
\end{array}\right].
\]
The constant term matrices are then
\[
{U}_{R}=\left[\begin{array}{rc}
-1 & 0\\
0 & 0\\
0 & 0\\
-3 & 0\\
0 & 1
\end{array}\right]~\mbox{and}~~{V}_{U}=\left[\begin{array}{cccrr}
1 & 0 & 0 & 2 & 0\\
0 & 1 & 0 & 0 & 0\\
0 & 0 & 1 & 0 & 0
\end{array}\right]
\]
with Gaussian-Jordan used to fnd a unimodular completion of $U_{R}$ as
\[
U_{L}^{*}=\left[\begin{array}{ccc}
1 & 0 & 0\\
0 & 1 & 0\\
0 & 0 & 1\\
0 & 0 & 0\\
0 & 0 & 0
\end{array}\right].
\]
 The determinant of $\mathbf{V}$ is then computed as
\[
\frac{\det\left(V_{U}U_{L}^{*}\right)}{\det\left(U^{*}\right)}=-\frac{1}{3}=2.
\]
Recursively computing the determinant of $\mathbf{G}_{1}$ and $\mathbf{G}_{2}$ gives $\det\mathbf{G}_{1}=x^{6}-x^{4}$ and $\det\mathbf{G}_{2}=x^{4}-x$.
Accumulating the above gives the determinant of $\mathbf{F}$ as
\[
\det\mathbf{F}=\det\mathbf{V}\cdot\det\mathbf{G}_{1}\cdot\det\mathbf{G}_{2}=2\left(x^{6}-x^{4}\right)\left(x^{4}-x\right)=2x^{10}-2x^{8}-2x^{7}+2x^{5}.
\]
\qed \end{example}

\subsection{Computational cost}
\begin{thm}
\label{thm:diagonalCost} Algorithm \prettyref{alg:determinant}
costs ${O\tilde{\phantom{\imath}}}\left(n^{\omega}s\right)$ field operations to compute
the determinant of a nonsingular matrix $\mathbf{F}\in\mathbb{K}\left[x\right]^{n\times n}$,
where $s$ is the average column degree of $\mathbf{F}$. \end{thm}
\begin{proof}
From \prettyref{lem:firstDiagonalBlock} and \prettyref{lem:secondDiagonalBlock}
the computation of the two diagonal blocks $\mathbf{G}_{1}$ and $\mathbf{G}_{2}$
costs $O^{\sim}\left(n^{\omega}s\right)$ field operations, which
dominates the cost of the other operations in the algorithm.

Now consider the cost of the algorithm on a subproblem in the recursive computation. If we let the cost
be $g(m)$ for a subproblem whose input matrix has dimension $m$, by \prettyref{lem:firstDiagonalBlock}
and \prettyref{lem:secondDiagonalBlock} the sum of the column degrees
of the input matrix is still bounded by $ns$, but the average column
degree is now bounded by $ns/m$. The cost on the subproblem is then
\begin{eqnarray*}
g(m) & \in & O^{\sim}(m^{\omega}\left(ns/m\right))+g(\left\lceil m/2\right\rceil )+g(\left\lfloor m/2\right\rfloor )\\
 & \subset & O^{\sim}(m^{\omega-1}ns)+2g(\left\lceil m/2\right\rceil )\\
 & \subset & O^{\sim}(m^{\omega-1}ns).
\end{eqnarray*}
 The cost on the original problem when the dimension $m=n$ is therefore
$O^{\sim}\left(n^{\omega}s\right)$.
\begin{comment}
From \prettyref{lem:firstDiagonalBlock} and \prettyref{lem:secondDiagonalBlock}
the computation of the two diagonal blocks $\mathbf{G}_{1}$ and $\mathbf{G}_{2}$
costs ${O\tilde{\phantom{\imath}}}\left(n^{\omega-1} \xi\right)$ field operations, where $\xi$  is the sum of the column degree of $\mathbf{F}$.
Now for the rest of the recursive algorithm, if we let its cost on a subproblem
be $g(m)$ for the input matrix of dimension $m$, by \prettyref{lem:firstDiagonalBlock}
and \prettyref{lem:secondDiagonalBlock} then the cost
\begin{eqnarray*}
g(n) & \in & {O\tilde{\phantom{\imath}}}(n^{\omega-1}\xi)+g(\left\lceil n/2\right\rceil )+g(\left\lfloor n/2\right\rfloor )\\
 & \in & {O\tilde{\phantom{\imath}}}(n^{\omega-1} \xi)+2g(\left\lceil n/2\right\rceil )\\
 & \in & {O\tilde{\phantom{\imath}}}(n^{\omega-1}\xi) = {O\tilde{\phantom{\imath}}}\left(n^{\omega}s\right).
\end{eqnarray*}
\end{comment}
\end{proof}

\section{Conclusion\label{sec:Future-Research}}

In this paper we have given a new, fast, deterministic algorithm for computing
the determinant of a nonsingular polynomial matrix. Our method relies on the efficient, deterministic computation of the diagonal elements of a triangularization of the input matrix. This in turn relies on recent efficient methods \cite{za2013,za2012} for computing shifted minimal kernel and column bases of polynomial matrices.

In a future report we will show how our triangularization technique results in a fast, deterministic algorithm for finding a Hermite normal form. Other directions of interest include making use of the diagonalization procedures in domains such as matrices of differential or, more generally, of Ore operators, particularly for computing normal forms. Partial results had been reported in \cite{davies-cheng:2006}, at least in the case of Popov normal forms.
