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Q: How to remove the background in Exception Handler gem in Rails 5? I am trying to add this gem https://github.com/richpeck/exception_handler to my website.
This is my config/application.rb
config.exception_handler = {
dev: true,
db: false, #-> defaults to :errors if true, else use :table_name
email: false, #-> need to integrate
layouts: {
'404' => 'application',
'400' => 'application',
'500' => 'application'
},
}
This is my app/views/exception_handler/exception/show.html.erb
<% provide(:title, 'Error') %>
<div class="jumbotronsignup nopadding">
<div class="container nopadding">
<div class="row">
<% if /^(5[0-9]{2})$/ =~ @exception.status.to_s %>
<div class="col-md-4 col-md-offset-4 labelcolor padding2">
<h3><%= "#{@exception.status} Error - #{details[:name]}" %></h3>
<%= details[:description] %>
<div class="thumbnail">
<strong>Our developers have been notified - we're working on it!</strong>
</div>
</div>
<% else %>
<div class="col-md-4 col-md-offset-4 labelcolor padding2">
<div class="thumbnail">
<strong><%= content_tag :div, details[:description], class: "message" %></strong>
</div>
</div>
<% end %>
</div>
</div>
</div>
I haven't changed the app/controllers/exception_handler/exception_controller.rb and app/helpers/exception_handler/application_helper.rb
I don't know why that background image is getting displayed.
If I delete the contents of app/assets/stylesheets/exception_handler/error.css.erb, then the image goes away and the content gets displayed as I want.
Where do I change to get that image away?
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,173
|
require 'spec_helper'
describe Volt::EJSON, '.parse' do
subject { Volt::EJSON }
let(:epoch) { 135820576553 }
let(:ruby_epoch) { epoch / 1000.0 }
context 'safe escaping' do
it 'does not parse date objects with invalid values' do
parsed = subject.parse '{"a" : {"$escape" : {"$date" : "something"}}}'
expect(parsed).to eq('a' => { '$date' => 'something' })
end
it 'only escapes one level down' do
parsed = subject.parse %({"$escape": {"$date": {"$date": #{epoch}}}})
expect(parsed).to eq('$date' => Time.at(ruby_epoch))
end
end
context 'parsing EJSON fields' do
context 'date' do
it 'is not parsed when given a bad value' do
expect(subject.parse '{"a": {"$date" : "something"}}').
to eq('a' => { '$date' => 'something' })
end
it 'parses proper $date EJSON fields' do
parsed = subject.parse '{"a" : {"$date": 135820576553}}'
expect(parsed['a']).to eq Time.at(ruby_epoch)
end
it 'parses nested EJSON date fields' do
parsed = subject.parse '{"a" : {"b" : {"$date": 135820576553}}}'
expect(parsed['a']['b']).to eq Time.at(ruby_epoch)
end
it 'parses nested $dates within $escapes' do
parsed = subject.parse(
'{"a" : {"$escape": {"$date" : {"date" : {"$date": 135820576553}}}}}'
)
expect(parsed['a']['$date']['date']).to eq Time.at(ruby_epoch)
end
it 'parses multiple EJSON date fields' do
ejson = begin
%({"when":{"$date":#{epoch}},"then":{"$date":#{epoch}}})
end
expect(subject.parse ejson).to eq(
"when" => Time.at(ruby_epoch),
"then" => Time.at(ruby_epoch)
)
end
end
end
end
describe Volt::EJSON, '.stringify' do
subject { Volt::EJSON }
context 'marshaling dates' do
let(:now) { Time.now }
let(:now_js_epoch) { now.to_i * 1_000 }
it 'does nothing with regular hashes' do
stringified = subject.stringify plain: 'jane'
expect(stringified).to eq '{"plain":"jane"}'
end
it 'marshals when given a date' do
stringified = subject.stringify when: now
expect(stringified).to eq %({"when":{"$date":#{now_js_epoch}}})
end
it 'marshals nested dates' do
stringified = subject.stringify how: { when: now }
expect(stringified).to eq %({"how":{"when":{"$date":#{now_js_epoch}}}})
end
it 'marshals multiple dates' do
stringified = subject.stringify when: now, then: now
expect(stringified.gsub(' ', '')).to eq(
%({"when":{"$date":#{now_js_epoch}},"then":{"$date":#{now_js_epoch}}})
)
end
it 'should convert symbols to strings' do
stringified = subject.stringify({something: :awesome})
expect(stringified).to eq('{"something":"awesome"}')
end
it 'escapes reserved key when type is incorrect' do
stringified = subject.stringify '$date' => 'something'
expect(stringified).to eq '{"$escape":{"$date":"something"}}'
end
end
end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 5,138
|
Buchang to Increase Stake in Tianyin-Buchang Alliance
Chengdu Tianyin Pharmaceutical Co., Inc.
CHENGDU, China, June 15, 2015 /PRNewswire/ -- Tianyin Pharmaceutical Co., Inc. (NYSE MKT: TPI), a pharmaceutical company that specializes in patented biopharmaceutical, modernized traditional Chinese medicine (mTCM), branded generics and active pharmaceutical ingredients (API) updated that during the advanced stage of the discussions between Chengdu Tianyin and Buchang Pharma (www.buchang.com) it is likely that Buchang Pharma will significantly increase its stake in the Tianyin-Buchang Alliance joint venture. The total registered capital for the joint venture is RMB 200 million (approximately $33 million), which TPI's wholly owned subsidiary Chengdu Tianyin Pharmaceutical Co., Ltd. owns 95% and Buchang Pharma owns 5%.
The above mentioned discussions follow the construction completion and the subsequent successful GMP certification (Certification No.: SC20140067, valid till July 1, 2020) according to the latest GMP standards at the Company's new manufacturing Qionglai Facility (QLF). The integration of sales network of TPI-Buchang Pharma platform is currently ongoing.
The TPI-Buchang Alliance
TPI and Buchang Pharmaceutical Co., Ltd. ("Buchang Pharma") in early 2015 established Tianyin-Buchang Strategic Alliance (the "Alliance") to synergize and accelerate the growth of the Company, boosting the mTCM franchise focusing on its cardiovascular revenue driver Gingko Mihuan (GMOL). The Alliance is led by TPI's Chairman Dr. Jiang, Guoqing and Buchang's senior executive vice president Wang Yimin. The Alliance is based upon TPI's newly completed Qionglai Tianyin Facility (QLF) with the expanded production capacities in mTCM pre-extraction, purification and formulation manufacturing, which is planned to synergize the current sales coverage with the Buchang Pharma's network resources (>15,000 hospitals nationwide) to enhance TPI's product portfolio focusing on TPI's lead revenue driver GMOL.
About Buchang Pharma
Buchang Pharmaceutical Co., Ltd., headquartered in Xi'an, established in 1993, by Prof. Buchang Zhao (founder, net worth estimated at $1.1 billion in 2014), is a pre-IPO targeting going public on Shanghai main board in 2015, (Citic Securities, 2015) pharmaceutical enterprise focusing on research, development, manufacturing and distribution of medicines and health care products in China. Buchang Pharma is one of the leading pharmaceutical companies in China and specializes in cardio-cerebral vascular (CCV) drugs and mTCM research and development. Within its comprehensive portfolio of over 60 nationally reimbursed products, Buchang Pharma's Naoxintong Capsules, Yinxin Granules and Danhong Injection are three proprietary cardiovascular products that delivered $1.1 billion total annual sales in 2013. Listed in the prospectus of the Company, Buchang's cardiovascular franchise ranked No. 1, making up 8.1% of the total of China's CCV market in 2012. The three lead cardiovascular drugs mentioned above delivered an accelerated growth curve with 2011, 2012, 2013 sales at $700 million, $900 million and $1.1 billion in total respectively.
With more than 10,000 professional sales representatives covering 15,000 hospitals and 130,000 pharmacies, Buchang Pharma has established a comprehensive network in China's large healthcare industry. The annual sales of Buchang Pharma were RMB 3.6 billion (approximately $510 million) in 2008, RMB 5.2 billion (approximately $560 million) in 2009, RMB 6.5 billion (approximately $1 billion) in 2010 and RMB 8.6 billion (approximately $1.4 billion) in 2013, more than doubled within 5 years. For additional information on Buchang Pharma in English, please click http://www.buchang.com/english/about.asp; or, in Chinese, http://www.buchang.com.
Headquartered at Chengdu, China, with Dr. Guoqing Jiang as Company's Chairman and CEO, TPI is a pharmaceutical company that specializes in the development, manufacturing, marketing and sales of patented biopharmaceutical, mTCM, branded generics and API. For more information about TPI, please visit: http://www.tianyinpharma.com.
The Statements which are not historical facts contained in this press release are forward-looking statements that involve certain risks and uncertainties including but not limited to risks associated with the uncertainty of future financial results, additional financing requirements, development of new products, government approval processes, the impact of competitive products or pricing, technological changes, the effect of economic conditions and other uncertainties detailed in the Company's filings with the Securities and Exchange Commission.
For more information, please visit: http://www.tianyinpharma.com
Tel: +86-28-8551-6696 (Chengdu, China)
Tianyin Pharmaceutical
23rd Floor, Unionsun Yangkuo Plaza
No. 2, Block 3, South Renmin Road
Chengdu, 610041
SOURCE Chengdu Tianyin Pharmaceutical Co., Inc.
http://www.tianyinpharma.com
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 318
|
Q: update an array inside an EntityAdapter I have the following EntityAdapter
export interface IDroneRoute {
assignedDroneId?: number;
routeId: string;
rerouting?: boolean;
waypoints: Waypoint[];
}
export const featureAdapter: EntityAdapter<IDroneRoute> = createEntityAdapter<IDroneRoute>({
selectId: model => model.routeId,
});
I would like to have an action that add, remove and delete a waypoint in the array
const ADD_ROUTE_POINT = (state: State, action: any) => {
return featureAdapter.updateOne({
id: action.payload.routeId,
changes: {// add waypoint},
}, state);
};
how do I access the current array of the item inside the changes so that I can update it ?
A: changes corresponds to the entity you want to update (IDroneRoute), so before you return featureAdapter.updateOne({ you can build your updated object.
const REMOVE_ROUTE_POINT = (state: State, action: any) => {
const droneRoute = {...state.entities[action.payload.routeId]}
droneRoute.waypoints = droneRoute.waypoints.filter(
wp => wp.id !== action.payload.waypoint.id);
return featureAdapter.updateOne({
id: action.payload.routeId,
changes: droneRoute,
}, state);
};
const ADD_ROUTE_POINT = (state: State, action: any) => {
const droneRoute = {...state.entities[action.payload.routeId]};
droneRoute.waypoints = [...droneRoute.waypoints, ...action.payload.waypoint];
return featureAdapter.updateOne({
id: action.payload.routeId,
changes: droneRoute,
}, state);
};
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 3,720
|
Man accused of throwing 5-year-old boy over Mall of America balcony was 'looking for someone to kill'
Ashley May
A 5-year-old boy was standing outside of the Rainforest Cafe restaurant at Mall of America with his mom when a stranger "looking for someone to kill" threw him off of a third-floor balcony, according to a criminal complaint filed Monday.
The boy fell nearly 40 feet after the Friday attack, and suffered head trauma and multiple broken bones. He is fighting for his life at a Minneapolis hospital.
"His condition has very little change at this point, but we are hoping to get some good news back from some upcoming tests," family friend Noah Hanneman shared in an update posted to a GoFundMe page Monday night.
The fundraising page set up for the family, which is requesting privacy, has raised more than $670,000 as of Tuesday morning.
"He is the sweetest, kindest 5-year-old you will ever meet," Hanneman said.
Emmanuel Aranda, 24, of Minneapolis, is charged with attempted premeditated first-degree murder. He said he was angry after being rejected by women at the mall and was "looking for someone to kill," the complaint said.
Bloomington police Chief Jeffrey Potts described the scene as "gut-wrenching."
More: Boy thrown nearly 40-feet from Mall of America balcony is a 'strong survivor'
Aranda had been banned from the mall – but the ban was not in effect at the time of the incident. He has a history of misdemeanor convictions; some cases were handled through a mental health court, Potts said.
He was arrested at the mall in 2015 and faced three charges after he threw an object off the mall's third level and became uncooperative with police, Potts said.
Monday's complaint said Aranda had become aggressive after "coming to the mall for several years and had made efforts to talk to women in the mall, but had been rejected."
He said he had come to the mall a day earlier looking to kill someone, but it didn't "work out." Aranda said he planned to kill an adult but then changed his mind and grabbed the boy.
More: An apparent stranger threw a 5-year-old boy nearly 40 feet from a mall balcony, police say
Contributing: Joel Shannon, USA TODAY; The Associated Press. Follow Ashley May on Twitter: @AshleyMayTweets
This article originally appeared on USA TODAY: Man accused of throwing 5-year-old boy over Mall of America balcony was 'looking for someone to kill'
Thousands of Amazon workers across Europe and the US are striking and protesting on Prime Day
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 6,125
|
The main focus of this book is on water quantity management, specifically floods, scarcity and droughts. The relevant EU requirements for water quantity management in transboundary waters and the way these have been implemented in a specific river basin in the EU, the Scheldt, are scrutinized. Moreover, a case study of the river basin mechanism governing the Delaware River in the United States has been conducted with the aim of identifying lessons learned for the EU. The key theme running through the book is based on the social-ecological resilience theory and the water security paradigm.
April 2018 | xviii + 378 pp.
A healthy water sector has been identified as a crucial contributing factor in reaching and maintaining a healthy society, from an environmental, human health and economic perspective. However, freshwater resources are under increasing pressure and climate change is expected to have a substantial impact on the hydrological cycle and freshwater resources. Considering the fact that the territories of 145 States worldwide, and 60 per cent of EU territory, run through transboundary lakes and river basins, their good governance is essential in tackling the challenges ahead. To this end, solid inter-regional and international upstream-downstream cooperation mechanisms are necessary.
The Law of the River takes a comparative perspective by analysing the relevant legal and policy frameworks in the European Union and the United States, with the goal of providing Critical Success Factors to transboundary river basin management. Each Critical Success Factor has resulted in a specific set of recommendations, both geared toward the level of the EU and the International River Basin Districts.
The main focus of this book is on water quantity management, specifically floods, scarcity and droughts. The relevant EU requirements for water quantity management in transboundary waters (International River Basin Districts) and the way these have been implemented in a specific river basin in the EU, the Scheldt, are scrutinized. Moreover, a case study of the river basin mechanism governing the Delaware River in the United States has been conducted with the aim of identifying lessons learned for the EU. The key theme running through the book is based on the social-ecological resilience theory and the water security paradigm.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 8,983
|
\section{Introduction}
Softly broken supersymmetric models contain a fairly large number of
scalar fields not present in the standard model. Their existence leads
to a complicated scalar potential, which might contain undesirable
minima which spontaneously break charge and/or color symmetry, a
situation which can not happen within the Standard Model. The
condition that the ``realistic'' minimum is the global minimum of the
theory can be used to obtain restrictions on the parameter space of
supersymmetric models, as already realized more than 20 years ago
\cite{Frere:1983ag,Claudson:1983et,Nilles:1982mp}. This way a
disadvantage of supersymmetry may turn into a virtue by shedding some
light into the unknown supersymmetry breaking mechanism itself.
Due to the enormous complexity of the full scalar potential in the
minimal supersymmetric extension of the standard model (MSSM) early
papers on this
subject~\cite{Frere:1983ag,Claudson:1983et,Nilles:1982mp,Komatsu:1988mt}
have only analyzed particular, but especially dangerous directions in
field--space. Casas et al \cite{casas:1997ze} have presented a more
detailed analysis of this subject. They were able to show that in the
constrained MSSM (CMSSM) with minimal supergravity boundary conditions
strong constraints arise ruling out sizeable parts of the parameter
space~\cite{casas:1997ze}.
Similar studies in R--parity violating versions of the MSSM, however,
have not been published~\footnote{The work of Abel and Savoy
\cite{Abel:1998ie} contains a discussion on the possibility of
lifting flat directions by adding explicit trilinear R--parity
violating terms to the superpotential. However, they discuss the
impact of bilinear terms only briefly. This is our main emphasis.}.
Our main goal is to present a detailed analysis of the
'unbounded--from--below' (UFB) as well as charge/colour breaking
minima (CCB) in the bilinear R--parity breaking model
(RMSSM)~\cite{Diaz:1997xc}. This model breaks lepton number and
R--parity explicitly through the simplest bilinear terms. The
justification for such emphasis is threefold.
First, it represents the simplest possible scheme of R--parity
violation, a mere six parameter extension of the MSSM. It is therefore
interesting to investigate the ``stability'' of the MSSM against such
``innocuous'' perturbation. For this reason we can also call this
model the generalized MSSM where R--parity breaks in the minimal way.
Second, this model is motivated by the fact that it produces the
paradigm for the idea that supersymmetry is the origin of neutrino
mass~\cite{Hirsch:2004he}, leading to a pattern of neutrino
masses~\cite{hirsch:2000ef} that successfully describes current
neutrino data~\cite{Maltoni:foc}. Last, but not least, it represents
the only model of R--parity breaking consistent with a spontaneous
violation of R--parity~\cite{Masiero:1990uj,Romao:1992vu}, where it is
the vacuum, not the fundamental theory, that breaks the symmetry.
In this model the atmospheric neutrino mass scale \cite{Fukuda:1998mi}
is generated at the tree--level, through the mixing of the three
neutrinos with the neutralinos~\cite{Ellis:1984gi}, in an effective
`low--scale'' variant of the seesaw mechanism. In contrast, the solar
mass and mixings needed to account for solar neutrino
data~\cite{Ahmad:2002jz,Eguchi:2002dm} are generated
radiatively~\cite{hirsch:2000ef}.
A very important difference between such a supersymmetric approach to
the origin of neutrino mass and seesaw--type schemes, is that here the
dimension--five operator responsible for (Majorana) neutrino masses is
generated at an accessibly low energy scale -- namely the weak scale.
This makes this model potentially testable by experiment.
In fact it has been shown that such a low--scale scheme for neutrino
masses has the advantage of being testable also ``outside'' the realm
of neutrino physics experiments. Although neutrino properties can not
be predicted from first principles, interpreting current neutrino data
in this framework implies unambiguous tests of the theory at
accelerator
experiments~\cite{Mukhopad:1998xj,Porod:2000hv,Hirsch:2002ys,Chun:2002rh,Hirsch:2003fe}
which can potentially be used to falsify the model.
This paper is organized as follows. In the next section we will
briefly recall some basics of the discussion on CCB and UFB bounds in
the MSSM. This will serve as a basis for section 3, where we will
discuss new features related to the R--parity violating terms. We show
how the bounds from unbounded--from--below directions have to be
modified, once non--zero bilinear R--parity violating (BRpV) terms are
allowed. We point out the novel possibility to generate a non--zero
vacuum expectation value of the charged Higgs field, albeit in regions
of parameter space which are now excluded by neutrino physics
\cite{Maltoni:foc}. We show that, given current data on neutrino
masses, bilinear R--parity violation can be understood as a small
perturbation of the MSSM. From the point of view of charge breaking
minima the RMSSM is thus as safe (or unsafe) as the MSSM itself. We
will then close with a short summary.
\section{Review of the MSSM results on UFB and CCB}
\noindent
To set up the notation, the superpotential of the MSSM can
be written as
\begin{eqnarray}
W&=&\varepsilon_{ab}\left[
h_U^{ij}\widehat Q_i^a\widehat U_j\widehat H_u^b
+h_D^{ij}\widehat Q_i^b\widehat D_j\widehat H_d^a
+h_E^{ij}\widehat L_i^b\widehat R_j\widehat H_d^a
-\mu\widehat H_d^a\widehat H_u^b
\right].
\label{eq:W}
\end{eqnarray}
Here, $h_U^{ij}$, $h_D^{ij}$ and $h_E^{ij}$ are $3\times 3$ Yukawa
matrices, $\widehat Q$, $\widehat U$ and $\widehat D$ are quark doublet and
singlet superfields and $\widehat L$ and $\widehat R$ are the usual lepton
doublet and singlet fields.
Supersymmetry must be broken and the most general set of soft breaking terms
allowed by the standard model gauge group under the assumption of
lepton number conservation can be written as
\begin{eqnarray}
\label{Vsoft}
{V}_{SB}&\hskip-5mm=\hskip-5mm&
M_Q^{ij2}\widetilde Q^{a*}_i\widetilde Q^a_j+M_U^{ij2}
\widetilde U_i\widetilde U^*_j+M_D^{ij2}\widetilde D_i
\widetilde D^*_j
+M_L^{ij2}\widetilde L^{a*}_i\widetilde L^a_j
+M_R^{ij2}\widetilde R_i\widetilde R^*_j
+\sum_{i=1}^2 m_{H_i}^2 H^{a*}_i H^a_i \cr
&&+\left[
- \ifmath{{\textstyle{1 \over 2}}} \sum_{i=1}^3 M_i\lambda_i\lambda_i
+\varepsilon_{ab}\left(
A_U^{ij}h_U^{ij}\widetilde Q_i^a\widetilde U_j H_u^b
+A_D^{ij}h_D^{ij}\widetilde Q_i^b\widetilde D_j H_d^a
+A_E^{ij}h_E^{ij}\widetilde L_i^b\widetilde R_j H_d^a
\right.\right.\cr
&&\left. \left. \hskip 45mm
-B\mu H_d^a H_u^b
\right) +h.c. \vb{18} \right]
\end{eqnarray}
The Higgs doublets giving mass to the standard model fermions are
\begin{equation}
\label{eq:2}
H_d=\left(
\begin{array}{l}
H_d^0\\
H_d^-
\end{array}
\right),
\qquad
H_u=\left(
\begin{array}{l}
H_u^+\\
H_u^0
\end{array}
\right)
\end{equation}
and the parameters in Eq. (\ref{Vsoft}) are to be understood at some
renormalization scale $Q$ chosen to minimize the effects of the one loop
corrections. This way we can neglect in the analysis the effect of the one
loop radiative corrections \cite{casas:1997ze}.
Without loss of generality, we now consider that the fields take the
following vev's\footnote{Our normalization here for the vev's differs
from Refs. \cite{Diaz:1997xc,hirsch:2000ef} by a factor of
$\sqrt{2}$.},
\begin{equation}
\label{eq:3}
\vev{H_u^+}=0,\quad \vev{H_d^-}=v_{-},\quad \vev{H_d^0}=v_d,\quad
\vev{H_u^0}=v_u
\end{equation}
to obtain
\begin{eqnarray}
\label{eq:4}
V_{\hbox{Higgs}}&=&\left(m^2_{H_u} + \mu^2\right) v_u^2
+\left(m^2_{H_d} + \mu^2\right) \left(v_d^2 +v_{-}^2 \right)
- 2 B \mu v_u v_d
-\frac{1}{2} g^2 v_u^2 v_d^2\nonumber \\[+2mm]
&&+
\frac{1}{8} \left(g^2 +g'^2\right) \left(v_u^4+v_d^4+v_{-}^4+2 v_d^2
v_{-}^2\right)
+\frac{1}{4} \left(g^2 -g'^2\right) \left( v_d^2 + v_{-}^2\right) v_u^2
\end{eqnarray}
This Higgs potential has the property that $v_{-}=0$. To see this
we note that the potential can be written in the form,
\begin{equation}
\label{eq:5}
V_{\hbox{Higgs}}= C_4 v_{-}^4 + C_2 v_{-}^2 + C_0
\end{equation}
where
\begin{eqnarray}
\label{eq:6}
C_4&=&\frac{1}{8} \left(g^2+g'^2\right)\nonumber \\
C_2&=&\frac{1}{4} \left(g^2-g'^2\right) v_u^2 +\frac{1}{4}
\left(g^2+g'^2\right) v_d^2 + \left(m^2_{H_d} + \mu^2\right)\nonumber \\
C_0&=&\frac{1}{8} \left(g^2+g'^2\right) \left(v_u^2-v_d^2\right)^2
+\left(m^2_{H_u} + \mu^2\right) v_u^2
+\left(m^2_{H_d} + \mu^2\right) v_d^2
-2 B \mu v_u v_d
\end{eqnarray}
Now since $g>g'$ we must have $C_2 >0$, unless $m^2_{H_d} + \mu^2 <0$
\footnote{Casas et al.~\cite{casas:1997ze} assume that only $m^2_{H_u}
+ \mu^2$ can be negative. Even though in mSugra at very large
$\tan\beta$ values $m^2_{H_d} + \mu^2 <0$ can occur in exceptional
cases, we will follow their assumption.}. Therefore the minimum of
the Higgs potential occurs for vanishing vev of the charged Higgs
boson.
By using the minimization equations,
\begin{eqnarray}
\label{eq:7}
0&=&-2 B \mu v_d + 2 \left(m^2_{H_u} + \mu^2\right) v_u - \frac{1}{2}
\left(g^2+g'^2\right) \left(v_d^2-v_u^2\right) v_u \nonumber \\[+2mm]
0&=&-2 B \mu v_u + 2 \left(m^2_{H_d} + \mu^2\right) v_d + \frac{1}{2}
\left(g^2+g'^2\right) \left(v_d^2-v_u^2\right) v_d
\end{eqnarray}
one can find the value of the Higgs potential at the real minimum,
\begin{eqnarray}
\label{eq:8}
V_{MIN}&=&-\frac{1}{8} \left(g^2+g'^2\right)
\left(v_u^2-v_d^2\right)^2
\end{eqnarray}
Eq. (\ref{eq:8}) will be important to compare with the values of other
(and potentially deeper) minima.
Before starting the discussion of the dangerous directions, a word of
caution should be added, namely, that the condition that the realistic
minimum is the global one might actually be too conservative. In fact,
it is possible that the universe resides in a false vacuum which is
stable because the tunneling time into the global minimum is large
with respect to the age of the universe. In this sense, CCB and UFB
constraints on the supersymmetric parameter space are sufficient but
might not be necessary, see for example
\cite{Kusenko:1996jn,Kusenko:1996xt}. However, we will not follow
this line of reasoning any further.
\subsection{UFB directions}
The 'unbounded--from--below' (UFB) directions are those where the
quartic D--terms vanish and some coefficient(s) quadratic in the vev's
are negative. Then the potential at the weak scale
seems to be unbounded from below. However, this is a slight
misnomer, since if one assumes that all soft masses are positive at
the high unification scale, it appears that these dangerous directions
are not really unbounded from below but there exists a true local
minimum at some large scale. It then must be checked that this local
minimum is not deeper than the physical one. As was shown in Ref.
\cite{casas:1997ze} there are three kinds of such directions. The
first and most obvious one corresponds to the D--flat direction where
$|v_u|=|v_d|$, all other vev's being zero. The potential along this
direction reads,
\begin{equation}
\label{eq:10}
V_{UFB-1}=\left(m^2_{H_u} + m^2_{H_d} +2 \mu^2 -2 |B \mu| \right) v_u^2
\end{equation}
and a sufficient condition to avoid developping a deep minimum at large
values of the field is
\begin{equation}
\label{eq:11}
m^2_{H_u} + m^2_{H_d} +2 \mu^2 -2 |B \mu| >0.
\end{equation}
In principle, one should check the depth of the true minimum along the
dangerous direction when this coefficient is negative. For simplicity, we
will stick however to the condition given in Eq. (\ref{eq:11}).
The second dangerous direction corresponds to the case where a slepton
$L_i$ takes a vev $v_i$. Then a combination of $v_u, v_d$ and $v_i$
can cancel the D--term and the potential reads,
\begin{equation}
\label{eq:12}
V_{UFB-2}=\left( m^2_{H_u} + \mu^2 + m^2_{L_i} - \frac{| B
\mu|^2}{m^2_{H_d}+\mu^2 -m^2_{L_i}} \right) v_u^2 -\frac{2
m^4_{L_i}}{g^2+g'^2}
\end{equation}
which constrains the coefficient of the quadratic term as
\begin{equation}
\label{eq:ufb2}
m^2_{H_u} + \mu^2 + m^2_{L_i} - \frac{| B
\mu|^2}{m^2_{H_d}+\mu^2 -m^2_{L_i}} > 0.
\end{equation}
Note that in the case of a universal $m_0$ at the unification scale
the $m_{L_i}$ are usually the smallest soft masses at the weak scale.
Dropping the universality assumption the bound obtained for $m_{L_i}$,
Eq. (\ref{eq:ufb2}), must be verified for the squark soft masses as
well.
Finally the last UFB direction corresponds to the case where $v_d=0$
but we have a neutral slepton $L_i$ with nonzero vev, like in the
UFB-2 case. This direction is both D-- and F--flat. The difference
with respect to UFB-2 is that the F--term is canceled by giving vev's
to the charged sleptons. The resulting potential reads
\begin{equation}
\label{eq:ufb3}
V_{UFB-3}=\left( m^2_{H_u} + m^2_{L_i} \right) v_u^2
+ \frac{|\mu|}{h_{e_j}} \left(m^2_{L_i}+ m^2_{L_j}+ m^2_{e_j}\right) v_u
-\frac{2 m^4_{L_i}}{g^2+g'^2}
\end{equation}
Since $m^2_{H_u}$ must be negative in order to break electroweak symmetry and
$m^2_{L_i}$ is small when one assumes universality of the soft terms, the
coefficient quadratic in $v_u$ is generally negative. As shown in
Refs.~\cite{casas:1997ze,Abel:1998ie} in the case of universal soft masses at
the GUT scale, the condition that the minimum along this UFB-3 direction is
not deeper than the physical minimum implies $m_0 > \alpha M_{1/2}$, where
$\alpha$ is a coefficient of ${\cal O}(1)$.
\subsection{CCB minima}
\label{sec:CCBMSSM}
\noindent
For the classical CCB minima, dangerous negative contributions to the
scalar potential are generated by cubic ($A$--type) soft supersymmetry
breaking terms. Therefore these directions cannot be F--flat, but they
are still D--flat. The traditional bound of Ref. \cite{Frere:1983ag}
corresponds to the case where
\begin{equation}
\label{eq:13}
\vev{Q^1}=\vev{H_u^2}=\vev{U}=v
\end{equation}
all other vev's vanishing. This choice cancels the D--term and the
potential reads,
\begin{equation}
\label{eq:14}
V_{CCB}=v^2 \left(3 h_u^2 v^2 + 2 A_u h_u v + m^2_{H_u}+\mu^2+m^2_Q
+m^2_U \right)
\end{equation}
In order to avoid a very deep color and charge breaking minimum we
must make sure that the parenthesis in Eq.~(\ref{eq:14}) never
vanishes, which happens if the corresponding second order equation can
not have real solutions. This leads to the well known condition,
\begin{equation}
\label{eq:16}
|A_u|^2 < 3 \left( m^2_{H_u}+\mu^2+m^2_Q +m^2_U \right)
\end{equation}
A more complete and general analysis of this and similarly dangerous
directions can be found in Ref. \cite{casas:1997ze}. Note again, that
the bound given in Eq.(\ref{eq:16}) for $A_u$ must be checked for all
$A$--terms in the general non--universal MSSM.
\section{UFB and CCB in the RMSSM}
The RMSSM is simply the bilinear R--parity violating model, defined by
the following superpotential~\cite{Diaz:1997xc}
\begin{eqnarray}
W&=&W_{MSSM} + \varepsilon_{ab}\epsilon_i\widehat L_i^a\widehat H_u^b
\label{eq:Wrpv}
\end{eqnarray}
and corresponding soft supersymmetry breaking terms,
\begin{eqnarray}
{V}_{SB}&=& V_{MSSM} +
B_i\epsilon_i\widetilde L^a_i H_u^b \,.
\label{eq:Vrpv}
\end{eqnarray}
It is therefore a rather mild extension of the MSSM. In the following
it will be sufficient to consider for simplicity only a one generation
version of the model~\footnote{We do not believe that this
simplification has any impact on the following discussion, since
neutrino oscillation data require $\frac{\epsilon}{\mu}\ll 1$ and
intergenerational effects between different families of leptons due
to BRpV terms scale as $(\frac{\epsilon}{\mu})^2$.}. We are mainly
interested in studying how the appearance of the new terms in the
superpotential (and in $V_{SB}$) changes the conclusions which hold
for the MSSM. Since the MSSM is the limit of the RMSSM when $\epsilon
\to 0$ we expect that the results of the MSSM will hold in that limit.
Note also that the structure of the trilinear terms is not modified,
so conclusions like those of Eq.~(\ref{eq:16}) are expected also to
hold in our case. Defining
\begin{equation}
\label{eq:17}
\vev{H_u^+}=0,\quad \vev{H_d^-}=v_{-},\quad \vev{H_d^0}=v_d,\quad
\vev{H_u^0}=v_u, \quad \vev{L^0}=v', \quad \vev{L^-}=v'_{-}
\end{equation}
one finds for the scalar potential
\begin{eqnarray}
\label{eq:15}
V&=& M^2_{H_u} v_u^2 + M^2_{H_d} \left(v_d^2 + v_{-}^2\right)
+ M^2_{L} \left( v'^2 + v'^2_{-}\right) - 2 B \mu\, v_d v_u + 2 B'
\epsilon\, v_u v' \nonumber\\[+1mm]
&&
+\epsilon^2 \left( v_u^2 + v'^2_{-} + v'^2 \right)
+\mu^2 \left( v_u^2 + v_d^2 +v^2_{-} \right)
-2 \mu \epsilon \left( v' v_d + v_{-} v'_{-} \right)\nonumber\\[+1mm]
&&
+\frac{g^2}{8} \left[
\left( v_u^2-v_d^2-v'^2 +v_{-}^2 +v'^2_{-} \right)^2
+ 4 \left(v_d v_{-} + v' v'_{-} \right)^2 \right] \nonumber\\[+1mm]
&&
+\frac{g'^2}{8} \left( v_u^2-v_d^2-v'^2 -v_{-}^2 -v'^2_{-} \right)^2
\end{eqnarray}
where $ B'$ characterizes the soft supersymmetry and R--parity
violating bilinear term. We note that it is not possible to have an
UFB direction with non vanishing charged vev's in this potential,
because the D--terms can not be made to vanish for $v_{-}$ and
$v'_{-}$ different from zero. The minimization equations can be found
in the usual way taking derivatives with respects to the fields
\begin{eqnarray}
\label{eq:18}
0&=&
\left[ 2 \left(M^2_{H_d} + \mu^2\right) -\frac{g^2}{2} \left(
v_u^2 -v_d^2 -v'^2 -v_{-}^2 +v'^2_{-} \right) -\frac{g'^2}{2} \left(
v_u^2 -v_d^2 -v'^2 -v_{-}^2 -v'^2_{-} \right)
\right] v_d \nonumber\\
&&
-\left( 2 \epsilon \mu -g^2 v_{-} v'_{-}\right) v'
-2 B \mu v_u\nonumber\\[+2mm]
0&\hskip-3mm=&\hskip-3mm
\left[ \frac{g^2}{2} \left(
v_u^2 -v_d^2 -v'^2 +v_{-}^2 +v'^2_{-} \right)
+\frac{g'^2}{2} \left(
v_u^2 -v_d^2 +v'^2 -v_{-}^2 -v'^2_{-} \right)
\right] v_u \nonumber\\
&&
+ 2 \left(M^2_{H_u} + \mu^2 + \epsilon^2 \right) v_u +
2 \left( B' \epsilon v' -B \mu v_d \right)\nonumber\\[+2mm]
0&\hskip-3mm=&\hskip-3mm
\left[ 2 \left(M^2_{L} + \epsilon^2\right) -\frac{g^2}{2} \left(
v_u^2 -v_d^2 -v'^2 +v_{-}^2 -v'^2_{-} \right) -\frac{g'^2}{2} \left(
v_u^2 -v_d^2 -v'^2 -v_{-}^2 -v'^2_{-} \right)
\right] v' \nonumber\\
&&
-\left( 2 \epsilon \mu -g^2 v_{-} v'_{-}\right) v_d
+2 B' \epsilon v_u\nonumber\\[+2mm]
0&\hskip-3mm=&\hskip-3mm
\left[ 2 \left(M^2_{H_d} + \mu^2\right) +\frac{g^2}{2} \left(
v_u^2 +v_d^2 -v'^2 +v_{-}^2 +v'^2_{-} \right) -\frac{g'^2}{2} \left(
v_u^2 -v_d^2 -v'^2 -v_{-}^2 -v'^2_{-} \right)
\right] v_{-} \nonumber\\
&&
-\left( 2 \epsilon \mu -g^2 v_d v' \right) v'_{-} \nonumber\\[+2mm]
0&\hskip-3mm=&\hskip-3mm
\left[ 2 \left(M^2_{L} + \epsilon^2\right) +\frac{g^2}{2} \left(
v_u^2 -v_d^2 +v'^2 +v_{-}^2 +v'^2_{-} \right) -\frac{g'^2}{2} \left(
v_u^2 -v_d^2 -v'^2 -v_{-}^2 -v'^2_{-} \right)
\right] v'_{-} \nonumber\\
&&
-\left( 2 \epsilon \mu -g^2 v_d v' \right) v_{-}
\end{eqnarray}
Since we are dealing with a set of five coupled equations this system
is difficult to solve for the vev's. We can however use the following
trick. Instead of solving for the five vev's we try to solve those
equations for the three soft masses squared $M^2_{H_u}$, $M^2_{H_d}$
and $M^2_{L}$~\cite{Romao:1992vu} and for the charged vev's. Using
this approach we could find two types of solutions.
Before discussing the general case, however, we consider first the
limit in which RMSSM is considered a perturbation of the MSSM. This
is a reasonable approach since the BRpV parameters must be small to
account for the neutrino data~\cite{hirsch:2000ef}. Therefore we can
pose the following question. Suppose that in the limit $\epsilon \to
0$ the parameters are such that the MSSM has no UFB directions or CCB
minima. This means $v_u\not=0\, , v_d\not=0$ and $v'=v_{-}=v'_{-}=0$.
If we now consider a small non--vanishing value for the $\epsilon$
what will be the corresponding minimum? In order to answer this
question in perturbation theory we write
\begin{equation}
\label{eq:23}
v_d=\sum_{i=0}^{\infty} v_d^{(i)}\, \epsilon^i, \
v_u=\sum_{i=0}^{\infty} v_u^{(i)}\, \epsilon^i, \
v'=\sum_{i=0}^{\infty} v'^{(i)}\, \epsilon^i, \
v_{-}=\sum_{i=0}^{\infty} v_{-}^{(i)}\, \epsilon^i, \
v'_{-}=\sum_{i=0}^{\infty} v{'}_{-}^{(i)}\, \epsilon^i
\end{equation}
Now we substitute back in the extremum Eq.~(\ref{eq:18}) and solve
order by order in perturbation theory. The result that we get is as
follows,
\begin{eqnarray}
\label{eq:24}
v_d&=&v_d^{(0)} +v_d^{(2)}\epsilon^2 +v_d^{(4)}\epsilon^4 + \cdots\nonumber\\
v_u&=&v_u^{(0)} +v_u^{(2)}\epsilon^2 +v_u^{(4)}\epsilon^4 + \cdots\nonumber\\
v'&=&v'^{(1)} \epsilon +v'^{(3)}\epsilon^3 +v'^{(5)}\epsilon^5 + \cdots\nonumber\\
v_{-}&=& 0\nonumber\\
v'_{-}&=& 0
\end{eqnarray}
where $v_u^{(0)}\, ,v_d^{(0)}$ are the MSSM values for $\epsilon=0$.
This is precisely the solution of type \textbf{I} that we will discuss
shortly. Note that if $\epsilon \not=0$ then also $v'\not=0$. In
fact,
\begin{equation}
\label{eq:25}
v'= \frac{\mu v_d^{(0)}
- B' v_u^{(0)}}{M^2_L- \frac{1}{4} (g^2 + g'^2)
\left(v_u^{(0)}{}^2 - v_d^{(0)}{}^2\right)}\, \epsilon +\cdots
\end{equation}
So we can formulate the following important result: {\it If we start
with the MSSM parameters such that in the limit $\epsilon
\rightarrow 0$ the minimum has no UFB or CCB problems, then by
turning on perturbatively a small value for $\epsilon$ we get a
correspondingly safe minimum of the RMSSM.} However, as we will now
discuss, in general there are two types of solutions for the minimum
equations.