Similarly we are interested in applying our block elimination techniques using kernal bases to computing the Dieudonn\'e determinant and quasideterminant of matrices for Ore polynomial rings. These are the two main generalizations of determinants for matrices of noncommutative polynomials.  Degree bounds for these noncommutative determinants have been used in \cite{markkim} for modular computation of normal forms.

\bibliographystyle{plain}


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text:
Tag: internet radio
Internet Radio – The Next Big Thing: Exaget Week in Review
Internet radio has entered its first teenage years. 2015 has marked its thirteenth year, and internet radio has already come a long way for something that's still relatively young and fresh. Whilst other radio platforms, such as DAB or the sage analogue, are struggling in keeping up with the hip competition that is online music streaming, internet radio is not only keeping up with the game, but come another thirteen years, could very well surpass it.
So this week, we are dedicating our Week in Review to Internet Radio. Happy Birthday chum!
Dutch go digital, apart from when it comes to radio
It looks like it's not just the UK that's being rather obstinate and slow to jump on the DAB world domination band-wagon. According to Dutch broadcaster Nos, the government's multi-million euro campaign to get people to make the DAB radio switch is failing. Experts in the Netherlands' radio industry say that switching off FM in 2017 is a fairy tale, and that it will take at least another ten years before people are ready. But it's not FM that's DAB's threat. It's internet radio. Sales of internet radios are much more popular, and more consumers have switched from FM to internet radio both at home and in their cars. Is the UK to soon see a familiar pattern?
Recruiting from radio: Apple hires Zane Lowe from BBC
Legendary BBC Radio 1 presenter Zane Lowe is making news waves as it emerged this week that he's now set on joining Apple after over a decade of BBC radio broadcasting. His exact role is as yet unknown, but nevertheless the news are enough to make one stroke one's chin and ponder, 'What is this going to mean for internet radio?' Apple is very much a tech company first and foremost, and much like Pandora depends on algorithms to 'interact' with its listeners. But now this tech-driven online music platform is reaching deep into broadcast radio and acquiring the presence of a real-life human being – the trusted host. Apple being Apple, of course it's going to be the first to set a new trend; and Apple being Apple, of course other companies are going to attempt to follow in its footsteps.
Five things internet radio should steal from broadcast
With Zane Lowe's announcement that he's to join Apple soon, it looks like the worlds of music streaming and broadcast radio are converging – and of course, who better to start this trend that Apple. Real life human presenters, who reach out to the audience and create a living relationship with them through the mutual love of music, is a big factor that internet radio is missing, and one that makes it, in contrast to analogue and DAB radio, rather soulless. But it's not just the human touch that internet radio can take from its bigger broadcast brother. This great insight looks at five other things that internet radio can steal from broadcast, including local programming, music and artist familiarity (which, in its bid to become a source of new undiscovered music, internet radio is overlooking), and audience building and ad selling through recurrents.
Internet radio is young, but it has all the potential and all the signs of becoming the next big thing.
If you are interested in becoming a broadcasting partner, or would like to know what our integrating technology can do for you, contact our Partnership Account Manager Matthew Layton – matthew.layton@exaget.com or +447533517396
If you are interested in advertising opportunities, please contact the CEO of Exaget, Shankar Meembat –shankar.meembat@exaget.com or +447411130680
The Importance of Content: Exaget Week in Review
In last week's Week in Review we looked at the growth and acquisition of some well-known and emerging music streaming services as this market becomes increasingly competitive.
This week we're looking at the various ways in which brands and companies use their content across a variety of platforms to reach new audiences while keeping their current ones happy.
BBC to test 'experimental' digital technology and content
The BBC has launched an online platform, BBC Taster, which will allow them to develop and test ideas for digital content and technology, which audiences will be able to watch and rate; such as interactive, short-form or social content, online features, as well as digital technology from BBC Future Media. The BBC hopes that this platform will enable them to respond to changing media habits as well as better serve its audience from gained feedback.
Umano offers streaming narrations of the web's written work
Quite simply, Umano reads the internet for you, so that you don't have to. The company supplies audio narrations of written web content, and currently has access to articles from several outlets, such as Forbes, Digital Trends, and VentureBeat. Umano's PR have stated all narrations have links back to the original written posts, which will drive new traffic to the original publishers. Available as a free app for iOS and Android, the programme has already seen millions of downloads and streams, according to their PR. It's good to see illiteracy levels being kept down….
Rdio launches in new countries & partners with Digicel
Rdio continues its empirical expansion into 24 new countries and territories across the Caribbean, Central America and Asia Pacific, as well as partnering with mobile phone network Digicel. 30 minutes of free Rdio internet radio listening will be offered to Digicel prepaid customers per day. A pay structure is, however, to be developed and launched in due time. These moves come following Rdio's recent launch in India, where last year they acquired music streaming service Dhingana. Rdio CEO Anthony Bay had previously hinted at expansion plans: 'Our ultimate goal is to be everywhere.'
Twitter tries to up its game with native video
Twitter is set to take on the likes of Facebook and YouTube in the world of native video content. Video is both a crucial and an important form of content for Twitter, as it drives engagement and generates more revenue than other forms of media. By launching its own video platform, users will be encouraged to upload their videos directly to Twitter rather than post links to clips on Facebook or YouTube, or any other video platform.
NPR One – The blueprint for mobile radio apps?