\subsubsection*{Type I}
This solution corresponds to the case where the charged vev's vanish.
We are then in the situation studied usually \cite{Diaz:1997xc} in the
bilinear R--parity model. We get
\begin{eqnarray}
\label{eq:19}
M^2_{H_d}&=&
\epsilon\, \mu\, \frac{v'}{v_d} - \mu^2 + B\, \mu\, \frac{v_u}{v_d}
+ \frac{g^2 + g'^2}{4} \left(v_u^2 -v'^2 - v_d^2 \right)
\nonumber\\[+2mm]
M^2_{H_u}&=&
-\epsilon^2\, - \mu^2 + B\, \mu\, \frac{v_d}{v_u}
-B'\, \epsilon\, \frac{v'}{v_u}
- \frac{g^2 + g'^2}{4} \left(v_u^2 -v'^2 - v_d^2 \right)
\nonumber\\[+2mm]
M^2_{L}&=&
-\epsilon^2 +\epsilon \left(\mu \frac{v_d}{v'}- B' \frac{v_u}{v'}\right)
+ \frac{g^2 + g'^2}{4} \left(v_u^2 -v'^2 - v_d^2 \right)
\nonumber\\[+2mm]
v_{-}&=&0
\nonumber\\[+2mm]
v'_{-}&=&0
\end{eqnarray}
This corresponds to the neutral Higgs potential that we will discuss
further below. Here we just note that the value of the potential at
the minimum can be shown to be
\begin{equation}
\label{eq:26}
V_{BRpV}= -\frac{g^2+g'^2}{8}
\left(v_u^2-v_d^2-v'^2\right)^2.
\end{equation}
\subsubsection*{Type II}
In the general case we can find the solutions of the minimization
equations in the following way. We start by solving the first three
equations in Eq.~(\ref{eq:18}) for the soft masses. We get,
\begin{eqnarray}
\label{eq:20}
M^2_{H_d}&=& M^2_{H_d}(0) -\frac{1}{4} \left(g^2-g'^2\right)
\left(v_{-}^2+ v'^2_{-}\right) \nonumber\\
M^2_{H_u}&=& M^2_{H_u}(0) -\frac{1}{4} \left(g^2+g'^2\right)
\left(v_{-}^2+ v'^2_{-}\right)
-\frac{1}{2}\, g^2\, \frac{v'}{v_d}\, v'_{-} v_{-}\nonumber\\
M^2_{L}&=&M^2_{L}(0) +\frac{1}{4} \left(g^2-g'^2\right) v_{-}^2
-\frac{1}{4} \left(g^2+g'^2\right) v'^2_{-}
-\frac{1}{2}\, g^2\, \frac{v'}{v_d}\, v'_{-} v_{-}
\end{eqnarray}
where $M^2_{H_d}(0)$, $M^2_{H_u}(0)$ and $M^2_{L}(0)$ are the soft
masses when $v_{-}=v'_{-}=0$ and are given in
Eq.~(\ref{eq:19}). Now we substitute Eq.~(\ref{eq:20}) into the last
two equations in Eq.~(\ref{eq:18}) to obtain,
\begin{eqnarray}
\label{eq:35}
0&\hskip-3mm=\hskip-3mm&
-g^2\left( v'^2 v_{-} - v' v_d v'_{-} +
v_{-}^2 v'_{-} \frac{v'}{v_d} - v_{-} v'^2_{-} \right)
+ 2 \epsilon \mu \left( v_{-}\frac{v'}{v_d} - v'_{-} \right)
+ 2 B \mu v_{-} \frac{v_u}{v_d} + g^2 v_{-} v_u^2\nonumber\\[+2mm]
0&\hskip-3mm=\hskip-3mm&
g^2 \left( v'^2 v_{-}
- v' v_d v'_{-} + v_{-}^2 v'_{-} \frac{v'}{v_d}
- v_{-} v'^2_{-} \right) \frac{v_d}{v'}
- 2 \epsilon \mu \left( v_{-}\frac{v'}{v_d} - v'_{-} \right)
\frac{v_d}{v'} \\
&&
- 2 B' \epsilon v'_{-} \frac{v_u}{v'} + g^2 v'_{-} v_u^2\nonumber
\end{eqnarray}
Multiplying the second of the equations in Eq.~(\ref{eq:35}) by
$v'/v_d$ and adding them one obtains,
\begin{equation}
\label{eq:36}
v'_{-}=\kappa\, v_{-}
\end{equation}
where
\begin{equation}
\label{eq:37}
\kappa=\frac{2 B \mu + g^2 v_d v_u}{2 B' \epsilon - g^2 v' v_u}
\end{equation}
\vspace{1mm}
\noindent
Finally we use Eq.~(\ref{eq:36}) to reduce either one of Eq.~(\ref{eq:35})
to
\begin{equation}
\label{eq:38}
0=v_{-} \Big( D_2\, v_{-}^2 - D_0 \Big)
\end{equation}
where
\begin{eqnarray}
\label{eq:39}
D_2&=& g^2 \left( \kappa^2 - \frac{v'}{v_d}\, \kappa \right)\nonumber\\
D_0&=&g^2 \left( v'^2 -v_d v' \kappa -v_u^2 \right)
- \left( B v_u + \epsilon v'\right) \frac{2 \mu}{v_d}
+ 2 \epsilon \mu \kappa
\end{eqnarray}
Eq.~(\ref{eq:38}) has the trivial solution $v_{-}=0$ which corresponds
to type \textbf{I}, the BRpV solutions. However, if
\begin{equation}
\label{eq:22}
\frac{D_0}{D_2} > 0
\end{equation}
we have a new type of solutions for the minimization equations,
\begin{equation}
\label{eq:40}
v_{-}=\pm \sqrt{\frac{D_0}{D_2}}, \qquad v'_{-}= \kappa\, v_{-}
\end{equation}
As $D_{0,2}$ do not have in general a well defined sign it can happen
that such solutions do exist for some combination of the
parameters. We will discuss this later in more detail.
\subsection{UFB Directions}
We have seen before that for the Higgs potential of the RMSSM the UFB
directions can only arise when the charged Higgs vev's vanish,
otherwise it is not possible to cancel the quartic D--terms. The
neutral Higgs potential obtained from Eq.~(\ref{eq:15}) when
$v_{-}=0,v'_{-}=0$ is given by
\begin{eqnarray}
\label{eq:27}
V_{Neutral}&=& \left( M^2_{H_u} +\epsilon^2 +\mu^2 \right) v_u^2
+ \left(M^2_{H_d} +\mu^2 \right) v_d^2
+ \left(M^2_{L} + \epsilon^2 \right) v'^2 \nonumber\\[+1mm]
&&- 2 B \mu\, v_d v_u + 2 B' \epsilon\, v_u v'
-2 \mu \epsilon v' v_d
+\frac{g^2+g'^2}{8}
\left( v_u^2-v_d^2-v'^2\right)^2
\end{eqnarray}
From this equation we can see that we can make the D--term vanish if
we choose the condition
\begin{equation}
\label{eq:28}
v_u^2=v_d^2+v'^2
\end{equation}
To implement this condition it is convenient to write
\begin{equation}
\label{eq:29}
v_d=v_u \cos\theta, \quad v'=v_u\sin\theta
\end{equation}
Then we get
\begin{equation}
\label{eq:30}
V_{Neutral}=B(\theta) v_u^2
\end{equation}
where
\begin{eqnarray}
\label{eq:31}
B(\theta)&=&
\left[\vb{14} M^2_{H_u} +\epsilon^2 +\mu^2
+ \left(M^2_{H_d} +\mu^2 \right) \cos^2\theta
+ \left(M^2_{L} + \epsilon^2 \right) \sin^2\theta \right.\nonumber\\[+1mm]
&&\left.\vb{14} \hskip 3mm
- 2 B \mu\, \cos\theta + 2 B' \epsilon\, \sin\theta
-2 \mu \epsilon \sin\theta \cos\theta \right]
\end{eqnarray}
Therefore the condition for avoiding an UFB direction is that,
\begin{equation}
\label{eq:32}
B(\theta_{\min}) > 0
\end{equation}
where $\theta_{\min}$ is the value of $\theta$ that corresponds to the
minimum of $B(\theta)$. Now consider Eq. (\ref{eq:31}) in the limit
$\epsilon \to 0$ and take the derivative,
\begin{equation}
\label{eq:Btheta}
\frac{dB}{d\theta}= 2\sin\theta \left[-( M^2_{H_d} +\mu^2-M^2_{L})\cos\theta +
B \mu\ \right]
\end{equation}
The right hand side vanishes when $\theta=0$ and when $\cos\theta =
\frac{B\mu}{M^2_{H_d} +\mu^2 - M^2_{L}}$. These two solutions
correspond to the UFB-1 and UFB-2 directions given in
Eqs.~(\ref{eq:11}) and (\ref{eq:ufb2}), respectively, when
$\epsilon=0$.
For $\epsilon \not=0$ it does not seem possible to have an analytical
expression for $\theta_{\min}$. However for a given set of parameters
it is always easy to verify whether Eq.~(\ref{eq:32}) holds for
$\theta \in [0, 2 \pi]$. It is also clear from Eq.~(\ref{eq:31}) that
the MSSM condition, Eq.~(\ref{eq:11}), is not enough to ensure that we
are free from UFB directions. This fact can be best illustrated from
figure (\ref{fig:1}) that shows a typical example.
\begin{figure}[ht]
\centering
\begin{tabular}{cc}
\includegraphics[width=0.45\textwidth,clip]{Btheta-fig3a.eps}&
\includegraphics[width=0.45\textwidth,clip]{Btheta-fig3b.eps}
\end{tabular}
\caption{$B(\theta)$ as a function of $\theta$ for an example where
$B(\theta_{min})<0$ but $B(0)>0$. The right panel is an enlarged
view of the left one close to the zeros of $B(\theta)$.}
\label{fig:1}
\end{figure}
One can see clearly that starting from a large value of $B(0)$ is not
enough to decide upon the sign of $B(\theta_{\min})$. However it is
easy to check numerically whether $B(\theta_{\min})>0$ or not.
Therefore, although we lack a simple analytical formula, the criterium
for avoiding UFB directions is easily implemented.
Finally we comment briefly on the direction UFB-3. It can be easily
shown that at large values of the field the potential in direction
UFB-3 is given as
\begin{equation}
\label{eq:ufb3mod}
V_{UFB-3}=\left( m^2_{H_u} + m^2_{L_i} + \epsilon B' \right) v_u^2
+ \cdots
\end{equation}
where the dots stand for irrelevant terms. Since in our notation
$\epsilon B' < 0$ this leads, in principle, to a slightly more
stringent requirement than the one corresponding to the R--parity
conserving MSSM. However, since $\frac{\epsilon}{\mu} \sim {\cal
O}(10^{-(3-4)})$ is required by neutrino oscillation data
\cite{hirsch:2000ef}, this modification is numerically irrelevant.
This is in agreement with the argument presented in
Ref.~\cite{Abel:1998ie}.
\subsection{Nonzero charged Higgs and Slepton Vev's}
We now turn to the solutions of type II. We have already seen in Eqs.
(\ref{eq:38}) - (\ref{eq:40}) that there are potentially dangerous
solutions for the Higgs potential with nonzero vev's for the charged
scalars. These solutions, if they exist, would provide new CCB
solutions different from those already present in the MSSM, as
explained above. As can be seen from Eq.~(\ref{eq:22}) such solutions
can exist if the parameters satisfy the relation $D_0/D_2 >0$, where
the $D_i$ are given in Eq.~(\ref{eq:39}).
Since it does not seem possible to give a strict analytic criterion
which relates the condition $D_0/D_2 <0$ (guaranteeing the absence of
unwanted minima) to the parameters of the potential we have resorted
to a numerical scan of the parameter space. Our approach to find the
minima of the potential was as follows. We always started with a
random set of parameters with zero charged vev's and subject to the
requirement that,
\begin{equation}
\label{eq:41}
v_u^2+v_d^2+v'^2=v^2=\left( 2 \sqrt{2} G_F\right)^{-1/2}= 174.1\,
\mathrm{GeV}
\end{equation}
\noindent Note that with this procedure we should always have,
\begin{equation}
\label{eq:42}
|\eta| =\frac{|v'|}{v} < 1.
\end{equation}
We then search for the global minimum numerically. If we find a minimum
deeper than the realistic minimum but which breaks charge this part of
parameter space should be discarded.
Two examples are shown in Fig. (\ref{fig:2}).
\begin{figure}[ht]
\centering
\begin{tabular}{cc}
\includegraphics[width=0.45\textwidth,clip]{tb105.eps}&
\includegraphics[width=0.45\textwidth,clip]{tb12.eps}
\end{tabular}
\caption{Range of RMSSM parameters where
nonzero charged vev's for the Higgs and slepton fields are
favoured over the realistic minimum for two examples of
$\tan\beta$, left $\tan\beta=1.05$, right $\tan\beta=1.2$. Here we
fix for convenience $B=B'=\mu=$ 100 GeV. For a discussion see
text.}
\label{fig:2}
\end{figure}
The results shown in Fig. (\ref{fig:2}) can be understood
qualitatively as follows. Starting with the definitions Eqs
(\ref{eq:37}) and (\ref{eq:39}) and taking into account the smallness
of $\frac{\epsilon}{\mu}$ one can show that in the limit $\epsilon \to
0$ we always have $D_2 >0$. On the other hand the condition $D_0>0$
requires
\begin{equation}
\label{eq:condd}
v'^2 > v^2\frac{\tan^2\beta-1}{1+\tan^2\beta} + \frac{2 B \mu}{g}
\frac{\tan^2\beta-1}{\tan\beta}.
\end{equation}
Note that this condition is not strictly valid for $\tan\beta \equiv
1$, because in this limit we can no longer neglect the terms
proportional to $\epsilon$ in the definitions of $D_0$ and $D_2$. Eq.
(\ref{eq:condd}) shows that charge breaking minima in the limit of
small values of $\epsilon$ require that $v'$ take up a sizeable
fraction of $v$. This trend is clearly visible from Fig.
(\ref{fig:2}). The figure also illustrates how these solutions
disappear very quickly with $\tan\beta$ greater than $1$.
Although we find it amusing that such solutions exist, we wish to
stress that consistency with neutrino data requires
$\frac{\epsilon}{\mu} \sim {\cal O}(10^{-(3-4)})$ and $\frac{v'}{v}
\sim {\cal O}(10^{-(3-4)})$. We therefore conclude that the RMSSM is
automatically safe from these unwanted minima in those ``physical''
parts of parameter space which account for the neutrino oscillation
data.
\section{Conclusions}
We have studied charge breaking minima and unbounded from below
directions within bilinear R--parity breaking supersymmetry. Such a
``reference model'' is nothing but the simplest broken R--parity
version of the Minimal Supersymmetric Standard Model. We have first
generalized some results obtained previously in the R--parity
conserving MSSM. Subsequently we discussed new ways to generate a
nonzero vacuum expectation value of the charged Higgs and slepton
fields. However, such unwanted solutions occur only in regions of
parameter space which are now excluded by neutrino oscillation data.
In summary it can be said that, given the data on neutrino masses,
bilinear R--parity violation can be understood as a small perturbation
of the MSSM. From the point of view of CCB and UFB directions the
RMSSM is as robust as the R--parity--conserving MSSM: it is equally
safe from unwanted minima in the same portions of parameter space.
\section{Acknowledgments}
This work was supported by Spanish grant BFM2002-00345, by the
European Commission Human Potential Program RTN network
HPRN-CT-2000-00148 and by the European Science Foundation network
grant N.86. M.H. is supported by a MCyT Ramon y Cajal contract.
JCR was supported by the Portuguese
\textit{Funda\c{c}\~ao para a Ci\^encia e a Tecnologia}
under the contract CFIF-Plurianual and grant POCTI/FNU/4989/2002.
We thank Werner Porod for useful discussions.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 4,279
|
\section{Introduction}
Collisions between classical wave packets have recently been studied
numerically for several interacting relativistic field theories
\cite{TR,GNV,GMMT,OWN}. Interest in this topic arose in connection with
expectations that the rate of multiparticle production processes in
electroweak interactions, which can manifest themselves, e.g., in
baryon number violation, might be unsuppressed at high energies \cite{RE}.
The non-perturbative nature of the baryon number violating amplitude
\cite{HFT} demands a corresponding non-perturbative approach as provided
by semiclassical techniques. The main difficulty in semi-classical
approaches is the treatment of the $2 \to$ many particle transition
amplitude, since the {\it initial} state of high energy particles is
not semiclassical at all, and loop contributions are essential in general
(see, e.g. \cite{VL}). Possible techniques for circumventing this
difficulty of the semiclassical approach have been proposed and studied
in the literature \cite{RST,GHP,RS}.
In the classical approach to scattering, the question is: does there
exist a mechanism for energy transfer from high frequency modes, which
corresponds to two high energy particles, to low frequency modes
representing a multiparticle final state? At first glance, the answer
to the question, formulated in terms of nonlinear dynamics, seems to be
affirmative since the gauge field theories are nonlinear. However, the
studies of $(1+1)$-dimensional abelian Higgs
model \cite{TR} and $\lambda\varphi^4$-theory \cite{GNV} have shown
no indication for a non-perturbative
mechanism providing the coupling between the initial
high and the final low frequency modes. For example, in \cite{TR} the
wave packets always passed through each other without being destroyed.
It is important to note that in \cite{TR} the initial states were always
chosen to have small amplitude, which made the nonlinear terms less important.
The important issue here is that the results are strongly influenced
by the nonlinearity due to the non-abelian spin-field coupling, which is
absent in abelian models. It is this coupling that is responsible for the
infrared instabilities of the pure non-abelian gauge theory. This can be
seen from the linearized equation describing small perturbations $a_{\mu}^c$
around an $SU(2)$ background field $A_\mu$ (in background gauge):
\begin{equation}
\label{eq1}
(D_{\mu}^2 a_{\nu})^a - 2g\;\varepsilon^{abc}F_{\mu\nu}^ba_{\mu}^c=0~,
\end{equation}
where $D_{\mu}\equiv\partial_{\mu}-ig[A_{\mu}, ~]$ is the gauge covariant
derivative. The second term in (\ref{eq1}) may have any sign. In particular,
this essentially non-abelian coupling drives an instability for
perturbations with isospin polarization orthogonal to the isospin of a
standing wave, which leads to a growth of low frequency modes from initial
high frequency modes \cite{GMMT}. This may imply the existence of classical
trajectories of the type required for multiparticle production \cite{GHP},
if this instability persists in more realistic case, e.g., collision of
localized gauge field wave packets.
{}From a more general point of view, the observed inability of the nonlinearity
to furnish a mechanism for the formation of strongly inelastic final states is,
in our opinion, intimately connected with the integrable nature of the
classical
systems considered in \cite{TR} and \cite{GNV}. It is well-known that
non-abelian
gauge theories are non-integrable in the classical limit , and exhibit
dynamical
chaos \cite{SERGEI,MT} \footnote{Strictly speaking, chaos only
sustains for solutions of finite energy {\it density} \cite{MT}. Finite energy
solutions in $(3+1)$-dimensions will spread out in space at late times and will
therefore
linearize. However, nummerical results indicate that at intermediate times
these
fields generally exhibit exponentially growing perturbations.}. This
dynamical stochasticity of the non-abelian gauge fields together with their
mentioned
dynamical instability are possible sources of the non-perturbative mechanism
for the
coupling between high frequency modes and low frequency modes. At the same
time, it
is important to recall the special role of the Higgs field as a mechanism for
the
suppression of the dynamical chaos of the non-abelian gauge fields
\cite{MATINYAN}.
With this in mind, we studied \cite{OWN} the collision
of two $SU(2)$ gauge field wave packets, homogeneous in the transverse
plane. As we expected, based on
previous results \cite{GMMT}, the collision of essentially non-abelian
initial configurations trigger the decay of initial high frequency modes
into many low frequency modes with dramatically different momentum
distributions, whereas for abelian configurations (parallel relative isospin
polarizations) wave packets pass through each other without interaction.
The present paper, which studies collisions of wave packets in the $SU(2)$
Higgs model, is a generalization of the earlier work in two directions.
Firstly, it is an extension of \cite{TR} to the non-abelian Higgs model.
Secondly, it is a generalization of the previous work \cite{OWN} to the
case where the $SU(2)$ gauge symmetry is spontaneously broken by a Higgs
field and the fundamental excitations of the gauge field are massive.
One expects that the explicit mass scale introduced by the Higgs field
will act as a cutoff on the low frequency excitations, potentially leading
to drastic changes in the coupling between high and low frequency modes.
We will see that the real situation is more complicated, and the ratio
$\lambda/g^2$ of the Higgs self-coupling $\lambda$ and gauge coupling
$g$ and the vacuum expectation value $v$ of the Higgs field are essential
parameters.
This paper is organized as follows. In Section II, we formulate the
problem. In Section III, we present results from our numerical simulations
and discuss their implications. Section IV is devoted to an extended
discussion of our results. In Section V, we conclude and indicate
possible directions for future research.
\section{Formulation Of The Problem}
In this section, we describe scattering of classical wave packets
in the non-abelian Higgs model and its numerical formulation on the
lattice. In particular, we give a brief discussion of the scaling
properties of the classical dynamics. This section is based on previous
work \cite{TR,OWN}.
\subsection{The non-abelian Higgs model}
Here we give a brief discussion on the spontaneously broken $SU(2)$
Yang-Mills theory, in which a charged scalar isodoublet field, the
Higgs field, is coupled to the gauge field. This model retains the
most relevant ingredients of the electroweak theory. The action
describing this model in $(3+1)$-dimensions is given by
\begin{equation}
S = \int {d^3x}{dt}\left[-{{1}\over{2}}{\rm tr}(F_{\mu\nu}F^{\mu\nu})
+ {{1}\over{2}} {\rm tr} \left( (D_{\mu}\Phi)^{\dag} D^{\mu}\Phi
\right) - \lambda \left( {1\over2}{\rm tr}(\Phi^{\dag}\Phi) - v^2 \right)^2
\right]
\end{equation}
with $D_{\mu}=\partial_{\mu}-igA_{\mu}^a \tau^a/2, \;
F_{\mu\nu} \equiv F_{\mu\nu}^a\tau^a/2 = (i/g)\left[D_{\mu}, D_{\nu}
\right]$ and
\begin{equation}
\Phi = \phi^{0}-i\tau^{a}\phi^{a}~,
\end{equation}
where $\tau^{a}$ ($a=1, 2, 3$) are Pauli matrices. Following the
notation of \cite{AAPS}, we represent the complex Higgs doublet by a
quaternion, which is convenient for numerical manipulation. Clearly,
this maintains the correct number of degrees of freedom in the Higgs field.
By a scaling transformation
\begin{equation}
\label{scaling}
x_{\mu}^{\prime}=gv x_{\mu},~~~ \Phi^{\prime}=\Phi/v,~~~
A^{\prime}_{\mu}=A_{\mu}/v~,
\end{equation}
we obtain the action in terms of the primed quantities
\begin{equation}
\label{prime_S}
S = (1/g^2) \int {d^3x^{\prime}}{dt^{\prime}}\left[-{{1}\over {2}}
{\rm tr}(F_{\mu\nu}^{\prime}F^{\prime\mu\nu}) + {1\over2}{\rm tr}
\left( (D^{\prime}_{\mu}\Phi^{\prime})^{\dag}D^{\prime\mu}\Phi^{\prime}
\right)- \lambda^{\prime} \left({1\over2}{\rm tr}(\Phi^{\prime\dag}
\Phi^{\prime}) - 1\right)^2\right]
\end{equation}
with $\lambda^{\prime}=\lambda/g^2$.
Within classical physics, the prefactor ${{1}/{g^2}}$ in (\ref{prime_S})
is irrelevant, leaving $\lambda^{\prime}=\lambda/g^2$ as the only relevant
parameter in the action. Note that $\lambda^{\prime}$ is proportional to
the square of ${M_H}/{M_W}$, the mass ratio of the Higgs and $W$-boson.
The elementary excitation modes $\rho$ and $W_{\mu}$ are best described
in the unitary gauge
\begin{eqnarray}
\Phi &=& (v+\rho/\sqrt{2})U(\theta)~, \\
A_{\mu} &=& U(\theta)W_{\mu}U^{-1}(\theta) -
(1/ig)\left(\partial_{\mu}U(\theta)\right) U^{-1}(\theta)~,
\end{eqnarray}
where $U(\theta)=\exp(i\tau^{a}\theta^{a})$, $\rho$ describes oscillation
of the Higgs field about its
vacuum expectation value, and $W_{\mu}$ is the field of the gauge boson.
$W_{\mu}$ and $\rho$ obey the following classical equations of motion
\begin{eqnarray}
[D_{\mu}, F^{\mu\nu}]+M_W^2 W^{\nu}+{{1}\over{\sqrt{2}}}g^2 v\rho W^{\nu}
+{{1}\over{4}}g^2\rho^2 W^{\nu} &=& 0~, \label{w_equation} \\
(\partial_{\mu}\partial^{\mu}+M_H^2)\rho+3\sqrt{2}\lambda v \rho^2
+\lambda\rho^3-{{\sqrt{2}}\over{4}}g^2 v W^{a}_{\mu}W^{a \mu} -
{1\over 4}g^2\rho W^{a}_{\mu}W^{a \mu} &=& 0~, \label{h_equation}
\end{eqnarray}
where $M_H=2v\sqrt{\lambda}$ and $M_W=gv/\sqrt{2}$. $D_{\mu}$ and
$F^{\mu\nu}$ are defined in terms of $W_\mu$. After a scaling
transformation similar to that in (\ref{scaling}), it is easy to see
that the above equations of motion depend on a single parameter: the
mass ratio $M_H/M_W$. However, in the simulation of colliding wave packets,
there are other parameters involved in the initial condition.
\subsection{Scattering of classical wave packets}
Our numerical study is based on the Hamiltonian formulation of lattice
$SU(2)$ gauge theory \cite{CRUK} (see \cite{OWN,GT} for more
details), in which the dynamic variables are link variables defined as
\begin{equation}
U_{\ell} ~=~ \exp(-igaA^c_{\ell}\tau^c/2)~,
\end{equation}
where $\ell$ stands for the link index. As in \cite{OWN}, we work on a
one dimensional lattice with a physical size $L=Na$, where $N$ is the
number of lattice sizes and $a$ the lattice spacing. We arrange initially
two Gaussian wave packets with average momenta ${\bf k}=(0,0,{\bar k})$,
and width $\Delta k$. Our goal is to simulate the collision of two $W$-boson
wave packets in the background of the Higgs condensate.
Before actually constructing the wave packets, one has to deal with the
gauge fixing problem. In the Hamiltonian formulation of lattice gauge
theory, temporal gauge $A_0=0$ is most convenient. On the other hand, one
must construct the $W$-boson wave packets in the unitary gauge and then
transform back to obtain the initial conditions in the temporal gauge.
The gauge field for a configuration of two well-separated wave packets
in the unitary gauge can be written as
\begin{equation}
W^{c,\mu}=W_{L}^{c,\mu}+W_{R}^{c,\mu}~,
\end{equation}
with $c$ being the isospin index and $\mu$ the Lorentz index.
$W_{L}^{c,\mu}$ is a left-moving wave packet, initially centered at
$z_L$; $W_{R}^{c,\mu}$ is a right-moving wave packet, initially
centered at $z_R$. In our simulation, $z_L$ and $z_R$ are chosen in a
way such that the two wave packets are positioned symmetrically about
the center of the lattice. Specifically, we take transversely polarized
wave packets
\begin{eqnarray}
W_{L}^{c,\mu} &=& (0, 0, 1, 0) n^{c}_{L}\psi (z-z_L, -t)~, \\
W_{R}^{c,\mu} &=& (0, 0, 1, 0) n^{c}_{R}\psi (z-z_R, +t)~,
\end{eqnarray}
with $n^{c}_L$ and $n^{c}_R$ being the polarization vectors in isospin
space. We choose $n^{c}_R=(0,0,1)$ fixed and leave $n^{c}_L$ free to be
varied. The above choice satisfies the relation $\partial_{\mu}W^{\mu}=0$.
Because we have chosen transversely polarized wave packets\footnote{Note
that under realistic conditions the luminosity for transversely polarized
gauge bosons in proton-proton system is typically two orders of magnitude
higher than for longitudinally polarized ones and increases with energy
\cite{Dawson}.}, they already satisfy the temporal gauge condition $W_0=0$.
If we had chosen, instead, longitudinally polarized wave packets (as in ref.
\cite{TR}), we would have needed to apply a gauge transformation
$U({\bf x},t)$ which transforms $W_{\mu}$ to $A_{\mu}$
\begin{equation}
A_{\mu}=U W_{\mu} U^{-1} - (1/ig) (\partial_{\mu}U)U^{-1}~,
\end{equation}
such that $A_0=0$, i.e.,
\begin{equation}
\partial_0 U = igU W_0~.
\end{equation}
In our case, obviously, $U=1$.
To construct the wave packets, we need to specify the functional form of
$\psi ({\bf x}, t)$. A right-moving wave packet centered at $z=0$ at
time $t=0$ with mean wave number $\bar k$, width $\Delta k$, and mean
frequency ${\bar \omega}=\sqrt{{\bar k}^2 + M_W^2}$ is described by
\begin{equation}
\psi (z, t) = {{\sqrt{\hbar}}\over{\sqrt{4\pi\sqrt{\pi}\Omega
\Delta k \sigma}}}\int_{-\infty}^{\infty} dk_z
e^{-(k_z-{\bar k})^2/{2(\Delta k)^2}} \left[ e^{i(\omega (k_z) t-k_z z)}
+ c.c. \right]~,
\end{equation}
with $\omega (k_z)=\sqrt{{k_z}^2+M_W^2}$ and
\begin{equation}
\Omega= {\bar \omega} \left[ 1+{1\over 4} \Big[ 1- \left( {\bar k
\over \bar \omega}\right)^2\Big] \left({\Delta k\over\bar \omega}\right)^2
+ {\cal O} \left( \Big( {\Delta k\over\bar \omega} \Big)^4 \right)\right]~,
\end{equation}
where the amplitude of the wave packet is fixed by requiring energy
equal to $\hbar {\bar \omega}$ (``one particle'') per cross sectional area
$\sigma$. In the following we will set $\hbar = 1$.
Performing the $k_z$-integral at $t=0$ gives
\begin{equation}
\label{init_phi}
\psi |_{t=0} = \sqrt{{2\Delta k\over\sqrt{\pi}\Omega\sigma}}
e^{-(\Delta k z)^2/2}\cos({\bar k}z)~.
\end{equation}
Since the differential equations are of second order in time, one also
needs to specify $\dot{\psi}\equiv \partial \psi/\partial t$ at $t=0$, which
is found to be
\begin{eqnarray}
\dot{\psi} |_{t=0}&=& {i\over\sqrt{4\pi\sqrt{\pi}\Omega
\Delta k \sigma}} \int_{-\infty}^{\infty} dk_z \omega (k_z)
e^{-(k_z-\bar k)^2/2(\Delta k)^2} \left[ e^{i(\omega (k_z) t-k_z z)}
-c.c.\right]_{t=0} \nonumber \\
&=& \sqrt{2\bar \omega\Delta k\over\sqrt{\pi}\sigma (\Omega/\bar\omega)}
e^{-(\Delta k z)^2/2} \left[\sin(\bar kz) +{\bar k\over\bar\omega}
{\Delta k\over\bar\omega}\Delta k z \cos(\bar kz) \right.
\nonumber \\
&&\qquad \left. +{1\over2} \left[ 1- \left({\bar k\over\bar\omega}\right)^2
\right] \left({\Delta k\over\bar\omega} \right)^2 [1-(\Delta k z)^2]
\sin(\bar kz)+{\cal O}\left( \Big({\Delta k\over\bar \omega}\Big)^3 \right)
\right]~.
\end{eqnarray}
Furthermore, the initial condition for the Higgs field is chosen as the
vacuum solution:
\begin{equation}
\phi ^0=v, ~~~ \phi ^a=0, ~~~ \dot{\phi ^0}=\dot{\phi ^a}=0 ~~~~~
{\rm at} ~~ t=0~.
\end{equation}
To determine the number of independent parameters, we make use of the
scaling transformation (\ref{scaling}) for $\psi |_{t=0}$. In terms of the
primed quantities, equation (\ref{init_phi}) reads
\begin{eqnarray}
\psi^\prime|_{t^\prime =0} &=& (1/v)\psi|_{t=0} \nonumber \\
&=& (1/\pi^{1/4})\sqrt{{\Delta k/M_W\over(\Omega/M_W)
(\sigma M_W^2/g^2)}} e^{-(\Delta k/M_W)^2 z'\,^2/4}
\cos[(\bar k/M_W)z^\prime/\sqrt{2}] , \label{amplitude}
\end{eqnarray}
where
\begin{equation}
{\Omega\over M_W}=\sqrt{1+(\bar k/M_W)^2} \;
\left[ 1+{1\over4}{(\Delta k/M_W)^2 \over[1+(\bar k/M_W)^2]^2} +
{\cal O} \Big( (\Delta k/\bar k)^4 \Big) \right]~.
\end{equation}
The above initial condition contains three dimensionless parameters:
${{\bar k}}/{M_W}$, ${\Delta k}/{M_W}$, and ${\sigma M_W^2}/{g^2}$.
There appears one more parameter in the initial condition, i.e., the
relative rotation in isospin space between the two wave packets, which
we denote by $\theta_c$.
Combining equations of motion and initial condition, our ansatz has
five independent parameters: ${M_H}/{M_W}$, ${\bar k}/{M_W}$,
${\Delta k}/{M_W}$, ${{\sigma M_W^2}/{g^2}}$, and $\theta_c$. The
parameter ${\bar k}/{M_W}$, which sets the energy of collisions in units
of the $W$-boson mass, is referred to as the energy parameter.
${\Delta k}/{M_W}$, whose inverse specifies the width of each wave packet
in position space, can be called the width parameter. The amplitude of
each wave packet depends on ${\bar k}/{M_W}$ as well as
${\Delta k}/{M_W}$, but more crucially, on ${\sigma M_W^2}/{g^2}$. In
our simulation, we always require $\bar k \gg \Delta k$ so that the
wave packets are well-defined objects. Furthermore, we choose
$\bar k \gg M_W$ to model high energy scattering.
In our numerical calculations, the $SU(2)$ coupling constant $g$ was fixed
to be $0.65$. However, due to
the scaling properties of the equations of motion and the initial
conditions, the results of our calculation do not depend on the
particular choice of $g$ and $v$. This can be verified by the fact
that the amplitude of the wave packets only depends on the ratio of
$\sigma$ and $g^2$. Also, since the dynamics does not depend on a
particular choice of $\sigma$ or $g$ as long as the ratio
$\sigma/g^2$ is fixed (assuming that $M_W$ and other parameters remain
fixed), we can predict, from the result for one coupling $g$ at a
certain value of $\sigma$, the result for another coupling $g'$ at a
different $\sigma' = (g'/g)^2\sigma$. Hence, a change of the value for
the gauge coupling $g$ simply corresponds to a rescaling of the
parameter $\sigma$ controlling the amplitude of initial wave packets.
\section{Numerical Results}
\subsection{Dependence on the mass ratio $M_H/M_W$}
As established in the previous work \cite{OWN}, the behavior of the
wave packet collisions is governed by the nonlinearity due to the
self-interaction of the gauge field. For two wave packets of parallel
isospin polarizations in the pure Yang-Mills theory, where the nonlinear
self-coupling in the gauge field is absent, we found no indication of
any interaction \cite{OWN}. This provided a check on our numerical
procedure and showed that the artificial interactions introduced by the
formulation in terms of compact lattice gauge fields did not affect the
results.
Here, for the Yang-Mills-Higgs system, the situation is more involved.
Besides the nonlinearities due to the gauge field self-interaction, there
exist other nonlinearities induced by the gauge-Higgs coupling and by the
Higgs self-interaction. However, in the case where most energy remains
contained in the gauge field and the Higgs field is only slightly excited,
one can expect that the gauge field self-interaction will be the major
contributor to the nonlinearities observed in the system. Note that the
amplitudes of the gauge and Higgs fields shown in the figures below are
in the temporal gauge. This means that the longitudinal part of the gauge
field is not fully represented in the figures.
The top rows of Figure 1 and Figure 2 show a few ``snapshots'' of the
space-time development of the colliding $W$-boson wave packets with
$M_H=M_W=0.126$, $\sigma=0.336$, $\bar k =\pi/5$, and $\Delta k=\pi/100$ for
parallel (Figure 1) and orthogonal (Figure 2) isospin polarization,
respectively. The figures show the absolute magnitude of the scaled gauge field
amplitude, $|{\bf A}^\prime|=|{\bf A}|/v$.
For parallel isospin orientations, the
result of the ``collision'' is a slight distortion of the initial wave
packets showing no sign of significant inelasticity. In contrast, the
top row of Figure 2 illustrates that the collision of two wave packets
with orthogonal relative polarizations in isospin space is strongly inelastic.
The difference between the two figures is even more clearly illustrated
by looking at the evolution of the absolute value of the Fourier
transform of the gauge invariant energy density (scaled by $v^2$)
\begin{equation}
\label{spectrum}
\widetilde{{\cal E}}\left({\bf k}, t\right)=\frac{{\cal E}\left({\bf k},
t\right)}{v^2} ~=~
\frac{1}{4 v^2}\,\left|\,\int {d^3x}~e^{i{\bf k}\cdot{\bf x}}~{\rm Tr}~
\left[\, {\bf E}^2\left({\bf x}, t\right) ~+~
{\bf B}^2\left({\bf x}, t\right) \,\right]\,\right|~,
\end{equation}
where ${\bf E}$ is the gauge electric field and ${\bf B}$ the gauge magnetic
field. It is seen that the spectrum for the parallel isospins (median
row in Figure 1) does not change its shape dramatically, while for the
case of orthogonal isospins (median row in Figure 2), the spectrum spreads
out widely. The spike at $k=0$ in these spectra corresponds to the total
energy contained in the transverse gauge field. From its slight decrease
in Figure 2, we see that the energy transferred to the Higgs and the
longitudinal gauge fields during the collision is small ($\approx 10\%$).
This reflects the fact that the nonlinearity due to the gauge field
self-coupling dominates. Furthermore, the bottom rows of Figures 1 and 2
illustrate the time evolution of the Higgs field excitations\footnote{As
seen from (\ref{h_equation}) oscillations of the gauge boson field act as
a source for Higgs field excitations. The equation (\ref{w_equation}) for
the gauge field does not possess a source term.} around its condensate
value $v$ (which is scaled to unity) accompanying the collision process
shown in the top rows of Figures 1 and 2. Here we have plotted the square
$|\Phi^\prime|^2=|\Phi|^2/{v^2}$ of the Higgs field as a function of space
coordinate at three different times. Throughout our simulations, we have kept
$k_{min}\ll\Delta k\ll\bar{k}\ll k_{max}$, where $k_{min}$ and $k_{max}$ are
the minimum and maximum momentum on the lattice, respectively. This
ensures that the wave packets
are smooth on the lattice. But during collisions, unlike
quantum mechanics, classical dynamics does not provide a mechanism for
stopping power from flowing to
very low frequency modes (close to $k_{min}$) or to very high frequency modes
(close to $k_{max}$). In our calculations, the power flowing to high frequency
modes does not cause a deterioration in the local smoothness of the gauge field
at the end of the simulations.
To display dependence on the mass ratio $r={{M_H}/{M_W}}$, the
top row of Figure 3 shows the collision of two orthogonally polarized
$W$ wave packets at the final time $(t=580)$ for three different values of
$r={M_H/ M_W}$. It is seen that the ``inelasticity'' is more pronounced
for small $r$. On the other hand, the distortions in the wave packets
still survive at large $r$ (even at $r=100$, not shown here). This can
be understood as follows. Remember that there are three sources of
nonlinearity, namely, gauge field self-coupling, gauge-Higgs coupling,
and Higgs self-coupling. As the Higgs mass increases, the Higgs modes
begin to decouple. As a result, the interaction between gauge and Higgs
field diminishes and hence contributes less to the nonlinear effects.
The gauge field self-interaction is not affected by the change in the
Higgs mass and acts as the main contributor of nonlinear effects observed
during the collision. The median row of Figure 3 is the analogue of
the top row of Figure 3 in momentum space, as defined in (\ref{spectrum}).
Again, it gives a clearer picture of the inelasticity of the collision
process. The bottom row of Figure 3 demonstrates that the amplitude of
the Higgs field excitations becomes smaller as the Higgs mass is increased,
while their frequency increases with $M_H$.
It is remarkable that for small Higgs mass, as seen for $r=0.1$ in Figure 3,
the Higgs field oscillates not about the vacuum expectation value $v$ but
rather
about zero. The
observed behavior holds even at larger values of $r$, up to $r \approx 0.5$
(not
shown here). This suggests that for not too large $r$, the collision of gauge
field wave packets, accompanied by energy transfer from gauge field to Higgs
field,
leads to restoration of the broken symmetry. This phenomenon occurs for gauge
field configurations with large amplitude \footnote{The idea that the
restoration of
vacuum symmetry is possible in the background of intense gauge fields was first
noted
in \cite{KLINDE}. Also see \cite{KPC}), where the role of external gauge fields
in the
restoration of broken symmetries was considered.}. Indeed, it is easy to see
that
$\rho=-\sqrt{2}v$ (i.e. $|\Phi|=0$) is an exact solution to equation
(\ref{h_equation}).
Inserting $\rho=-\sqrt{2}v$ into equation (\ref{w_equation}) leads to the pure
Yang-Mills
equation for massless
$W$-bosons. In terms of excitations around this state, $\chi=\rho+\sqrt{2}v$,
we rewrite
equations (\ref{w_equation}) and (\ref{h_equation}) as
\begin{eqnarray}
[D_{\mu}, F^{\mu\nu}]+\frac{1}{4}g^2\chi^2 W^{\nu} &=& 0~,
\label{wprime_equation} \\
\left[\partial_{\mu}\partial^{\mu}-M_H^2(1+\frac{g^2W^2}{8\lambda v^2})\right]
\chi
+ \lambda\chi^3 &=& 0~, \label{chi_equation}
\end{eqnarray}
where $W^2=-(W_i^a)^2 < 0$ for transverse polarized wave packets (the sum over
spatial index
$i$ and isospin index $a$ is assumed here and in below). After dropping a
constant term
$\lambda v^4$, the corresponding effective potential describing the excitations
$\chi$ has the following form:
\begin{equation}
V(\chi,~W_{\mu})=-\lambda v^2(1-\eta)\chi^2+\frac{\lambda}{4}\chi^4~,
\label{potential}
\end{equation}
where we denote
\begin{equation}
\eta \equiv \frac{g^2(W_i^a)^2}{8\lambda v^2}
= \frac{1}{r^2} \left( \frac{W_i^a}{v} \right)^2~. \label{ETA}
\end{equation}
In the following we use $\eta$ as a parameter in which the true
intensity $(W_i^a)^2$ of the high frequency gauge field pulses is replaced by
its
space-time average $\langle W^2 \rangle$. Depending on whether $\eta<1$ or
$\eta > 1$,
the potential (\ref{potential}) has two different {\it stable} minima:
\begin{eqnarray}
{\rm for}~ \eta<1, &~& \chi_{min}=\pm\sqrt{2}v(1-\eta)^{1/2}~, ~~~{\rm i.e.}~~~
|\Phi|=v(1-\eta)^{1/2}~, \\
{\rm for}~ \eta \geq 1, &~&\chi_{min}=0~, ~~~{\rm i.e.}~~~ |\Phi|=0~.
\end{eqnarray}
Stable excitations about these ``vacua'' have the following squared masses:
\begin{eqnarray}
{\widetilde{M}}_W^2 &=& M_W^2(1-\eta) \theta(1-\eta) \label{WMASS} \\
{\widetilde{M}}_H^2 &=& \frac{M_H^2}{2}(1-\eta) [1+\theta(1-\eta)]
\label{HMASS}
\end{eqnarray}
Thus for $\eta > 1$ , the broken symmetry is restored and oscillations of the
scalar
field occur about the symmetrical state $|\Phi|=0$, not about $|\Phi|=v$. The
effective
mass of the gauge bosons in the region where the symmetry is restored vanishes.
For $\eta<1$,
the ratio between the effective masses ${\widetilde{M}}_H$ and
${\widetilde{M}}_W$ has
no dependence on $\eta$ and remains $r=M_H/M_W$. Relations
(\ref{WMASS}) and (\ref{HMASS}) are characteristics of a second order phase
transition.
The expression (\ref{ETA}) for $\eta$ shows that in the regime of large
$(W_i^a)^2 > v^2$,
this phase transition can occur for experimentally favorable mass ratio $r>1$.
Oscillations of the scalar field around the new symmetrical minimum $|\Phi|=0$
are clearly
seen for $r=0.1$ where $\eta \approx 22.3 $ (see Figure 3). These numerical
results provide indications for transition from the phase with spontaneously
broken
$SU(2)$ symmetry and asymmetric vacuum to the phase with restored $SU(2)$
symmetry
and symmetric vacuum as a result of the collisions.
Since $\eta$ is the only relevant parameter in question here,
this transition can occur either for small $\lambda$ (light Higgs) or for large
$\lambda$
(heavy Higgs) if amplitude of the gauge field is large enough. In Figure 3, it
is also
interesting to notice that the spatial region showing symmetry restoration
seems to be
wider than the region
where the colliding wave packets stay visibly large.
It is clear that the phenomenon discussed above does not depend on the
one-dimensionality
of space in our calculations. However, it is to be expected that the symmetry
restoration
would not persist as long in three dimensions as the wave packets disperse more
rapidly after
the collision causing the squared amplitude $\langle W^2 \rangle$ to decay more
rapidly.
\subsection{Yang-Mills and BPS limit}
In the light of the previous work \cite{OWN}, it is instructive to study
the limiting case of the present system as $M_H, ~ M_W
\rightarrow 0$ while fixing $r={{M_H}/{M_W}}$ (which is chosen
to be $1$ here). Of course, this corresponds to the limit $v \rightarrow 0$,
where one expects that the gauge field in the Yang-Mills-Higgs system behaves
most closely to that in a pure Yang-Mills system. In Figure 4, the
top row shows snapshots of the collision of two orthogonally polarized
wave packets with $M_H=M_W=0.001$ and the bottom row exhibits the
corresponding spectra. Qualitatively, these figures show that the time
evolution is very similar to that seen in the pure Yang-Mills system
(see Figures 2 and 4 in \cite{OWN}).
The second interesting limit is the Bogomolny-Prasad-Sommerfield (BPS)
limit \cite{BPS} where $M_H\rightarrow 0$ but $M_W$ is finite
($\lambda\rightarrow 0$, $v$ fixed). Figure 5 shows the snapshots and
spectra for this case with $M_W=0.126$ and $r=0.01$. Again, we display
only the orthogonal case, which reveals complete destruction of the wave
packets as in the pure Yang-Mills limit. It is interesting to note that
in this limit the static force between equally charged $W$-bosons
vanishes due to the precise cancellation between the photon and (massless)
Higgs exchange diagrams, which is a result of the electromagnetic duality
\cite{MO}. For a pair of oppositely charged $W$-bosons, the contributions
from these diagrams add to each other, doubling the attraction.
\subsection{Dependence on the initial amplitude and energy}
In our simulation, the most crucial role is played by the initial
amplitude of the wave packets. As in the pure Yang-Mills case \cite{OWN},
we find that the amount of ``inelasticity'' observed in the present
system is closely linked to the magnitude of the dimensionless amplitude
(\ref{amplitude}). This amplitude depends on several independent
parameters: $\sigma M_W^2 / g^2$, ${\Delta k}/ M_W$, and
${\Omega}/{M_W}\approx {\bar k}/{M_W}$ (for ${\bar k}\gg M_W$),
each of which has a different physical meaning. Noting that the gauge
coupling constant is fixed to be $g=0.65$ throughout our simulation
and $M_W$ is a fixed quantity in reality, the best way to study the
amplitude dependence is to vary $\sigma$ without changing anything else.
By varying $\sigma$, we find that the nonlinear effects increase with
amplitude. For a very large $\sigma$ (very small amplitude), we find
no indication of ``inelasticity'' in the colliding wave packets at the
end of the simulation.
To search for the energy dependence, we have to study the dependence on
$\bar k$, which determines the energy of the initial wave packet. In
the meantime, we fix $\sigma$, $M_W$, and $M_H$. $M_W$
and $M_H$ are chosen to be much smaller than $\bar k$ to model high
energy scattering. Furthermore, as we change $\bar k$, $\Delta k$ is
either fixed or changed proportionally to fix the ratio ${\Delta k}/{\bar k}$.
In Figure 6, we display snapshots of collisions at the final time for
different sets of $\bar k$ and $\Delta k$. Figure 7 shows the
corresponding spectra. The orthogonal isospin cases in Figures 6 and 7
are shown in the left column with their parallel isospin counterparts in the
right column.
Clearly, the observed nonlinear effects in the orthogonal cases are
qualitatively similar for different $\bar k$ or $\Delta k$; while in
the parallel cases, regardless of $\Delta k$, the nonlinear effects
disappear as $\bar k$ is increased from $\pi/25$ to $\pi/5$.
\section{Discussions}
\subsection{Amplitude Dependence}
Our numerical calculations show for a wide range of parameters that
the wave packet collisions with orthogonal isospin orientation are
strongly inelastic if the scaled initial amplitude (see equation
(\ref{amplitude}), $k\gg M_W$)
\begin{equation}
\left({2\Delta k\over\sqrt{\pi}\bar k\sigma v^2}\right)^{1/2} \label{24}
\end{equation}
is of the order of unity. We recall that the expression (\ref{amplitude})
for the scaled amplitude was determined by the condition that the wave packet
contains one particle per transverse area $\sigma$.
Although, in the strict sense, our configurations describe wave packets
which are infinitely extended in the transverse direction and hence
contain infinitely many particles, only a finite transverse area
influences the dynamics over a finite period of time. As argued in
\cite{OWN}, causality restricts that area to $\sigma (T_s) = \pi T_s^2$
where $T_s$ is the elapsed time after the impact of the two
wave packets. The relevant number of particles in the initial state is
therefore given by
\begin{equation}
N_i^{\rm eff} = {\sigma(T_s)\over\sigma} = {\pi T_s^2\over \sigma}.
\end{equation}
What is the lower bound on $N_i^{\rm eff}$ under realistic conditions,
for which strongly inelastic events occur? Let us first estimate the
constraints on our parameters from a realistic point of view. Clearly,
we must have $\bar k\gg v$. The natural spread of any $W$-boson wave packet
produced in high energy interactions is of order $\Delta k\sim v$ in
the comoving reference frame. Therefore the typical transverse area
of the $W$-boson wave packet is of order $\sigma \approx 1/v^2$. Due
to Lorentz contraction, its longitudinal momentum spread will generally
be much larger than $v$, or of order $\Delta k_{\Vert}\sim \gamma
v$, where $\gamma \approx \bar k/M_W$ is the Lorentz factor. As a result,
$\Delta k_{\Vert}/\bar k$ will be approximately independent of the
collision energy, with a value not much smaller than one. Assuming,
e.g., $\Delta k/\bar k \approx 0.5$ in (\ref{24}), we obtain an amplitude of
order unity implying that a few $W$-bosons per area $\sigma$ in the
initial state could produce strong inelasticity. Of course, the
precise lower bound on the particle number will depend on the detailed
shape of the wave packets and requires a full three-dimensional
analysis. But our estimate shows that strongly inelastic events are
not excluded for collisions of wave packets containing few particles.
In this respect, the results of our analysis correspond to those of
Singleton and Rebbi \cite{RS} who found that few-particle initial states
may not be excluded for baryon number nonconserving processes
resulting in multi-particle final states.
As mentioned above, the finite transverse size of order $v^{-1}$
limits the applicability of our calculation for the real
three-dimensional case to times $T_s \le v^{-1}$. Since the
inelasticity is clearly revealed for times $T_s\sim 100$ (see e.g.
Figure 5), our numerical results apply most confidently to very high
energy where $\bar k/v \ge 10^2$.
\subsection{Energy Dependence}
We now turn to the question of the energy dependence of the nonlinear
effects seen in the wave packet collisions. In the $(1+1)$-dimensional
abelian Higgs model, the nonlinearities were clearly found to decrease
with energy \cite{TR}. For the non-abelian Higgs model discussed here,
the answer is given in Figures 6 and 7. The inelasticity seen in the
orthogonal isospin cases does not change significantly with energy,
while it dies out in the parallel isospin cases as $\bar k$ increases.
This shows the fundamental role of the non-abelian nature of the
$W$--$W$ interaction in the formation of strongly inelastic final states.
{}From Figures 6 and 7 one can also see that the inclusion of the Higgs field
produces new phenomena which are not seen in the pure Yang-Mills
system: For initial configurations with parallel isospin, in which case
nonlinear interactions of the gauge bosons are absent, lowering of
the parameter $\bar k$ leads to inelastic final states. This is
exclusively due to the Higgs field since the collision of wave packets
with parallel isospin configurations in the pure Yang-Mills theory
always leads to elastic final states independently of $\bar k$ \cite{OWN}.
Of course, this pattern indicates that the influence of the Higgs coupling
to the gauge field increases for smaller $\bar k$. How does one understand
this behavior? For this purpose, we recall that all our calculations
are in the regime of high energy ($\bar k \gg v, M_W$). For the highest
energy of the collisions ($\bar k =\pi/5$) where parallel polarized
wave packets scatter elastically, one may think that the transversely
polarized $W$--$W$ scattering (elastic in these collisions) proceeds via
exchanges of the gauge and of the Higgs bosons in the tree approximation.
The first contribution prevails at high energy, but it does not contribute
to the inelastic final states for the parallel isospin orientation.
Inelasticity may arise here only from the nonlinear coupling of the gauge
and Higgs fields or, in diagrammatic language, due to the Higgs exchange
whose contribution increases with the lowering of $\bar k$.
\section{Conclusion}
We have numerically studied collisions between classical wave packets
of transversely polarized gauge bosons in the spontaneously broken
Yang-Mills-Higgs theory. Our main results are the following:
\begin{enumerate}
\item We have found evidence for the creation of final states with
dramatically different momentum distributions (strongly ``inelastic''
events) for a wide range of the essential parameters.
\item These inelastic events persist at the highest investigated energies
$(\bar k/M_W \sim 10^2)$ for collisions with orthogonal isospin
polarization, reflecting the essentially non-abelian character of the
interaction. For parallel isospin configurations, in contrast, the
inelastic events, which are solely due to the Higgs field, occur only for
lower energies.
\item Under more realistic conditions as discussed in Section IV.A, the
inelastic
events are not excluded for initial configurations with few particles.
\item We have observed, at least for $r \leq 0.5$ (with fixed amplitude for
the gauge field wave packets), the phenomenon of symmetry restoration as a
result of the wave packet collisions. This transition from the asymmetrical
state to
the symmetrical one is
governed by a single parameter $\eta$, which depends on both the mass ratio $r$
and
the amplitude of the wave packets.
\end{enumerate}
Summarizing, we conclude that the introduction of the Higgs field (in
the broken symmetry phase) does not in general spoil the inelasticity
of the final state in collisions with orthogonal isospin orientation.
Our results provide a strong motivation for exploring related
phenomena in $(3+1)$ dimensions. This would allow one to study
collision between realistically shaped wave packets and investigate the
particle number content of inelastic final states. Last, but not
least, it would be interesting to study the winding number change
associated with these collisions.
\acknowledgements
We thank S. D. H. Hsu for discussions and useful comments. Especially, we
want to thank the referee for numerous constructive comments and suggestions,
which were very useful in preparation of a revised version of this paper.
This work was supported, in part, by grants DE-FG05-90ER40592 and
DE-FG02-96ER40945 from the U.S. Department of Energy, and by the North Carolina
Supercomputing Center.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 0
|
package org.apache.flink.runtime.rest.messages;
import org.apache.flink.runtime.jobgraph.JobVertexID;
import org.apache.flink.runtime.rest.handler.job.JobVertexDetailsHandler;
import org.apache.flink.runtime.rest.messages.job.SubtaskExecutionAttemptDetailsInfo;
import org.apache.flink.runtime.rest.messages.json.JobVertexIDDeserializer;
import org.apache.flink.runtime.rest.messages.json.JobVertexIDSerializer;
import org.apache.flink.shaded.jackson2.com.fasterxml.jackson.annotation.JsonCreator;
import org.apache.flink.shaded.jackson2.com.fasterxml.jackson.annotation.JsonIgnore;
import org.apache.flink.shaded.jackson2.com.fasterxml.jackson.annotation.JsonProperty;
import org.apache.flink.shaded.jackson2.com.fasterxml.jackson.databind.annotation.JsonDeserialize;
import org.apache.flink.shaded.jackson2.com.fasterxml.jackson.databind.annotation.JsonSerialize;
import java.util.Collections;
import java.util.List;
import java.util.Objects;
import static org.apache.flink.util.Preconditions.checkNotNull;
/** Response type of the {@link JobVertexDetailsHandler}. */
public class JobVertexDetailsInfo implements ResponseBody {
public static final String FIELD_NAME_VERTEX_ID = "id";
public static final String FIELD_NAME_VERTEX_NAME = "name";
public static final String FIELD_NAME_PARALLELISM = "parallelism";
public static final String FIELD_NAME_MAX_PARALLELISM = "maxParallelism";
public static final String FIELD_NAME_NOW = "now";
public static final String FIELD_NAME_SUBTASKS = "subtasks";
@JsonProperty(FIELD_NAME_VERTEX_ID)
@JsonSerialize(using = JobVertexIDSerializer.class)
private final JobVertexID id;
@JsonProperty(FIELD_NAME_VERTEX_NAME)
private final String name;
@JsonProperty(FIELD_NAME_PARALLELISM)
private final int parallelism;
@JsonProperty(FIELD_NAME_MAX_PARALLELISM)
private final int maxParallelism;
@JsonProperty(FIELD_NAME_NOW)
private final long now;
@JsonProperty(FIELD_NAME_SUBTASKS)
private final List<SubtaskExecutionAttemptDetailsInfo> subtasks;
@JsonCreator
public JobVertexDetailsInfo(
@JsonDeserialize(using = JobVertexIDDeserializer.class)
@JsonProperty(FIELD_NAME_VERTEX_ID)
JobVertexID id,
@JsonProperty(FIELD_NAME_VERTEX_NAME) String name,
@JsonProperty(FIELD_NAME_PARALLELISM) int parallelism,
@JsonProperty(FIELD_NAME_MAX_PARALLELISM) int maxParallelism,
@JsonProperty(FIELD_NAME_NOW) long now,
@JsonProperty(FIELD_NAME_SUBTASKS) List<SubtaskExecutionAttemptDetailsInfo> subtasks) {
this.id = checkNotNull(id);
this.name = checkNotNull(name);
this.parallelism = parallelism;
this.maxParallelism = maxParallelism;
this.now = now;
this.subtasks = checkNotNull(subtasks);
}
@JsonIgnore
public List<SubtaskExecutionAttemptDetailsInfo> getSubtasks() {
return Collections.unmodifiableList(subtasks);
}
@Override
public boolean equals(Object o) {
if (this == o) {
return true;
}
if (null == o || this.getClass() != o.getClass()) {
return false;
}
JobVertexDetailsInfo that = (JobVertexDetailsInfo) o;
return Objects.equals(id, that.id)
&& Objects.equals(name, that.name)
&& parallelism == that.parallelism
&& maxParallelism == that.maxParallelism
&& now == that.now
&& Objects.equals(subtasks, that.subtasks);
}
@Override
public int hashCode() {
return Objects.hash(id, name, parallelism, maxParallelism, now, subtasks);
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 4,147
|
George Sandys (ur. 2 marca 1578 w Bishopsthorpe, zm. w marcu 1644 w Boxley) – angielski polityk, podróżnik i poeta. Brat polityka Edwina Sandysa (1561–1629).
Życiorys
Sandys urodził się jako najmłodszy, siódmy syn arcybiskupa Yorku, Edwina Sandysa. Studiował w St Mary Hall w Oksfordzie, ale nie uzyskał dyplomu. W 1610 roku zaczął podróżować po Europie, Azji, Afryce i Ameryce. Najpierw odwiedził Francję, potem przez Wenecję udał się do Konstantynopola, dalej do Egiptu, na górę Synaj i do Palestyny, a w drodze powrotnej na Cypr, Sycylię, do Neapolu i wreszcie do Rzymu. Relację z tej długiej podróży zadedykował królowi Karolowi I Stuartowi. Była ona ważnym źródłem geograficznym i etnograficznym.
W kwietniu 1621 roku Sandys rozpoczął karierę polityczną. Został skarbnikiem Kompanii Wirginijskiej (Virginia Company). Udał się do Ameryki w towarzystwie Francisa Wyata, męża swojej bratanicy, który został nowym gubernatorem. Kiedy Wirginia uzyskała oficjalnie status angielskiej kolonii, Sandys stał się członkiem tamtejszej rady. Piastował to stanowisko w 1626 i 1628 roku. W 1631 roku bezskutecznie starał się o uzyskanie miejsca w komisji do spraw modernizacji rolnictwa. Wkrótce potem na dobre wrócił do Anglii. Zajął się wtedy pracą literacką. Nie założył rodziny. Zmarł w Boxley, koło Maidstone w hrabstwie Kent w 1644 roku.
Twórczość
Za najważniejsze dzieło Sandysa uchodzi przekład Metamorfoz Owidiusza. Poeta wydał też Paraphrase upon the Psalms and Hymns Dispersed throughout the Old and New Testaments i tłumaczenie łacińskiego dzieła Męka Chrystusa Grotiusa. W 1641 roku opublikował swoje ostatnie dzieło Paraphrase of the Song of Songs. Uważany jest za poetę, który przyczynił się do rozwoju dystychu bohaterskiego (heroic couplet), czyli parzyście rymowanego pentametru jambicznego. John Dryden nazwał go najlepszym wersyfikatorem (the ingenious and learned Sandys, the best versifier of the former age).
Przypisy
Linki zewnętrzne
Angielscy poeci metafizyczni
Brytyjscy tłumacze
Brytyjscy politycy
Brytyjscy podróżnicy i odkrywcy
Urodzeni w 1578
Zmarli w 1644
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 9,788
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package TeamTwoHTMLEditor;
/**
* Created with IntelliJ IDEA. User: Kocsen Date: 3/22/13 Time: 2:58 PM
* Distributor/Controller class - Contains a reference to FileManager
*/
public class CommandDistributor{
private FileManager fileManager;
public CommandDistributor(FileManager fManager){
fileManager = fManager;
}
public FileManager getFileManager(){
return fileManager;
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 9,034
|
» Extension
Organisation of a Primary Dairy Cooperative
1.1. Survey of a village:
To assess whether any project or industry would be viable in a certain area, a survey of available resources in that particular area is carried out. While conducting a survey of the villages concerning milk procurement, the following aspects are studied in detail.
Ø The existing cattle and buffalo population
Ø The production and utilization / disposal pattern of milk and milk products
Ø Marketing channels for surplus milk
Ø Returns from the sale of milk realized by the farmers
Ø Agricultural facilities and production patterns
Ø Basic amenities such as communication links, educational facilities, etc.
Ø Other sources of income
Ø Performance of other institutions including multipurpose cooperatives, etc.
Ø Different communities living in a village and their inter-relationship
Ø Other relevant information if any
Such a study helps in assessing the future prospects of a milk cooperative society. It also helps in finding out the interest and faith of farmers in collective activity. Thus, survey forms the basis for establishing any milk cooperative society.
The Union's field staff conducts the survey. The study is carried out in the village itself. A suitable format is designed for this purpose so that all the information is collected (formats on the following page). The following steps are taken for conducting survey of a village before setting up a milk producers' cooperative society:
Ø The field supervisor proceeds to the village.
Ø He contacts the progressive farmers, village Sarpanch or Pradhan and other important persons of the village.
Ø He explains to them the purpose of his visit and the entire scheme.
Ø He collects the basic information about the village from Panchayat office.
Ø He moves from door-to-door to collect information about individual villagers.
Ø He visits the people belonging to all communities and areas in a village.
Ø He also collects information regarding agriculture and animals from the records of district office.
Ø All information thus collected is crosschecked for validity.
After conducting the survey, the field staff should be in a position to judge whether the people are interested in forming a cooperative society for milk or not. He should record his opinion on the format accordingly. He also decides whether the village can be considered for setting up a cooperative in the very first stage, or it should qualify for the same at a later date.
This information is then submitted to the milk procurement section of the Union for review. The union analyses this information carefully. And on the basis of marks allotted to each section of information, the merit of a village is finally assessed. Depending on the merit, further action for organizing cooperative society is decided.
Survey of Village – Format A
Name of village Date of survey
Name of Taluka/Block Area (sq. kms)
Name of District Human population
Name of milkshed No. of house holds
A. Animal Statistics B. Public Facilities Available
Buff.
Cross bred
Animals in milk
Animals dry
Service bulls
Average milk yield
Total milk production
Educational facilities with standard
Government/Pvt./Nil
Veterinary facilities
Pvt.
Deep tube well/ well/Nil/Pvt.
A.I. Facilities
C. General
Village connected by
Metal/Kachha Road
- Village Panchayat
Individual / group
Distance of metal road from village
- Name of Sarpanch
Nearest village connected by road.
Name and distance
- Important crops grown in village
Days for which village not accessible in monsoon
- Name of fodder crops grown
Distance and name of nearest town
- Total area for fodder crops
Distance of village from dairy plant/ chilling centre
- Sources of irrigation
Existing Milk Disposal Details
I. Liquid
No. of agents
Total Qty. per ltrs.
Basis of payment Quality
Price offered/ ltr.
Payment frequency Advance/ weekly/
Where disposes the milk
No. of farmers supplying
Village vendors
Vendors from other villages
Any coop. Society Name
Private / Public organised sector Name
II. Product Conversion Details
No. of creameries/ shops converting milk into products
Qty. of milk converted (Ltrs.)
Price/kg. product
Price offered to producer Rs./ lit.
Skimmed milk disposal/ utilization if any
No. of producers supplying milk
1. Ghee
2. Khoa
4.Chhana
5. Curd
6. Cream
7. Others
Existence of Cooperative Society other than Milk:
1. Does any coop. society exist: _____________ Yes / No
2. If yes, name and financial status: _____________ In profit / In loss
3. General view of villagers about
above cooperative _____________ Unsatisfactory/Satisfactory/Good
Milk Producers Cooperative Organisation:
a) Land holdings Large Small Marginal Landless Remarks
farmers farmers farmers labourers
No. of farmers in village
No. of farmers expected to become
milk coop. Approx. No.
b) Marketable Flush Lean Mean
surplus milk
(in kg.)
c) Expected milk supply to the society, if formed
d) Name/No. of milk route in which society will fall
Recommendation: Society to be organized __________________________ Yes / No.
To complete the above format, a supplementary format is required to be filled. This is possible only if door-to-door survey is conducted. In other words, a realistic survey has to be done to assess the position correctly. The design of the format (B) is given on the following page.
MODEL OF SUPPLEMENTARY FORMAT – B
Name of village: _____________________________
Name of prod-ucer
No. of milch animals
Milk prodn. Lts/day
Cow Buff
Home consu-mption
Ltr./day
Marketa-ble surplus of family
ltrs./day
of dis-posal
Rate of dis-posal Rs./lit.
Freque-ncy of receiving payment, advance/ monthly/ weekly
In milk
Satisfied or not with existing system Yes/No.
Land Holding Status
L.F.* S.F. M.F. L.L.
Whether willing to become member of the society Yes/No.
* L.F. – Large farmers – having more than 5 acres of land
S.F. - Small farmers – having 2.5 to 5.0 acres of land
M.F. - Marginal farmers – having less than 2.5 acres of land
L.L. - Landless labourers – having no land
Analysis of the Survey Format and Ratings:
The format (A) consists of 6 important sections from A to F. Each section has been allotted certain points. On analyzing, each section should at least score the minimum marks as explained below for deciding to organize the society in a particular village:
Sections A B C D E F Total
Maximum marks 5 5 7 13 5 10 45
Minimum marks 3 3 4 6 3 4 23
The above table is based on the following criteria:
Section A – (5 marks) Criteria Points awarded
Total milk production – 500 litrs. and above / day 4
Between - 300 litrs. to 500 litrs. / day 3
Less than - 200 litrs./ day 1
Veterinary / A.I. facilities in village by
Government / Private / Other agency 1
No such facility in the village 0
Section B – (5 marks)
Post office facility 1
Bus service / Railway service 2
Electricity in village 1
Education facilities 1
Section C – (7 marks)
Metal road up to village 3
Katcha road up to village 1
No road up to village / only foot path 0
Distance from nearest town more than 5 kms. 1
Distance from nearest town less than 5 kms. 0
Village not accessible in rainy season for about 30 days 1
Village not accessible in rainy season for more than 30 days 0
Good fodder cultivation in village 2
Average fodder cultivation in village 1
No fodder cultivation in village 0
Section – D (13 marks)
Village vendors operating 1
No village vendors operating 3
Vendors from other villages operating 1
No vendors from other villages operating 2
Organised sector collecting milk 1
No organized sector collecting milk 2
Entire milk converted into products 0
About 50% milk converted into products 3
No milk is converted into products 5
Section E – (5 marks)
General idea of villagers about societies performance
Unsatisfactory 0
Satisfactory 3
Section F – (10 marks)
More number of small and marginal farmers 4
More number of large farmers 2
More number of landless farmers 2
Retention of milk by villagers
- Less than 30% of production 5
- Between 30-60% of production 2
- More than 60% of production 1
Rating Total points awarded
Rank – A Between 35 to 42
B " 25 to 34
C " 15 to 24
D Less than 15
After the format (A) is filled out and marks allotted to each section by the surveyor, he should add all the marks and rate the village in either of the above-mentioned categories.
Final Selection of a Village for Society Organisation
The villages with rank 'A' and 'B' can be easily selected in the first phase itself. The villages ranking as 'C' may be taken up for filling in the gaps at a later stage. However, villages falling under category 'D', as far as possible be avoided for organising independent societies as the same may not be an economical proposition.
However, this classification should be used only as a guideline as sometimes a village may not obtain the required minimum score but still may be considered for organising a society due to one single reason such as potentiality of village in terms of milk. In such cases the milk procurement sectional head has to use his own discretion based on practical experience.
1.2. Organisation and Registration of society:
After the Survey, villages are categorised on the basis of milk potential and other related factor such as approachability and location in the proposed milk route. The milk union's personnel initiate work pertaining to the organisation of a dairy cooperative society once the categorisations of villages are complete and proposed area for the route is decided. The State Cooperative Societies Act and Rules form the basis for organisation and registration of a society. Normally following steps are taken to form a society:
Organising Gram Sabha
This involves the following activities to be undertaken:
Ø One person from the milk union's procurement wing visits the selected villages and arranges meeting of villagers. This meeting is called as gram-sabha and the interested villagers participate in the same.
Ø A well accepted elderly person from the village is requested to preside.
Ø The officer / staff of the milk union explains the purpose and advantages of organising the dairy cooperative society in the village. The principles and concept of cooperation and the activities and functioning of the society are explained.
Ø Once the milk producers have decided to form a milk producers' cooperative society, an organiser is selected from amongst them.
Ø The organiser is authorised to collect the share subscription (as per the State Cooperative Societies Act, Rules, model by-laws of the society etc.) and entrance fee from all those milk producers who are interested in becoming members (promoters) of the society. The share collection takes a few days and normally the concerned supervisor keeps a close watch on the developments.
Ø After a sufficient number of milk producers become members (depending on the expected quantity of milk procurement, number of milk producers in the village etc.), the amount of share money and entrance fee is deposited to a local bank in the name of the proposed society.
Society Organisation Meeting
A general meeting of all the milk producers who have subscribed to the share deposit of the proposed society is convened. At this meeting, one of the members is elected as Chairman to preside over the meeting. The following issues are discussed and resolved. These resolutions are then minuted in the Proceeding Book.
Ø To form a milk producers' cooperative society on the lines of bye-laws as suggested by the milk union, named ----Milk Producers' Cooperative Society and to apply for registration in due course under the State Cooperative Societies Act. Till the registration certificate is obtained, this will be called Proposed Society.
Ø To decide the area of operation of the society (Revenue village, part of village, Khatian/Daag No, Tola, Hamlets etc.).
Ø To constitute an ad-hoc managing committee comprising members as per rule to look after the society's affairs till the registration.
Ø To elect the Chairman (Chief Promoter) of the proposed society as per rule.
Ø To authorise the managing committee to appoint society staff for day-to-day work (normally on honorary basis for initial period). Generally at the beginning only a Secretary is appointed and than as the procurement goes up, other supporting staff are appointed. The staff should be the resident of the same village.
Ø To authorise the Chairman and Secretary to open a bank account in the name of the Proposed Society at the nearest branch. The Chairman and Secretary will operate this account jointly.
Ø To obtain tangible security from the Secretary to become eligible for operating bank account and handling of cash.
Ø To regularise the collection of share money and entrance fees from milk producers towards membership.
Ø To make the dairy cooperative society duty bound to follow all directions and suggestions given by the Milk Union to which the society desires to be affiliated.
Ø To collect milk from all the members and supply the same to the milk union as suggested/directed by the milk union.
Ø To supply the inputs on cost to the members as provided by the milk union.
Ø To select the milk collection centre/location/premise for the society in the village which desirably a centrally located position and accessible by most of the members.
Ø To procure the Milk Cans, Milk Collection and Testing equipment, Stationary, Chemicals for testing etc. before the date of commencement of milk procurement by the society.
Ø To decide the modalities of milk transportation (Head Load) if the society is not on the main road/lifting point of the milk truck.
Ø To raise fund /deposit from individual or to request milk union for an advance to facilitate quick payment in the beginning.
It may please be noted that constitution of ad-hoc managing committee / Chief promoter, collection of the share money, application for registration etc. are governed and decided by the State Cooperative Societies Act, Rules and the Milk Union's policy of organisation and registration of society.
Registration of Society
In normal circumstances a proposed society (which has been organised as per bye-laws) is allowed to function as such for a period up to which the milk union assess its attainment of sustainability. A performance review of the functioning of the society is done and if satisfied with its growth and sustainability, the milk union proposes for its registration. The proposal is recommended by the milk union and forwarded to the concerned office of the Registrar, Cooperative Societies of the State. The general procedure for preparing the proposal for registration is indicated below:
Ø The application form for registration is collected.
Ø All members including those on the ad-hoc managing committee sign the application as Promoters.
Ø The application is submitted to the appropriate authority for consideration along with the following documents. The requirement may vary from state to state.
a) Number of copies (as prescribed in the application form) of the bye-laws signed by the Chief Promoter.
b) Number of copies (as prescribed in the application form) of the list of members (promoters) with number of shares held by each of them.
c) Number of copies (as prescribed in the application form) of the resolutions passed at the proposed society's organisation meeting.
d) Number of copies (as prescribed in the application form) of the proposed society's bank balance certificate issued by the bank.
e) Number of copies (as prescribed in the application form) of the accounts statement for the period it has worked as proposed society.
f) A certificate regarding jurisdiction of village Panchyat under which this village is located.
The society is considered registered only when a registration certificate is obtained by the society with a registration number and date, issued by the registering authority.
1.3. First General Body Meeting of the Registered Society:
Once the society is registered, a general body meeting of all the members is convened by the Secretary of the proposed society with the permission /consultation of the Chairman. The following suggestive / indicative agenda items are considered in the meeting (depending upon the state act, rules etc.).
Ø Selection of a person to chair this meeting.
Ø Thanks to the registering authority and accepting the registered bye-laws.
Ø Election to the regular Managing Committee and Chairman of the Society as per bye-laws.
Ø Regularising / terminating the existing staff / appointing new staff, if required.
Ø Accepting the statements of accounts for the period it functioned as a proposed society.
Ø Informing the bank about the registration of the society and request them to make the account of the proposed society in the name of the registered society.
Ø Regularisation of membership according to the bye-laws. Enrollment of new members.
Ø Affiliation of the society with the Cooperative Milk Union and other related organisations.
Ø Appointment of local auditor.
Ø Any other items with the permission of the Chair.
1.4. Organisation and registration of Milk Union:
Once sizeable number of societies (40-50) are organised and registered in a milkshed, the steps for organising the District level milk union are taken. The responsibility of organising the union lies with the implementing agency along with concerned societies. The societies form the basic unit (member) of a union. The organisational work is done as per the approved bye-laws for union which are available from the office of the Registrar, Cooperative Societies or his representative office at District level. In some case the implementing agency (Government/Corporation/Federation) may nominate the union directors and ask the union to organize the societies. This happens when a cooperative dairy project is to be started from a scratch.
Nominated/Adhoc Body
In pursuance of the union bye-laws, the Chief Executive Officer of the implementing agency invites the society representatives (normally Chairman of all the registered milk societies) to hold a general body meeting which is called as an organisation meeting for union. For this purpose a communication in writing is sent to all the registered societies, stating purpose, date, time and place of meeting.
The proceedings of this meeting may differ on the basis of provisions in bye-laws of the union. In some cases the adhoc board is democratically elected in this meeting itself while in others the State Government/Registrar Cooperative Societies, nominates the first board. In former case the board continues functioning till the union is registered and holds its first general body meeting to elect the Board as per the bye-laws. In latter case the nominated board continues to function for the whole term as specified in bye-laws (normally 3 yrs) unless changes are made by the Registrar Cooperative Societies himself.
The meeting in both cases resolves around the formation of District Cooperative Milk Produces' Union in accordance with bye-laws. Also an interim board and Chairman are elected for a period of 3 months or till the union is registered. In the latter case the meeting resolves all the other matters but election of Board and Chairman which is subsequently nominated.
Registration of Union
The proposal for registration of Union is made on the prescribed application form available from District Registrar's office. This is accompanied by 4 copies of bye-laws duly signed by promoter-members, a copy of minutes of organisation meeting, bank balance certificate and other necessary resolutions as prescribed in bye-laws Acts with a request to register the union.
Post Registration General Body Meeting
After the union is registered, an agenda stating date, place, time and purpose of meeting is issued by the Chief Promoter to all member societies. In this meeting only those member societies are eligible to participate which have signed the original proposal of registration in the organisation meeting and who have also purchased shares of the union. This is called the first General Body Meeting of the union after registration. The agenda of this meeting contains following points to be considered:
Ø Selection of President of the meeting
Ø Acceptance of registered bye-law
Ø Election of regular board
Ø Approval of accounts for the proposed period
Ø Fixing the borrowing limit for union
Ø Any other work with the permission of chair.
The election of office bearers is done according to norms prescribed in the bye-laws/Rules and Acts of the State and thus a regular board is installed.
Meeting of Board of Directors
The board conducts its meeting soon after the general body meeting and decides about appointing the staff and taking further actions for achievement of the objectives as per bye-laws of the Union.
‹ Manuals up Cooperative Principles ›
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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 6,045
|
Would you know what to do in the case of a disaster? Would you know the best place to go, who to contact in your community, or where to get reliable information? You can get answers to those, and many other questions by attending a New York State Citizen Preparedness Corps training.
Since 2014, the Citizen Preparedness Corps, have been giving New York residents the tools and resources needed to prepare for any type of disaster. By taking this training you will know the best way to respond and how to recover as quickly as possible. The New York National Guard, working with experts from the Division of Homeland Security and Emergency Services' Office of Emergency Management and Office of Fire Prevention and Control, lead the training.
The next training session in the Hudson Valley is this Wednesday, June 13 from 6:00 pm- 7:30 pm at the Mount Hope Senior Center, on 7-11 Baker Street in Otisville. You'll learn about responding to a natural or man-made disaster, how to properly prepare for any disaster, including developing a family emergency plan and stocking up on emergency supplies. Click here to register for this event.