Statistically, online radio listening is increasing year-on-year, with the biggest percentage of listeners falling in the 12-24 years of age bracket; and it's the same story for music streaming services. As both audio platforms try to boost their listener percentage, they must look at what makes them different from their competitors. But online radio looks like it might have an advantage…
BURSTING AT THE SEAMS
There is no denying that the online music streaming industry is over-saturated. Just off the top of your head you would probably be able to name Spotify, Pandora, Deezer, SoundCloud and Grooveshark. And that's just the big international players – imagine how many more, local, music streaming services there are the world over. Just last week it was announced that Tesco's ex-music streaming service, Blinkbox Music, is to be sold to Guvera, yet another such service, hailing from Australia. French service Deezer acquired US based Muve Music to expand their music streaming footprint in America. And yet again this week we have been informed of two – yes, two – more music streaming services that we should keep our ears peeled for – Boomio and Nusiki, who both lay claims to providing users with services that are different, and better, than their competitors.
'IF INSTAGRAM AND SPOTIFY HAD A KID'
Brian Hewitt, co-founder of Chicago-based Nusiki, has described this new app as 'if Instagram and Spotify had a kid'. The secret, it seems, in launching these new apps, is in implementing small features which other apps have overlooked and making a big fuss over that. Spotify shares music too publicly? Ok, we'll make our sharing system more controlled, as in the case of Nusiki. After all, it's the little things that make the difference, a phrase that seems to carry a lot of weight in the world of music streaming.
Boomio's mantra seems to be 'sharing is caring' as users pick a song to listen to and share, and at the end are prompted to either re-share in order to hear the next song or buy the track on iTunes. Sharing can be done to an individual, a group, or a social network.
But at the end of the day, music streaming services are limited in what they can offer to the listener when compared to the content of radio. Radio stations are of course already available on mobile phones, but they often lack that element of personalisation that such services as Spotify and Pandora offer. But what if there was an app that brought to you relevant news and stories, in bite sized chunks, from your local radio station as well as internationally, with the curation aspect of music streaming services?
Larry Rosin, president of Edison Research, has recently talked about one such app – NPR One. Dubbed 'Public radio made personal', it is available only in the US, although users worldwide can still download it and listen in. The app itself has many great qualities, but it's not just good; it could well be a blue-print for future radio apps with which to take the online audio platform by storm.
'PANDORA-ITISATION OF CONTENT'
The advantages of radio are numerous and well-known. One of the oldest social mediums, it still continues to have a large relevance in people's day-to-day lives. What NPR One does so well is offer their listeners efficiency. Up-to-date relevant news and stories, in under 5 or 10 minutes. Like the music streaming services, you can skip stories, flag your favourite, and share. But it also reminds the listener that there is a local public radio station as part of its programme, and one that needs financial support. Through this scheme the app inspires a wholesome community feel; radio really does bring people together.
Of course, NPR One only deals with news and stories; there is no music, no presenter tete-a-tete, no real-time traffic and weather updates. But all of these typical radio features could be merged with NPR One's principal concept to create great personalised radio apps, which would have a better value to listeners than all the current numerous music streaming services which fundamentally all do the same thing, albeit in differently packaged ways.
And it's not just broadcasters and listeners who would benefit from such apps; advertisers too could cash in by the implementation of personalised user-targeted ads.
The moral of the story? NPR One have a great mission and concept. Taken on a global scale and implemented by other radio apps, mobile radio would certainly offer much more than music streaming services – the varied content of radio, with the curated personalisation of music streaming, and adverts tailored to both listener and broadcaster. We all know that radio as a medium is still going strong, with audience figures constantly on the up, and it's refreshing to see that younger listeners haven't been completely sucked in by the world of streaming – at least, not in the UK.
The Tide Turns for Music Streaming: Exaget Week in Review
In our last Week in Review, we took a look into our crystal ball to see what new ventures may be coming out of the woodwork this year – including the futuristic concept of smart glasses.
This week, however, we turn our attention back to something that is already a big, popular, and sought-after phenomena – music streaming services. With Tesco last week announcing its sale of Blinkbox, the streaming services scene is about to become even more competitive as two new rivals are set to emerge this year:
Tesco close to selling Blinkbox Music
Last week, one of Britain's largest retailers sold their video streaming service, Blinkbox Movies, to telecoms business TalkTalk in a bid to reel in cash spend – and profit loss. This week they are set to sell Blinkbox Music, their music streaming service, to Australian company Guvera, who are already big in Asia and partnered with Lenovo. Guvera will use this acquisition as a means to get their foot into the UK and European market. Under their management, Blinkbox Music will undergo a face transplant in the form of new branding.
Deezer acquires Muve Music
We bring our attention back to European players – more specifically, to French music streaming service Deezer. They already launched in the US in September 2014 following a partnership with Sonos, but now, with the acquisition of Muve Music, they are set to expand their presence in the US – which is also home to perhaps their biggest rival, Pandora. What will make Deezer different? Access to an impressive 35 million tracks, and a tantalising price of $6 per month, compared to the $10 that most other services charge. Will this launch them into a big player on the scale of Pandora? Watch this space…
Why mobile is key to Spotify's future growth
Swedish music streaming behemoth Spotify is this week celebrating 15m paid subscribers and 60m active users; and more than half of these users are streaming via their mobile devices. Statistics show that 42% stream on smartphones, and 10% on tablets. Their free streaming on mobile through their shuffle feature increased their amount of mobile listeners dramatically; but now their goal is to transfer these listeners into paid subscribers. But with Apple to automatically install Beats Music on their iPhones, it will be interesting to monitor how this will affect Spotify's iOS users.