Each family participating will receive a free Citizen Preparedness Corps Response Starter Kit, to assist in the immediate aftermath of a disaster. By taking this training, you will not only be able to help out your family and friends but your neighbors and your community too.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 9,168
|
package ca.ryangreen.apigateway.generic;
import com.amazonaws.ClientConfiguration;
import com.amazonaws.auth.AWSCredentialsProvider;
import com.amazonaws.auth.AWSStaticCredentialsProvider;
import com.amazonaws.auth.BasicAWSCredentials;
import com.amazonaws.http.AmazonHttpClient;
import com.amazonaws.http.HttpMethodName;
import com.amazonaws.http.apache.client.impl.SdkHttpClient;
import com.amazonaws.regions.Region;
import com.amazonaws.regions.Regions;
import java.util.Arrays;
import java.util.List;
import org.apache.http.HttpResponse;
import org.apache.http.HttpVersion;
import org.apache.http.client.methods.HttpUriRequest;
import org.apache.http.entity.BasicHttpEntity;
import org.apache.http.message.BasicHttpResponse;
import org.apache.http.message.BasicStatusLine;
import org.apache.http.protocol.HttpContext;
import org.junit.Assert;
import org.junit.Before;
import org.junit.Test;
import org.mockito.Mockito;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.util.HashMap;
import java.util.Map;
import static org.junit.Assert.assertEquals;
import static org.mockito.Matchers.any;
import static org.mockito.Matchers.argThat;
import static org.mockito.Mockito.times;
public class GenericApiGatewayClientTest {
private GenericApiGatewayClient client;
private SdkHttpClient mockClient;
@Before
public void setUp() throws IOException {
AWSCredentialsProvider credentials = new AWSStaticCredentialsProvider(new BasicAWSCredentials("foo", "bar"));
mockClient = Mockito.mock(SdkHttpClient.class);
HttpResponse resp = new BasicHttpResponse(new BasicStatusLine(HttpVersion.HTTP_1_1, 200, "OK"));
BasicHttpEntity entity = new BasicHttpEntity();
entity.setContent(new ByteArrayInputStream("test payload".getBytes()));
resp.setEntity(entity);
Mockito.doReturn(resp).when(mockClient).execute(any(HttpUriRequest.class), any(HttpContext.class));
ClientConfiguration clientConfig = new ClientConfiguration();
client = new GenericApiGatewayClientBuilder()
.withClientConfiguration(clientConfig)
.withCredentials(credentials)
.withEndpoint("https://foobar.execute-api.us-east-1.amazonaws.com")
.withRegion(Region.getRegion(Regions.fromName("us-east-1")))
.withApiKey("12345")
.withHttpClient(new AmazonHttpClient(clientConfig, mockClient, null))
.build();
}
@Test
public void testExecute_happy() throws IOException {
Map<String, String> headers = new HashMap<>();
headers.put("Account-Id", "fubar");
headers.put("Content-Type", "application/json");
GenericApiGatewayResponse response = client.execute(
new GenericApiGatewayRequestBuilder()
.withBody(new ByteArrayInputStream("test request".getBytes()))
.withHttpMethod(HttpMethodName.POST)
.withHeaders(headers)
.withResourcePath("/test/orders").build());
assertEquals("Wrong response body", "test payload", response.getBody());
assertEquals("Wrong response status", 200, response.getHttpResponse().getStatusCode());
Mockito.verify(mockClient, times(1)).execute(argThat(new LambdaMatcher<>(
x -> (x.getMethod().equals("POST")
&& x.getFirstHeader("Account-Id").getValue().equals("fubar")
&& x.getFirstHeader("x-api-key").getValue().equals("12345")
&& x.getFirstHeader("Authorization").getValue().startsWith("AWS4")
&& x.getURI().toString().equals("https://foobar.execute-api.us-east-1.amazonaws.com/test/orders")))),
any(HttpContext.class));
}
@Test
public void testExecute_happy_parameters() throws IOException {
Map<String, String> headers = new HashMap<>();
headers.put("Account-Id", "fubar");
headers.put("Content-Type", "application/json");
Map<String,List<String>> parameters = new HashMap<>();
parameters.put("MyParam", Arrays.asList("MyParamValue"));
GenericApiGatewayResponse response = client.execute(
new GenericApiGatewayRequestBuilder()
.withBody(new ByteArrayInputStream("test request".getBytes()))
.withHttpMethod(HttpMethodName.POST)
.withHeaders(headers)
.withParameters(parameters)
.withResourcePath("/test/orders").build());
assertEquals("Wrong response body", "test payload", response.getBody());
assertEquals("Wrong response status", 200, response.getHttpResponse().getStatusCode());
Mockito.verify(mockClient, times(1)).execute(argThat(new LambdaMatcher<>(
x -> (x.getMethod().equals("POST")
&& x.getFirstHeader("Account-Id").getValue().equals("fubar")
&& x.getFirstHeader("x-api-key").getValue().equals("12345")
&& x.getFirstHeader("Authorization").getValue().startsWith("AWS4")
&& x.getURI().toString().equals("https://foobar.execute-api.us-east-1.amazonaws.com/test/orders?MyParam=MyParamValue")))),
any(HttpContext.class));
}
@Test
public void testExecute_noApiKey_noCreds() throws IOException {
client = new GenericApiGatewayClientBuilder()
.withEndpoint("https://foobar.execute-api.us-east-1.amazonaws.com")
.withRegion(Region.getRegion(Regions.fromName("us-east-1")))
.withClientConfiguration(new ClientConfiguration())
.withHttpClient(new AmazonHttpClient(new ClientConfiguration(), mockClient, null))
.build();
GenericApiGatewayResponse response = client.execute(
new GenericApiGatewayRequestBuilder()
.withBody(new ByteArrayInputStream("test request".getBytes()))
.withHttpMethod(HttpMethodName.POST)
.withResourcePath("/test/orders").build());
assertEquals("Wrong response body", "test payload", response.getBody());
assertEquals("Wrong response status", 200, response.getHttpResponse().getStatusCode());
Mockito.verify(mockClient, times(1)).execute(argThat(new LambdaMatcher<>(
x -> (x.getMethod().equals("POST")
&& x.getFirstHeader("x-api-key") == null
&& x.getFirstHeader("Authorization") == null
&& x.getURI().toString().equals("https://foobar.execute-api.us-east-1.amazonaws.com/test/orders")))),
any(HttpContext.class));
}
@Test
public void testExecute_non2xx_exception() throws IOException {
HttpResponse resp = new BasicHttpResponse(new BasicStatusLine(HttpVersion.HTTP_1_1, 404, "Not found"));
BasicHttpEntity entity = new BasicHttpEntity();
entity.setContent(new ByteArrayInputStream("{\"message\" : \"error payload\"}".getBytes()));
resp.setEntity(entity);
Mockito.doReturn(resp).when(mockClient).execute(any(HttpUriRequest.class), any(HttpContext.class));
Map<String, String> headers = new HashMap<>();
headers.put("Account-Id", "fubar");
headers.put("Content-Type", "application/json");
try {
client.execute(
new GenericApiGatewayRequestBuilder()
.withBody(new ByteArrayInputStream("test request".getBytes()))
.withHttpMethod(HttpMethodName.POST)
.withHeaders(headers)
.withResourcePath("/test/orders").build());
Assert.fail("Expected exception");
} catch (GenericApiGatewayException e) {
assertEquals("Wrong status code", 404, e.getStatusCode());
assertEquals("Wrong exception message", "{\"message\":\"error payload\"}", e.getErrorMessage());
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 7,150
|
Piano for everybody is a lesson plan for those beginners. Many music teachers concentrate on teaching learners to sight read from the start, going note by learning and note that the correspondence between musical notation and the computer keyboard.
It's acceptable for adults and teenagers not young children who desire to know piano and also have results in a quick moment.
Piano for It's sold as being a lesson plan comprising 10 eBooks, which include video and audio demonstrations, as well as training exercises for the student. The file is almost 500MB, though the web site does offer the option to down load the novels individually so students can begin their lessons while other books are downloading.
The Piano for Each program comes with a fully collection of interactive stuff to relish sitting at the piano and playing with. It is aimed at developing a solid ground to help create a business playing style in record time. That's why it was well organized and https://musichedge.com/pianoforall-review carefully planned. The guidelines can lead you to simply learn to play piano by ear, then in the first location, then improvise, make your own personal compositions and eventually read piano sheet music.
With due consideration, I think that Piano for All is a worthwhile option. Hall certainly includes a dedication to teaching at a useful, readily understood way. The class was made both accessible and affordable, with a multimedia piano on the web combination. Students who can not afford regular courses, or students who find themselves remote from face-to-face teachers but have broadband access, will get this resource extremely helpful. Furthermore, Hall delivers direct customer support via their own email address, also supplies a 60-day money back guarantee.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 6,620
|
{"url":"http:\/\/theory.cs.uchicago.edu\/abstract.php?id=kulkami&year=2008","text":"# Seminar: March 30, 2009\n\n## Any Monotone Property of Sparse Graphs is Evasive\n\nWe call an n-vertex graph \"sparse\" if its number of edges is O(n). A graph property is said to be ''evasive'' if, in order to decide its membership, one needs to query all {n \\choose 2} possible edges in wosrt case. Karp conjectures that any non-trivial monotone graph property must be evasive. It is a longstanding open question. We prove Karp's conjecture when restricted to 'sparse' graphs, i.e., we show that any non-trivial monotone decreasing property of n-vertex 'sparse' graphs is 'evasive' for all large enough n.\n\nWe use the topological approach proposed by Kahn, Saks and Sturtevant [1984] as a black box. The extra component of our method is a further connection to analytic number theory. In particular, we construct new group actions which rely crucially on some deep and interesting properties of the numbers. Under the Generalized Reimann Hypothesis, we can further stregthen our result to show that any monotone property of ''weakly sparse'' graphs is evasive, where 'weakly sparse' means that the number of edges are bounded by O(n^{5\/4 - \\epsilon}). We give an evidence that this can be further improved to O(n^3\/2) but these bounds are far from the desired {n \\choose 2} bound.\n\nThis is a joint work with Anandam Banerjee, Department of Mathematics, Northeastern University and Vipul Naik, Department of Mathematics, University of Chicago.","date":"2017-11-19 10:16:28","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8049484491348267, \"perplexity\": 858.7422594420119}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-47\/segments\/1510934805541.30\/warc\/CC-MAIN-20171119095916-20171119115916-00249.warc.gz\"}"}
| null | null |
Ле-Тей () — колишній муніципалітет у Франції, у регіоні Нормандія, департамент Орн. Населення — осіб (2011).
Муніципалітет був розташований на відстані близько 140 км на південний захід від Парижа, 130 км на південний схід від Кана, 50 км на південний схід від Алансона.
Історія
До 2015 року муніципалітет перебував у складі регіону Нижня Нормандія. Від 1 січня 2016 року належав до нового об'єднаного регіону Нормандія.
1 січня 2016 року Ле-Тей, Жемаж, Л'Ермітьєр, Маль, Ла-Руж i Сент-Аньян-сюр-Ерр було об'єднано в новий муніципалітет Валь-о-Перш.
Демографія
Розподіл населення за віком та статтю (2006):
Економіка
У 2010 році в муніципалітеті числилось 794 оподатковані домогосподарства, у яких проживали 1861,5 особи, медіана доходів виносила євро на одного особоспоживача
Посилання
Ле-Тей на сайті французького Національного інституту географії
[ Розташування муніципалітету Ле-Тей на мапі Франції та сусідні муніципалітети]
Див. також
Список муніципалітетів департаменту Орн
Примітки
Колишні муніципалітети департаменту Орн
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 3,032
|
<?php
namespace Crisu83\Conversion\Quantity\ApparentPower;
use Crisu83\Conversion\Quantity\Quantity;
/**
* Class ApparentPower
* @package Crisu83\Conversion\Quantity\ApparentPower
*/
class ApparentPower extends Quantity
{
/**
* @var string native unit name
*/
protected static $native = Unit::VOLT_AMPERE;
/**
* @var array conversion map (unit => native unit)
*/
protected static $conversionMap = array(
Unit::VOLT_AMPERE => 1,
Unit::KILOVOLT_AMPERE => 1000,
);
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 6,045
|
The Australian Historical Fencing League is a platform which unites the nation's major tournaments and events. For members of the Australian Historical Fencing community, the League provides access to a circuit of major national tournaments. In order to further populate the vastness of a national circuit, smaller state-wide tournaments have been incorporated into the League as 'Second-Tier Events'.
The League provides a ranking system which evaluates the performance of individual fencers and their HEMA/WMA Clubs. The League actively promotes the diversity in rule sets to which the Australian Historical Fencing community has always known. The League will protect the autonomy of events and clubs as they work to deliver unique and personalised events for the community's benefit.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 1,496
|
{"url":"https:\/\/mechcontent.com\/instantaneous-acceleration\/","text":"# Instantaneous acceleration: Definition, Formula, Examples\n\nOn the basis of the time interval considered for calculation, the acceleration is classified as average acceleration and instantaneous acceleration. In this article, we are discussing instantaneous acceleration in detail.\n\nContents\n\n## What is instantaneous acceleration?\n\nInstantaneous acceleration is the acceleration of the object at a specific instant during the motion. It indicates the change in velocity per unit time measured for a very small interval \u2018dt\u2019.\n\nThe object moving in a straight line may undergo an increase or decrease in acceleration or it may move with a uniform acceleration or zero acceleration. Thus in such cases, the average acceleration does not describe the motion of the object at every instant.\n\nThe average acceleration only provides the mean value of the acceleration instead of the actual acceleration of the object during the motion. While the instantaneous acceleration gives the exact acceleration at every instant during the motion.\n\nIn the above acceleration-time graph, the a_{\\text{average}} indicates the average acceleration of the object throughout the motion while the a_{1} and a_{2} indicates the instantaneous acceleration of the object at specific instant t_{1} and t_{2} respectively.\n\n## Equations:\n\nIn the form of limits, the instantaneous acceleration of the object is given by,\n\nIn the form of differentiation, the instantaneous acceleration of the object is given by,\n\n## How to find the instantaneous acceleration?\n\nIt can be found by use of the following two methods:-\n\n1] Analytical method:\n\nThis method is used to find the instantaneous acceleration when the equation of velocity in terms of time is given. It can be solved by using the method of limits or by using differentiation.\n\nBy using limits, the instantaneous acceleration is calculated as,\n\na_{\\text{instantaneous}} = \\lim_{\\Delta t \\to 0} \\frac{V_{(t + \\Delta t)}-V_{t}}{\\Delta t}\n\nBy using differentiation, the instantaneous velocity can be calculated as,\n\na_{\\text{instantaneous}} = \\frac{dV}{dt}\n\n2] Graphical method:-\n\nThis method is used for calculating instantaneous acceleration from the velocity-time graph.\n\n## How to find instantaneous acceleration from a velocity-time graph?\n\nThe instantaneous acceleration from the different profiles of a velocity-time graph is calculated as follows:-\n\nCase 1] When a velocity-time graph is linear:-\n\nIf the velocity-time plot has a linear nature, then it means that the object is moving with constant acceleration throughout its motion.\n\nThus in this case, the instantaneous acceleration is equal to the average acceleration of the object.\n\nV_{\\text{Instantaneous}} = V_{\\text{Average}}\n\nV_{\\text{Instantaneous}} = \\frac{\\Delta V}{\\Delta t}\n\nV_{\\text{Instantaneous}} = \\frac{V_{2}-V_{1}}{t_{2}-t_{1}}\n\nCase 2] When velocity-time profile is non-linear:-\n\nIf the velocity time profile is non-linear thus it means that the acceleration of the objeat is changing throughout the motion.\n\nThus in this case, the instantaneous acceleration of an object is different from the average acceleration. From such a graph, the instantaneous acceleration can be calculated by the use of the following steps:-\n\nStep 1] Locate a point of a curve at a required time:-\n\nStep 2] At this point draw a tangent to the curve:-\n\nStep 3] Find the slope of the tangent:- The instantaneous acceleration is the slope of the tangent drawn to the velocity-time curve at that instant.\n\n\u2234 The instantaneous acceleration is given by,\n\na_{\\text{Instantaneous}} = Slope(1-2) = \\frac{V_{2}-V_{1}}{t_{2}-t_{1}}\n\n## Solved examples:\n\nGiven:\nV = (5t^{2} +3t) m\/s\nt = 45 seconds\n\nSolution:-\n\nMethod 1:- Using limits\n\nThe instantaneous acceleration of the object is given by,\n\na_{t} = \\lim_{\\Delta t \\to 0} \\frac{V_{(t + \\Delta t)}-V_{t}}{\\Delta t}\n\na_{t} = \\lim_{\\Delta t \\to 0} \\frac{[5(t + \\Delta t)^{2} + 3(t + \\Delta t)] \u2013 [5t^{2} +3t]}{\\Delta t}\n\na_{t} = \\lim_{\\Delta t \\to 0} \\frac{5t^{2} + 10t\\Delta t + 5\\Delta t^{2}+3t+3\\Delta t-5t^{2}-3t}{\\Delta t}\n\na_{t} = \\lim_{\\Delta t \\to 0} \\frac{5\\Delta t^{2}+10t\\Delta t+3\\Delta t}{\\Delta t}\n\na_{t} = \\lim_{\\Delta t \\to 0} 5\\Delta t + 10t + 3\n\na_{t} = 10t + 3\n\nNow the acceleration of the object at t = 45 seconds is given by,\n\na_{(t=45)} = 10(45) + 3\n\nMethod 2:- Using differentiation\n\na_{t} = \\frac{dV}{dt}\n\na_{t} = \\frac{d}{dt}(5t^{2} + 3t)\n\na_{t} = 10t + 3\n\nThe acceleration at t = 45 seconds is given by,\n\na_{(t=45)} = 10(45) + 3\n\nGiven:\nt = 3.5 seconds\n\nSolution:-\n\nStep 1] Locate point on curve at time t = 3.5 seconds:\n\nStep 2] Draw a tangent to the curve at point x:\n\nStep 3] Find the slope of the tangent:\n\n\u2234 The instantaneous acceleration at t = 3.5 second is given by,\n\na_{(t=3.5)} = Slope(1-2) = \\frac{V_{2}-V_{1}}{t_{2}-t_{1}}\n\nFrom above figure,\n\nV_{2} = 0.5 m\/s, V_{1}= 3 m\/s,\nt_{2} = 6 seconds, t_{1} = 1 second.\n\na_{(t=3.5)} = \\frac{0.5-3}{6-1}\n\na_{(t=3.5)} = \u2013 0.5 m\/s\u00b2\n\nGiven:\nV = (6t^{2} + 2t) m\/s\na_{\\text{average}} = 6 m\/s\u00b2\n\nSolution:-\n\nThe instantaneous acceleration of the particle is given by,\n\na_{\\text{instantaneous}} = \\frac{dV}{dt}\n\na_{\\text{instantaneous}} = \\frac{d}{dt}(6t^{2} + 2t)\n\na_{\\text{instantaneous}} = 12t + 2\n\nThe time at which the V_{\\text{average}} is equals to the V_{\\text{instantaneous}} is given by,\n\na_{\\text{average}} = a_{\\text{instantaneous}}\n\n6 = 12t + 2\n\n## FAQs:\n\n1. Why instantaneous acceleration is important?\n\nIt gives the acceleration of the object at a specific instant during the motion.\n\n2. Is instantaneous acceleration always changing?\n\nFor the object moving with constant acceleration or constant retardation, the instantaneous acceleration never changes while for the object moving with continuously changing its acceleration, the instantaneous acceleration of the object always changes.\n\nRead also this article:","date":"2022-08-14 13:29:25","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8146302700042725, \"perplexity\": 1033.8299452236201}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-33\/segments\/1659882572033.91\/warc\/CC-MAIN-20220814113403-20220814143403-00104.warc.gz\"}"}
| null | null |
Marc Davis puede referirse a:
Marc Fraser Davis, animador en los Estudios Walt Disney.
Marc Davis (astrofísico), astrofísico y profesor en la Universidad de California en Berkeley.
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Purple Heart postage stamp honors veterans' sacrifices
WASHINGTON — The U.S. Postal Service continues to honor the sacrifices of the men and women who serve in the U.S. military with the issuance of the new Purple Heart Medal Forever stamp.
First issued as a 37-cent First-Class stamp in 2003, this new Forever Stamp differs from the 2011 Forever Stamp design displaying a slightly larger image of the Medal on a pure white background.
Available nationwide today in sheets of 20, the stamps can be purchased online at usps.com/shop or by calling 800-STAMP-24 (800-782-6724).
The date and location of the special dedication ceremony will be announced at a later time.
"The Postal Service salutes America's veterans for their selfless sacrifice in defending our great nation," said Stamp Service Manager Stephen Kearney. "We hope Americans will buy and use these Forever stamps when corresponding with loved ones and friends to honor these courageous men and women, who in many cases gave the ultimate sacrifice."
World's Oldest Military Decoration
The Purple Heart is awarded in the name of the President of the United States to members of the U.S. military who have been wounded or killed in action. According to the Military Order of the Purple Heart, an organization for combat-wounded veterans, the medal is "the oldest military decoration in the world in present use and the first award made available to a common soldier."
Established by General George Washington during the Revolutionary War, the badge of distinction for meritorious action — a heart made of purple cloth — was discontinued after the war. In 1932, on the 200th anniversary of Washington's birth, the decoration was reinstated and redesigned as a purple heart of metal bordered by gold, suspended from a purple and white ribbon. In the center of the medal is a profile bust of George Washington beneath his family coat of arms.
Customers may view the Purple Heart Medal Forever Stamp, as well as many of this year's other stamps, indicate which stamps they like and vote for their favorite stamp on Facebook at facebook.com/USPSStamps, through Twitter @USPSstamps or on the website Beyond the Perf at beyondtheperf.com/2012-preview. Beyond the Perf is the Postal Service's online site for background information on upcoming stamp subjects, first-day-of-issue events and other philatelic news.
How to Obtain the First-Day-of-Issue Postmark
Customers have 60 days to obtain the first-day-of-issue postmark by mail. They may purchase new stamps at a local Post Office, at The Postal Store website at usps.com/shop or by calling 800-STAMP-24. They should affix the stamps to envelopes of their choice, address the envelopes to themselves or others and place them in larger envelopes addressed to:
Purple Heart Medal Stamp
Special Cancellations
After applying the first-day-of-issue postmark, the Postal Service will return the envelopes through the mail. There is no charge for the postmark. All orders must be postmarked by Nov. 5, 2012.
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\section{Introduction}
\noindent In \cite{Casas} Casas-Alvero found a decomposition of higher order polars
of an irreducible singular plane curve. Generalizing the results of \cite{Merle}, he
proved that the irreducible components of the higher order polar curves
of a plane branch $f(x,y)=0$ are
branches that have \textit{characteristic contacts} with $f(x,y)=0$,
which means that their contacts with $f(x,y)=0$ are the characteristic exponents
$b_1/b_0,\ldots,b_h/b_0$ of $f(x,y)=0$. If the contact between a branch $h(x,y)=0$ and $f(x,y)=0$
is equal to the characteristic exponent $b_i/b_0$
then
$b_1/b_0,\ldots, b_{i-1}/b_0$ are the first characteristic exponents of $h(x,y)=0$.
\medskip
\noindent Casas-Alvero's decomposition of the $k$th higher order polar curve of $f(x,y)=0$ involves writing
$\frac{\partial ^k}{\partial y^k}f(x,y)$ as a finite product of power series, not necessarily irreducible,
called {\it bunches}, where each bunch is in turn the product of all irreducible factors
of $\frac{\partial ^k}{\partial y^k}f(x,y)$ having the same contact value with $f(x,y)=0$.
\noindent
Note that with only the information about the contact value we cannot determine
the equisingularity type (in the sense of Zariski) of the irreducible components
of $\frac{\partial ^k}{\partial y^k}f(x,y)=0$ from the equisingularity type of $f(x,y)=0$.
It is well-known that the equisingularity type of the polar curve can vary in a family of
equisingular branches. The family $\{f_a=y^3+x^{11}+ax^8y\}_{a\in \mathbf{C}}$ (see \cite[Exemple 3]{Pham}) is equisingular; the first polar curve of $f_a(x,y)=0$ has two different smooth branches for $a\neq 0$, but it has a double smooth branch for $a=0$.
\bigskip
\noindent In this paper we refine Casas-Alvero's decomposition. We show that every Casas-Alvero's bunch $\Gamma$ of $\frac{\partial ^k}{\partial y^k}f(x,y)$ is the product of two power series $\Gamma_1\cdot \Gamma_2$, where
all irreducible factors of $\Gamma_2$ called {\em threshold semi-roots},
have the same Puiseux characteristic depending only on the Puiseux characteristic of $f(x,y)=0$. The remaining irreducible factors of $\Gamma$ constitute $\Gamma_1$. The existence of threshold semi-roots is a new phenomenon observed for the higher order polars, because we note that the first order polar does not have such branches. We also prove that the number of Newton-Puiseux roots of $\Gamma_1=0$ and $\Gamma_2=0$ depends only on the Puiseux characteristic of $f(x,y)=0$.
\medskip
\noindent In \cite{LMW} the authors determine the possible components of the exceptional divisor $E$ of the minimal resolution of the branch $f(x,y)=0$ where the strict transform of $\frac{\partial}{\partial y}f(x,y)=0$ intersects $E$. For higher order polars the result of \cite{LMW} remains true and we make it precise for threshold semi-roots: the strict transforms of branches defined by threshold semi-roots are smooth and intersect transversely ({\it curvetta}) the rupture components of the exceptional divisor $E$ (components of $E$ intersecting at least three other components). We observe that threshold semi-roots are not {\it semi-roots} (in the sense of Abhyankar).
\medskip
\noindent The decomposition theorem of the first polar of a plane reduced curve $f(x,y)=0$ allowed to describe in \cite{GB-T} the phenomenon of {\em Lipschitz-Killing curvature concentration } on the Milnor fiber
$f(x,y) = \lambda \subseteq \mathbf{C}^2 $ for
$ \vert (x,y)\vert< \epsilon$ when $ \lambda,\epsilon \to 0,\, \vert \lambda \vert << \epsilon$. This is a multiscale phenomenon
(as the multiscale phenomenon shown in Example \ref{GL}) depending only on the equisingularity type of the curve. It would be expected that the decomposition of the higher order polars presented in this paper will help in the description of the metric and topological properties of the fibers of singular complex analytic morphisms.
\medskip
\noindent
In order to refine Casas-Alvero's factorization we deal with Newton-Puiseux roots
of~$\frac{\partial ^k}{\partial y^k}f(x,y)$.
For any characteristic exponent $q$ of $f$ we count the number of
roots that have a contact $q$ with $f$. Moreover our approach allows to find
the coefficients $c_q$ of the monomial $x^q$ in these roots.
The Newton-Puiseux roots with $c_q=0$ are the roots of $\Gamma_1=0$
and the others are the roots of $\Gamma_2=0$.
\medskip
\noindent All the results of this paper remain true if we replace $\mathbf{C}$ by any algebraically closed field $\mathbf{K}$ of characteristic zero.
\section{ Formal Puiseux power series}
Denote by $\mathbf{C}[[x]]^*$ the set of formal Puiseux power series. The {\em order} of any nonzero formal Puiseux power series is the minimal degree of its terms. By convention the order of the zero formal Puiseux power series is $+\infty$.
For every $\phi,\psi\in \mathbf{C}[[x]]^*$ we define $O(\phi,\psi)$ to be
the order of the difference $\phi-\psi$ and we call it
the {\em contact order} of $\phi$ and $\psi$.
It is well-known that for any $\phi_1,\phi_2,\phi_3\in \mathbf{C}[[x]]^*$ the {\em Strong Triangle Inequality (STI)}
$O(\phi_1,\phi_3)\geq \min \{O(\phi_1,\phi_2),O(\phi_2,\phi_3)\}$ holds.
\medskip
\noindent Let $\alpha \in\mathbf{C}[[x]]^{*}$ and $r$ be a positive rational number. The set $B=\{\,\psi \in\mathbf{C}[[x]]^{*}: O(\alpha,\psi) \geq r \,\}$ is called a \textit{pseudo-ball of height} $r$. Note that any two pseudo-balls of height $r$ are either disjoint or are equal. To prove it observe that by STI if $O(\alpha_1,\phi), O(\alpha_2,\phi), O(\alpha_1,\psi)\geq r$ then $O(\alpha_2,\psi) \geq r$. Hence if
the pseudo-balls $\{\psi \in\mathbf{C}[[x]]^{*}: O(\alpha_1,\psi) \geq r \,\}$ and $\{\psi \in\mathbf{C}[[x]]^{*}: O(\alpha_2,\psi) \geq r \,\}$ have a non empty intersection then they are equal.
\medskip
\noindent Take a pseudo-ball $B$ of height $r$. Every formal Puiseux power series $\gamma(x)\in B$ has the form
$\gamma(x)=\lambda_B(x)+c_{\gamma}x^r+ \hbox{\em higher order terms}$, where $\lambda_B(x)$ is obtained from an arbitrary $\alpha(x)\in B$ by omitting all its terms of order bigger than or equal to $r$. We call the number $c_{\gamma}$ the {\em leading coefficient of } $\gamma$ {\em with respect to} $B$ and denote it $\mathrm{lc}_B \gamma$. Remark that $c_{\gamma}$ can be zero.
\medskip
\noindent Hereinafter, for brevity, formal Puiseux power series will be called Puiseux series.
\section{Newton-Puiseux roots of higher order polars}
\noindent Let $f(x,y)\in \mathbf{C}[[x,y]]$ be such that $1<\mathrm{ord}\, f(0,y)=n<+\infty$. Fix a positive integer $k<n$. Then the order of $\frac{\partial ^k}{\partial y^k} f(0,y)$ equals $n-k$.
The Newton-Puiseux factorizations of $f(x,y)$ and $\frac{\partial ^k}{\partial y^k} f(x,y)$ have the form
\[
f(x,y)= u(x,y)\prod_{i=1}^n (y-\alpha_i(x)),
\]
\begin{equation}
\label{ppp2}
\frac{\partial^k}{\partial y^k}f(x,y)=\tilde u(x,y)\prod_{j=1}^{n-k} (y-\gamma_j(x)),
\end{equation}
where
$u(x,y)$, $\tilde u(x,y)$ are units in $\mathbf{C}[[x,y]]$ and $\alpha_i(x)$, $\gamma_j(x)$
are Puiseux series of positive order called {\em Newton-Puiseux roots} of $f(x,y)=0$ and $\frac{\partial^k}{\partial y^k}f(x,y)=0$, respectively. We denote by $\mathrm{Zer} g$ the set of Newton-Puiseux roots of $g(x,y)=0$ for any $g(x,y)\in
\mathbf{C}[[x,y]]$.
\medskip
\noindent Let $B$ be a pseudo-ball. We put
\[
F_B(z):=\prod_{j\;:\;\alpha_j\in B}(z-\mathrm{lc}_B \alpha_j).
\]
\noindent Remark that the above polynomial is equal up to multiplication by a constant,
to the polynomial introduced in \cite[Lemma 3.3]{Gwo} (see also \cite[ Formula~(2.2)]{K-P}).
\medskip
\begin{Lemma}
\label{GL}
Let $B$ be a pseudo-ball. Assume that $k< \deg F_B(z)$. Then
\[
\frac{d^k}{d z^k}F_B(z)= \hbox{\rm constant} \cdot \prod_{j\;:\;\gamma_j\in B}(z-\mathrm{lc}_B \gamma_j).
\]
\end{Lemma}
\noindent \begin{proof}
Let $r$ be the height of $B$. Fix the weight $\omega$ such that $\omega(x)=1$, $\omega(y)=r$
and denote by $\mathrm{in}\,_{\omega}(h)$ the weighted initial part of $h\in \mathbf{C}[[x^{1/N},y]]$, where $N\in \mathbf{N}$.
First assume that $\lambda_B(x)=0$. Then
\[
\mathrm{in}\,_{\omega}f(x,y)=\hbox{constant } x^A\prod_{i\;:\alpha_i\in B}(y-\mathrm{lc}_B \alpha_i \cdot x^{r}),
\]
and
\[
\mathrm{in}\,_{\omega}\frac{\partial^k}{\partial y^k}f(x,y)=\hbox{constant } x^{A'}\prod_{j\;:\gamma_j\in B}(y-\mathrm{lc}_B \gamma_j \cdot x^{r}),
\]
where $A,A'$ are rational numbers.
If $k\leq \deg F_B(z)$ then $\frac{\partial^k}{\partial y^k} \mathrm{in}\,_{\omega} f(x,y)$ is nonzero and consequently $\frac{\partial^k}{\partial y^k} \mathrm{in}\,_{\omega} f(x,y)=\mathrm{in}\,_{\omega}\frac{\partial^k}{\partial y^k} f(x,y)$.
For $x=1$ we get
\[
\frac{d^k}{dy^k}\prod_{i\;:\alpha_i\in B}(y-\mathrm{lc}_B \alpha_i)=\hbox{constant } \cdot \prod_{j\;:\gamma_j\in B}(y-\mathrm{lc}_B \gamma_j ).
\]
\noindent If $\lambda_B(x)\neq 0$ then taking $g(x,y):=f(x,y+\lambda_B(x))$
we reduce the proof to the first case.
\end{proof}
\section{Properties of branches}
\noindent Denote by $\mathbf{U}_m$ the multiplicative group of the $m$th complex roots of unity. This group acts on $\mathbf{C}[[x^{1/m}]]$ in the following way: for $\epsilon \in \mathbf{U}_m$ and $\alpha=\sum_ia_i x^{i/m}$
\begin{equation}
\label{star}
\epsilon *_m\alpha=\sum_ia_i\epsilon^ix^{i/m}.
\end{equation}
\noindent The {\em star operation} defined in (\ref{star}) preserves the contact, that is
$O(\alpha_1,\alpha_2)=O(\epsilon*_m\alpha_1,\epsilon*_m\alpha_2)$.
\medskip
\noindent Let $\alpha$ be a Puiseux series. The smallest natural number $n$ such that $\alpha\in \mathbf{C}[[x^{1/n}]]$ is called the {\em index} of $\alpha$. Denote by $*$ the star operation of $\mathbf{U}_n$ on $\mathbf{C}[[x^{1/n}]]$ introduced in (\ref{star}).
\noindent
Observe that if the Puiseux series $\alpha$ has index $n$ then $\epsilon_1 *\alpha\neq \epsilon_2 *\alpha$, for any two different $n$-th roots of the unity $\epsilon_1,\epsilon_2$ (see \cite[Lemma 3.9]{Hefez}).
\medskip
\noindent For a Puiseux series $\alpha=\sum_ia_i x^{i/n}$ of positive order and index $n$ we introduce two sequences $(e_i)$ and $(b_i)$ of natural numbers as follows:
\begin{itemize}
\item $e_0=b_0=n$,
\item if $e_k\neq 1$ then
$b_{k+1}:=\min \{i\;:\; i\not\equiv 0\; \hbox{\rm mod } e_{k}\; \mbox{and } a_i\neq 0\}$,
\item $e_k=\gcd(e_{k-1},b_k)$.
\end{itemize}
\noindent The sequence $e_i$ is strictly decreasing and for some $h\in \mathbf{N}$ we have $e_h=1$. We get
$\mathbf{U}_n=\mathbf{U}_{e_0} \supset \mathbf{U}_{e_1} \supset \cdots \supset \mathbf{U}_{e_h}=\{1\}$. After \cite[Lemma 6.8]{Hefez} if $\epsilon \in \mathbf{U}_{e_{k-1}}\backslash \mathbf{U}_{e_{k}}$ then $\epsilon^{b_k}\neq 1$. Consequently
\begin{equation}
\label{contact}
O(\alpha,\epsilon*\alpha)=\frac{b_k}{n} \;\;\hbox{\rm for } \epsilon \in \mathbf{U}_{e_{k-1}}\backslash \mathbf{U}_{e_k}.
\end{equation}
\medskip
\noindent Let $\alpha$ be a Puiseux series of index $n$ which is a Newton-Puiseux root of an irreducible power series $f(x,y)\in \mathbf{C}[[x,y]]$. Then $\mathrm{Zer} f=\{\epsilon * \alpha \;:\; \epsilon \in \mathbf{U}_n\}$ and consequently $\mathrm{ord}\, f(0,y)=n$ (see \cite[Theorem 3.10]{Hefez}). The {\em characteristic} of an irreducible power series $f(x,y)\in \mathbf{C}[[x,y]]$ is the sequence $(b_0,b_1,\ldots,b_h)$, associated to any Newton-Puiseux root of $f$. By (\ref{contact}) the set $\mathrm{Char} f:=\left \{\frac{b_1}{b_0},\cdots, \frac{b_h}{b_0}\right\}$ is the set of contacts between the Newton-Puiseux roots of $f$. We call $\mathrm{Char} f$ the set of {\em characteristic exponents} of $f$.
\medskip
\noindent Let $T_i(f)$ be the set of pseudo-balls of height $\frac{b_i}{b_0}$ having non-empty intersection with $\mathrm{Zer} f$.
\begin{Property}\label{PR2}
For every characteristic exponent $b_i/b_0$ the set $T_i(f)$ consists of $e_0/e_{i-1}$
pairwise disjoint pseudo-balls.
Every $B\in T_i(f)$ contains $e_{i-1}$ elements of $\mathrm{Zer} f$ and
$F_B(z)=(z^{e_{i-1}/e_i}-c_B)^{e_i}$ for some $c_B\neq 0$.
\end{Property}
\noindent \begin{proof} Let $B\in T_i(f)$ and
$\alpha \in B\cap \mathrm{Zer} f$. By (\ref{contact}) $B\cap \mathrm{Zer} f=\{\epsilon * \alpha \;:\; \epsilon \in \mathbf{U}_{e_{i-1}}\}$, which shows that $B$ contains $e_{i-1}$ elements of $\mathrm{Zer} f$. Consequently $T_i(f)$ consists of $e_0/e_{i-1}$
pairwise disjoint pseudo-balls.
\noindent We get
\[
F_B(z)=
\prod_{\epsilon^{e_{i-1}}=1}(z-\mathrm{lc}_B(\epsilon * \alpha))=
\prod_{\epsilon^{e_{i-1}}=1}(z-\epsilon^{b_i}a_{b_i})=
(z^{e_{i-1}/e_i}-a_{b_i}^{e_{i-1}/e_i})^{e_i},
\]
where $a_{b_i}$ is the coefficient of the monomial $x^{b_i/b_0}$
of $\alpha$. The last equality follows from \cite[Lemma 3.4]{Acta}.
\end{proof}
\medskip
\newpage
\begin{Example}
\label{GL}
Consider the irreducible complex convergent power series
$f(x,y)=((y^3-x^4)^4+x^{17}y^3)^2+x^{22}(y^3-x^4)^5$
of characteristic $(24,32,62,137)$.
Let $\alpha_i(x)$, $i=1,\dots, 24$ be the Newton-Puiseux roots of $f(x,y)=0$.
\noindent Take $\epsilon>0$ small enough.
A higher contact order between $\alpha_i(x)$, $\alpha_j(x)$ means a smaller Euclidean distance
between $\alpha_i(\epsilon)$, $\alpha_j(\epsilon)$. Thus the pseudo-balls of~$T_i(f)$, $i=1,2,3$ correspond to groups of roots of $f(\epsilon,y)=0$.
These roots, for $\epsilon=0.75$, are drawn on the left side of Figure 1.
\noindent Fix $B\in T_2(f)$ and $E\in T_3(f)$.
Using \cite[Lemma 3.3]{Gwo} one can show that there are constants
$C_{\epsilon},D_{\epsilon}\in \mathbf{C} $ such that,
\begin{equation}
\label{convergence}
\begin{array}{ll}
C_{\epsilon}\cdot f(\epsilon, \lambda_B(\epsilon)+z\cdot \epsilon^{62/24}) \rightarrow F_B(z), \;&
\\
D_{\epsilon}\cdot f(\epsilon, \lambda_E(\epsilon)+z\cdot \epsilon^{137/24}) \rightarrow F_E(z), \;&\end{array}
\end{equation}
when $\epsilon \rightarrow 0$.
This asymptotic property is illustrated on the right side of Figure 1.