Radio still beats digital for music discovery
Despite the influx of music streaming services vying for your attention, ears, and wallets, the days of the radio are still going strong. The latest statistics from Nielsen have shown that 51% of music consumers in the US find new songs through the radio – that's an impressive 243 million. The figures include all platforms of radio; car radios, AM/FM sets, and online radio. They also show that listening in the car is the most common way of enjoying music; and that Disney's Frozen soundtrack is the number one listened to. It looks like there's no letting go of it…..see what we did there?
'Cars will have radios in 2015'
Roger Lanctot, thought-leader in the connected-car space, has recently made this prediction: that cars in 2015 will have radios. Now, that might seem a little bit obvious at first glance, but with the increasing rise of online audio streaming services and podcasts, it may look as though radio is in danger. But we disagree. Radio, across its various platforms, is here to stay – it's just evolving.
There is something about silence in a car that is discomforting and awkward. A silent car with passengers puts strains on social etiquette as you grapple for something inane to say. We need audio in our cars. But AM/FM radio is struggling to maintain its presence as the UK may or not be poised on the brink of a national DAB switchover. The glitch with AM/FM? The hissing and crackling of radio white noise, which is an infuriating and teeth-grinding experience. It was all very well listening to your favourite Capital FM while you whizzed around London, but dare to venture into a neighbouring home county and you'd be met with white noise and no choice but to browse for a local radio's reception, or switch to a CD.
And it's not just DAB that's threatening AM/FM – younger generations are becoming increasingly dependent on and attached to their mobile devices, increasing radio listening among mobile users. And at this year's Consumer Electronics Show, a new potential craze really came to the fore – the connected car.
Both the CES, held in Las Vegas this year, and the North American International Auto Show in Detroit – dubbed the 'Motor City' – aimed their focus on the future of the connected-car and the probability of bringing this concept one step closer to consumer production. And whilst Mercedes-Benz's self-driving model is a stretch beyond our imagination and not due to hit any car dealerships any time soon, the first connected-cars may well be on roads this year. And as the name suggests, they are connected to the internet.
Connected cars, with their fancy apps, could make the radio obsolete as they sidle over to the dark side of music streaming services. Rdio, one such service, is to pair up with Bosch, an interface manufacturer for connected cars. In Jaguars and Land Rovers, which use Bosch's system, Rdio will be the only subscription music app. Except that the automakers are also planning on partnering with Apple and their own connected-car system, Carplay. Add into this mix Spotify, Pandora, and Google's Android Auto and it's all a bit of a kerfuffle from the business perspective.
But whilst streaming services are cool and popular, there are two fundamental downsides to having them in your car as a radio replacement. Firstly, streaming services could potentially be a hazard to drivers. Think about how frequently you flick through a playlist to get to the song you want, and then compare that to how frequently you'd flick through radio stations. That's extra seconds of attention taken off the road. Secondly, there can be no denying that radio is the original social medium. Real-time traffic updates, weather reports, the latest news – just the sound of two presenters nattering away at each other makes us feel more connected and part of the world, unlike streaming, which is automated, impersonal, and cold.
And let's not forget mobile radio. Hundreds – thousands – of radio stations worldwide can be accessed anywhere by anybody on their mobile while they're mobile. Pair this with the connected car, and all of the relevance that radio in a connected car can deliver can be offered today. For example, imagine having the most relevant and up-to-date traffic information to where you are travelling, or an offer from the service station at the exit you are approaching – something that music streaming services cannot provide. The relevance that being connected can add to the radio experience has the potential for stations to build even more loyal listeners. After all, radio have been voted as the most important feature for new car buyers, alongside connectivity. A mobile radio may be the best solution for broadcasters, advertisers, listeners, and automakers.
Another reason for radio to stay: radio listeners are less likely to switch channels during adverts than television audiences. Which, combined with the potential to deliver highly relevant ads to the listener, is golden news for advertisers.
This is the concept that drives Exaget's forward-thinking technology. Using a refined blend of database-analysing technology and a dash of common sense, we are able to create an overall profile of a radio listener, and target relatable adverts their way. Adverts that are not only compatible with the radio station, but with the radio listener themselves. The interaction does not just consist of 'sports radio = listener more likely to be a man = insert ad for booking a test drive', but also works on a 'listener-radio station-advertiser' relationship platform, adding value to all three parties involved.
But with cars looking to become connected to the internet of things in the foreseeable future, who's to say that mobile radio, with its interactive and relevant ads, won't make a progression onto dashboards? But if that's a bit too futuristic for you to digest right now, you can at least take away this with you – radio is here to stay. It's just in the process of getting a face lift. It may or may be DAB; it will more likely be mobile; but it will still be 'the radio'.
If you are interested in becoming a broadcasting partner, or would like to know what our integrating technology can do for you, contact our Partnership Account Manager Matthew Layton –matthew.layton@exaget.com or +447533517396
Take a stroll through Middle-earth – Exaget Week in Review
Welcome to our first Week in Review of 2015! We hope you've had a relaxing break and the year has started off well. As you may remember, in our last Week in Review we took a sneak peak at what's set to be trending this year – including the ubiquitous 'programmatic advertising'!
This week we're continuing to look at what's set to be trending, including wearables for consumers and businesses alike to keep an eye out for (no pun intended), as well as two new business developments that may turn our recreational audio and video habits on their heads.
Twitter to be new Youtube
The little blue bird of Twitter is squaring up to take on video behemoth YouTube this year as they prepare to release a new video service on their platform. Such a move could prove pivotal to maintaining their relevance amongst users and their investors happy following a fall of their share price, which they are still struggling to recover.
Why you should look out for smart glasses in 2015
Smartwatches hit the consumer market in 2014 in the form of Android Wear, and are set to boom into greater popularity with the upcoming release of Apple's Apple Watch range. But the market for wearable tech could be a very lucrative one, with BK Yoon, CEO and President of Samsung, stating that wearables would be as important as smartphones. And with Intel investing up to $25 million in internet-connected eyewear maker Vuzix, smart glasses are set to be the next big trend to look out for. One range will even allow you to take a stroll through the Shire with none other than Gandalf himself.
2015 Prediction – 'Cars will have radios'
A thought leader in the connected-car space has this week made a thought-provoking statement that cars in 2015 will have radios. Mind = Blown. With so many of us relying on internet-connected devices (smartphones, laptops, tablets et al.), there is a risk that car radios will be ripped out of dashboards and replaced by – internet modems? Self-driving technology? A directory of streaming companies? No, that would be too silly, best to just stick to a driver's best friend, the tried-and-tested car radio. Any chance we could bring back the cassette player though? Some of us have still kept our Spice Girls memorabilia…
4 Tips to Making a Succesful Radio Ad
Week in Review – June Week 2
Risk-Taking – Two Strangers and a Wedding
3 Things to Remember When Tweeting for Your Radio Station
The #SteveHarvey Morning Show has now reached 100 affiliates! ow.ly/ztsW30czVsy @RadioInk
Check out these 5 ways to become a better #radiopresenter! ow.ly/dBt930czRiY
The @verge enters partnership with Anchor to trial new #podcast ideas ow.ly/fIyx30czQZ1 via @RAINtwitter
Take a look at @podtrac's publisher rankings! ow.ly/n1Nh30cxP53 #podcasts via @RAINtwitter
These 4 tips to making a quality #radioadvert will be sure to give you a higher #ROI ow.ly/fMWQ30cA0Fc
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Fourteen Years On
https://www.steynonline.com/7166/fourteen-years-on
Fourteen years after 9/11, an army of Muslim men marches into Europe
On Thursday I made my weekly appearance on The Hugh Hewitt Show. We'll save some of the other subjects we discussed for a little later, but toward the end of our conversation (which you can find here, somewhat unreliably transcribed), Hugh asked me about today's anniversary:
HUGH HEWITT: Now speaking of blown sky high – "9/11" tomorrow. I asked Jeb Bush about this in the first hour. And the question was, fourteen years later, the first seven years of that were run by your brother and then the second seven years were run by President Obama. Are we safer today than we were on 9/12, 2001. What do you Mark Steyn – Jeb Bush's answer is posted over at HughHewitt.com.
MARK STEYN: I think the problem is that we defined what we were up against in the fall of 2001, 2002 too narrowly - and I think you can see that actually at the time of the first anniversary in 2002. We are in an ideological struggle... And we've seen that that ideology is very seductive to people who hold the passports of Western nations. We are a hole, we are a vacuum - and something fills the vacuum, which is what we see in Europe and to a lesser extent over here. And you can't fight this war even with the most brilliant military in the world because it's as I said in America Alone all those years ago - it's not my line, it's from Basil Liddell Hart, the great military strategist – it's not about blowing up their tanks and it's not about shooting their planes out of the sky – and nobody can beat Western militaries for doing that - but if you don't understand that you're up against this ideology and you don't target that ideology, then you can never win. And that's why I find this anniversary about as dispiriting as any of the fourteen since that Tuesday morning all those years ago.
I don't know why I said that this ideological faintheartedness was evident even at the time of the first anniversary in 2002. So, after the show, I turned to The Face of the Tiger, my account of the first year of the new war. Back then 9/11 was "the day everything changed". With hindsight, very little changed, with the exception of Muslim immigration, which accelerated. So, as I said to Hugh, I find these anniversaries more dispiriting with each passing year. Here's what I had to say on September 11th 2002, all of which applies to 2015, only more so:
WE ARE BACK to September 10th 2001, at least if the National Education Association is anything to go by. Their attractive series of classroom lessons and projects for September 11th, sponsored by Johnson & Johnson, begins with a little light non-judgmentalism: the NEA advises teachers not to "suggest any group is responsible" for the, ah, "tragic events". Just because Osama bin Laden and al-Qa'eda boasted they did it is no reason to jump to conclusions:
Blaming is especially difficult in terrorist situations because someone is at fault. In this country, we still believe that all people are innocent until solid, reliable evidence from our legal authorities proves otherwise.
So instead the NEA thinks children should:
Explore the problems inherent in assigning blame to populations or nations of people by looking at contemporary examples of ethnic conflict, discrimination, and stereotyping at home and abroad."
And by that you mean...?
Internment of Japanese Americans after Pearl Harbor and the backlash against Arab Americans during the Gulf War are obvious examples.
Not that obvious: for one thing, the "backlash against Arab Americans during the Gulf War" is entirely mythical. But you get the gist. Don't blame anyone. But, if you have to, blame America...
President Bush has won the first battle (Afghanistan) but he's in danger of losing the war. The war isn't with al-Qa'eda, or Saddam, or the House of Saud. They're all a bunch of losers. True, insignificant loser states can cause their share of trouble when they're proxies for the great powers. But, in a unipolar world, it's clear that the most powerful enemy in this war is ourselves, and our determination to sleepwalk to cultural suicide in order to demonstrate our sensitivity... On my car radio, John McCain pops up on behalf of the Office of Civil Rights every ten minutes sternly reminding Americans not to beat up Muslims.