Notice that by Property~\ref{PR2} we have
$F_B(z)=(z^4-c_1)^2$ and $F_E(z)=z^2-c_2$ for some nonzero constants $c_1$, $c_2$.
\begin{center}
\begin{tikzpicture}[scale=0.35]
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\draw[->,thin] (0,-11)--(0,11) ;
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\draw [blue](6.75,0) circle (2.5cm);
\draw [blue](-3.35,5.82) circle (2.5cm);
\draw [blue](-3.35,-5.82) circle (2.5cm);
\draw [red](5.64,1.18) circle (0.5cm);
\draw [red](5.64,-1.18) circle (0.5cm);
\draw [red](7.95,1.05) circle (0.5cm);
\draw [red](7.95,-1.05) circle (0.5cm);
\draw [red](-4.85,6.35) circle (0.5cm);
\draw [red](-3.84,4.30) circle (0.5cm);
\draw [red](-3.08,7.39) circle (0.5cm);
\draw [red](-1.8,5.48) circle (0.5cm);
\draw [red](-4.85,-6.35) circle (0.5cm);
\draw [red](-3.84,-4.30) circle (0.5cm);
\draw [red](-3.08,-7.39) circle (0.5cm);
\draw [red](-1.8,-5.48) circle (0.5cm);
\draw [olive](5.1,9.4) node[above]{$T_1(f)=\hbox{\rm the olive ball}$} ;
\draw [blue](5,4.8) node[above]{$T_2(f)=\hbox{\rm 3 blue balls}$};
\draw [red](5,2.8) node[above]{$T_3(f)=\hbox{\rm 12 red balls}$} ;
\draw [blue](5.6,-3.5) node[above]{$B$} ;
\draw [red](7.3,1.1) node[above]{$E$} ;
\draw (15,-3.5) node[above]{$\hbox{\rm roots of }F_B$} ;
\draw (20.5,-3.5) node[above]{$\hbox{\rm roots of }F_E$} ;
\draw (6.5,-13.5) node[above]{\hbox{\rm Figure 1}} ;
\draw[->,thin] (13,0)--(17,0) ;
\draw[->,thin] (15,-2)--(15,2) ;
\node[draw,red, circle,inner sep=1pt,fill=red] at (15.7,0.7){};
\node[draw,red, circle,inner sep=1pt,fill=red] at (15.7,-0.7){};
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\node[draw,red, circle,inner sep=1pt,fill=red] at (14.3,-0.7){};
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\draw[->,thin] (18,0)--(22,0) ;
\draw[->,thin] (20,-2)--(20,2) ;
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\node[draw,circle,inner sep=1pt,fill] at (20.25,0.35){};
\draw [red](20,0) circle (1cm);
\end{tikzpicture}
\end{center}
\noindent The convergence in (\ref{convergence}) is almost uniform. Hence there are similar limits for higher derivatives. This explains why we could detect the position of the roots of the $k$th derivative of $f$ by the position of the roots of the polynomials $F^{(k)}_B(z)$.
\end{Example}
\subsection{Contact of branches}
\noindent Let $f, g\in\mathbf{C}[[x,y]]$ be irreducible power series
coprime with $x$.
For every Puiseux series $\gamma$ we define
$\mathrm{cont}(f,\gamma)=\max\{ O(\alpha,\gamma):\alpha\in\mathrm{Zer} f\}$
and call this number the {\em contact} between $f$ and $\gamma$. By abuse of notation we put
\[ \mathrm{cont}(f,g)=\max\{ O(\alpha,\gamma):\alpha\in\mathrm{Zer} f,\gamma\in\mathrm{Zer} g\}. \]
\noindent In this section we take $m\in \mathbf{N}$ such that $\mathrm{Zer} f,\mathrm{Zer} g\subset \mathbf{C}[[x^{1/m}]]$ and we consider the star operation $*_m$ of $\mathbf{U}_m$ in $\mathbf{C}[[x^{1/m}]]$ introduced in (\ref{star}). If $\alpha=\sum_ia_i x^{i/n}$ is a Newton-Puiseux root of $f(x,y)=0$ of index $n$ then $m=q n$ for some $q \in \mathbf{N}$. Then $\alpha=\sum_ia_i x^{i q/m}$ and $\theta *_m\alpha=\theta^q *_n \alpha$, where $*_n$ is the star operation of $\mathbf{U}_n$ on $\mathbf{C}[[x^{1/n}]]$. Since $\mathbf{U}_n=\{\theta^q\;:\;\theta\in \mathbf{U}_m\}$, the action of $\mathbf{U}_m$ permutes $\mathrm{Zer} f$ and for every $\alpha, \alpha'\in \mathrm{Zer} f$ there exists $\epsilon \in \mathbf{U}_m$ such that $\alpha'=\epsilon *_m \alpha$. Up to the end of this section we denote $*_m$ by $*$.
\begin{Property}
\label{contact-roots}
For every $\gamma\in\mathrm{Zer} g$\quad $\mathrm{cont}(f,\gamma)=\mathrm{cont}(f,g)$.
\end{Property}
\noindent \begin{proof}
It is enough to show that for all $\gamma,\gamma'\in\mathrm{Zer} g$ the sets
of contact orders
$\{O(\alpha,\gamma):\alpha\in\mathrm{Zer} f\}$ and
$\{O(\alpha,\gamma'):\alpha\in\mathrm{Zer} f\}$ are equal.
\noindent Take $\epsilon\in \mathbf{U}_m$ such that $\gamma'=\epsilon* \gamma$.
Then $O(\alpha,\gamma)=O(\epsilon*\alpha,\gamma')$ for all $\alpha\in\mathrm{Zer} f$.
Since the action of $\mathbf{U}_m$ permutes $\mathrm{Zer} f$ the sets under consideration are equal.
\end{proof}
\begin{Property}
\label{contact-exponents}
For every $q<\mathrm{cont}(f,g)$\quad $ q\in\mathrm{Char} f$ if and only if $q\in\mathrm{Char} g$.
\end{Property}
\noindent \begin{proof}
Let $q<\mathrm{cont}(f,g)$ be a characteristic exponent of $f$. By definition of
the characteristic exponent $O(\alpha,\alpha')=q$ for some $\alpha, \alpha'\in\mathrm{Zer} f$.
Following Property~\ref{contact-roots}
$\mathrm{cont}(g,\alpha)=\mathrm{cont}(g,\alpha')=\mathrm{cont}(g,f)$.
Hence there exist $\gamma,\gamma'\in\mathrm{Zer} g$ such that
$O(\gamma,\alpha)=O(\gamma',\alpha')=\mathrm{cont}(g,f)=\mathrm{cont}(f,g)$.
By STI we get
$O(\gamma,\gamma')\geq\min\{O(\gamma,\alpha),O(\alpha,\alpha'),O(\alpha',\gamma')\}=q$.
Suppose that $O(\gamma,\gamma')>q$. Then we would have
$O(\alpha,\alpha')\geq\min\{O(\alpha,\gamma),O(\gamma,\gamma'), O(\gamma',\alpha')\}>q$
which is absurd. Hence $q=O(\gamma,\gamma')$ is a characteristic exponent of $g$.
\end{proof}
\medskip
\noindent Let $\alpha=\sum_ia_ix^{i/n} \in \mathbf{C}[[x]]^*$ be a Puiseux series. The {\em support of} $\alpha$ is the set $\{i/n\;:\;a_i\neq 0\}$.
\begin{Property}
\label{contact-nonzero}
If $q=\mathrm{cont}(f,g)$ is a characteristic exponent of $f$ and there exists
a Puiseux series $\gamma\in\mathrm{Zer} g$ such that $q$ is in the support of $\gamma$ then $q$ is a characteristic exponent of $g$.
\end{Property}
\noindent \begin{proof}
Take $\alpha,\alpha'\in\mathrm{Zer} f$ such that $O(\alpha,\gamma)=O(\alpha,\alpha')=q$ and let
$\epsilon\in \mathbf{U}_m$ be such that $\alpha'=\epsilon * \alpha$.
Put $\gamma'=\epsilon *\gamma$.
\noindent By STI we get
$O(\gamma,\gamma')\geq\min\{O(\gamma,\alpha),O(\alpha,\alpha'),O(\alpha',\gamma')\}=q$.
The equality $O(\alpha,\alpha')=q$ implies that $\epsilon *x^q\neq x^q$.
Thus the monomial $x^q$ appears in the difference $\gamma-\epsilon * \gamma$ with a nonzero
coefficient which proves that $O(\gamma,\gamma')=q$. Therefore $q\in\mathrm{Char} g$.
\end{proof}
\section{Roots of derivatives of special polynomials}
In this section we study the roots of the complex polynomial
$\frac{d^k}{dz^k}(z^n-c)^e$.
\begin{Property}\label{P1}
Let $F(t)=H(t^n)$ be a complex polynomial.
If $t_0$ is a nonzero root of~$F(t)$ of multiplicity $m$ then $(t^n-t_0^n)^m$ divides $F(t)$.
\end{Property}
\begin{proof}
It is enough to factorize $F(t)$ in the ring $\mathbf{C}[t^n]$ and notice that $t_0$ is a
root of a factor $t^n-a$ if and only if $a=t_0^n$.
\end{proof}
\begin{Lemma}\label{L1}
Let $F(t)$ be a real polynomial of positive degree of the form
\[F(t)=C \cdot t^{a}(t^n-1)^{b}\prod_{i=1}^{d}(t^n-c_i), \]
\noindent where $a$, $b$, $d$ are nonnegative integers
and $c_i$ are pairwise distinct real numbers from the interval $(0,1)$.
Then the derivative of $F(t)$ has the form
\[F'(t)=C' \cdot t^{a'}(t^n-1)^{b'}\prod_{i=1}^{d'}(t^n-c_i'),\]
\noindent where $c_i'$ are pairwise distinct real numbers from the interval $(0,1)$.
Moreover:
if $a>0$ then $a'=a-1$,
if $a=0$ then $a'=n-1$,
if $b>0$ then $b'=b-1$,
if $b=0$ then $b'=0$.
\end{Lemma}
\begin{proof}
Let $a'$ be the multiplicity of $0$ as a root of $F'(t)$,
let $b'$ be the multiplicity of $1$ as a root of $F'(t)$
and let $d'$ be the number of distinct real roots of $F'(t)$ in the interval~$(0,1)$.
We will check that
\begin{equation}\label{E2}
(a'-a)+[(b'-b)+(d'-d)]n \geq -1
\end{equation}
\noindent which is equivalent with
\begin{equation}\label{E1}
a'+(b'+d')n \geq \deg F'(t) .
\end{equation}
\medskip
\noindent Consider several cases
depending on the values of $a$ and $b$.\\
\noindent (I) $a,b>0$.
The polynomial $F(t)$ has $d+2$ distinct real roots in the closed interval $[0,1]$.
These roots divide $[0,1]$ to $d+1$ sub-intervals.
By Rolle's Theorem inside each sub-interval there is at least one root of $F'(t)$.
Hence $d'\geq d+1$.
The differentiation decreases the multiplicity of a root of a polynomial by $1$.
Thus $a'=a-1$ and $b'=b-1$. \\
(II) $a>0$ and $b=0$.
By similar arguments as before we get $a'=a-1$, $b'\geq 0$, and $d'\geq d$.\\
(III) $a=0$ and $b>0$.
In this case $F(t)$ is a polynomial of $t^n$. Taking the derivative we get $a'\geq n-1$.
Moreover $b'=b-1$ and $d'\geq d$.\\
(IV) $a=b=0$.
We get $a'\geq n-1$, $b'\geq 0$ and $d'\geq d-1$.\\
\noindent One easily verifies that inequality~(\ref{E2}) holds in each case.
\medskip
\noindent Let $t_1$, \dots, $t_{d'}$ be the pairwise distinct real roots of $F'(t)$ from the interval $(0,1)$.
Consider the polynomial
$P(t)=t^{a'}(t^n-1)^{b'}\prod_{i=1}^{d'}(t^n-t_i^n)$.
Inequality~(\ref{E1}) reads $\deg P(t)\geq \deg F'(t)$.
By Property~\ref{P1} $P(t)$ divides $F'(t)$.
Hence $P(t)$ and $F'(t)$ are equal up to a multiplication by a constant.
This proves the first statement of the lemma.
\medskip
\noindent By the form of $F'(t)$ we get $\deg F'(t)=a'+(b'+d')n$.
Consequently the inequality ``$\geq$'' in ~(\ref{E2}) can be replaced by ``$=$''.
This implies that all weak inequalities obtained in the above case-by-case analysis must be equalities and proves the second statement of the lemma.
\end{proof}
\begin{Lemma}
\label{AL}
Let $F(z)=(z^n-c)^{e}$ be a complex polynomial.
Then for $1\leq k<\deg F(z)$ one has
$\frac{d^k}{dz^k}F(z)=C z^{a}(z^n-c)^{b}\prod_{i=1}^{d}(z^n-c_i)$, where $C\in \mathbf{C}$ and
\begin{enumerate}
\item[(1)] $0\leq a <n$ and $a+k\equiv 0 \pmod n$,
\item[(2)] $b=\max\{e-k,0\}$,
\item[(3)] $d=\min\{e,k\}-\lceil \frac{k}{n} \rceil$, where $\lceil x \rceil$ denotes the smallest integer number larger than or equal to $x$,
\item[(4)] $a +(b+d)n=ne-k$,
\item [(5)] $c_i\neq c_j$ for $1\leq i<j\leq d$ and $0\neq c_i\neq c$ for $1\leq i\leq d$.
\end{enumerate}
\end{Lemma}
\begin{proof}
Without loss of generality we may assume that $c=1$. The general case
reduces to this case by replacing $F(z)$ by the polynomial
$c^{-e}F(\sqrt[n]{c}z)$.
\medskip
\noindent The polynomial $F(z)=(z^n-1)^e$ satisfies the assumptions of Lemma \ref{L1}.
Applying this lemma to subsequent derivatives of $F(z)$ we see
that the $k$th derivative of $F(z)$ has the form
$\frac{d^k}{dz^k}F(z)=C_k z^{a_k}(z^n-1)^{b_k}\prod_{i=1}^{d_k}(z^n-c_{i,k})$
and verifies the assumptions of Lemma~\ref{L1}, for $0\leq k<\deg F(z)$.
This implies (4) and~(5). By Lemma~\ref{L1} we get $0\leq a_k \leq n-1$.
The congruence $a_k+k\equiv 0 \pmod n$ is a consequence of (4), and we conclude (1).
Remark that $b_0=e$ and by Lemma~\ref{L1} we have $b_{i+1}=b_i-1$ if $b_i>0$
and $b_{i+1}=0$ if $b_i=0$. This gives~(2). Now we will prove (3). By (2) we get $e-b_k=\min \{e,k\}$ and by (1) the quotient $\frac{a_k+k}{n}$ is the smallest integer number larger than or equal to $\frac{k}{n}$. Computing $d_k$ from (4) we get $d_k=e-b_k-\frac{a_k+k}{n}=\min\{e,k\}-\lceil \frac{k}{n} \rceil$.
\end{proof}
\begin{Corollary}
\label{CC}
Let $F(z)=(z^n-c)^{e}$ be a complex polynomial.
Then every nonzero derivative $\frac{d^k}{dz^k}F(z)$ has no multiple complex roots
except $0$ and the roots of $z^n=c$.
\end{Corollary}
\section{Higher order polars of a branch}
\noindent Let $i_k$ be the nonnegative number such that $e_{i_k}\leq k < e_{i_k-1}$. Remember that the $k$th
partial derivative of $f(x,y)$ admits a decomposition $\frac{\partial^k} {\partial y^k}f(x,y)=\hbox{\rm unit }\prod_{j=1}^{n-k}(y-\gamma_j)$, where $\gamma_j$ are Puiseux series of positive order.
\medskip
\noindent Hereafter the notation $\left[a \;\;\hbox{\rm mod } n\right]$ for an integer $a$ and a natural number $n$ means the remainder of the division of $a$ by $n$.
\begin{Lemma}
\label{TL}
Let $f(x,y)\in \mathbf{C}[[x,y]]$ be an irreducible power series of characteristic $(b_0,b_1,\ldots,b_h)$.
\begin{enumerate}
\item For every $\gamma_j\in \mathrm{Zer} \frac{\partial^k} {\partial y^k}f$ we have $\mathrm{cont}(f,\gamma_j)\in \left \{\frac{b_1}{b_0},\ldots, \frac{b_{i_k}}{b_0}\right\}$.
\item If $i< i_k$ then the number of $\gamma_j$'s with $\mathrm{cont}(f,\gamma_j)=\frac{b_i}{b_0}$ equals $\left(\frac{b_0}{e_i}-\frac{b_0}{e_{i-1}}\right)k$.
\item If $i= i_k$ then the number of $\gamma_j$'s with $\mathrm{cont}(f,\gamma_j)=\frac{b_i}{b_0}$ equals ${b_0}-\frac{b_0}{e_{i-1}}k$.
\item If $i\leq i_k$ then the number of $\gamma_j$'s with $\mathrm{cont}(f,\gamma_j)=\frac{b_i}{b_0}$ and such that ${b_i/b_0}$ is not in the support of $\gamma_j$ equals $\frac{b_0}{e_{i-1}}\left[-k \;\;\hbox{\rm mod } n_i\right]$, where $n_i=\frac{e_{i-1}}{e_i}$.
\item If $i\leq i_k$ then the number of $\gamma_j$'s with $\mathrm{cont}(f,\gamma_j)=\frac{b_i}{b_0}$ and such that ${b_i/b_0}$ is in the support of $\gamma_j$ equals $\frac{b_0}{e_{i}}\left(\min\{e_i,k\}-\lceil \frac{k}{n_i}\rceil\right)$.
\end{enumerate}
\end{Lemma}
\begin{proof} Let $i\leq i_k$. Take a pseudo-ball $B\in T_i(f) $. After Property \ref{PR2} the polynomial $F_B(z)$ has the form $(z^{n_i}-c)^{e_i}$ for some $c\neq 0$, so its degree is
$e_{i-1}$ and after the choice of $i$ we get $k< e_{i_k-1}\leq e_{i-1}=\deg F_B(z)$. By Lemma \ref{AL} we get
\begin{equation}
\label{ad}
\frac{d^k}{dz^k}F_B(z)=C z^{a}(z^{n_i}-c)^{b}\prod_{j=1}^{d}(z^{n_i}-c_j).
\end{equation}
\noindent By Lemma \ref{GL} the number of $\gamma_j$'s in $B$ such that $\mathrm{cont}(f,\gamma_j)=\frac{b_i}{b_0}$ equals
$i_B:=a+dn_i$. After Lemma \ref{AL} we have
\[
i_B=\left\{
\begin{array}{rl}
(n_i-1)k & \hbox{\rm if } i< i_k\\
e_{i_k-1}-k & \hbox{\rm if } i=i_k.\\
\end{array}
\right.
\]
\noindent For every $\gamma_j$ satisfying $\mathrm{cont}(f,\gamma_j)=\frac{b_i}{b_0}$ there is a unique pseudo-ball $B\in T_i(f)$ containing $\gamma_j$. By Property \ref{PR2} the total number of $\gamma_j$'s with $\mathrm{cont}(f,\gamma_j)=\frac{b_i}{b_0}$ equals $i_B\frac{b_0}{e_{i-1}}$. This gives the second and third statements. As a consequence the number of $\gamma_j$'s with $\mathrm{cont}(f,\gamma_j)\in \left \{\frac{b_1}{b_0},\ldots, \frac{b_{i_k}}{b_0}\right\}$
equals
\[
\sum_{i=1}^{i_k-1} \left(\frac{b_0}{e_i}-\frac{b_0}{e_{i-1}}\right)k+{b_0}-\frac{b_0}{e_{i_k-1}}k=b_0-k,
\]
\noindent which is the total number of Newton-Puiseux roots of $\frac{\partial^k} {\partial y^k}f(x,y)=0$. This proves the first statement.
\medskip
\noindent Given $B\in T_i(f)$, consider all $\gamma_j\in B$ such that $\mathrm{cont}(f,\gamma_j)=b_i/b_0$. By Lemma$\,$\ref{GL} the number of such $\gamma_j$'s with $\mathrm{lc}_B\gamma_j=0$ equals $a$ while the number of such $\gamma_j$'s with $\mathrm{lc}_B\gamma_j\neq 0$ equals $n_id$, where $a$ and $d$ are from (\ref{ad}).
\medskip
\noindent Recall that there are $\frac{b_0}{e_{i-1}}$ pseudo-balls in $T_i(f)$. We finish the proof of the last two statements computing the values $\frac{b_0}{e_{i-1}}a$ and $\frac{b_0}{e_{i-1}}n_id=\frac{b_0}{e_{i}}d$ using the first and the third items of Lemma \ref{AL}.
\end{proof}
\medskip
\noindent The next theorem is an improvement of \cite[Theorem 3.1]{Casas}.
\begin{Theorem}
\label{main}
Let $f(x,y)\in \mathbf{C}[[x,y]]$ be an irreducible power series of cha\-rac\-teristic $(b_0,b_1,\ldots,b_h)$. Put $e_s=\gcd(b_0,\ldots,b_s)$.
Fix $1\leq k<\mathrm{ord}\, f(0,y)$, and let $i_k$ be the nonnegative integer number such that $e_{i_k}\leq k < e_{i_{k-1}}$. Then $\frac{\partial^k} {\partial y^k}f(x,y)$ admits a factorization as following:
\[\frac{\partial^k} {\partial y^k}f(x,y)=\Gamma^{(1)}\cdots \Gamma^{(i_k)},\]
\noindent where $\Gamma^{(i)}$ are power series, not necessarily irreducible, verifying:
\begin{enumerate}
\item For each $1\leq i\leq i_k$, all branches of $\Gamma^{(i)}$ have contact $b_i/b_0$ with $f(x,y)=0$. The order of $\Gamma^{(i)}(0,y)$ equals $\left(\frac{b_0}{e_i}-\frac{b_0}{e_{i-1}}\right)k$, for $i< i_k$ and ${b_0}-\frac{b_0}{e_{i-1}}k$ for $i=i_k$.
\item $\Gamma^{(i)}$ can be written as a product $\Gamma^{(i)}_1\Gamma^{(i)}_2$, where for any irreducible factor $g$ of $\Gamma^{(i)}_1$ the first $i-1$ characteristic exponents of $f$ and $g$ are the same
and
$\frac{b_i}{b_0}\not\in \mathrm{Char} \, g$; and $\left \{\frac{b_1}{b_0},\ldots,\frac{b_{i}}{b_0}\right\}$ is the set of characteristic exponents of any irreducible factor of $\Gamma_2^{(i)}$.
\item The order of $\Gamma_1^{(i)}(0,y)$ equals $\frac{b_0}{e_{i-1}}\left[-k \;\;\hbox{\rm mod } n_i\right]$, where $n_i=\frac{e_{i-1}}{e_i}$.
\item The order of $\Gamma_2^{(i)}(0,y)$ equals $ \frac{b_0}{e_{i}}\left(\min\{e_i,k\}-\lceil \frac{k}{n_i}\rceil\right)$.
\item The power series $\Gamma_2^{(i)}$ has $\min\{e_i,k\}-\lceil \frac{k}{n_i}\rceil$ irreducible factors.
\end{enumerate}
\end{Theorem}
\noindent \begin{proof}
\noindent We factorize $\prod_{j=1}^{n-k} (y-\gamma_j)$ into $\bar{\Gamma}^{(1)}\cdots\bar{\Gamma}^{(i_k)}$, where every $\bar\Gamma^{(i)}$ is the product $\prod (y-\gamma_j)$ running over $\gamma_j\in \mathrm{Zer} \frac{\partial^k} {\partial y^k}f$ with $\mathrm{cont}(f,\gamma_j)=\frac{b_i}{b_0}$. By Property \ref{contact-roots} if $g$ is an irreducible factor of $\frac{\partial^k} {\partial y^k}f$ and $\gamma,\gamma' \in \mathrm{Zer} g$ then $\mathrm{cont}(f,\gamma)=\mathrm{cont}(f,\gamma')$. Hence
$\bar\Gamma^{(i)}$ is the product of irreducible power series, so it is a power series. By$\,$(\ref{ppp2}) we have
\[\frac{\partial^k} {\partial y^k}f(x,y)=\Gamma^{(1)}\cdots \Gamma^{(i_k)},\]
\noindent where $\Gamma^{(i)}$ equals $\bar\Gamma^{(i)}$, up to multiplication by a unit, for $1\leq i\leq i_k$.
\medskip
\noindent The first statement of the theorem is a consequence of the first three statements of Lemma \ref{TL}, since the order of $\Gamma^{(i)}(0,y)$ is the number of $\gamma_j$'s with $\mathrm{cont}(f,\gamma_j)=\frac{b_i}{b_0}$.
\medskip
\noindent By Property \ref{contact-exponents}
for any irreducible factor $g$ of $\Gamma^{(i)}$ the first $i-1$ characteristic exponents of $f$ and $g$ are the same. We define $\Gamma^{(i)}_1$ (respectively $\Gamma^{(i)}_2$) as the product of all irreducible factors $g$ of $\Gamma^{(i)}$ such that $\frac{b_i}{b_0}$ is not in the support of the Newton-Puiseux roots of $g$ (respectively $\frac{b_i}{b_0}$ is in the support of the Newton-Puiseux roots of $g$). We will prove that $\left \{\frac{b_1}{b_0},\ldots,\frac{b_{i}}{b_0}\right\}$ is the set of characteristic exponents of any irreducible factor of $\Gamma_2^{(i)}$. By Property \ref{contact-nonzero}, the first $i$ charac\-te\-ris\-tic exponents of $g$ are $\frac{b_1}{b_0},\ldots, \frac{b_i}{b_0}$.
Suppose that there exists a rational number $r> \frac{b_i}{b_0}$ which is also a characteristic exponent of $g$. Let $\gamma$ be a Newton-Puiseux root of $g$. By (\ref{contact}) there is $\gamma'\in Zer g$, $\gamma'\neq \gamma$ such that $O(\gamma,\gamma')=r > \frac{b_i}{b_0}$. Consider the pseudo-ball $B\in T_i(f)$ containing $\gamma$. We get $\mathrm{lc}_B \gamma=\mathrm{lc}_B\gamma'$. Hence $\mathrm{lc}_B \gamma$ is a multiple root of $\frac{d^k}{dz^k}F_B(z)$, which contradicts Corollary \ref{CC}.
\medskip
\noindent The third and fourth statements of the theorem are a consequence of the fourth and fifth items of Lemma \ref{TL}.
\medskip
\noindent For any irreducible factor $g$ of $\Gamma_2^{(i)}$ the order of
$g(0,y)$ is the least common denominator of the elements of
$\mathrm{Char} \, g=\left \{\frac{b_1}{b_0},\ldots,\frac{b_{i}}{b_0}\right\}$, that is $\frac{b_0}{e_i}$.
The number of irreducible factors of the power series $\Gamma_2^{(i)}$ is the quotient of the
order of $\Gamma_2^{(i)}(0,y)$ by $\frac{b_0}{e_i}$, which finishes the proof.
\end{proof}
\bigskip
\noindent The first part of Theorem \ref{main} is \cite[Theorem 3.1]{Casas}. For $k=1$ the power series $\Gamma_2^{(i)}$ is a unit and consequently $\Gamma^{(i)}=\Gamma_1^{(i)}$ for every factor of Casas-Alvero's decomposition.
\medskip
\begin{Corollary}
\label{coro1}
With the notations and assumptions of Theorem~\ref{main}:
\begin{enumerate}
\item If $k=e_{i-1}-1$ then $\Gamma^{(i)}$ is irreducible and
$\mathrm{Char} \, \Gamma^{(i)}=\left \{\frac{b_1}{b_0},\ldots,\frac{b_{i-1}}{b_0}\right\}$.
\item If $k=e_{i-1}-n_i$ then $\Gamma^{(i)}$ is irreducible and
$\mathrm{Char} \, \Gamma^{(i)}=\left \{\frac{b_1}{b_0},\ldots,\frac{b_{i}}{b_0}\right\}$.
\end{enumerate}
\end{Corollary}
\noindent\begin{proof}
If $k=e_{i-1}-1$ then by the first and the third statements of Theorem \ref{main} we get $\mathrm{ord}\, \Gamma_1^{(i)}(0,y)=\mathrm{ord}\, \Gamma^{(i)}(0,y)=n_1\cdots n_{i-1}$.
\noindent On the other hand, by the second statement of Theorem \ref{main}, the first $i-1$ characteristic exponents of any branch $g$ of
$\Gamma_1^{(i)}$ are $\frac{b_1}{b_0},\ldots,\frac{b_{i-1}}{b_0}$, and consequently the order of $g(0,y)$ is greater than or equal to $n_1\cdots n_{i-1}$. So there exists a unit $u\in \mathbf{C}[[x,y]]$ such that $\Gamma^{(i)}=ug$ and $\Gamma^{(i)}$ is irreducible with
$\mathrm{Char} \, \Gamma^{(i)}=\left \{\frac{b_1}{b_0},\ldots,\frac{b_{i-1}}{b_0}\right\}$.
\medskip
\noindent If $k=e_{i-1}-n_i>0$ then $\mathrm{ord}\, \Gamma^{(i)}(0,y)=\mathrm{ord}\, \Gamma_2^{(i)}(0,y)=n_1\cdots n_{i-1}$. By the fifth statement of Theorem \ref{main} we conclude that $\Gamma^{(i)}$ is irreducible and by the second statement of Theorem \ref{main} we get
$\mathrm{Char} \, \Gamma^{(i)}=\left \{\frac{b_1}{b_0},\ldots,\frac{b_{i}}{b_0}\right\}$.
\end{proof}
\begin{Remark}
\label{equisingular} The characteristic sequence or equivalently the set of characteristic exponents determines the equisigularity class (in the sense of Zariski) of an irreducible singular curve.
Since the contact orders of the irreducible power series~$f$ and the branches of its higher order polars $\frac{\partial^k} {\partial y^k}f(x,y)$, for $k<e_{h-1}$ are precisely the characteristic exponents of $f$, they determine the equisingularity class of $f(x,y)=0$.
The case $k=1$ is well-known after \cite[page 110]{Merle}.
\end{Remark}
\medskip
\noindent Remember that if $f(x,y)\in \mathbf{C}[[x,y]]$ is irreducible with $\mathrm{Char} \, f=\left\{\frac{b_1}{b_0}, \ldots, \frac{b_h}{b_0}\right\}$ then an irreducible power series $g$ is called an $i-1$-{\em semi-root} of $f$ if $\mathrm{Char} \, g=\left\{\frac{b_1}{b_0}, \ldots, \frac{b_{i-1}}{b_0}\right\}$ and $\mathrm{cont}(f,g)=\frac{b_{i}}{b_0}$. In the language of resolution of singularities, a branch with characteristic contact is a semi-root if and only if its strict transform is a curvetta of the divisor corresponding to an end vertex of valency1 (different to the root) of the dual resolution graph of $f(x,y)=0$.
\medskip
\noindent Assume that $1\leq i\leq i_k$. Proceeding as in the proof of Corollary \ref{coro1} we can show that
if $k+1\equiv 0$ (mod $n_i$) then $\Gamma^{(i)}_1$ is an $(i-1)$-semi-root of $f$.
\medskip
\noindent We call an irreducible power series $g$ an $i$-{\em threshold semi-root} of $f$ if $\mathrm{Char} \, g=\left\{\frac{b_1}{b_0}, \ldots, \frac{b_{i}}{b_0}\right\}$ and $\mathrm{cont}(f,g)=\frac{b_{i}}{b_0}$. Remark that an $i$-{\em threshold semi-root} of $f$ is not an $i$-semi-root since its contact with $f$ is not hight enough.
\medskip
\noindent The irreducible factors of $\Gamma^{(i)}_2$ are {\em $i$-threshold semi-roots}.
\medskip
\noindent Figure 2 is the schematic picture of the dual resolution graph of the curve $f\cdot \Gamma^{(i)}_2 \cdot f^{(i-1)}\cdot f^{(i)}$, where $f^{(j)}$ is a $j$-semi-root of $f$, $E_j$ denotes the $j$-th rupture point and $\overline g$ means the strict transform of $g=0$. Here we assume that $x=0$ and $f=0$ are transverse.
\begin{center}
\begin{picture}(100,70)(0,0){
\put(-40,0){\line(1,0){138}}}
\put(100,0){\vector(1,1){20}}\put(120,20){$\overline f$}
\put(-42,-2.5){$\bullet$}
\put(-14.5,0){\line(0,1){42}} \put(-17,38){$\bullet$}
\put(-17,-2.5){$\bullet$}\put(-17,-10){$E_1$}
\put(20.5,0){\line(0,1){42}}
\put(18,-2.5){$\bullet$}\put(19,-10){$E_i$}
\put(20,-1){\vector(1,1){20}}
\put(20,-1){\vector(1,2){20}}
\put(38,22){$\vdots$}
\put(41.5,25){$\overline{\Gamma^{(i)}_2}$}
\put(18,38){$\bullet$}
\put(59.5,0){\line(0,1){42}}
\put(57,-2.5){$\bullet$}\put(56,-10){$E_{i+1}$}
\put(57,38){$\bullet$}
\put(59,40){\vector(1,1){20}}\put(79,60){$\overline{f^{(i)}}$}
\put(20,40){\vector(1,1){20}}\put(40,60){$\overline{f^{(i-1)}}$}
\put(-4,38){$\dots$}
\put(99.5,0){\line(0,1){42}}
\put(74,38){$\dots$}
\put(97,-2.5){$\bullet$}\put(96,-10){$E_h$}
\put(97,38){$\bullet$}
\put(39,-25.5) {\hbox{\rm Figure 2}} ;
\end{picture}
\end{center}
\vspace{0.6cm}
\begin{Example}
\label{Ex1}
Consider $f(x,y)=(y^3-x^4)^2-x^9\in \mathbf{C}[[x,y]]$.
The curve $f(x,y)=0$ is irreducible of characteristic $(b_0,b_1,b_2)=(6,8,11)$.
Then for the first partial derivative
$\frac{\partial} {\partial y}f(x,y)=\Gamma^{(1)}\Gamma^{(2)}$
where $\Gamma^{(1)}=6y^2$, $\Gamma^{(2)}=y^3-x^4$.
If $2\leq k \leq 5$ then $\frac{\partial^k}{\partial y^k}f(x,y)=\Gamma^{(1)}$.
For $k=2$ we have $\Gamma^{(1)}=\Gamma^{(1)}_1\Gamma^{(1)}_2$, where $\Gamma^{(1)}_1=6y$ and $\Gamma^{(1)}_2=5y^3-2x^4$.
For $k=3$ the factor $\Gamma^{(1)}_1$ is a unit, while for $k\in \{4,5\}$ the factor $\Gamma^{(1)}_2$ is a unit.
In Figure 3 the dual resolution graph of the curve $y\cdot (y^3-x^4) \cdot (5y^3-2x^4) \cdot f$ is drawn. Here $E_j$ denotes the $j$th-divisor and $\overline g$ means the strict transform of $g=0$.
\begin{center}
\begin{tikzpicture}[scale=2]
\draw [-](0,0) -- (2,0);
\node[draw,circle,inner sep=1.5pt,fill=black] at (0,0){};
\node[draw,circle,inner sep=1.5pt,fill=black] at (1,0) {};
\node[draw,circle,inner sep=1.5pt,fill=black] at (2,0) {};
\draw [-](1,0) -- (1,1);
\node[draw,circle,inner sep=1.5pt,fill=black] at (1,0.5) {};
\node[draw,circle,inner sep=1.5pt,fill=black] at (1,1) {};
\draw [-](2,0) -- (2,1);
\node[draw,circle,inner sep=1.5pt,fill=black] at (2,0.5) {};
\node[draw,circle,inner sep=1.5pt,fill=black] at (2,1) {};
\draw (0,-0.1) node[below]{$E_1$} ;
\draw (1,-0.1) node[below]{$E_4$} ;
\draw (2,-0.1) node[below]{$E_7$} ;
\draw (1,0.5) node[left]{$E_3$} ;
\draw (1,1) node[left]{$E_2$} ;
\draw (2,0.5) node[left]{$E_6$} ;
\draw (2,1) node[left]{$E_5$} ;
\draw [->](2,0)--(2.5,-0.5);
\draw [->](1,0) -- (1.5,-0.5);
\draw [->](1,1) -- (1.5,0.5);
\draw [->](2,1) -- (2.5,0.5);
\draw (2.5,-0.5) node[right]{$\overline f$} ;
\draw (1.5,-0.5) node[below]{$\overline{5y^3\!-\!2x^4}$} ;
\draw (1.5,0.5) node[below]{$\overline{y}$} ;
\draw (2.5,0.5) node[right]{$\overline{y^3\!-\!x^4}$} ;
\draw (1.5,-1.2) node[above]{\hbox{\rm Figure 3}} ;
\end{tikzpicture}
\end{center}
\end{Example}
\medskip
\noindent {\bf Acknowledgements:} The authors thank Bernard Teissier
for suggesting the name {\em threshold semi-root}.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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Manuel José Homem da Costa Noronha Ponce de Leão (Angra, 14 de março de 1784 — Angra, 5 de julho de 1824), morgado, grande proprietário, fidalgo cavaleiro da Casa Real e coronel do Regimento de Milícias de Angra. Era primo de Teotónio de Ornelas Bruges, o 1.º conde da Vila da Praia da Vitória, e pai de Pedro Homem da Costa Noronha (1809-1870) e de Manuel Homem da Costa Noronha (1807-1832), dois jovens que se destacaram entre os principais apoiantes da causa liberal na Terceira.
Biografia
Manuel Homem da Costa de Noronha Ponce de Leão foi filho de Pedro Homem da Costa Noronha e D. Jerónima Ludovina do Canto e Castro. Foi cavaleiro fidalgo da Casa Real e Coronel do regimento de milícias de Angra do Heroísmo. Foi Herdeiro e Senhor da casa e morgados de seus antepassados. No dia 25 de Março de 1784 foi baptizado na igreja de Nossa Senhora da Conceição, da cidade de Angra do Heroísmo. Faleceu no ano de 1824. Casou em 1804 com D. Úrsula Cândida do Canto e Castro Pacheco.
Filhos de Manuel Homem da Costa de Noronha Ponce de Leão com D. Úrsula Cândida do Canto e Castro Pacheco:
1 - Pedro Homem da Costa Noronha Ponce de Leão, casou com D. Maria Teotónia Augusta de Ornelas Bruges.
2 - Manuel Homem da Costa Noronha, nasceu no dia 2 de Janeiro de 1807, na ilha Terceira. Foi Tenente-coronel das milícias de Angra do Heroísmo. Foi assassinado na ilha de São Miguel, no Vale das Furnas, em casa de Diogo José do Rego, por partidários do rei D. Miguel, no mês de Setembro do ano de 1832.
Referências
História dos Açores
Família Noronha
Senhores do Reino de Portugal
Açorianos
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
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\section{Introduction}
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\begin{table}
\begin{center}
\begin{tabular}{|l|c|}
\hline
Method & Frobnability \\
\hline\hline
Theirs & Frumpy \\
Yours & Frobbly \\
Ours & Makes one's heart Frob\\
\hline
\end{tabular}
\end{center}
\caption{Results. Ours is better.}
\end{table}
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{\small
\bibliographystyle{ieee_fullname}
\section{Introduction}
\begin{figure}[ht]
\centering
\includegraphics[width=\linewidth,keepaspectratio]{figure.pdf}
\vspace{-7mm}
\caption{Performance analysis on NLPR dataset \cite{peng2014rgbd}. Note that better models are shown in the upper left corner (i.e., with a larger mean F-measure and smaller MAE). The circle size denotes the model size. Our proposed MGSnet for RGB SOD achieves the best performance with the lightest model size. The MGS design can also be embedded to the state-of-the-art RGBD model HDFnet \cite{pang2020hierarchical} to enable further progress (denoted as $*+MGS$).}
\label{fig:perform}
\vspace{-5mm}
\end{figure}
\begin{figure*}[ht]
\centering
\includegraphics[width=\linewidth,keepaspectratio]{net_new.pdf}
\vspace{-5mm}
\caption{(a) Conventional RGB models \cite{liu2019simple,zhang2017learningsingle,wu2019cascaded} insert additional modules to learn geometry-invariant features. (b) RGBD models \cite{fu2020jldcf,zhao2020single,pang2020hierarchical} adopt fusion-wise design to learn both photometric and geometric information. (c) Our proposed MGSnet which takes only RGB image for both training and testing. We use depth prior to guide sampling position on RGB feature map through a subnetwork design to compensate the master streaming.}
\label{fig:MGS}
\vspace{-5mm}
\end{figure*}
In the last decade, RGB-based deep learning models for salient object detection (SOD) \cite{zhang2017learningsingle,deng2018r3net,liu2019simple,wu2019cascaded,zhao2019egnet} achieved significant success thanks to the advances of GPU and CNN. Given an input image, the goal of SOD is to compute the pixel-wise location of the prominent objects that visually attract human attention the most. However, RGB SOD models focus more on photometric information instead of geometry. This is due to the fixed shape and size kernel design of CNN that is not invariant to scale changes and to 3D rotations. By the lack of geometric information on the input side, it is inevitable for RGB models to add additional learning modules in the network to attend to salient objects, resulting in model complexity and computational cost.