And, of course, let us not forget Britain's great comic figure Baroness Kennedy of the Shaws, QC, who thinks that it's too easy to go on about "Islamic fundamentalists":
"What I think happens very readily," she said, "is that we as western liberals too often are fundamentalist ourselves. We don't look at our own fundamentalisms."
And what exactly does Lady Kennedy mean by western liberal fundamentalism?
One of the things that we are too ready to insist upon is that we are the tolerant people and that the intolerance is something that belongs to other countries like Islam. And I'm not sure that's true.
If I follow correctly, Lady Kennedy is suggesting that our tolerance of our own tolerance is making us intolerant of other people's intolerance. To complain about Islamic fundamentalism is to ignore how offensive others must find our own western fundamentalisms – votes, drivers' licenses for women, no incentives to mass murder from the pulpit of Westminster Cathedral.
AMERICA'S had a year to wise up, but instead it's retreating to its illusions. George W Bush had a rare opportunity after September 11th. He could have attempted to reverse the most poisonous tide in the western world: the gloopy multiculturalism that insists all cultures are equally valid, even as they're trying to kill us. He could have argued that western self-loathing is a psychosis we can no longer afford. He could have told the teachers' unions that there was more to the Second World War than the internment of Japanese-Americans and it's time they started teaching it to our children.
But he chose not to...
The 90% poll numbers were always going to come down. It was just a question of where they stabilised, and what Bush would manage to accomplish while they were up in the stratosphere. By that measure, he squandered his opportunity.
In devoting his energies to the war, the President let his domestic agenda die. Even as the USAF were strafing Tora Bora, Senator Pat Leahy, a wily Vermont Democrat, continued to stall the President's judicial nominations; Ted Kennedy gutted the Bush education bill; and their fellow Democrats obstructed plans for oil-drilling in the Arctic National Wildlife Refuge. At that moment, with his poll numbers in the eighties, it would have been so easy for Bush to do to Leahy what Clinton did to Gingrich. The President could have said that, with so many suspected terrorists and their accomplices in custody, we can't afford vacancies and backlogs in our courthouses and my good frien' Pat needs to stop playin' politics with the Federal judiciary. September 11th is not just an event, hermetically sealed from everything before and after, but a context. Everything that's wrong with the environmental movement, with the teachers' unions, with the big-government bureaucracies can be seen through the prism of their responses to that day...
But he ducked the rhetorical challenge. Bush has allowed the culture to lapse back into its default mode of psychobabbling self-absorption... Mona Charen summed it up in a column on the increasing pressure to pretend that September 11th 2001 was not what it was – an act of war – but instead some sort of unfortunate "tragedy". It is, she says, "a kind of moral disarmament of the nation. Before there can be an army, navy and air force capable of protecting us, there must be a citizenry that believes we are worth defending."
If it sounds extreme to put it in those terms, consider how far many in the west are prepared to go not to defend themselves... Five days before 9/11, the Norwegian newspaper Dagbladet reported that 65% of the country's rapes were committed by "non-western" immigrants – a category which, in Norway, is almost wholly Muslim. A professor at the University of Oslo explained that one reason for the disproportionate Muslim share of the rape market was that in their native lands "rape is scarcely punished" because it is generally believed that "it is women who are responsible for rape".
So Muslim immigrants to Norway should be made aware that things are a little different in Scandinavia?
Not at all! Rather, the professor insisted, "Norwegian women must take their share of responsibility for these rapes" because their manner of dress would be regarded by Muslim men as inappropriate. "Norwegian women must realize that we live in a multicultural society and adapt themselves to it." Or to modify Queen Victoria's apocryphal wedding-night advice to her daughter: lie back and think of Yemen...
Whether or not certain cultures are more prone to rape is a delicate question we shall explore another day. But what's interesting is how easily even this most extreme manifestation of multiculturalism is subsumed within the usual pieties. Norwegian women must learn to be, in a very real sense, less "exclusionary"...
After September 11th, a friend in London said to me she couldn't stand all the America-needs-to-ask-itself stuff because she used to work at a rape crisis centre and she'd heard this blame-the-victim routine a thousand times before. America was asking for it: like those Norwegian women, it was being "provocative". Even so, it comes as a surprise to realize the multiculti apologists do exactly the same to actual rape victims. After the OJ verdict, it was noted by some feminists that "race trumped gender". What we've seen since September 11th is that multiculturalism trumps everything. Its grip on the imagination of the western elites is unshakeable...
I believe western culture – rule of law, universal suffrage, etc – is preferable to Arab culture: that's why there are millions of Muslims in Scandinavia, and four Scandinavians in Syria. Follow the traffic. I support immigration, but with assimilation. Without it, like a Hindu widow, the west is slowly climbing on the funeral pyre of its lost empires. You see it in European foreign policy already: they're scared of their mysterious, swelling, unstoppable Muslim populations... The Islamists are militarily weak but ideologically secure. A year on, the west is just the opposite. There's more than one way to lose a war.
~excerpted from Mark's book The Face of the TIger
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explore What Your Doctor Isn't Telling You
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What Your Doctor Isn't Telling You
Aviation, Medicine and Other Potential Technology Disasters
David Sherer
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About What Your Doctor Isn't Telling You
Dr. David Sherer is bold enough to tell you what others in the medical profession haven't the courage to say, with inside information on health, healthcare, related public policy and the latest in prevention, diagnosis and treatment of disease.