Recent RGBD-based SOD has motivated research interest thanks to the accessibility of cross-modal information from the input side. State-of-the-art RGBD models \cite{fu2020jldcf,piao2020a2dele,pang2020hierarchical,zhao2020single} achieve superior performance over the RGB baseline, affirming the effectiveness of learning from two modalities. Most architectures adapt fusion-wise models, such as early fusion \cite{zhao2020single} where the depth map is fed as the fourth channel to RGB image, or multi-scale and late fusion \cite{pang2020hierarchical} where two-stream networks are adopted. However, early fusion contains more low-level features than semantic ones. Multi-scale or late fusion inevitably requires more learning parameters. As shown in Figure \ref{fig:perform}, the size of RGBD models is often larger than that of RGB networks.
We explore differently the relationship between depth map and RGB image. Taking human beings as an example, to distinguish salient objects from the 3D world, the input is the visual appearance through human eyes. With the color information and thanks to the depth estimation capability, humans further discover geometric information. This prior guides the understanding of RGB images. It should be the same case for intelligent machines.
To this end, we propose a novel Modality-Guided Subnetwork (MGSnet) which adaptively transforms convolutions by fusing information from one modality to another (e.g., depth to RGB or RGB to depth). Our network matches perfectly both RGB and RGB-D data and dynamically estimates depth if not available by simply applying an off-the-shelf depth prediction model. We design a subnetwork mechanism alongside the master streaming pipeline. The subnetwork can be treated like a light residual-addition branch as the ResNet \cite{He2016Residual}. It takes one modality map as the master input, e.g. RGB, and enhances its robustness by deforming the convolution kernel with the supervision of the complementary modal prior, e.g. depth, and vice versa.
In summary, the main contributions of this paper are listed as follows :
\begin{itemize}
\vspace{-2mm}
\setlength{\itemsep}{2pt}
\setlength{\parsep}{0pt}
\setlength{\parskip}{0pt}
\item By exploiting the nature of CNN sampling position, we propose a novel cross-modal fusion design (MGS) for salient object detection, where we use a subsidiary modality, i.e., RGB/depth, to guide the main modality streaming, i.e., depth/RGB.
\item For RGB-only input, we suggest using an off-the-shelf depth prediction model to mimick the multi-modality input. Our MGSnet enables dramatical performance gain on benchmark datasets and achieves state-of-the-art performance among RGB SOD models.
\item The proposed MGS can also be embedded in RGBD two-stream network with the advantage of cross-modality cues while being lightweight.
\end{itemize}
\section{Related Work}
\textbf{RGB SOD:} In the past decade, the development of GPU and CNN contributes to the advances of RGB SOD. One core problem is understanding the geometric information from the image. Fully Convolutional Network (FCN) \cite{Long2015FCN} is a pioneering work in leveraging spatial information in CNN. Most recent researches dominating RGB SOD are FCN-based, such as \cite{zhang2017learningsingle} which designs a single stream encoder-decoder system, \cite{li2016deepmulti} which adopts a multi-scale network on input, and most currently \cite{deng2018r3net,liu2019simple,wu2019cascaded,zhao2019egnet} which fuse multi-level feature map. Some branch designs also have achieved impressive results such as C2S-Net \cite{li2018contour} which bridges contour knowledge for SOD. By inserting additional transformation parameters in networks, it contributes to the model performance. Nevertheless, the inference time and computational cost become more significant.
\textbf{RGBD SOD:} The complementary depth map may provide extra clues on the geometry. How to efficiently joint RGB and depth modality is the key challenge for RGBD SOD. One possible solution is to treat the depth map as an additional channel and adapt a single-stream system as shown in DANet \cite{zhao2020single}. It further designs a verification process with a depth-enhanced dual attention module. An alternative is to realize multi-stream networks followed by a feature fusion mechanism. PDNet \cite{zhu2019pdnet} designs a depth-enhanced stream to extract geometric features and further fuses with the RGB features. D3net \cite{fan2020rethinkingd3} adopts separate networks to respectively extract features from RGB, depth map, and RGBD four-channel input. A late fusion is further realized. HDFnet \cite{pang2020hierarchical} adopts two streaming networks for both RGB image and depth map. These features are further fused to generate region-aware dynamic filters. JL-DCF \cite{fu2020jldcf} proposes joint learning from cross-modal information through a Siamese network. Generally, RGBD networks achieve superior performance compared to RGB as shown in Figure \ref{fig:perform}. However, these methods rely on the quality and accessibility of the depth map. A high-quality depth map requires expensive depth sensors and is still sparse compared to an RGB image as suggested in \cite{fu2020jldcf,fan2020rethinkingd3}. To this end, DCF \cite{ji2021calibrated} proposes to calibrate the raw depth to improve the quality. Nevertheless, the high computational cost due to the two-streaming network requires more development.
Some recent researches \cite{piao2020a2dele,ji2020accurate,zhao2020depth} propose to learn from RGBD images and tests on RGB. This design enables an RGB CNN to achieve a comparable result with RGBD SOD during testing. Different from it, we propose to firstly discover the hidden geometric modality behind RGB images by simply using an off-the-shelf depth prediction method. With the estimated depth, we further propose a Modality-Guided Subnetwork mechanism to enhance the master RGB network understanding of the contour problem. Our proposed MGSnet achieves state-of-the-art performance with real-time inference speed compared to other RGB models. It can also be embedded in RGBD two-stream models to enable further progress with raw depth.
\section{Modality-Guided Subnetwork}
\subsection{Overview}
In Figure \ref{fig:MGS} (c), our network only takes RGB as input that then estimates the pseudo-depth. Our MGSnet only takes the pseudo-depth to deform the RGB streaming. In other words, only the RGB modality is fed through Conv\_4.
Note that our model is not limited by the nature of the modality. It can be a depth-guided RGB convolution as well as an RGB-guided depth convolution. Figure \ref{fig:rgbdmgs} presents our model embedded on an RGBD two-streaming network and Figure \ref{fig:guided} illustrates the idea of modality-guided sampling position. We learn the offset from both semantic RGB and depth features to create a cross supervision mechanism.
\begin{figure}[ht]
\centering
\includegraphics[width=\linewidth,keepaspectratio]{rgbd_mgs.pdf}
\vspace{-7mm}
\caption{Illustration of embedded MGS on a RGBD two-streaming network.}
\label{fig:rgbdmgs}
\vspace{-5mm}
\end{figure}
For simplicity, we present in the following section a depth-guided subnetwork for RGB features. It contains three parts: a master RGB streaming network, an off-the-shelf prediction model to estimate a pseudo-depth map if not available, and a depth-guided subnetwork design. For simplicity, VGG-16 \cite{simonyan2014vgg} architecture is adopted as our basic convolutional network to extract RGB features for its wide application in SOD. We use RFB \cite{liu2018rfb} on the steamer layers ($f_3, f_4, f_5$) which contains high level features for SOD as suggested in \cite{piao2020a2dele,pang2020hierarchical,fu2020jldcf}. We further embed our subnetwork to enhance the edge understanding of the encoder output. We take the same decoder as proposed in \cite{piao2020a2dele} and a simple binary cross-entropy (BCE) as the loss.
\begin{figure*}[ht]
\begin{subfigure}{.495\textwidth}
\centering
\includegraphics[width=0.98\linewidth]{rgb_cnn.png}
\caption{Depth-guided sampling position on RGB image}
\end{subfigure}
\begin{subfigure}{.495\textwidth}
\centering
\includegraphics[width=0.98\linewidth]{depth_cnn.png}
\caption{RGB-guided sampling position on depth image}
\end{subfigure}
\vspace{-3mm}
\caption{Visual comparison of MGSnet. A pair of RGB and depth images from an RGBD dataset are illustrated on the left. While extracting features through two streaming networks, the cross-modal information beyond the fixed sampling position is not utilized (second left). Our proposed modality-guided sampling position breaks the limit of fixed-local configurations. The new sampling position incorporates supporting modality into the basic function of CNN on the main modality: the fixed sampling position is replaced by relevant neighbors defined by the supporting modality without limitation (right).}
\label{fig:guided}
\vspace{-3mm}
\end{figure*}
\subsection{Depth-guided Subnetwork}
To proceed with the geometric prior, the depth map D and the RGB feature map (output of $Conv\_4$) are fed together to our model. We use $f_4 \in \mathbb{R}^{b\times 512\times h \times w}$ to denote the input RGB feature. The depth prior and RGB feature maps are articulated through an adaptive convolution to compute depth-aware RGB feature maps as output. The last is added to the master RGB stream to form the final feature map.
The subnetwork contains three convolutions of different filter sizes: $1\times1, 3\times3$, and $1\times1$. It shares the same architecture of plain baseline of ResNet \cite{He2016Residual} that the $1\times1$ layers are used for reducing (512$\rightarrow$64) and then increasing dimensions (64$\rightarrow$512), allowing the $3\times3$ layer with smaller input/output dimensions. We denote $\mathcal{D}$ and $\mathcal{U}$ for the first and the last $1\times1$ convolution, which stands for down-sample and up-sample, respectively. This design can significantly reduce the learning parameters, which contributes to the lightweight design of our subnetwork. Different from ResNet that uses the three layers as a bottleneck, we use them as the residual-addition branch which serves as complementary information to the plain network.
A standard convolution is formulated as:
\begin{equation}
\textbf{y}(p) = \sum_{p_n\in\textbf{R(p)}} \textbf{w}(p_n) \cdot \textbf{x}(p + p_n).
\end{equation}
with \textbf{R(p)} the sampling grid for point $p$. Physically it represents a local neighborhood on input feature map, which conventionally has regular shape with certain dilation $\Delta d$, such that :
\begin{equation}
\textbf{R(p)} = a \Vec{u} + b\Vec{v}
\label{eq:2dgrid}
\end{equation}
where $(\Vec{u}, \Vec{v})$ is the pixel coordinate system of input feature map and $(a,b) \in (\Delta d \cdot \{-1, 0 , 1\})^2$ for a $3\times3$ convolution or $(a,b) \in (\{0\})^2$ for $1\times1$ convolution.
We further replace the conventional $3\times3$ convolution by deformable convolution (DeformConv) \cite{dai2017deformable}, where the kernels are generated with different sampling distributions which is adapted to depth modality. Mathematically, we have:
\begin{equation}
\textbf{y}(p) = \sum_{p_n\in\textbf{R(p)}} \textbf{w}(p_n) \cdot \textbf{x}(p + p_n + \Delta p_n)
\label{eq}
\end{equation}
The convolution may be operated on the irregular positions $p_n+\Delta p_n$ as the offset $\Delta p_n$ may be fractional. To address the issue, we use the bilinear interpolation which is the same as that proposed in \cite{dai2017deformable}. The adapted convolution is denoted as $\mathcal{A}$.
Thanks to the depth input of the subnetwork, the scale and geometric transformation of objects on the RGB feature map can be directly analyzed with the adapted offsets. This process is expressed as:
\begin{equation}
\Delta p_n = \eta (D)
\label{eq:offset}
\end{equation}
We present two types of offset generators according to different plain networks. More details are discussed in the following section. The newly defined sampling position becomes depth-aware and helps to better articulate the RGB feature and geometric information. Finally, the output of MGS is added to the master stream, which serves as complementary depth-aware guidance on RGB features.
The entire process to compute the modality-guided feature $f_M$ can be formulated as follows:
\begin{equation}
\begin{split}
f_M & = MGS(f_4, D) \\
& = \mathcal{U}(\mathcal{A}(\mathcal{D}(f_4), \eta(D)))\\
\end{split}
\end{equation}
The output of RGB encoder can be formulated as :
\begin{equation}
out = f_5 + \lambda f_M
\label{eq:reg}
\end{equation}
where $\lambda$ is the weight parameter.
\subsection{Offset generator}
We use another modal prior to deform the main stream convolution. When the offset exceeds the input size, the output will be computed as if the zeros padding is applied. For RGB input, the pseudo-depth is used to deform the RGB sampling position. The offset is generated through Z-ACN \cite{wu:zacn}. It firstly back-projects the 2D conventional grid to form a 3D point cloud according to the depth. Based on the point cloud, it extracts a depth-aware 3D plan and further creates a depth-aware 3D regular grid. Then it projects the 3D regular grid to the image plan to form the deformable sampling position. More details can be found in Z-ACN \cite{wu:zacn} paper. Different to DeformConv \cite{dai2017deformable} that learns offset from the RGB feature map to deform RGB sampling position, Z-ACN computes offset according to low-level geometric constraint (one-channel depth) and does not require gradient descent, thus perfectly matches our light-weight subnetwork design. The computed offset allows the RGB convolution to be scale and rotation independent. We verify through experiments the superior performance of our model in the ablation study.
For RGBD input, current Sconv \cite{chen2021spatial} suggests learning the RGB offset from a semantic depth feature map. We share the same motivation as Sconv. However, Sconv firstly projects the depth into a high-dimensional feature space and secondly learns a depth-aware offset and mask. Unlike Sconv, we learn the offset from the encoder or high-level features to avoid the additional projection. In other words, in our case, the offset generator $\eta$ is realized through a simple $3\times3$ convolution to minimize the computational cost. Furthermore, we adapt to different modalities as input, i.e., it learns offset from both RGB and depth, while Sconv only learns from depth.
\subsection{Understand adaptive sampling position}
Our model aims to compensate for the single modality streaming. As shown in Figure \ref{fig:guided}, while extracting features from RGB images, the conventional sampling position is limited by the lack of capability to include geometry due to the fixed shape. We propose to use the depth prior to accurately locate the sampling position. For RGB input without depth prior, we suggest mimicking the depth map by using a monocular depth estimation model. Some pseudo-depth images may be inaccurate due to the domain gap between SOD and monocular depth estimation. In such a case, the offset will converge to 0 so that the deformation becomes minimal and local. The contribution of the depth-aware RGB feature is further regularized by the weight parameter $\lambda$ of Eq. \ref{eq:reg}. In Fig. \ref{fig:rgb}, we show that our method is robust to non-optical depth through several examples.
While extracting features from raw depth, conventional sampling positions may produce sub-optimal results due to some inaccurate measurements. The raw depth maps for SOD are obtained by camera measurements such as Kinect and Light Field cameras, or estimated by classic computer vision algorithms as \cite{sun2010secrets,liu2010sift}. Thus, the raw depth images may contain noise and ambiguity. We can visualize several low-quality samples on the third row of Figure \ref{fig:rgb}. To this end, we propose to use the RGB image to deform the depth sampling position. In such a case, the RGB-guided sampling position can make up for the measurement error on geometry.
\section{Experiments}
\subsection{Benchmark Dataset}
To verify the effectiveness of our method, we conduct experiments on seven following benchmark RGBD datasets. DES \cite{cheng2014depth} : includes 135 images about indoor scenes captured by Kinect camera. LFSD \cite{li2014saliency}: contains 100 images collected on the light field with an embedded depth map and human-labeled ground truths. NLPR \cite{peng2014rgbd}: contains 1000 natural images captured by Kinect under different illumination conditions. NJUD \cite{ju2014depth}: contains 1,985 stereo image pairs from different sources such as the Internet, 3D movies, and photographs taken by a Fuji W3 stereo camera and with estimated depth by using optical flow method \cite{sun2010secrets}. SSD \cite{zhu2017ssd}: contains 80 images picked up from stereo movies with estimated depth from flow map \cite{sun2010secrets}. STEREO \cite{niu2012leveraging}: includes 1000 stereoscopic images downloaded from the Internet where the depth map is estimated by using SIFT flow method \cite{liu2010sift}. DUT-RGBD \cite{piao2019depth}: contains 1200 images captured by Lytro camera in real-life scenes.
\subsection{Experimental Settings}
Our model is implemented basing on the Pytorch toolbox and trained with a GTX 3090Ti GPU. We adopt several generally-recognized metrics for quantitative evaluation: F-measure is a region-based similarity metric that takes into account both Precision (Pre) and Recall (Rec). Mathematically, we have : $F_{\beta} = \frac{(1+\beta^2) \cdot Pre \cdot Rec}{ \beta^2 \cdot Pre + Rec}$. The value of $\beta^2$ is set to be $0.3$ as suggested in \cite{achanta2009frequency} to emphasize the precision. In this paper, we report the \textbf{maximum F-measure} ($F_{\beta}$) score across the binary maps of different thresholds, the \textbf{mean F-measure} ($F_{\beta}^{mean}$) score across an adaptive threshold and the \textbf{weighted F-measure} ($F_{\beta}^{w}$) which focuses more on the weighted precision and weighted recall.
\textbf{Mean Absolute Error ($MAE$)} studies the approximation degree between the saliency map and ground-truth map on the pixel level.
\textbf{S-measure ($S_m$)} evaluates the similarities between object-aware ($S_o$) and region-aware ($S_r$) structure between the saliency map and ground-truth map. Mathematically, we have: $S_m= \alpha \cdot S_o + (1 - \alpha) \cdot S_r$, where $\alpha$ is set to be $0.5$.
\textbf{E-measure ($E_m$)} studies both image level statistics and local pixel matching information. Mathematically, we have: $E_m= \frac{1}{W\times H} \sum_{i=1}^{W} \sum_{j=1}^{H} \phi_{FM}(i,j)$, where $\phi_{FM}(i,j)$ stands for the enhanced-alignment matrix as presented in \cite{fan2018enhanced}.
\subsection{Performance Comparison with RGB Input}
\begin{table*}
\setlength\tabcolsep{0pt}
\setlength\extrarowheight{1pt}
\begin{center}
\begin{tabular*}{0.98\textwidth}{@{\extracolsep{\fill}}*{18}{c}}
\hline
Dataset & &\multicolumn{3}{c}{DES} & \multicolumn{3}{c}{NLPR} & \multicolumn{3}{c}{NJUD} & \multicolumn{3}{c}{STEREO} & \multicolumn{3}{c}{DUT-RGBD} \\
\cline{3-5} \cline{6-8} \cline{9-11} \cline{12-14} \cline{15-17}
Metric & \small $Size\downarrow$ & \small $MAE\downarrow$ & \small $F_{\beta}^{mean}\uparrow $ & \small $F_{\beta}^{w}\uparrow$ & \small $MAE\downarrow$ &\small $F_{\beta}^{mean}\uparrow $ & \small $F_{\beta}^{w}\uparrow$ &\small $MAE\downarrow$ & \small $F_{\beta}^{mean}\uparrow $ & \small $F_{\beta}^{w}\uparrow$ & \small $MAE\downarrow$ & \small $F_{\beta}^{mean}\uparrow $ & \small $F_{\beta}^{w}\uparrow$ & \small $MAE\downarrow$ & \small $F_{\beta}^{mean}\uparrow $ & \small $F_{\beta}^{w}\uparrow$ \\
\hline
\multicolumn{17}{c}{RGB input}
\\
$R^{3} Net_{18}$
&225 &.066 &.728 &.693 &.101 &.649 &.611 &.092 &.775 &.736 &.084 &.800 &.752 & .113 &.781 &.709\\
$PoolNet_{19}$
&279 &.031 &.852 &.814 &.046 &.791 &.771 &.057 &.850 &.816 &.045 &.877 &.849 & .049 &.871 &.836 \\
$CPD_{19}$
&112 & \rr{.028} &.860 &\rr{.841} &.037 &.840 &.829 &.059 &.853 &.821 &.046 &.880 &.851 & .055 &.872 &.835 \\
$AFNet_{19}$
&144 & .034 &.840 &.816 &.043 &.807 &.796 &.056 &.857 &.832 &.046 &.876 &.850 & .064 &.851 &.817 \\
$EGNet_{19}$
&412 & .035 &.831 &.797 &.047 &.800 &.774 &.060 &.846 &.808 &.049 &.876 &.835 & .059 &.866 &.805 \\
\multicolumn{17}{c}{+ Pseudo Depth (86 Mb extra model size)} \\
$HDFnet_{20}$ &177 (+86)
& .070 &.721 &.664 &.062 &.758 &.741 &.124 &.716 &.656 & .106 &.743 &.684 & - & - & - \\
$CoNet_{20}$ &171 (+86)
& .037 &.820 &.808 &.049 &.744 &.835 &.068 &.827 &.795 & .050 &.848 &.825 & .045 &.865 &.847 \\
$Ours$ & \rr{62} (+86) & \rr{.028} &\rr{.871} &\bb{.837} &\rr{.025} &\rr{.888} &\rr{.874} &\rr{.047} &\rr{.882} &\rr{.856} &\rr{.041} &\rr{.881} &\rr{.857} &\rr{.037} &\rr{.906} &\rr{.889} \\
\hline
\hline
\end{tabular*}
\end{center}
\vspace{-6mm}
\caption{Quantitative comparisons of with RGB input. The off-the-shelf depth estimation is realized with MiDaS \cite{ranftl2019midas} which presents 86Mb model size. $\uparrow \& \downarrow$ denote larger and smaller is better, respectively. (\rr{red}: best, \bb{blue}: second best).}
\label{tab:rgb}
\vspace{-4mm}
\end{table*}
We firstly compare with RGB models, including R3Net \cite{deng2018r3net}, PoolNet \cite{liu2019simple}, CPD \cite{wu2019cascaded}, AFnet \cite{feng2019attentive}. All saliency maps are directly provided by authors or computed by authorized codes. For fair comparisons, we adopt the same training set as suggested in \cite{piao2020a2dele}, which contains 1485 samples from NJUD, 700 samples from NLPR, and 800 samples from the DUT-RGBD dataset. The remaining images of all listed datasets are used for testing. The quantitative comparison is presented in Table \ref{tab:rgb}. Our model is trained with 50 epochs with $256\times256$ input image size.
For the RGB model, we can conclude from Table \ref{tab:rgb} that the improvement on the saliency map is attributed to different learning modules, which results in high computational cost (size). Different from traditional RGB models which do not exploit the depth information, we propose to take full advantage of the pseudo-geometry estimated with an existing monocular depth estimation method.
We re-train two RGB-D SOD network (HDFnet \cite{pang2020hierarchical}, CoNet \cite{ji2020accurate}) with the additional estimated pseudo-depth. We observe a significant performance gap between the recent RGB-D models and the previous RGB models. The main reason is the quality of depth estimation: the domain gap between the depth estimation dataset and the SOD dataset leads to some failure depth maps. This can be noticed in the poor performance of HDFnet that extracts features from both RGB and depth images. CoNet, however, is more robust to the depth quality since the depth map is only used to supervise the feature extraction on RGB images. Our model shares the same motivation as CoNet to use depth prior to guide SOD but in a completely different manner. In our model, we directly learn a geometric-aware offset from the depth map to the sampling position on the RGB image. Our model achieves consistent superior performance compared with other models.
\subsection{Performance Comparison with RGB-D Input}
\begin{table*}
\begin{center}
\setlength{\tabcolsep}{1mm}{
\begin{tabular}[ht]{||c l|| c c c | c c c m{1cm}| c c m{1cm} ||}
\hline
\hline
& & \multicolumn{3}{c|}{Extract RGB feature} & \multicolumn{7}{c||}{Extract RGBD feature}\\
\hline
& & $CoNet_{20}$& $A2dele_{20}$ & $Ours$ & $DANet_{20}$ & $cmMS_{20}$ & $HDFnet_{20}$ & $HDF+Ours$ & $DSA2F_{21}$ &$HDFnet_{20}$ & $HDF+Ours$ \\
\multicolumn{2}{||c||}{Backbone} & Resnet101 & \multicolumn{2}{c|}{-- VGG16 -- } & \multicolumn{4}{c|}{-- VGG16 -- } &\multicolumn{3}{c||}{-- VGG19 --}\\
\hline
& $Size\downarrow$
&167 &\underline{57} & \bl{62} & \underline{102} & 430 &\underline{177} & \bl{178} & - & \underline{220} & \bl{221}\\
& $FPS\uparrow$
&- &120 & \bl{150} & 32 & &\underline{62} & \bl{58} & - & - & -\\
\hline
\multirow{4}{*}{\rotatebox[origin=c]{90}{DES}}
& $MAE \downarrow$
&\underline{.027} &.029 &\bl{.028} &.023 &- &.030 & \bl{.019} & .021 &.017 & \bl{.017} \\
& $F_{\beta}^{mean}\uparrow$
&.862 & .870 &\bl{.871} &.887 &- &.843 &\bl{.920} & .896 &.918 & \bl{.923} \\
& $S_m \uparrow$
&\underline{.910} & .881 &\bl{.882} &.904 &- &.899 &\bl{.935} & .920 &.937 & \bl{.937}\\
& $E_m \uparrow$
&\underline{.945} & .918 &\bl{.922} &.967 &- &.944 &\bl{.979} & .962 &.976 & \bl{.979}\\
\hline
\multirow{4}{*}{\rotatebox[origin=c]{90}{NLPR}}
& $MAE \downarrow$
&.031 &.031 &\bl{.025} &.028 &.027 &.027 & \bl{.025} & \underline{.024} &.027 & \bl{.025} \\
& $F_{\beta}^{mean}\uparrow$
&.848 & .871 &\bl{.888} &.871 &.869 &.878 &\bl{.885} & \underline{.891} &.883 & \bl{.882} \\
& $S_m \uparrow$
&.908 & .889 &\bl{.908} &.915 &.899 &.898 & \bl{.918} & .918 &.915 & \bl{.918} \\
& $E_m \uparrow$
&.934 & .937 &\bl{.952} &.949 &.945 &.948 &\bl{.954} & .950 &.951 & \bl{.951} \\
\hline
\multirow{4}{*}{\rotatebox[origin=c]{90}{NJUD}}
& $MAE \downarrow$
&.047 &.052 &\bl{.047} &.045 &.044 &.039 & \bl{.037} & .039 &.038 & \bl{.035} \\
& $F_{\beta}^{mean}\uparrow$
&.872 & .873 &\bl{.882} &.871 &.886 &.887 &\bl{.893} & .898 &.887 & \bl{.898} \\
& $S_m \uparrow$
&\underline{.895} & .867 &\bl{.879} &.899 &.900 &.907 &\bl{.911} & .903 &.911 & \bl{.912}\\
& $E_m \uparrow$
&.911 & .914 &\bl{.928} &.922 &.914 &.931 &\bl{.935} & .923 &.932 & \bl{.942}\\
\hline
\multirow{4}{*}{\rotatebox[origin=c]{90}{STEREO}}
& $MAE \downarrow$
&\underline{.037} &.044 &\bl{.041} &.047 &.043 &.042 & \bl{.039} & .039 &.040& \bl{.039} \\
& $F_{\beta}^{mean}\uparrow$
&\underline{.885} & .875 &\bl{.881} &.858 &\underline{.879} &.864 &\bl{.864} & \underline{.893} &.875 & \bl{.878} \\
& $S_m \uparrow$
&\underline{.908} & .878 &\bl{.887} &.901 &.895 &.900 &\bl{.904} & .897 &.903 & \bl{.902}\\
& $E_m \uparrow$
&.928 & .929 &\bl{.936} &.914 &.922 &.929 &\bl{.937} & .933 &.934 & \bl{.938}\\
\hline
\hline
\end{tabular}}
\end{center}
\vspace{-5mm}
\caption{Quantitative comparisons of with recent RGBD models. $\uparrow \& \downarrow$ denote larger and smaller is better, respectively. MGS can also be embedded to the HDFnet \cite{pang2020hierarchical} to enable further progress. The scores/numbers better than ours are \underline{underlined} (extracting RGB feature, extracting RGBD feature with VGG16, and extracting RGBD feature with VGG19 models are labeled separately). More details on all RGB-D dataset can be found in the Supplementary Material. }
\label{tab:rgbd}
\vspace{-1mm}
\end{table*}
We also compare with state-of-the-art RGBD models with raw depth input in the Table \ref{tab:rgbd}, including CoNet \cite{ji2020accurate}, A2dele \cite{piao2020a2dele}, DANet \cite{zhao2020single}, cmMS \cite{li2020rgb}, HDFnet \cite{pang2020hierarchical}, and DSA2F \cite{sun2021deep}. For fair comparisons, all saliency maps and the FPS are directly provided by authors or computed by authorized codes. Note that the FPS depends on the GPU for inference. Thus, only the FPS of HDFnet is tested on the same GPU as ours.
While depth is only used as supervision during training and only RGB image is required during testing, our model surpasses existing efficient A2dele significantly on performance with only an + around 5Mb model size. Compared to CoNet, the model size is minimized by 63\% and achieves a comparable result. As presented in Figure \ref{fig:guided}, our proposed module can take advantage of cross-modality cues while being lightweight. Thus, we further incorporate with the HDFnet \cite{pang2020hierarchical} to show the performance gain by integrating our approach. It achieves the state-of-the-art (SOTA) performance on VGG16 based models ($HDF+Ours$). To better demonstrate the superiority of the proposed method, we also use a larger backbone (VGG19) to compare with the plain version HDFnet and the SOTA method DSA2F. Note that DSA2F uses neural architecture search to automate the model architecture while ours is hand-designed. Our model enables significant gains on the plain version with minimal cost (+ around 1 Mb on model size) and achieves comparable results with the DSA2F.
\subsection{Qualitative Evaluation}
We present the qualitative result with some challenging cases in Figure \ref{fig:rgb}: low density ($1^{st}$ columns), similar visual appearance between foreground and background ($2^{nd} - 5^{th}$ columns), small objects ($6^{th}$ columns), far objects ($7^{th}-9^{th}$ columns), human in scene ($10^{th}$ columns), and similar and low contrast on depth map ($11^{th}-13^{th}$ columns). It can be seen that our MGSnet yields the results closer to the ground truth mask in various challenging scenarios, especially for the last three columns with low-quality depth clues. Different from two-stream networks that tend to treat sub-optimal depth equally as RGB input, MGSnet extracts features from RGB images while the depth map serves only as complementary guidance, thus becoming robust to depth bias. By analyzing the response on HDFnet (sixth row) and HDFnet with embedded MGS (seventh row), we observe that our approach enables the plain network better discrimination of salient objects from the background.
\section{Ablation Study}
\begin{figure*}[ht]
\centering
\includegraphics[width=\linewidth,keepaspectratio]{rgbd.pdf}
\vspace{-6mm}
\caption{Visual comparison between our proposed MGSnet and the state-of-the-art RGB/RGBD methods. $*$ denotes that the ground truth depth is used during testing. We also embed MGS on the HDFnet \cite{pang2020hierarchical} to enable further improvement, denoted as $*HDF+Ours$. More examples can be found in the Supplementary Material.}
\label{fig:rgb}
\vspace{-8mm}
\end{figure*}
\begin{table*}
\setlength\tabcolsep{0pt}
\setlength\extrarowheight{1pt}
\begin{center}
\begin{tabular*}{0.98\textwidth}{@{\extracolsep{\fill}}*{14}{l}}
\hline
& Dataset &\multicolumn{2}{c}{DES} &\multicolumn{2}{c}{LFSD} & \multicolumn{2}{c}{NLPR} & \multicolumn{2}{c}{NJUD} &\multicolumn{2}{c}{SSD} & \multicolumn{2}{c}{STEREO} \\
\cline{3-4} \cline{5-6} \cline{7-8} \cline{9-10} \cline{11-12} \cline{13-14}
\# & Metric &$MAE\downarrow$ & $F_{\max}\uparrow $ &$MAE\downarrow$ & $F_{\max}\uparrow $ &$MAE\downarrow$ & $F_{\max}\uparrow $ &$MAE\downarrow$ & $F_{\max}\uparrow $ &$MAE\downarrow$ & $F_{\max}\uparrow $ &$MAE\downarrow$ & $F_{\max}\uparrow $
\\
\hline
1 & RGB Baseline
& .036 & .880 &.104 &.835 &.037 &.883 &.059 &.877 &.082 &.785 &.054 &.882
\\
2 & RGB + Self Deform
& .042 & .860 &.110 &.798 &.031 &.885 &.052 &.879 &\underline{.062} &\underline{.814} &.046 &.882
\\
3 & RGB pseudo D Fusion
& .032 & .888 &.093 &.819 &.029 &.893 &.061 &.863 &.077 &.776 &.049 &.878
\\
4 & RGB + Depth-Deform
& \bl{.028} & \bl{.899} &\bl{.078} &\bl{.849} &\bl{.025} &\bl{.905} &\bl{.047} &\bl{.897} &\bl{.063} &\bl{.801} &\bl{.041} &\bl{.898}
\\
\hline
5 & RGB-D Baseline (B)
& .020 & .933 &.089 &.856 &.028 &.921 &.039 &.922 &.054 &.867 &.042 &.911
\\
6 & B + Self Deform
& .019 & .936 &.089 &.853 &.026 &.916 &.038 &.925 &.053 &.878 &.044 &.895
\\
7 & B + Cross-Modal Deform
& \bl{.019} & \bl{.936} &\bl{.079} &\bl{.871} &\bl{.025} &\bl{.921} &\bl{.037} &\bl{.925} &\bl{.049} &\bl{.867} &\bl{.039} &\bl{.917}
\\
\hline
\hline
\end{tabular*}
\end{center}
\vspace{-6mm}
\caption{Ablation study of modality-guided sampling position}
\label{tab:ablation}
\vspace{-4mm}
\end{table*}
\textbf{Effect of Modality-Guided Sampling Position}: Our modality-guided sampling position aims to incorporate multi-modal information through the basic function of CNN - the sampling position of convolution. This pattern is integrated in Eq. \ref{eq} and Eq. \ref{eq:offset}. To verify the effectiveness of the proposed modality-guided sampling position, a series of experiments with different learning strategies are realized.
(1) - (4) are experiments on RGB model: (1) RGB Baseline. (2) Self-guided deformable sampling position. We learn the offset from the RGB feature map. (3) RGB pseudo-depth early fusion. We form a four-channel input with pseudo depth. (4) Depth-guided deformable position. We compute an offset from pseudo-depth using Z-ACN to guide RGB streaming. (5) - (7) are experiments on RGBD model: (5) Baseline. We use the same architecture as HDFnet. (6) Self-guided deformable sampling position. The offset applied to RGB streaming is learned from the RGB feature. Idem for depth streaming. (7) Cross modality-guided deformable position. We learn an offset from depth to guide RGB streaming, and vice versa.
\begin{figure}[ht]
\centering
\vspace{-1mm}
\includegraphics[scale = 0.61]{ablation.pdf}
\vspace{-4mm}
\caption{Visual analysis of embedded depth with MGSnet.}
\label{fig:data}
\vspace{-5mm}
\end{figure}
Table \ref{tab:ablation} (1) and (3) compare the performance of the baseline RGB three-channel input and mimicked RGBD four-channel input with pseudo-depth, respectively. The mimicked multi-modality early fusion achieves better performance, indicating that the pseudo-depth provides additional semantic. However, by comparing (3) and (4), we observe that the proposed depth-guided deformable sampling position can better use the complementary information to supervise RGB streaming, compared with early fusion. By comparing (2) and (4), we show that the depth-guided deformable position is more accurate on saliency compared to that of the self/RGB-guided. This verifies the assumption that depth cues can help the RGB model to better distinguish the foreground and background. Note that in (4) we only extract features from RGB images. The additional awareness of the geometry is only treated as a 2D offset to better locate the sampling position. This new integration design contributes to the model performance with minimal cost. For better understanding, the qualitative result presented in Figure \ref{fig:data} shows that our approach provides more accurate saliency maps with better contrast. On the RGBD model (5-7), we also observe the superior performance with the cross-modality deformable sampling position achieves as it directly compensates for the single modal streaming.
\textbf{Performance with different depth qualities}:
We also conduct an experiment to show the impact of depth quality. We choose the HDFnet \cite{pang2020hierarchical} as the baseline and further embed it with our method. We present the average metric on all testing datasets in Table \ref{tab:estimated} with pseudo-depth (estimated) and raw depth from the RGBD dataset. Results obtained with pseudo-depth are denoted with *.
\begin{table}[ht]
\begin{center}
\begin{tabular}[ht]{l | c c | c c }
\hline
\small{AvgMetric} & $HDFnet*$ & $+Ours*$ & $HDFnet$ & $+Ours$ \\
\hline
$MAE \downarrow$
&.1053 &\rr{.0758} & .0405 & \rr{.0375} \\
$F_{\beta}\uparrow$
&.8410 &\rr{.8599} & .9121 & \rr{.9166}\\
$F_{\beta}^{mean}\uparrow$
&.7326 &\rr{.7868} & .8730 & \rr{.8831} \\
$F_{\beta}^{w}\uparrow$
&.6789 &\rr{.7488} & .8569 & \rr{.8672} \\
$S_m \uparrow$
&.8010 &\rr{.8390} & .9013 & \rr{.9053} \\
$E_m \uparrow$
&.8359 &\rr{.8797} & .9312 & \rr{.9377} \\
\hline
\hline
\end{tabular}
\end{center}
\vspace{-4mm}
\caption{Performance variation with different depth qualities. (*) denotes results obtained with pseudo-depth.}
\label{tab:estimated}
\vspace{-5mm}
\end{table}
It shows that the quality of depth has an important influence on performance. Features extracted from raw depth describe better the salient object and were in line with our expectations. However, in both cases, our MGS can significantly enable progress compared to the plain networks. For pseudo-depth, the contribution of our MGS is more significant, which can be explained by the effectiveness of our RGB-guided sampling position for depth streaming. It can efficiently help to alleviate depth errors.
\section{Conclusions}
In this paper, we propose a modality-guided module (MGSnet) for RGB-D salient object detection models. The depth channel can either be the input or be estimated using a state-of-the-art monodepth network. Our model adaptively transforms convolutions that their size and shape are built by fusing information from one modality to another (e.g., depth to RGB and/or RGB to depth), thus enabling a cross-modality interaction. Extensive experiments against RGB baselines demonstrate the performance gains of the proposed module, and the addition of the proposed module to existing RGB-D models further improved results.
\section*{Acknowledgements}
We gratefully acknowledge Zhuyun Zhou for her support and proofreading. We also thank Jilai Zheng, Zhongpai Gao, and Yonglin Zhang for the discussion. This research is supported by the French National Research Agency through ANR CLARA (ANR-18-CE33-0004) and financed by the French Conseil R\'egional de Bourgogne-Franche-Comt\'e.
{\small
\bibliographystyle{ieee_fullname}
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ELIS Catalogue
ELIS Quicklinks
ELIS Getting Answers Gateway
ELIS Information Sources Gateway
NZ's International Trade - Q & A
New Zealand's Trade History
ELIS Archives
TraLIS blog
Other Trade Libraries & Information Services
Country Quizzes - the Answers
Significant Dates in New Zealand's Trade History
This is a list of significant dates for New Zealand's international trade. They are significant for a variety of reasons and some people may disagree with this choice. If you would like to suggest additional dates with your reasons for choosing them please email: info@export.ac.nz
2010 (March) New Zealand joins negotiations for a broadened free trade agreement based on the existing Trans-Pacific Strategic Economic Partnership Agreement or P4 which would include the United States, now a significant market for New Zealand products.
2008 (7 April) China-New Zealand Free Trade Agreement signed in Beijing. New Zealand is the first developed country to sign such a deal with China. It entered into force on 1 October 2008.
2004 (29 February) Sir Peter Jackson receives an Oscar for his direction of The Lord of the Rings: The Return of the King. This cements the importance of New Zealand's creative industries as part of our international trade.
2001 (October) Fonterra, New Zealand's largest company was launched. It has become the world's leading dairy exporter.
1999 (1 September) Mike Moore, former New Zealand Prime Minister, took up the position of Director-General of the World Trade Organization. His term of office ended in 2002 and currently he is New Zealand's Ambassador to the United States.
1995 (1 January) The World Trade Organization (WTO) officially commenced, replacing the General Agreement on Tariffs and Trade (GATT), which started in 1948 (see 1947 below). New Zealand was a founding member.
1983 (1 January) The Closer Economic Relations (CER) Agreement between New Zealand and Australia came into effect. The actual treaty was signed in Canberra on 28 March 1983 but then Prime Minister Robert Muldoon had earlier signed a "Heads of Agreement" on 14 December 1982 that allowed the basic provisions of the agreement to take effect from 1 January 1983. This was New Zealand's first free trade agreement.
1973 (1 January) Britain, formerly New Zealand's most important export market, joins the European Economic Community (EEC) later to become the EU. As a result New Zealand has to find new markets for its exports.
1970 Growth of sunrise industries and exports: horticulture (including kiwifruit), fish and wine.
1953 First shipment of meat to Japan.
1947 (30 October) GATT (General Agreement on Tariffs and Trade) signed in Geneva. New Zealand was one of the original contracting parties.
1940 Exports to the United Kingdom peak. 88% of New Zealand's trade by value went to the UK.
1932 (10 July–20 August) The Ottawa Agreements: a series of trade agreements between Britain and its Dominions including New Zealand were signed. It introduced a system of Imperial Preference, under which agricultural products from the Dominions were allowed to enter Britain free of duty. In return, New Zealand and the other Dominions gave preferential treatment to manufactured goods imported from Britain.
1882 (15 February) First shipment of frozen meat left for the United Kingdom from Port Chalmers, on the sailing vessel Dunedin.
1853 Official trade statistics compiled for the first time by the Government situated in Auckland.
1830 (January – August) New Zealand exported 500 tons of flax, 69,000 pounds of salt, as well as timber, potatoes, maize, seal skins, whale oil and pigs to New South Wales, Australia. Much of the agricultural produce was grown by Māori entrepreneurs. From Australia, New Zealand imported 7000 bricks, beer, flour, bread, as well as cutlasses, gunpowder and muskets.
1820s Trade in flax began with Australia with the product being worked and traded by Māori from stations on the coasts of Northland, Waikato, Taranaki, Coromandel, Bay of Plenty, the East Coast, Southland, both sides of Cook Strait and Banks Peninsula. The flax trade was a generator of early growth but peaked in 1831.
1794 New Zealand's export trade began when the British Royal Navy ship 'Fancy' took 200 kauri trees for spars from Doubtless Bay in Northland and the Coromandel Coast in 1794.
Selected Resources:
Callaghan, Sir Paul (2011) From where I sit (Part 1). NZ manufacturer v.2 no.5 (July) p.12
King, Michael (2003) The Penguin history of New Zealand. Auckland: Penguin Books.
McKinnon, Malcolm (Ed.) (1997) Bateman New Zealand historical atlas | Ko Papatuanuku e Takoto Nei. Wellington: David Bateman in association with Historical branch, Dept. of Internal Affairs.
McLintock, A. H. (Ed.) (1966) An encyclopaedia of New Zealand. Wellington: Govt.Printer. 3 v.
If you have found this information useful and would like to copy it all, here is a pdf version which may be freely copied. NZ Trade history sig dates enl..pdf(318.89 KB)
Page last updated 25 August 2011
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\section{Results}
\subsection{Dissipation mechanisms and synchronization}
We consider generic networks of $N$ nonresonant, coupled
quantum harmonic oscillators, given by the Hamiltonian
\begin{equation}\label{HS}
H_S
= \frac{1}{2} \left( \bf{p}^T {\bf{p}} + {\bf{q}}^T \mathcal{H} {\bf{q}} \right)
\end{equation}
where ${\bf{q}}^T = (q_1, ..., q_N)$ is the vector of canonical position operators and ${\bf{p}}$
are momenta, satisfying $[q_j,p_j]= i$
(we take $\hbar=1$ throughout the paper), and
$\mathcal{H}_{m,n}=\omega_m^2 \delta_{mn} +
\lambda_{mn}(1-\delta_{mn})$ is the matrix containing the
topological properties of the network (frequencies $\omega_m$ and couplings $\lambda_{mn}$).
The eigenmodes of the system $\bf{Q}$ result from diagonalization of
this Hamiltonian through the transformation matrix $\mathcal{F}$.
\begin{figure}
\includegraphics[width=8cm]{fig_1.eps}
\caption{
(A) Network of oscillators (represented by the network nodes) dissipating into separate baths (SB,
represented by the gray circles surrounding the nodes).
Links, representing couplings, have different strengths (lines thickness) and nodes have different natural frequencies (corresponding to
different colors as given in the color bar). (B) Network of oscillators dissipating into a common bath (CB). (C)
Network of oscillators with dissipation restricted to one node, local bath (LB).
\label{fig_1}}
\end{figure}
Any realistic model needs to include also environment effects \cite{Weiss,Schloss,gardiner} and,
depending on system and bath correlations lengths, different forms of dissipation can be envisaged for
an extended network (see Methods). All units can dissipate into separate identical baths (SB),
Fig.\ref{fig_1}A, as cavity optical modes \cite{Weiss,gardiner}. Otherwise, if the coherence length of
the environment is larger than the size of the system (here given by the spatial extension occupied by
the oscillators network in Eq.\eqref{HS}), all the nodes feel a 'similar' dissipation. This
common bath (CB), Fig.\ref{fig_1}B, is known to create decoherence-free subspaces \cite{dfs,Viola}
and asymptotic entanglement
\cite{klesse,paz-roncaglia,liu,galve2010}. A third, limiting, case (LB) in which a specific oscillator
$d$ dissipates much faster than any other node (Fig.\ref{fig_1}B) is also considered (local bath).
One of the key insights of our work comes from noting that the coupling of real oscillators to the bath (taken here to be equal, $\gamma$) differs from
those of eigenmodes. The latter are found to be
$\gamma\kappa_m$ (with $\kappa_m^{CB}=\sum_n\mathcal{F}_{nm}$, $\kappa_m^{SB}=1$ and $\kappa_m^{LB}=\mathcal{F}_{dm}$) meaning that, except the SB situation, the eigenmodes have
different decay rates. Then for CB and LB only the least dissipative eigenmode will survive to thermalization, thus governing the motion of all oscillators overlapping with it. It is then
useful identifying the less dissipating normal mode with
smallest {\it effective coupling}, $\kappa_\sigma$, and also the
following one, $\kappa_\eta$, such that $|\kappa_\sigma|\le
|\kappa_\eta|$. Further, in the case of an Ohmic bath with cut-off-frequency larger than
the frequencies of the system, the normal-mode
damping rates simplify to the form $ \Gamma_{i} = \gamma ~
\kappa_i^2$
\subsection{Conditions for synchronization in a network}
Knowledge of the normal modes of a complex network and of their
dissipation rates (or effective couplings) allows to fully
characterize a large variety of phenomena. Indeed this is a
simple but powerful approach, even if diagonalization of the
problem needs to be performed numerically except in a few
(highly symmetric) configurations. By the diagonalization
matrix $\mathcal{F}$ and system-bath interaction Hamiltonian we
obtain the conditions to have a dominating mode during a
transient. This mode dissipating most slowly,
$|\kappa_\sigma|<|\kappa_j|$ $\forall j\neq\sigma$, is found
either for CB or LB. Even more important, it is possible to
identify normal modes completely protected against dissipation,
so that some network's nodes do not thermalize. Indeed, a
normal mode $\sigma$ is protected against decoherence if
$\kappa_\sigma=0$. For a pair of oscillators interacting with a
CB, this condition is accomplished only in the trivial case of
identical frequencies \cite{paz-roncaglia,galve2010} but this
is not the case when more than two nodes are considered. We
find that asymptotic synchronized quantum states can then be
observed even in random networks where all nodes have different
natural frequencies.
Full characterization of the quantum state evolution of the
network comes from moments of all orders of the oscillator
operators ${{q}_j}$ and ${{p}_j}$ \cite{gardiner}.
For SB, average positions (and momenta) are
characterized by irregular oscillations before
thermalization (Fig. \ref{fig_2}A). On the other hand, for
dissipation in CB and after a transient, regular phase locked
oscillations can arise, as shown in Fig. \ref{fig_2}B.
Synchronization between detuned nodes can be found during a
rather long and slow relaxation, like in the case of
just one pair \cite{PRAsync}. Further, the oscillations can
remain robust even asymptotically if the condition
$\kappa_\sigma=0$ is satisfied.
\begin{figure}
\includegraphics[width=7cm]{fig_2.eps}
\caption{
First order moments for initial conditions $-\langle q_1\rangle=\langle q_3\rangle=1.0$, $\langle q_2\rangle=0.0$, and vanishing
momenta in the case of an open chain of three oscillators with $\omega_1=1.2~\omega_2$, $\omega_3 = 1.8 ~\omega_2$,
non-vanishing couplings $\lambda_{12}=\lambda_{23}=0.4~\omega_2^2$, temperature $T=10~ \omega_2$
(Boltzmann constant taken to be unity), $\gamma= 0.07~ \omega_2^2$, bath cutoff $50~\omega_2$, for SB (A) and
for CB (B). Time is scaled in units of the inverse of the reference frequency $\omega_2$.
\label{fig_2}}
\end{figure}
Beyond the classical limit given by average positions and momenta, let us
now consider the full quantum dynamics stemming from the
evolution of higher moments (see SI). At the microscopic level,
quantum fluctuations also oscillate in time (even for initial
vacuum states for which first order moments vanish at any time).
This collective periodic motion is
associated to a slow energy decay and witnesses the presence of
robust quantum correlations against decoherence \cite{Schloss}.
Our approach points to a wide range of appealing possibilities
in quantum networks. In the following we show how a whole
random network (or a part of it) can be brought to a
synchronized state retaining quantum correlations via local
tuning of just one of the nodes, or how two external
oscillators can be linked to a random network leading to their
entanglement and locked oscillations.
\subsection{Collective synchronization by tuning one oscillator}
Let us consider an Erd\"os-R\'enyi random and dissipative network
\cite{Arenas} of oscillators with different node frequencies,
links and weights (Fig. \ref{fig_1}) focusing on the
relaxation dynamics of energy and quantum correlations. The
node dynamics is mostly incoherent and even if initializing the
network in a non-classical state, quantum correlations
generally disappear due to decoherence \cite{Schloss}.
Independently on the form of the network, for dissipation in
SB, all nodes thermalize on a time scale $\gamma^{-1}$
(see Eq. \eqref{HISB} and Methods). As anticipated
before, this is not the case in the presence of a dissipation
acting not-uniformly within the network.
\subsubsection{Common dissipation bath}
In presence of CB, an arbitrary network of $N$ nodes can reach
a synchronized state before thermalization if there is a
weakest effective coupling $\kappa_\sigma$. As a matter of fact
just by tuning one of the node frequencies, $\omega_v$, even
maintaining fixed the rest of the network frequencies
$\{\omega_{l\neq v}\}$ and its topology ($\lambda_{ij}$
couplings) it is possible to decrease the weakest coupling
$\kappa_\sigma$. This means that an extra oscillator of
properly selected frequency $\{\omega_{l\neq v}\}$ (like a
synchronizer) can be added to a random network, even if weakly
coupled, and it will lead to a collective synchronization of
the whole system at some frequency ($\Omega_\sigma$), generally
different from $\omega_v$.
Fig. \ref{fig_3} displays the
average global synchronization and quantum correlations
established in the network. Synchronization arises after a
transient across the whole network by tuning one of the
frequencies $\omega_v$ to a particular value $\bar\omega_v$,
while it is not present when moving a few percent away from
this value. Equivalently one could have tuned one of the couplings
$\lambda_{vv'}$.
In the following we consider separately the case in
which $\kappa_\sigma$ is significantly smaller than the other
effective couplings and the case in which it vanishes.
Conditions for global synchronization follow from small ratio
between the damping rates of the two slowest normal modes
$R=\kappa_\sigma/\kappa_\eta\rightarrow 0$. Interestingly, this
is a necessary but not sufficient condition for $collective$
synchronization. This is due to the fact that the presence of a
slowly dissipating normal mode into the system needs to be
accompanied by a significant overlap between this mode
($Q_\sigma$), or virtual oscillator, and all the real ones
($q_1, ...,q_N$). An analytical estimation of the
synchronization time is found taking into account both the
importance (overlap with individual oscillator) and decay of
few normal modes in the system. The time for oscillator $j$
to start oscillating at the less damped frequency
$\Omega_\sigma$ reads:
\begin{equation}\label{time_sync}
t^{(j)} \equiv \max_{\{ k \neq \sigma \}} 2
\frac{\log{\mathcal{F}_{j k}}-\log{\mathcal{F}_{j \sigma}}}
{\Gamma_{k} - \Gamma_{\sigma}} \ ,
\end{equation}
maximizing over all modes $k$ different from the
slowest one $\sigma$ (see SI). Collective synchronization time
corresponds to $t_{sync} = \max_{\{j\}} \{ t^{(j)}\}$, i.e.
when even the last oscillator joins the synchronous dynamics
dominated by the less damped mode. Then phase-locking in the
evolution of all oscillators, namely in their (all order)
moments, can arise before thermalization, when there is
significant separation between largest time decays
$\Gamma_{\eta},\Gamma_{\sigma}$, and overlap between slowest
normal modes and each system node. Global network
synchronization (see Methods) obtained from the
full dynamical evolution and the estimated synchronization time
$t_{sync}$ are in good agreement, as seen in Fig.
\ref{fig_3}A.
For the same network, the ratio $R$, the collective synchronization $\mathcal{S}$ and mean discord $\langle\delta\rangle$ at long times
can be seen in Fig. S1 (see SI).
\begin{figure}
\begin{center}
\includegraphics[width=8cm]{fig_3.eps}
\end{center}
\caption{(A) Time evolution of synchronization $\mathcal{S}$,
and (B) quantum correlations quantified by the discord $\langle\delta\rangle\times 10^{3}$ , when varying one
node frequency $\omega_v$. Results are shown for a random network (connection probability
$p=0.6$) of $10$ oscillators. Frequencies of nodes are sampled from a uniform distribution
from $0.9 \omega_0$ to $1.2\omega_0$ and couplings from a
Gaussian distribution around $-0.1\omega_0^2$ with standard deviation $0.05 \omega_0^2$.
Environment parameters (here and in the following figures) are
$\gamma = 0.01\omega_0^2$, $T = 10 \omega_0$ and cut-off frequency $\Lambda=50 \omega_0$ (see Methods).
Time units are chosen so
that $\omega_0=1$. Collective synchronization $\mathcal{S}$ and (averaged and filtered)
discord $\delta$ (see Methods) are obtained considering all oscillator pairs of the network.
Dashed line identifies the frequency $\bar\omega_v$
for which $\kappa_\sigma=0$. Continuous line in (A) corresponds to the estimated synchronization time
$t_{sync}$.
\label{fig_3}}
\end{figure}
We now look at the quantumness of the state in presence of
collective synchronization. Generally decoherence is
independent on the specific features such as the oscillation
frequency in a system \cite{CaldeiraLeggett}. Still,
synchronization is a consequence of a reduced dissipation in
some system mode and indeed witnesses the robustness of quantum
correlations, as evident form the average discord $\langle\delta\rangle$ in
the network represented in Fig.\ref{fig_3}B. After a transient
dynamics in which the couplings in the network create quantum
correlations \cite{Plenio}, even when starting from separable states,
discord does
actually decay to small values for $\omega_v$ different from
$\bar\omega_v$ (non-synchronized network) while it maintains
large values for the case of a properly tuned node
($\omega_v\sim\bar\omega_v$).
The case $\omega_v=\bar\omega_v$, leading to $ \kappa_\sigma =
0$, needs special attention.
After a transient
all the nodes will oscillate at a locked common frequency, the
one of the undamped normal mode $\Omega_\sigma$, which we call
a {\sl frozen} mode. As before (Eq.\eqref{time_sync}), the
possibility to synchronize the whole network also requires a
second condition, namely that the undamped mode involves all
the network nodes. (The case in which the latter condition
applies only to some nodes is discussed below.)
When both the conditions
\begin{equation}\label{eq_CB_sync}
\kappa_\sigma = \sum_{k=1}^N \mathcal{F}_{k \sigma}= 0 \text{ ,
and } \mathcal{F}_{k \sigma}\neq 0 \text{ } \forall k
\end{equation}
are met, there is a frozen normal mode linking all oscillators.
This leads to collective synchronization in the whole network and
allows for mutual information and quantum correlations
remaining strong even asymptotically, being orders of magnitude
larger than for the fully thermalized state, when
synchronization is not present (Fig.\ref{fig_3}). The
undamped mode gives actually rise to a decoherence-free
dynamics for the whole system of oscillators where quantum
correlations and mutual information survive.
The phenomena above are found for nodes dissipating at equal
rates into a CB, while in the presence of $N$
independent environments (SB) all oscillators thermalize
incoherently, synchronization is not found, and decoherence
times for all oscillators are of the same order. As a final
observation
we mention the special case in which
the center of mass of the system is one of the
normal modes; then there will be a large decoherence-free
subspace (corresponding to the other $N-1$
modes) but no synchronization will appear for a CB.
\subsubsection{Local dissipation bath}
Common and separate baths correspond to two extreme situations
in which all oscillators have equivalent interactions with the
environment(s). We now consider the case of a local bath, as a
limit case in which one oscillator is dissipating stronger,
Fig.\ref{fig_1}C.
A frozen normal mode $\sigma$ must not overlap with the
dissipative oscillator (labeled by $d$) while involving all the
other nodes ($ \mathcal{F}_{i\sigma} \neq 0$
$\forall~ i \neq d$). Then,
synchronization of the whole network (except for the
dissipative oscillator) arises.
This occurs when
\begin{equation}\label{eq_LB_sync}
\mathcal{F}_{d \sigma} = 0 \text{ , with } \mathcal{F}_{d j} \neq 0
\text{ }\forall~ j \neq \sigma
\end{equation}
meaning that the undamped mode $ \sigma$ involves a cluster of
oscillators not including the lossy one.
We find synchronization and
robust quantum effects across the network as
for CB, with the difference that for LB the dissipating node is
now excluded (further details are discussed in SI).
\subsection{Synchronization of linear motifs}
The possibility to synchronize a
whole network, in presence of different dissipation mechanisms,
just by tuning one local parameter opens-up the
perspective of control that can be explored considering the
dynamical variation of a control-node frequency. In particular
we find similar qualitative results both for random networks
and for disordered lattices consisting of regular networks
with inhomogeneous frequencies and couplings, being the latter largely studied in ultracold
atomic gases \cite{lew}. Local tuning to collective
synchronization is not only a general feature of different kind
of networks but can also be established in motifs within the
network. As we show in the following, the system can be tuned
to a partial synchronization, involving some nodes of a network
independently of the rest of it. Indeed, even if the whole
system is coupled to a CB, we can identify the
conditions for having a synchronized cluster, like the 3-node
linear motif in Fig. \ref{figure4}. Two non-directly linked
nodes $a$ and $b$ of the motif are then asymptotically
synchronized through another one, here $c$, and this leads to
a common oscillation dynamics along the whole motif $a$-$c$-$b$. The
condition for synchronization of a cluster, namely its
dependence on a frozen normal mode, reads
\begin{equation}\label{eq_wire_k0}
\frac{\lambda_{a c}}{\Omega_\sigma^2 - \omega_a^2} + \frac{\lambda_{b c}}{\Omega_\sigma^2 - \omega_b^2} = -1
\end{equation}
with $\Omega_\sigma$ frequency of the frozen mode (see details in SI).
\begin{figure}
\includegraphics[width=8cm]{fig_4.eps}
\caption{(A) Synchronization factors $\mathcal{S}_C$ and (B) average
discord $\delta_C\times 10^2$ evaluated for linear 3-node motifs
(hence the subindex $\mathcal{C}$) in a random network (connection probability $p=0.6$) of
$15$ oscillators (shown in C). A tuned non-dissipative motif $\mathcal{C}_1$ composed by the three nodes
$(a-c-b)$ is compared with another equivalent non-tuned motif $\mathcal{C}_2$ composed by nodes
$(d-f-e)$. Frequencies in the network are sampled from a uniform distribution from $\omega_0$ to $1.8
\omega_0$, and couplings with a Gaussian distribution around $-0.1\omega_0^2$ with standard deviation $0.05
\omega_0^2$. In order to avoid dissipation in the $(a-c-b)$
motif we have set $\omega_c = 1.51~ \omega_0$, being $\lambda_{a c}=-0.09~ \omega_0^2$ and
$\lambda_{b c} = - 0.11~\omega_0^2$. Time units such that $\omega_0=1$.\label{figure4}}
\end{figure}
This case is an example of the general result stating that
given any network, a part of it (in our case a linear motif,
$\mathcal{C}_1$) can be synchronized by tuning one of its
components, for instance a frequency or coupling of the motif.
A key point is that this is independent of the frequencies and
links of the rest of the network, provided the motif is
properly embedded in the network. The links between
$\mathcal{C}_1$ and the rest of the network should satisfy
\begin{equation}\label{eq_wire_coupl}
\left( \frac{\lambda_{a c}}{\Omega_s^2 - \omega_a^2} \right) \lambda_{a j} +
\left( \frac{\lambda_{b c}}{\Omega_s^2 - \omega_b^2} \right) \lambda_{b j}+
\lambda_{c j} = 0 \ ,\ \forall j \ .
\end{equation}
This is equivalent to saying that a synchronized motif with
robust quantum correlations can preserve these features when
linked to an $arbitrary$ network, if some constraints on the
reciprocal links are satisfied. For instance, each node of
the synchronized motif needs to share with the rest of the
network more than one link. In Fig.
\ref{figure4} we compare the behavior of two linear motifs of
a large network, where a first motif $\mathcal{C}_1$ is
synchronized, satisfying
Eqs.\eqref{eq_wire_k0}-\eqref{eq_wire_coupl} while the second
one $\mathcal{C}_2$ is not. After a transient a frozen mode
tames the dynamics of $\mathcal{C}_1$, which then shows a
synchronous evolution and robust correlations. It can also be
shown that quantum purity and energy reach higher values of
a stationary non-thermal state. This is
compared with the non-synchronized motif $\mathcal{C}_2$ whose
dynamics quickly relaxes to a thermal state. The case of a
three oscillator chain is an example showing the possibility
to tune synchronization and quantum effects in a motif within
the network when the proper link conditions are satisfied.
\subsection{Entangling two oscillators through a network}
The same technique discussed in the previous section can be
applied to the case in which we aim to synchronize few, even if
not directly connected, elements of a network. But this does
not mean that any set of nodes can be synchronized
asymptotically. In fact, we find that for a CB we can only
synchronize two different and not directly linked
($\lambda_{ab}=0$) oscillators if we synchronize with them also
other intermediate linked elements (like in the linear motif
example, Fig. \ref{figure4}) or when these two oscillators are
identical, like we discuss in the present section.
\begin{figure}
\includegraphics[width=8cm]{fig_5.eps}%
\caption{ (A) Energy evolution and (B) entanglement (logarithmic negativity) between two nodes with
identical frequency $\omega_0$ (we call these nodes $a$ and $b$ and are plotted
in red in the network displayed in panel (C)). The network is a random one (connection probability
$p=0.6$ of 15 oscillators and same frequency and couplings distribution as in Fig. \ref{figure4}. We
compare the situations in which the couplings from the red nodes to the rest of the network (they are
directly connected to other nodes called $c$ and $d$) are properly balanced in order to avoid dissipation
$(\lambda_{a c} = \lambda_{b c}= -0.15 \omega_0^2$ and $\lambda_{a d} = \lambda_{b d}= -0.12 \omega_0^2)$
with the case when this balance is perturbed $(\lambda_{a c} + 0.04\omega_0^2$ and $\lambda_{a d} + 0.04
\omega_0^2)$ .The third line in panel (B) shows the entanglement between other two arbitrary oscillators
in the situation in which $a$ and $b$ are balanced. Time units such that $\omega_0=1$
\label{figure5}}
\end{figure}
We consider the case of two identical oscillators (i.e. with
$\omega_a=\omega_b$) prepared in a separable state, with some
local squeezing. They are not directly coupled
($\lambda_{ab}=0$) but are connected through an arbitrary
network. In general they will dissipate reaching the thermal
state, but with the proper conditions we find an
important result: because their frequencies are identical it is
possible to construct a frozen normal mode involving only these
two nodes, given by $ Q_\sigma = \mathcal{F}_{a \sigma} ~q_a +
\mathcal{F}_{b \sigma} ~q_b, $ with $ \mathcal{F}_{a
\sigma},\mathcal{F}_{b \sigma} \neq 0$ and this can be
obtained, for instance, by properly attaching them to the
network. In other words, by tuning their couplings to the
network it is possible to have both oscillators relaxing onto
a frozen mode, so that they will be synchronized and will keep
a higher energy than otherwise. Most importantly, in this case
entanglement can actually be generated between oscillators
initially in a separable state and remains high asymptotically.
In order to entangle the oscillators, their coupling to the rest of the network needs to
fulfill the condition
\begin{equation}\label{eq_lobes}
\sum_{k=a,b} \mathcal{F}_{k \sigma} \lambda_{k j} = 0,
\end{equation}
(similar to Eq. \eqref{eq_wire_coupl}), achieved by proper
tuning of coupling strengths of the active links ($j$) with the
rest of the network $\lambda_{a j},\lambda_{b j}$. In Fig.
\ref{figure5}A and B we show the evolution of energy and
entanglement of the oscillators $a$ and $b$ when linked to a
random network. As we see in Fig. \ref{figure5}C there is not
direct link between $a$ and $b$ ($\lambda_{ab}=0$) and the
whole system dissipates in a common environment. The case where
the oscillators $a$ and $b$ are coupled to the network
following the prescription \eqref{eq_lobes} is compared to
another case in which their links are not properly balanced (we
slightly change the coupling strengths). Both
energy and entanglement are shown to be
sensitive to the structure of the reciprocal links and the
possibility to actually bring the added nodes into an entangled
state that will survive asymptotically is guaranteed by Eq.
\eqref{eq_lobes}. The importance of this result is twofold: in
terms of applications it shows that it is possible to
dynamically generate entanglement between two non-linked nodes
embedded in a random network by tuning their connections to it,
and on the other hand it enlarges the scenario for asymptotic
entanglement generation through the environment. It is known
that large entanglement can be generated between far
oscillators during a transient due to a sudden-switch
\cite{Plenio} or through parametric driving \cite{Galve}. On
the other hand, a common environment leads to
entanglement between a pair of spins \cite{dfs}
or oscillators \cite{paz-roncaglia}.
\section{Discussion}
Our results on synchronization in dissipative harmonic networks and its
optimization give a flavor of all the possibilities that show up once the
mechanism behind the phenomenon is understood. At difference from widely
considered self-sustained non-linear oscillators, here we focus in a linear
system showing how synchronization can emerge after a transient for
dissipation processes introducing inhomogeneous decay rates among the systems
normal modes. A synchronous oscillation is predicted, for the first time,
either in a long transient during relaxation to the equilibrium state or in a
stationary non-thermal state. We considered the most significant examples of
correlation length of the bath larger than the system size (CB) and of a node
of the network more strongly exposed to dissipation (LB), displaying
synchronous dynamics. On the other hand, for independent environments (SB) on
different nodes the resulting dynamics remains incoherent even when increasing
the strength of the reciprocal couplings in the network.
The presence of synchronization in the whole or a part of the network witnesses
the survival of quantum correlations and entanglement between the involved
nodes. This connection between a coherent oscillation in the network and its
non-classical state is a powerful result in the context of complex quantum
systems, considering the abundance of this phenomenon. Indeed, the condition
underlying synchronization provides a strategy to protect a system subspace
from decoherence. Our discussion and methodological approach are general, but
we show specific consequences of our analysis, such as global or partial
synchronization in a network through local tuning in one node (synchronizer) as
well as the possibility of connecting two nodes (not linked between them) to a
network and synchronize and entangle them, even starting from separable states.
Even if the reported results refer to random networks, our analysis applies to
generic ones, also including homogeneous and disordered lattices and do not
require all-to-all connectivity.
In some sense, tuning part of a network so that the rest of it
reaches a synchronous, highly correlated state can be seen as a
kind of reservoir engineering, where here the tuned part of the
network would be a part of the reservoir. This is to be
compared with recent proposals of dissipative engineering for
quantum information, where special actions are performed
to target a desired non-classical state
\cite{Diehl,Barreiro2010,cirac2009,blatt2011}.
In the context of quantum communications and considering recent results
on quantum Internet \cite{Kimble,Ritter},
our study can offer some insight
in designing a network with coherent information transport properties.
Furthermore implications of our approach can be explored in the context of
efficient transport in biological systems
\cite{Panitchayangkoon,Engel} .
An interesting methodological
connection is also with transport through (classical) random networks
\cite{transport}. On the other hand, our
analysis, when restricted to the classical limit, also gives
some insight about vibrations in an engineering context,
providing the conditions for
undamped normal modes and their effect \cite{Rayleigh,Engineering}.
\section{Methods}
\subsection{Interaction with the environment}
The Hamiltonian of the system $H_S$ as defined in Eq. (\ref{HS})
is diagonalized in the basis of its eigenmodes $\bf{Q}=\mathcal{F}^T\bf{q}$ yielding
$\Omega=\mathcal{F}^T\mathcal{H}\mathcal{F}$.
In a microscopic description with independent oscillators modeling the
environment, the system-bath interaction Hamiltonian for SB takes the form
\begin{equation}\label{HISB}
H_I^{SB} = - \gamma \sum_{m=1}^{N} q_m B^{(m)} \text{ , with }
B^{(m)}=\sum_{\alpha=1}^{\infty} \lambda_{\alpha} X_{\alpha}^{(m)},
\end{equation}
being $\gamma$ the system-bath coupling strength
(explicitly shown for the ease of understanding),
$X_{\alpha}^{(m)}$ the position operators for each
environment oscillator $\alpha$ (representing for instance a
vibrational mode, or an optical one, etc...) of the bath $B^{(m)}$ in
which the network unit $(m)$ is dissipating.
As explained in the main text, this situation occurs when the coherence length
of the environment is smaller than the spatial extension of the system. Thus
each oscillator dissipates to its own heat bath. In the opposite case, a common bath
is seen by all oscillators, resulting in an interaction Hamiltonian
\begin{equation}\label{HICB}
H_I^{CB} = - \gamma \sum_{m=1}^{N} q_m B,
\end{equation}
and actually involving only the average position (here the center
of mass) of the network, Fig. \ref{fig_1}B. Notice that in the eigenmodes basis
\begin{equation}\label{HICB_nm}
H_I^{CB} = - \gamma \sum_m \kappa_m Q_m B \text{ , with }\kappa_m = \sum_n \mathcal{F}_{n m}.
\end{equation}
The \textit{effective couplings} $\kappa_m$ are different and determined by
characteristics of the network such as topology, coupling
strengths, and frequencies, as encoded in the diagonalization matrix $\mathcal{F}$.
This is in stark contrast to the case of
identical SB \eqref{HISB} where all normal modes have equal effective
couplings to the baths (to see this, notice that we can transform the bath operators $X_\alpha^{(m)}$
to a new basis which exactly cancels the transformation $\mathcal{F}$; these new `oscillators' can be shown
to have the same statistical properties as the others, thus resulting in equivalent heat baths).
Finally, the case of a given node $d$ dissipating much faster than any other is modeled by
\begin{equation}\label{HILB}
H_I^{LB} = - \gamma q_d B.
\end{equation}
This local bath (LB) situation does also lead to non-uniform
environment interaction in some of the normal modes with
effective couplings ${\kappa_m}$:
\begin{equation}\label{HILB2}
H_I^{LB} = - \gamma \sum_m {\kappa_m} Q_m B \text{ , with }
{\kappa_m} = \mathcal{F}_{d m}.
\end{equation}
All the mentioned situations of
separate, common and local bath can be described by different
master equations \cite{Weiss} for the evolution of the network
state.
\subsection{Master equation}
A standard procedure allows to obtain from the total
Hamiltonian of system, bath and reciprocal interaction the
evolution of the reduced density matrix for the state of the
system, in our case a network of different oscillators. After a
(post-trace) rotating wave approximation, the master equations in the weak coupling limit
for separate, common, and local baths are in the Lindblad form,
guarantying a well-behaved system dynamics. These
equations (given in SI) are obtained by generalization of the
problem of a pair of coupled oscillators \cite{PRAsync}. For
the purpose of our analysis it is interesting to consider the
master equation in the normal-mode basis $([Q_k,P_l]=i\delta_{k
l})$.
\begin{eqnarray}
&&\frac{d \rho(t)}{dt}=-i[H_S,{\rho}(t)]- \nonumber\\
&-& \frac{1}{4} \sum_{n} i \Gamma_{n} \left( [Q_n,\{P_n,\rho(t)\}] -[P_n,\{Q_n,\rho(t)\}] \right) + \nonumber\\
&+& D_{n} \left( [Q_n,[Q_n,\rho(t)]] - \frac{1}{\Omega_{n}^2} [P_n,[P_n,\rho(t)]] \right)
\end{eqnarray}
where $\Omega_n$ are the normal-mode frequencies of $H_S$ and
the damping and diffusion coefficients, for an Ohmic bath
with spectral density
$J(\omega) = (2\gamma/\pi)\omega \Theta(\Lambda - \omega)$,
are, at temperature $T$ far away from the frequency cutoff $\Lambda$:
$\Gamma_{n}= \kappa_n^2 \gamma$ and $D_{n} = \kappa_n^2 \gamma
\Omega_n \coth(\frac{\Omega_n}{2 T}) $, being $\kappa_n$ the
effective couplings (see Eqs. \eqref{HICB_nm} and
\eqref{HILB2}). Boltzmann constant is taken to be unity. With
the appropriate definition of the couplings this equation is
valid both for common and local bath while for CB
we have: $\Gamma_{n}= \gamma$ and $D_{n} = \gamma \Omega_n
\coth(\frac{\Omega_n}{2 T}) $ i.e. we obtain the same damping
coefficient for all normal modes. The main differences in the
models of dissipation here proposed reside in these expressions
for the master-equation coefficients that will produce
different friction terms in the equations of motion determining
collective or individuals behaviors (See SI). We stress that
the choice of this master-equation representation is not
critical for our main conclusions, as also shown in
\cite{PRAsync}.
\subsection{Synchronization factor}
Synchronization between two time series $f(t)$ and $g(t)$ can
be characterized by a commonly used indicator, namely
$C_{f,g}(t,\Delta t)=\overline{ \delta f \delta
g}/\sqrt{\overline{\delta f^2} \ \overline{\delta g^2} }$ where
the bar stands for a time average $\overline{f}=\frac{1}{\Delta
t}\int_{t}^{t+\Delta t}dt'f(t')$ with time window $\Delta t$
and $\delta f=f-\overline{ f}$. For `similar' and in phase
(anti-phase) evolutions $C\sim 1$ ($-1$), while it tends to
vanish otherwise. As a figure of merit for global
synchronization in the whole network we look at the product
(neglecting the sign) of the indicator for all pairs of
oscillators in the system.
When the time series
correspond to positions second moments we have
$\mathcal{S}=\Pi_{i<j}|C_{\langle
q_i^2\rangle\langle q_j^2\rangle}|$. This collective
synchronization factor $\mathcal{S}$ can reach unit value
only in presence of synchronous dynamics between all the pairs
of oscillators in the network.
\subsection{Mutual information, discord and entanglement}
The total amount of correlations present in a bipartite system can be measured by the mutual
information $\mathcal{I}=S_A+S_B-S_{AB}$ with $S_i$ the entropy
of the reduced system $i=A,B$ and $S_{AB}$ the total entropy.
It can be decomposed in a purely classical part
$\mathcal{J}_{A:B}=\min [S_A-S_{A|E_j^B}]$, with
$S_{A|E_j^B}=\sum_ip_iS(\varrho_{A|E_i^B})$, $p_i={\rm
Tr}_{AB}(E_i^B\varrho)$ and $\varrho_{A|E_i^B}=
E_i^B\varrho/{p_i} $
(where $i$ labels the possible outcomes of a general measurement
with operators $E_i^B$ acting on $B$
occurring with
probability $p_i$ and resulting in a density matrix $\varrho_{A|E_i^B}$),
and a quantum part which is just the difference
$\delta_{A:B}=\mathcal{I}-\mathcal{J}_{A:B}$, the quantum
discord \cite{disc0,disc1,disc2}.
As a quantifier for entanglement we have
used the logarithmic negativity $E_N=\max(0,-\ln \nu_-)$, with
$\nu_-$ the smallest symplectic eigenvalue of the partially
transposed density matrix \cite{horodecki_review}.
We quantify correlations between pairs of (linked or unlinked)
nodes by applying these definitions to different pairs of oscillators in the network.
Average
quantities ($\langle .\rangle $) for all pairs in the network can
be considered to assess globally the network.
\begin{acknowledgments}
This work was partially supported by MINECO (Spain), FEDER, CSIC and Govern Balear
through projects FISICOS (FIS2007-60327), TIQS (FIS2011-23526) and JdC and JAE programs.
\end{acknowledgments}
\section*{Author contributions}
RZ and FG planned the research. GM did most calculations and numerical simulations. All authors contributed analysing and discussing results and writing the manuscript.