Sadly, recent world news has fixated on the disastrous second crash in five months of a Boeing 737 Max aircraft, a plane that was supposed to be the pinnacle of performance, technology and even safety. The plane, an Ethiopian Airways jet (owned by the same airline I flew last summer to a medical mission in Tanzania), was lost shortly after takeoff on March 10, killing all 157 people aboard. Boeing insisted the plane is safe and that the crashes have nothing to do with defects in the plane. Owners of the plane are skeptical, leading many airlines in nations including (after a conspicuous and controversial delay) the United States to ground their fleet of 737 Max's until the question of safety and/or defects is resolved.
The FBI is currently involved in a potential criminal probe of Boeing, related to whether the company had knowledge of the software defect that is believed to have led to the crashes. So, too, there have been recent stories of "jump seat" pilots having to take over from perplexed and panicked pilots who were not trained, briefed or otherwise skilled to handle this seemingly prevalent flaw that kept turning the plane's nose down.
How does any of this apply to medical practice and patients, you might ask? Easy—technology and the increasingly limited role of human operator control. There have long been comparisons made between aviation safety and medical safety, particularly in the areas of anesthesia and surgery. Indeed, in my own specialty of anesthesiology, inducing anesthesia has often been compared to "take-off," and emergence from it has been likened to "landing" the patient. What happens between those events has often been compared to maintaining stability, avoiding turbulence and keeping the ride (and anesthetic course) smooth.
But as companies who make planes, anesthesia equipment, surgical equipment and self-driving cars (who have had their share of injuries and even deaths) might not want to admit, this move away from operator control towards automation, often showcased to drive profits with technologic glitz and sexiness, might turn out to be a dangerous one. This is nowhere more evident than in this entry from the front page of The Washington Post on March 12th, 2019, where reporters Aaron Gregg and Christian Davenport write:
"The crash…puts the spotlight on Boeing, which already faced scrutiny for its October crash in Indonesia and concerns that a software update to the 737 could make it hard to override a malfunctioning autopilot system when it steers the plane into a nose dive."
It is this possible inability to override that reminded me of personal experience with some anesthesia and surgical equipment that has, in the past, caused or could have caused patient harm. I recall one case where a woman was undergoing a hysteroscopy, where fluid is flushed in the uterus to help visualize the female reproductive tract with an endoscope. Everyone was paying attention to the screen where the interior of the uterus was visible, but no one was really paying attention to the patient. Instead, an alarm system that kept going off due to imbalances in fluid-in versus fluid-out of the patient occupied much of the staff's attention and efforts. Repeated fiddling with warning sounds controls and real-time trouble-shooting the equipment cost valuable attention to the patient, whose lungs were rapidly filling with fluid due to a severe fluid imbalance caused by faulty input to the monitor. The patient went into severe congestive heart failure and required a tracheostomy (cutting a breathing hole in her neck to her trachea) because of an inability to intubate her (which involves inserting a breathing tube down the windpipe). Eventually she did well, but it was a close call.
Similarly, I remember when laparoscopic gall bladder removal first emerged in the early 1990's. Prior to that, gall bladders were removed with a large, open incision in the upper abdomen. The learning curve to skillfully operate the laparoscopy equipment for abdominal surgery required extra time, effort and attention by the surgeon. Bells and whistles went off like crazy, as pressure gauges, electrocautery connections and gas supply meters to insufflate (blow gas into) the abdomen all needed attention. This took critical attention away from the patient and onto equipment. The very technology that was supposed to help patients instead, at least in the learning phase of practice, ended up putting the patient at risk. Not only that, as surgeons came to rely on laparoscopic gall bladder removal as the primary method, they lost their skills in the old method, a method that sometimes they might have to fall back on in case the laparoscopic way failed. Many newer surgeons are not even adequately trained in the older method.
The point of this discussion is that in medicine, as in aviation, more technology and fancy equipment may not be better. In fact, anything that takes away from human operator control, flawed as that might be, might actually be more dangerous than previously thought. The same Post article concluded by saying:
"…the controversy revived an ongoing debate about what degree of automation is safest for airplanes—and how much human pilots should maintain."
So what can you, the patient, do to protect yourself? Unfortunately, not a lot, short of telling your medical team, "Remember me and pay close attention, not to just your equipment!"
What really needs to happen is that both the medical and aviation industries, as well as any industry entrusted with the public safety, ensure that skilled operators are well versed in the use and design of their equipment…have the ability to understand and override faulty warning systems…and, most importantly, are enabled to devote primary attention to what they were trained to do, whether that would be wielding a scalpel, steering clear of turbulence or landing a multi-ton plane full of hundreds of people safely. After all, pilots, doctors and even cab drivers were meant and trained to do a job with their heads and their hands, not troubleshoot overly complex systems that might well have been designed to make the product used appear to be more sophisticated, modern and appealing.
For more with Dr. Sherer, click here for his podcast and video interviews, or purchase his memoir, The House of Black and White: My Life with and Search for Louise Johnson Morris.


Why your time is so precious.
I have spent a lot of my time working with people on goal planning and more recently work/life balance. The importance of this was brought home to me on the 26th of June. This is a date that I wish didn't feature on my calendar as an anniversary, unfortunately, with the recent atrocities in London and Manchester this date has become even more entrenched in my mind than ever. On this day in 2015 alone gun man walked along a beach in Sousse and with grenades and bullets of hate, he prematurely ended the lives of 38 innocent people!!
I knew two of those people. They were my friends. A few weeks before they travelled to Sousse to celebrate a birthday, I had witnessed how happy this pair were and the love that they shared for each other. One danced care free as you do when you celebrate your 50th, the other offering encouragement and support as he always did.
Bill and Lisa, used their time well and deserved many more days. Their friends and family loved them dearly. They lived each moment for their daughter, Holly, and they live on in her. They live on in all of us including a wee Dachshund called Bailey. I can still hear Bill cracking bad jokes and know that Lisa still doesn't find them funny!
Time is the most precious thing available to us. There are only 24 hours in every day; ultimately how you choose to use those 24 hours will decide how happy and fulfilled you will be? Use them wisely, the only thing we don't know is how many of those 24 hours we will have.
Want to get more out of what you want from your 24hours?


Some background is available on the about page. Use the contact form to get in touch.
Offroading is a site my brother and I put together in 1998. It contains, amongst other 4x4-related information, off-road driving and vehicle recovery guidance.
Offroad GPS was my first attempt at a Windows Phone application, and was submitted to the app store in February 2011. It's also how I got to work for Nokia on Maps.
The Stopwatch was an experiment in universal Windows apps. Submitted to the app store in September 2014.
The Debt Register is an (incomplete) proof of concept I built for an innovation drive at work. It's mostly re-purposed code from a risk management app I created a few years ago.


Main features of this issue: Groundbreaking set for bioscience center. Diversity to be celebrated at annual conference. Honoring outstanding public service. Scholarships for EMBA students. Celebrating 175. Spotlight on National Technichal Institute of the Deaf. News briefs. Walk away with art at Gallery benefit. Gannett talk showcases music, diversity. Ludacris brings hip-hop to RIT spring festival. Black tie optional, but big appetite required. Six more weeks of school predicted on "Shadow Day". D&C debuts Barnes' column. A true testament to the power of lifelong learning. Viewpoints. Next big invention could be in RIT's backyard. Engineering Wall of Fame unveiled. CAST faculty assume new roles. Breakfast with Peter Cottontail. United Way campaign update. Generosity 101.


It was late October 2004. Two of my friends stayed with me on Fyn, a small island in the middle of Denmark. We had a week full of fly-fishing ahead of us and were keen on doing the first casts. The weather was warm; the sun was shining from a clear blue sky and the wind was almost calm.
We stayed in the area near Bogense in the north of Fyn, in a comfortable house. Everything was nearly like we had expected it.
Especially their behaviour regarding taking the fly - or unfortunately not taking the fly.
We saw sea trout splashing and saw their dorsal fins and tails close to the edge of the water.
We fished large flies and small flies. We were retrieving the line in fast strips and in slow strips. We were changing places and tried every tactic we could think of, but couldn't get a single take at all.
After two fruitless days I felt a strong resignation. With a sobbing sound I fell to my knees close to the water and pounded my fists into the sand.
After 10 minutes lying there in pure desperation, something from deep down in my weary angler's head told me to consult my fly box one last time.
After a coffee break I followed this miraculous inspiration out of nowhere and found two unbelievable ugly flies - bright green body, orange tail and a grizzly-hackle tied around the body.
After storing my wet handkerchief in my pocket, I took a closer look on the illuminating flies and swore to do good for every desperate angler I'd meet, if these flies caught me a fish.
Making sure no one saw me, I tied the forbidden fly on.
With a feeling of "if I'm in guilty I will pay" I entered the water, made a few casts and - immediately caught my first sea trout!
Not a big one, but a fish!
Since that day I've caught so many fish on this green fly, which Martin has called "Kai's Green Terror", that I always carry a good amount of these flies in my fly box.
So, if one day you should lie on the bank pounding your fists into the sand in frustration and someone sneaks around the corner offering you a chartreuse coloured fly, perhaps it's me.
But if you would like to tie some of these flies yourself (since I can't hang around the world's waters all the time), please read the instructions in this article.
Now position a single grizzly hackle.
Protect the the hook shank with a layer of varnish. Necessary or not?
Tie in the chartreuse body material.
Comb the body material with a brush.
In the united states we call this fly a wooly worm,one of the first flies I learned to tye " holds a warm spot in my heart",caught a lot of different species of fish on every color you can think of,My first stellie was caught on a # 10 pink wooly worm with a red tail over 20 years ago, good to see the simple flies still catch fish,I use everything from flash chenille,cotton chenille,dubbing,and yarn for the body to yarn or hackle fibers for the tail weighted or not you can't go wrong with a wooly worm,add a marabou tail a "wala" wooly bugger how simple is that.
Finally a website that finally gives step by step instructions for fly tying with good quality close-up pics.
I hope to tie Kai's Green Terror and try it salmon fishing.
Very similar to the one I use here in eastern Canada. Works very well with brook trout in rivers and brooks. I also tie them weighted.
Sorry for my late responds, but a bad flu brought me down.
Normally I fish the fly wet, directly under the surface, because of no weight.
But one time, during my summer holidays in Denmark 07 in the very early morning, I saw rainbows cruising around just under the surface and try to fish it dry – and it worked properly.
But I think this was a quit an unusual behaviour.
When fishing the fly wet, I retrieve it in small strips and from time to time I diversify the speed from low to medium low.
Until now I've got very low experience with fishing the fly in rivers and lakes, so perhaps it's up to you to help with some practise and please let me know of your results.
Few question: what is the way of fishing this fly? Was it tried in salt water only? What about lakes or rivers?
Do you fish it also as a dry fly?