\section*{Additional Information}
Competing Financial Interests: None.
|
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{"url":"https:\/\/discourse.julialang.org\/t\/comparison-of-automatic-differentiation-tools-from-2016-still-accurate\/8341?page=2","text":"Comparison of automatic differentiation tools from 2016 still accurate?\n\n1 Like\n\nI can\u2019t speak to the performance issue at the moment, but why are you defining all these different functions? Just define\n\nmyfunc(x) = 2 * (x + 1) + 3x^2\n\n\nand run the autodifferentiation on that.\n\nEdit: Try to run this:\n\nfoo(x) = 2 * (x + 1) + 3x^2\nfdiff(f, x, d=0.001) = (f(x + d) - f(x)) \/ d\n\nv = 5.0\n@btime fdiff(foo, $v) @btime dualpart(foo($v + \u03b5)) # v + \u03b5 is equivalent to Dual(v, 1)\n@btime ForwardDiff.derivative(foo, $v) I\u2019m having some problems with ForwardDiff on version 0.7, but I expect some significant speedups on 0.7\/1.0 when it comes to compiling away wrapper-types, etc. In this very simple case, though, I doubt that you can expect speedups when using ForwardDiff over finite diff. Not sure exactly in what situations that should even happen. The great advantage of autodiff is accuracy with almost finitediff performance. 1 Like Actually, all the talks at Juliacon were livestreamed this year! So the videos were available immediately. Everything is already on Youtube And \u2013 they used screen-capture instead of shaky-cam for the slides, so the whole experience was much improved over previous jcons. 1 Like defining all different functions is just for clarity \u2026 the point is: doing maths with dual number is at least doubling the operations compared to that on float. e.g. 3.0 * (x + \u03b5) has two operations: 3.0 * x, and 3.0 * \u03b5. And for more complicated operations, the cost could be much higher even, consider: (x + \u03b5) * (x + \u03b5) becomes the operations: x * x, x * \u03b5, x * \u03b5, \u03b5 * \u03b5, (+) \u2026 i.e. 5 operations compared to 1 operation in x * x so, for almost all maths operations on dual numbers, the time cost is more than doubled. now, for finite differences, the time cost is simply: 2 times O(f), one for (x + delta), one for ( \/ delta) \u2026 i.e. basically constant 2 times of that of f(x). so I would say that AD by Dual is almost certainly much slower than finite differences \u2026 a solution I could imagine is \u201csymbolic dual number\u201d. For example, for the function myfunc(x) = 2 * (x + 1) + 3x^2 if we could symbolically evaluate the dual part of it: dualpart(2.0 * (x + \u03b5) + 3.0 * (x + \u03b5) ^ 2) = dualpart(2.0x + 2.0\u03b5 + 3.0 * (x^2 + 2x\u03b5 + \u03b5*\u03b5) ) = dualpart(2.0x + 2.0\u03b5 + 3.0(x^2) + (6.0 * x)\u03b5 + 0.0) = dualpart(3.0(x^2) + 2.0x + (2.0 + (6.0 * x) )\u03b5) = 2.0 + (6.0 * x) and let g(x) = 2.0 + (6.0 * x) then we could evaluate g(x) for different values of x, e.g. g(5.0), g(5.1), etc., very quickly OK, but I think it instead ended up a lot less clear. Very confusing to read through at first. In general, I recommend that you use type annotations very carefully, and only specify types when you really need them. Generic code is considered idiomatic in Julia, and is normally both clearer, shorter and more powerful. I\u2019m not prepared to go into a discussion on the relative performance of dual numbers vs finite differences. I don\u2019t know enough about it, but I don\u2019t really expect them to be faster in the simplest case. I just want to note that I don\u2019t think (x + \u03b5) * (x + \u03b5) expands to that many operations \u2013 \u03b5*\u03b5 is not calculated, for example, since it is already known to be zero. You probably just do x*x, x*\u03b5 and \u03b5*x. Quick benchmark that may not be too useful: v = 5.0 d = dual(v, 1) 0.6.3> @btime$v * $v 1.457 ns (0 allocations: 0 bytes) 0.6.3> @btime$d * $d 1.745 ns (0 allocations: 0 bytes) BTW, the big reason your ForwardDiff code is so slow, is that you wrap your value inside a vector, and then access that, instead of just using scalar math. That has a gigantic performance cost. 1 Like do you see any hope that we could do something like: gradfunc = ForwardDiff.symbolicgradient(f) i.e. generates a function rather than the numeric gradient at a specific x? the generation of gradfunc may be costly (as I imagine it would use something like \u201csymbolic dual number\u201d), but it costs only once. Afterwards, we could evaluate it very quickly. This works for a simple function, but quickly becomes enormously difficult. Imagine doing this while combining the effects of several complicated functions with loops, if-statements, special type constructs and so on! I think this may be related to the source-transformation approach to autodiff. You could try to google that. could you show me how to use ForwardDiff.gradient() passing a function that accepts a scalar as argument? I got the following error if f() accepts a scalar rather than a vector: julia> function forwarddifffunc(x) 2.0 * (x + 1.0) + 3.0 * (x * x1) end forwarddifffunc (generic function with 1 method) julia> ForwardDiff.gradient(forwarddifffunc, 5.0) ERROR: MethodError: no method matching gradient(::#forwarddifffunc, ::Float64) You may have intended to import Base.gradient Closest candidates are: gradient(::Any, ::StaticArrays.SArray) at \/Applications\/JuliaPro-0.6.3.1.app\/Contents\/Resources\/pkgs-0.6.3.1\/v0.6\/ForwardDiff\/src\/gradient.jl:42 gradient(::Any, ::StaticArrays.SArray, ::ForwardDiff.GradientConfig) at \/Applications\/JuliaPro-0.6.3.1.app\/Contents\/Resources\/pkgs-0.6.3.1\/v0.6\/ForwardDiff\/src\/gradient.jl:43 gradient(::Any, ::StaticArrays.SArray, ::ForwardDiff.GradientConfig, ::Val) at \/Applications\/JuliaPro-0.6.3.1.app\/Contents\/Resources\/pkgs-0.6.3.1\/v0.6\/ForwardDiff\/src\/gradient.jl:44 ... Stacktrace: [1] macro expansion at \/Applications\/JuliaPro-0.6.3.1.app\/Contents\/Resources\/pkgs-0.6.3.1\/v0.6\/Atom\/src\/repl.jl:118 [inlined] [2] anonymous at .\/<missing>:? This is what you\u2019re looking for, still in beta though With juliacon video at https:\/\/youtu.be\/R81pmvTP_Ik?t=9m34s 3 Likes wow amazing, thx ! If you want symbolic derivatives, there\u2019s no need to involve dual numbers at all: using XGrad xdiff(:(2 * (x + 1) + 3x^2); x=1.0) which gives quote tmp372 = 3 tmp368 = 2 tmp369 = 1 tmp370 = x + tmp369 tmp371 = tmp368 * tmp370 tmp374 = x ^ tmp368 tmp375 = tmp372 * tmp374 tmp376 = tmp371 + tmp375 dtmp376!dtmp371 = 1.0 dtmp376!dx__2 = tmp368 * dtmp376!dtmp371 dtmp376!dtmp374 = tmp372 * dtmp376!dtmp371 tmp380 = tmp368 - tmp369 tmp381 = x ^ tmp380 dtmp376!dx__1 = tmp368 * tmp381 * dtmp376!dtmp374 dtmp376!dx = dtmp376!dx__1 .+ dtmp376!dx__2 tmp385 = (tmp376, dtmp376!dx) end Code is optimized for tensors so may look a bit ugly, but it should give you pretty good performance. (I think Calculus.jl used to give beautiful expressions for scalar derivatives, but I can\u2019t see it in their README anymore). The problem with symbolic approach is that it works really badly with things like conditions, loops, recursion, and, more generally, dynamic computation graphs (e.g. XGrad requires code to be a fixed list of correct algebraic expressions). It\u2019s fine in most cases, but if you encounter a task with dynamic graph - even if it\u2019s fixed for a specific execution - you have to fall back to (more) pure AD. In (more) pure AD you have a choice of forward-mode AD, which relies on dual numbers and works well for functions R \\rightarrow R^n, and reverse-mode AD, which is usually implemented using some kind of tracked arrays or, in case of future Cassette-based solutions, function call interception, and which is designed for R^n \\rightarrow R problems. Note, that reverse-mode AD may also be fully dynamic and construct graph on each run (I think AutoGrad.jl does this) or statically compile derivatives for performance after the first run, making it closer to symbolic approach (ReverseDiff.jl and Capstan.jl do this). (Currently I explore possibility to combine and compare both approaches in a single package Yota.jl). As a bottom line: dual numbers aren\u2019t the only approach to AD 1 Like in this simple example, direct gradient by dual number maths is 2.34X time-costly compared to finite differences. using ForwardDiff AD is even worse, it\u2019s 4271.75X !!! This is a fairly ridiculous comparison - you\u2019re comparing apples to oranges here by pitting a very limited handrolled scalar AD vs. an interface that\u2019s documented to allocate because it\u2019s expected to be used with far more substantial inputs. Furthermore, you changed the target function between differentiation implementations. Here, why not use this for comparison (also remember to interpolate variables correctly when using BenchmarkTools): julia> myfunc(x) = 2.0 * (x + 1.0) + 3.0 * (x * x) myfunc (generic function with 1 method) julia> @btime ForwardDiff.derivative(myfunc,$(5.0))\n1.525 ns (0 allocations: 0 bytes)\n32.0\n\n\nAnd even if you did want to change the target function to forwarddifffunc:\n\njulia> using StaticArrays\n\n1.530 ns (0 allocations: 0 bytes)\n1-element SArray{Tuple{1},Float64,1,1}:\n32.0\n\n\nAlso note that, for scalar differentiation, AD is generally faster than finite differences (regardless of the AD implementation, as long as it\u2019s decent and in a language that supports fast scalar ops).\n\n6 Likes\n\nUse ForwardDiff.derivative, not gradient.\n\nThere\u2019s also a mistake in your function, x1 is undefined.\n\nFinally, I suggest using integer literals, since they will help you preserve input types better:\n\nfoo(x) = 2 * (x + 1) + 3x^2 # use x^2 not x * x, it's more readable.\n\n\nyeah! a lot of good stuffs!\n\nanyway, any good website\/pdf\/docs that cover a review of various AD technologies to suggest?\n\nYou can check out these links:\nhttp:\/\/www.autodiff.org\/\n\n2 Likes\n\nNumerical Optimization by Nocedal and Wright has a very nice intro chapter on forward, reverse, and mixed, and why you would use one or the other.\n\n@misc{nocedal2006numerical,\ntitle={Numerical optimization 2nd},\nauthor={Nocedal, Jorge and Wright, Stephen J},\nyear={2006},\npublisher={Springer}\n}\n\n\nYou can check out these links:\nhttp:\/\/www.autodiff.org\/ 2\n\nNumerical Optimization by Nocedal and Wright has a very nice intro chapter on forward, reverse, and mixed, and why you would use one or the other.\n\nthanks!\n\n1 Like\n\nThis turns out to be fixable, actually. The symbolic approach effectively operates on a single block of SSA-form IR, and generalising that IR to contain control flow is not too difficult. Will put up more of a writeup on this at some point.\n\ngeneralising that IR to contain control flow is not too difficult.\n\nIs it? I\u2019m curious how would you preserve looping and SSA, e.g. in:\n\nfunction foo(x)\nfor i=1:100\nx = x + 1\nend\nreturn x\nend\n\n\nYou either break SSA-form for x or unroll the loop, or make a subgraph in which x is only assigned once. Breaking SSA-form essentially makes the function non-differentiable, AFAICT. Unrolling the loop only works when the number of iterations is constant, which isn\u2019t true in general case.\n\nThe only meaningful option I found is making a subgraph, but it brings another set of questions: how to incorporate it into the main graph, how to map variables inside the subgraph to variables before and after the loop, how should derivative of a loop \/ subgraph look like, etc.\n\nAll of these made me switch to a much simpler approach and just support separately dynamic graphs with possible performance penalty and static graphs with all the optimizations, but it will be cool if you derive correct derivatives for general-purpose loops and conditions.","date":"2022-07-05 22:20:05","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.42351779341697693, \"perplexity\": 1915.7408252412945}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-27\/segments\/1656104628307.87\/warc\/CC-MAIN-20220705205356-20220705235356-00588.warc.gz\"}"}
| null | null |
; dushlan.asm
;
; Copyright (c) 2016 Peter McQuillan
;
; All Rights Reserved.
;
; Distributed under the BSD Software License (see license.txt)
;
;
;; The iNes Header
.db "NES", $1a ; iNes identifier
.db $02 ; number of PRG-Rom blocks the game has 1 = 16KB, 2 = 32KB
.db $01 ; number of CHR-Rom blocks the game has (CHR-ROM blocks are 8KB)
.db $00, $00 ; control bytes
.db $00, $00, $00, $00, $00, $00, $00, $00
;; Constants and Variables
include "ggsound.inc"
include "defines.inc"
;----------------------------------------------------------------
; variables
;----------------------------------------------------------------
.enum $0000
include "ggsound_zp.inc"
include "variables1.inc"
.ende
.enum $0400
include "ggsound_ram.inc"
include "variables2.inc"
.ende
;; Set the code starting point
.org $8000
;; 4. The RESET routine
RESET:
;;;;;;TURN THINGS OFF AND INITIALIZE;;;;;;;
SEI ; SEI tells the code to ignore
; interrupts for the routine
LDA #$00 ; Load 0 into the accumulator
STA $2000 ; disables the NMI
STA $2001 ; disables rendering
STA $4010
STA $4015
LDA #$40 ; Loads HEX value 40, which = dec value 64
STA $4017
CLD ; disables decimal mode
LDX #$FF ; loads value 255
TXS ; initializes the stack
BIT $2002
vBlankWait1:
BIT $2002
BPL vBlankWait1
; we clear out memory
LDA #$00 ; loads zero into the accumulator
LDX #$00 ; loads zero into x
;;;;;;NOW WE'RE READY TO START MEMORY CLEAR LOOP;;;;;;;;
ClearMemoryLoop:
STA $0000,x ; Store accumulator (0) into
; address $0000 + x
STA $0100,x ; Store accumulator (0) into
; address $0100 + x
STA $0200,x ; Store accumulator (0) into
; address $0200 + x
STA $0300,x ; Store accumulator (0) into address
; $0300 + x
STA $0400,x ; Store accumulator (0) into
; address $0400 + x
STA $0500,x ; Store accumulator (0) into
; address $0500 + x
STA $0600,x ; Store accumulator (0) into
; address $0600 + x
STA $0700,x ; Store accumulator (0) into
; address $0700 + x
INX ; x goes up by one, so all of those
; +x's at the end that were zero
; the first time through are increased.
BNE ClearMemoryLoop
;; This will branch up to the loop again if X is not 0
;; All memory locations from $0000 to $07FF will be
;; loaded with zero.
vBlankWait2:
BIT $2002
BPL vBlankWait2
JSR HideAllSprites
;; load the main palette
LDA #<MainPalette
STA paletteaddr
LDA #>MainPalette
STA paletteaddr + 1
JSR LoadPalette
; initialise variables
JSR InitPPULookupTable
JSR InitShapeData
JSR InitBlockLookupTable
JSR InitGhostLookupTable
JSR InitGhostOffset
JSR InitRandom
JSR InitTileNumLookupTable
JSR InitHighScore
LDA #0
STA buttonspressed
STA backgroundmode
STA textoffset
STA ingamemusic
STA frameTimer
STA difficulty
STA controlleroption
LDA #$01
STA sensitivity
LDA #$02
STA dropmethod
LDA #TOPYWHENUPSIDEDOWN
STA starty
LDA #BOTTOMY-2
STA upsidedownstarty
LDA #15
STA startx
LDA #$10
STA plx
STA ply
STA tmpx
STA tmpy
LDA #15
STA blockshapes
LDA #0
STA blockshapes+1
LDA #02
STA nextshape
; this resets titlearrowpos (so its pointing at start game)
LDA #0
STA titlearrowpos
; this resets startgamerequested
LDA #0
STA startgamerequested
;;;;;;;TURN THINGS BACK ON NOW THAT WE'RE SET UP;;;;;;;;
JSR ClearScreen ; this will clear the screen, set it to all blank
; and will activate NMI and enable rendering
JSR GetTVSystem
STA tvsystem
; initialise music
;0: NTSC, 1: PAL, 2: Dendy; 3: unknown
; if we have identified tv system as PAL or Dendy, set sound to PAL, otherwise NTSC
LDA tvsystem
CMP #1
BEQ setsound1
CMP #2
BEQ setsound1
; not PAL or Dendy, so set to NTSC sound
LDA #SOUND_REGION_NTSC
JMP setsound2
setsound1:
LDA #SOUND_REGION_PAL
setsound2:
STA sound_param_byte_0
LDA #<song_list
STA sound_param_word_0
LDA #>song_list
STA sound_param_word_0+1
LDA #<sfx_list
STA sound_param_word_1
LDA #>sfx_list
STA sound_param_word_1+1
LDA #<envelopes_list
STA sound_param_word_2
LDA #>envelopes_list
STA sound_param_word_2+1
LDA #<dpcm_list
STA sound_param_word_3
LDA #>dpcm_list
STA sound_param_word_3+1
JSR sound_initialize
; load the splash screen for Teuthida
JSR WaitFrame ; wait for the NMI VBlank
JSR ClearScreen
JSR LoadTeuthidaScreen
LDA #song_index_Teuthida
STA sound_param_byte_0
JSR play_song
JSR FadeInTeuthidaScreen
LDX #0
teuthidaloop1:
TXA
PHA
JSR SmallDelay
PLA
TAX
INX
CPX #20
BNE teuthidaloop1
JSR pause_song
JSR SmallDelay
JSR SmallDelay
LDA #0
STA backgroundmode
JMP TitleScreen
;; 5. The NMI
NMI:
;;; push the registers to the stack to preserve them
PHA ; this pushes the accumulator to the stack.
TXA ; This loads whatever is in X into the accumulator
PHA ; and pushes the accumulator to the stack
; now the old A is on the bottom and X is on top of it.
TYA ; This loads whatever is in Y into the accumulator
PHA ; and pushes the accumulator to the stack
; now y is on top. A is on bottom, X is in middle.
;;;;;;;;==============
;;DO NMI STUFF HERE
INC frameTimer ; increase frame time every time NMI is hit
INC countdownframeTimer
LDA #$00 ; puts zero into the accumulator
STA $2003 ; sets the low byte of the sprite RAM address
LDA #$02 ; puts 02 into the accumulator
STA $4014 ; sets high byte of the RAM address
; and starts transfer. This has
; loaded low byte of 00, high byte of 02,
; meaning it's 16 bit address is
; high+low, or 02+00 or $0200.
; Later, we'll be using the address $0200
; for our sprite data. This is why.
; load the palette
; The palette for the background runs from VRAM $3F00 to $3F0F
; the palette for the sprites runs from $3F10 to $3F1F
LDA #$3f
STA $2006
LDX #$00
STX $2006
nmipal:
LDA palette,x
STA $2007
INX
CPX #$20
BNE nmipal
LDA bgupdaterequired
CMP #$01
BNE ppucleanup
BIT $2002 ; read from PPUSTATUS (occasional corruption if do not do this before writing)
JSR MakeBackgroundChanges
ppucleanup:
;;This is the PPU clean up section, so rendering the next frame starts properly.
; LDA #%10010000 ; enable NMI, sprites from Pattern Table 0, background from Pattern Table 1
LDA backgroundmode
CMP #1
BNE ppuc1
LDA #%10010000
STA $2000
JMP ppuc2
ppuc1:
LDA #%10000000
STA $2000
ppuc2:
LDA #%00011110 ; enable sprites, enable background, no clipping on left side
STA $2001
LDA #$00 ;;tell the ppu there is no background scrolling
STA $2005
STA $2005
setsleeping:
LDA #0 ; clear the sleeping flag so that WaitFrame will exit
STA sleeping
soundengine_update
ExitNMI:
;;; pull the registers FROM the stack and restore them.
PLA ;; Pulls the top stack and puts it in accumulator.
TAY ;; puts that value into y
;; now y is restored to what it was before NMI.
PLA ;; pulls second stack value and puts in accumulator
TAX ;; puts that value into x
;; now x is restored to what it was before NMI
PLA ;; pulls third stack value and puts in accumulator
;; now y,x,and a are all restored to what they were
RTI ;; at the end of the NMI, we want to
;; 'return from the interrupt'.
;; The RTI will put us back into the code
;; in whatever place we were when the frame ended
; this fades in the Teuthida screen by cycling through the palettes
FadeInTeuthidaScreen:
JSR VerySmallDelay
JSR WaitFrame ; wait for the NMI VBlank
LDA #$0C ; cyan colour
STA palette+15
JSR VerySmallDelay
JSR WaitFrame ; wait for the NMI VBlank
LDA #$00 ; gray colour
STA palette+15
JSR VerySmallDelay
JSR WaitFrame ; wait for the NMI VBlank
LDA #$10 ; light gray colour
STA palette+15
JSR VerySmallDelay
JSR WaitFrame ; wait for the NMI VBlank
LDA #$20 ; white colour
STA palette+15
RTS
; this loads the palette into RAM, ready to be processed by the NMI
LoadPalette:
LDY #$00
iploop:
LDA (paletteaddr),y
STA palette,Y ; store in the palette in RAM
INY
CPY #$20
BNE iploop
RTS
;; Start game
StartGame:
JSR NewGameInitialisation
;seed our random number generator
LDA frameTimer
STA randomtemp
LDX #0
sgloop:
JSR rnd
INX
CPX randomtemp
BNE sgloop
; lets draw the screen
JMP NewLevel
; this setups the variables for a new level and draws the screen
NewLevel:
JSR SetUpLevel
JSR InitPlayArea
JSR DrawScreen
;reset frameTimer and pretim
LDA frameTimer
STA pretim
JMP MainGameLoop
; this sets up the variables for a new level
SetUpLevel:
LDA #0
STA upsidedown
LDA currentlevel
CMP #3
BEQ sul1
JMP sul2
sul1:
LDA #1
STA upsidedown
sul2:
; reset allowed swap
LDA #1
STA allowedswap
LDA #0
STA totalrowscompletednum
; this calculates the number of pieces required to complete for this level
LDX currentlevel
DEX
LDA linesneededperlevel,x
STA targetlinesforthislevelnum
; reset the number of pieces played this level
LDA #0
STA piecesplayedthislevel
; reset the bombs found
LDA #0
STA bombsfound
STA bombsfoundpreviouscount
RTS
; this is the routine that draws the screen
DrawScreen:
JSR WaitFrame
JSR ClearScreen ; clear the screen
JSR PrintUpcomingLevel
JSR WaitFrame
JSR LoadMainGameGraphics
JSR DrawBase
JSR PrintHighScore
JSR PrintLevelTarget
JSR WriteNameOfLevel
; draw the saved shape
JSR DrawSavedShape
; draw the text lines (or bombs)
JSR DrawLinesOrBombs
; print the number of lines completed or bombs defused (zero)
JSR PrintLinesOrBombsCompleted
; draw anything that may be specific to that level
JSR DrawLevelSpecificItems
; print the current score
JSR PrintScore
; print the current ghost setting
JSR PrintGhostSetting
; we call selectnewpiece twice so we have a value for current and next shape
JSR SelectNewPiece
JSR SelectNewPiece
JSR ShowAllShapes
; finally we reset the number of pieces played this level
LDA #0
STA piecesplayedthislevel
LDA currentlevel
CMP #7
BNE ds1
; if level 7 we need to display the number of pieces left to play
LDA #<pieces_left_str
STA textprintaddr
LDA #>pieces_left_str
STA textprintaddr + 1
JSR WriteTextToScreen
JSR CalculateNumberOfPiecesLeft
JSR PrintNumberOfPiecesLeft
ds1:
RTS
; draw the bottom of the board
DrawBase:
LDX #0
LDA #12
STA bgbuf, x
INX
STX bgbufidx
; now write the PPU address
LDA upsidedown
CMP #1
BEQ dbase1
LDX #BOTTOMY
JMP dbase2
dbase1:
LDX #TOPYWHENUPSIDEDOWN
dbase2:
LDA ppu_lookup1, x
LDX bgbufidx
STA bgbuf, x
INX
STX bgbufidx
LDA upsidedown
CMP #1
BEQ dbase3
LDX #BOTTOMY
JMP dbase4
dbase3:
LDX #TOPYWHENUPSIDEDOWN
dbase4:
LDA ppu_lookup2, x ; this gives us the value for the start if the row
CLC
ADC #LEFTWALLX
LDX bgbufidx
STA bgbuf, x
INX
LDA upsidedown
CMP #1
BEQ dbase5
LDA #$0B ; tile for bottom left bend
JMP dbase6
dbase5:
LDA #$1B ; tile for top left bend
dbase6:
STA bgbuf, x
INX
LDY #10
drawbaseloop:
LDA #$0C
STA bgbuf, x
INX
DEY
CPY #0
BNE drawbaseloop
LDA upsidedown
CMP #1
BEQ dbase7
LDA #$0D ; tile for bottom right bend
JMP dbase8
dbase7:
LDA #$1C ; tile for top right bend
dbase8:
STA bgbuf, x
INX
; terminate the buffer
LDA #0
STA bgbuf, x
JSR CommitChange
RTS
; This draws on screen anything that may be specific to that level
DrawLevelSpecificItems:
LDA currentlevel
CMP #6
BEQ dlsi1
RTS
dlsi1:
JSR populatebombs
JSR DrawPlayAreaFromBuffer
; draw the clock seperator
LDA #<clock_seperator_str
STA textprintaddr
LDA #>clock_seperator_str
STA textprintaddr + 1
JSR WriteTextToScreen
LDA #LEVEL6ALLOWEDTIME
STA leveltimer
LDA #0
STA countdownframeTimer ; reset
JSR PrintOnScreenTimer
RTS
; this draws the text 'LINES' or 'BOMBS' as appropriate
DrawLinesOrBombs:
LDA currentlevel
CMP #6
BEQ dlob1
LDA #<lines_str
STA textprintaddr
LDA #>lines_str
STA textprintaddr + 1
JSR WriteTextToScreen
RTS
dlob1:
LDA #<bombs_str
STA textprintaddr
LDA #>bombs_str
STA textprintaddr + 1
JSR WriteTextToScreen
RTS
;; Read from controller 1 and place result in buttonspressed
ReadFromController1:
JSR ReadController1
LDA buttonspressed
STA controllertemp1
JSR ReadController1
LDA buttonspressed
STA controllertemp2
JSR ReadController1
LDA buttonspressed
STA controllertemp3
LDA controllertemp2
ORA controllertemp3
AND controllertemp1
STA controllertemp1
LDA controllertemp2
AND controllertemp3
ORA controllertemp1
STA buttonspressed
RTS
; this is called by ReadFromController1 to actually read the values
ReadController1:
; latch
LDA #$01
STA $4016
LDA #$00
STA $4016
LDX #$00
readcontroller1values:
CPX #$08
BPL endreadcontroller1
LDA $4016
AND #%00000001
ASL buttonspressed
ORA buttonspressed
STA buttonspressed
INX
JMP readcontroller1values
endreadcontroller1:
RTS
;; 6. The Main Game Loop
MainGameLoop:
LDA frameTimer ; load the variable
CheckFrameTimer:
CMP frameTimer ; check to see if it's the same
BEQ CheckFrameTimer
; if it is, don't move on, just loop
; only if frame has increase can we go on.
LDA buttonspressed
STA lastbuttonspressed
JSR ReadFromController1
LDA buttonspressed
CMP #$00 ; if equal to 0 then no buttons pressed
BEQ nobuttonspressed
JMP handlebuttonactions
nobuttonspressed:
JSR DropPieceIfTapped
LDA #0
STA dropbuttonpresscount
handlebuttonactions:
; Button status for each controller is returned in the following order: A, B, Select, Start, Up, Down, Left, Right.
LDA buttonspressed
AND #%10000000
CMP #$00
BEQ ReadB
; do stuff for A button
LDA controlleroption
CMP #1
BEQ reada1
JSR DoClockwiseAction
JMP ReadB
reada1:
JSR DoDropAction
ReadB:
LDA buttonspressed
AND #%01000000
CMP #$00
BEQ ReadSelect
; Do stuff for B button
LDA controlleroption
CMP #1
BEQ readb1
JSR DoAntiClockwiseAction
JMP ReadSelect
readb1:
JSR DoSwapAction
ReadSelect:
LDA buttonspressed
AND #%00100000
CMP #$00
BEQ ReadStart
; Stuff for Start button
JSR ChangeGhostSetting
JSR SmallDelay
ReadStart:
LDA buttonspressed
AND #%00010000
CMP #$00
BEQ ReadUp
; Stuff for Start button
JSR DoPauseAction
ReadUp:
LDA buttonspressed
AND #%00001000
CMP #$00
BEQ ReadDown
; Stuff for Up button
LDA controlleroption
CMP #1
BEQ readup1
JSR SwapShape
JMP ReadDown
readup1:
JSR DoAntiClockwiseAction
ReadDown:
LDA buttonspressed
AND #%00000100
CMP #$00
BEQ ReadLeft
; Stuff for Down button
LDA controlleroption
CMP #1
BEQ readdown1
JSR DoDropAction
JMP ReadLeft
readdown1:
JSR DoClockwiseAction
ReadLeft:
LDA buttonspressed
AND #%00000010
CMP #$00
BEQ ReadRight
; Stuff for Left button
JSR MoveLeft
JSR SmallDelay
ReadRight:
LDA buttonspressed
AND #%00000001
CMP #$00
BEQ NotRight
; Stuff for Right button
JSR MoveRight
JSR SmallDelay
NotRight:
; if level 6 then we need to decrement the timer
LDA currentlevel
CMP #6
BNE main1
; if PAL 50 frames a sec, if NTSC 60
LDA tvsystem
CMP #1 ; PAL
BNE main5
LDA countdownframeTimer
CMP #50
BCS main6
JMP main1 ; a second has not passed yet, keep going
main5:
LDA countdownframeTimer
CMP #60
BCS main6
JMP main1
main6:
; a second has passed, update the on-screen timer
DEC leveltimer
LDA #0
STA countdownframeTimer
JSR PrintOnScreenTimer
main1:
LDA difficulty
CMP #0
BNE main2
LDA frameTimer
SEC
SBC pretim
CMP #45 ; have 45 frames elapsed yet?
BCS main4
JMP main3
main2:
; difficulty hard
LDA frameTimer
SEC
SBC pretim
CMP #15 ; have 15 frames elapsed yet?
BCS main4
main3:
JMP MainGameLoop ;not time to drop piece yet, continue main loop
main4:
LDA frameTimer
STA pretim
JSR AutoDropPiece
; the following will send us back to MainGameLoop if level not complete, otherwise
; it will send us to NewLevel
JMP CheckLevelComplete
; end main game loop
; if the button pressed corresponds to drop
DoDropAction:
JSR DropPiece
INC dropbuttonpresscount
; if drop method is 1 (while held), we make the delay very small
LDA dropmethod
CMP #1
BEQ dda2
; if drop method is 2 (mixture) and the dropbuttonpresscount is >=2 then make the delay very small too
LDA dropmethod
CMP #2
BNE dda1
; if here then the drop method is mixture
LDA dropbuttonpresscount
CMP #2
BCS dda2
dda1:
JMP SmallDelay
dda2:
JMP VerySmallDelay
; if the button pressed corresponds to anticlockwise
DoAntiClockwiseAction:
JSR MoveAntiClockwise
JMP SmallDelay
; if the button pressed corresponds to clockwise
DoClockwiseAction:
JSR MoveClockwise
JMP SmallDelay
; if the button pressed corresponds to save/swap
DoSwapAction:
JSR SwapShape
JMP SmallDelay
; this is the pause action
DoPauseAction:
JSR pause_song
LDA #<paused_str
STA textprintaddr
LDA #>paused_str
STA textprintaddr + 1
JSR WriteTextToScreen
JSR SmallDelay
JSR SmallDelay
dpause1:
JSR ReadFromController1
LDA buttonspressed
AND #%00010000
CMP #$00
BEQ dpause1
LDA #<notpaused_str
STA textprintaddr
LDA #>notpaused_str
STA textprintaddr + 1
JSR WriteTextToScreen
JSR resume_song
JSR SmallDelay
RTS
; this calculates the number of pieces left allowed to play in the level and stores the result in piecesleftthislevel
CalculateNumberOfPiecesLeft:
LDA #LEVEL7ALLOWEDPIECES
SEC
SBC piecesplayedthislevel
STA piecesleftthislevel
RTS
; this prints on-screen the number of pieces allowed to play this level (used by level 7)
PrintNumberOfPiecesLeft:
LDA piecesleftthislevel
CMP #255
BEQ pnopl1
JMP pnopl2
pnopl1:
; we just display 0 if number has wrapped around
LDA #0
pnopl2:
STA digittemp
JSR Print2Digit
LDA #PIECESCOUNTDOWNX
STA printnumbersx
LDA #PIECESCOUNTDOWNY
STA printnumbersy
JSR PrintNumbers
RTS
; this prints on screen the number of secs remaining to play this level
PrintOnScreenTimer:
LDA leveltimer
CMP #240
BCS post1
CMP #180
BCS post2
CMP #120
BCS post3
CMP #60
BCS post4
; time is less than 60 seconds
LDA #0
JSR PrintOnScreenTimerMinutes
LDA leveltimer
STA timertemp
JMP post5
post1:
; time is 4 minutes or greater
LDA #4
JSR PrintOnScreenTimerMinutes
LDA leveltimer
SEC
SBC #240
STA timertemp
JMP post5
post2:
; time is 3 minutes or greater
LDA #3
JSR PrintOnScreenTimerMinutes
LDA leveltimer
SEC
SBC #180
STA timertemp
JMP post5
post3:
; time is 2 minutes or greater
LDA #2
JSR PrintOnScreenTimerMinutes
LDA leveltimer
SEC
SBC #120
STA timertemp
JMP post5
post4:
; time is 1 minute or greater
LDA #1
JSR PrintOnScreenTimerMinutes
LDA leveltimer
SEC
SBC #60
STA timertemp
post5:
; print the seconds component
LDA timertemp
STA digittemp
JSR Print2Digit
LDA #CLOCKSECX
STA printnumbersx
LDA #CLOCKSECY
STA printnumbersy
JSR PrintNumbers
RTS
; This prints the minute component. Minute gets passed in A
PrintOnScreenTimerMinutes:
STA digittemp
JSR Print2Digit
LDA #CLOCKMINX
STA printnumbersx
LDA #CLOCKMINY
STA printnumbersy
JSR PrintNumbers
RTS
; This plays the appropriate in-game music (or silence if that is what was chosen)
PlayInGameMusic:
LDA ingamemusic
CMP #0
BEQ pigm1
CMP #1
BEQ pigm3
CMP #2
BEQ pigm5
JMP pigm7
pigm1:
; Theme A selected, now see if fast or slow
LDA difficulty
CMP #1
BEQ pigm2
LDA #song_index_Slow_Theme_A
STA sound_param_byte_0
JMP play_song
pigm2:
LDA #song_index_Fast_Theme_A
STA sound_param_byte_0
JMP play_song
pigm3:
; Theme B selected, now see if fast or slow
LDA difficulty
CMP #1
BEQ pigm4
LDA #song_index_Slow_Theme_B
STA sound_param_byte_0
JMP play_song
pigm4:
LDA #song_index_Fast_Theme_B
STA sound_param_byte_0
JMP play_song
pigm5:
; Theme C selected, now see if fast or slow
LDA difficulty
CMP #1
BEQ pigm6
LDA #song_index_Slow_Theme_C
STA sound_param_byte_0
JMP play_song
pigm6:
LDA #song_index_Fast_Theme_C
STA sound_param_byte_0
JMP play_song
pigm7:
JMP pause_song
; Routine to pick a new block. Holds this in next shape and makes currentshape the old value of nextshape
; levels 2,5,7 and 9 have extra shapes added
SelectNewPiece:
LDA nextshape
PHA ; save the nextshape to the stack, this will become currentshape
LDA currentlevel
CMP #$02
BEQ snp2
CMP #$05
BEQ snp2
CMP #$07
BEQ snp2
CMP #$09
BEQ snp2
; if get to here then using the standard set
;this picks the random numbers when just using standard set
snp1:
JSR rnd
AND #%00000111 ;bitmask bits 0, 1 and 2
CMP #$07
BEQ snp1
JMP snp3
; this picks the random numbers when using the extended set
snp2:
JSR rnd
AND #15 ;bitmask bits 0, 1, 2 and 3 (7 for standard set)
CMP #12
BEQ snp2
CMP #13
BEQ snp2
CMP #14
BEQ snp2
CMP #15
BEQ snp2
snp3:
STA nextshape
JSR DrawNextShape
PLA
STA currentshape ; retrieve the previous next shape from the stack and make it the current shape
LDA startx
STA plx
LDA starty
STA ply
; if upside down we need to update the starting y position
LDA upsidedown
CMP #$01
BEQ snp5
JMP snp6
snp5:
LDA upsidedownstarty
STA ply
snp6:
; reset allowed swap
LDA #$01
STA allowedswap
; now that we have picked the shape, we set its tile type
LDX currentshape
LDA tilenumlookuptable, x
STA tilenum
snp7:
; now check if end game
LDA plx
STA tmpx
LDA ply
STA tmpy
JSR CheckMove
LDA allowedmove
CMP #$01
BEQ snp4
; the start position is not valid so its end game
JMP GameOver
snp4:
LDA #$00
STA currentorientation
JSR SetBlockShapes
INC piecesplayedthislevel
JSR LevelSpecialAction; this does the special action required per level (may not do anything)
RTS
; This handles the swap piece functionality. A player is allowed swap once till a new shape is selected automatically
; by the drop process. We swap the current piece with the saved shape
SwapShape:
LDA allowedswap
CMP #0
BNE ssh1
RTS ; allowedswap was set to 0, not currently allowed swap
ssh1:
LDA #sfx_index_sfx_Store
JSR PlaySoundEffect
LDA #0
STA allowedswap ; stop any more swapping of this shape
LDA savedshape
PHA ; save the saved shape to the stack
LDA currentshape
STA savedshape
JSR DrawSavedShape
PLA ; get the saved shape from the stack
STA currentshape ; now we have swapped shapes
LDA startx ; swapped piece starts from the top of the screen
STA plx
LDA starty
STA ply
; if we are upside down we need to update the y position
LDA upsidedown
CMP #1
BNE ssh4
ssh3:
LDA upsidedownstarty
STA ply
ssh4:
; now that we have picked the shape, we set its tile type
LDX currentshape
LDA tilenumlookuptable, x
STA tilenum
LDA #$00
STA currentorientation
; now check if end game
LDA plx
STA tmpx
LDA ply
STA tmpy
; player has swapped, but maybe the piece will not fit at the top of the screen (and thus game over)
JSR CheckMove
LDA allowedmove
CMP #$01
BEQ ssh2
; the start position is not valid so its end game
JMP GameOver
ssh2:
; ok, so we can draw the shape ok
JSR SetBlockShapes
JSR ShowAllShapes
RTS
; This drops the piece down by one square if possible, if not possible then it starts a new piece
AutoDropPiece:
LDA upsidedown
CMP #$01
BEQ adp3
LDA ply
STA tmpy
INC tmpy ; we are trying to move down
JMP adp4
adp3:
; this is the section called if upside down
LDA ply
STA tmpy
DEC tmpy ; we are trying to move up (as we are upside down)
adp4:
LDA plx
STA tmpx
JSR CheckMove
LDA allowedmove
CMP #$00
BEQ adp1 ; not possible to auto drop piece
LDA upsidedown
CMP #$01
BEQ adp5
INC ply ; move is valid so increment y
JMP adp2
adp5:
DEC ply ; move is valid so decrement y (as upside down)
JMP adp2
adp1:
; if we are here then it was not possible to drop the block, choose a new block
; first we redraw back the piece then choose our new one
; we also add to the score
; Add 20 to the score.
LDA #sfx_index_sfx_Lock_or_Move
JSR PlaySoundEffect
TYA
PHA ; push Y to the stack as we are going to overwrite it
LDA #<score
STA updatecountaddr
LDA #>score
STA updatecountaddr + 1
LDY #4 ; the 10's column
LDA #2
STA increaseamount ; 2 tens, increase score by 20
JSR UpdateCount
PLA
TAY ; restore Y from the stack
JSR PrintScore ;print this new score
LDX plx
LDY ply
JSR ConvertShapeToBg
JSR HideAllSprites ; sprite has been converted to background, temporarily hide
JSR CheckPlayArea ; see if a winning line (or lines) exists
JSR SelectNewPiece
; we need to reset lastbuttonspressed - otherwise if someone has taps the down key just before the
; selectnewpiece routine is called, then the next piece will immediately fall down as it appears
; First we read from the controller (to clear anything cached), then we reset the values
JSR ReadFromController1
LDA #0
STA lastbuttonspressed
STA buttonspressed
adp2:
JSR ShowAllShapes
RTS
; this draws the saved shape
DrawSavedShape:
LDA #SAVEDSHAPEX
STA tmpx
LDA #SAVEDSHAPEY
STA tmpy
JSR ClearInfoArea
; we temporarily set blockshapes to be our saved shape
LDA #$00
STA blockpointer
LDX savedshape
CPX #$00
BEQ dss1
LDA blocklookuptable,x
STA blockpointer
dss1:
LDX blockpointer
LDA shapedata, x
STA blockshapes
INX
LDA shapedata, x
STA blockshapes + 1
LDX savedshape
LDA tilenumlookuptable, x
STA tilenum
; so we have now successfully temporarily set blockshapes
LDX #SAVEDSHAPEX
LDY #SAVEDSHAPEY
LDA #0 ; disable adding blocks to playarea buffer
STA bufferaddactive
JSR ConvertShapeToBg
LDA #1 ; re-enable adding blocks to playarea buffer
STA bufferaddactive
RTS
; this draws the next shape to be displayed
DrawNextShape:
LDA #NEXTSHAPEX
STA tmpx
LDA #NEXTSHAPEY
STA tmpy
JSR ClearInfoArea
; we temporarily set blockshapes to be our nextshape
LDA #$00
STA blockpointer
LDX nextshape
CPX #$00
BEQ dns1
LDA blocklookuptable,x
STA blockpointer
dns1:
LDX blockpointer
LDA shapedata, x
STA blockshapes
INX
LDA shapedata, x
STA blockshapes + 1
LDX nextshape
LDA tilenumlookuptable, x
STA tilenum
; so we have now successfully temporarily set blockshapes
LDX #NEXTSHAPEX
LDY #NEXTSHAPEY
LDA #0 ; disable adding blocks to playarea buffer
STA bufferaddactive
JSR ConvertShapeToBg
LDA #1 ; reenable adding blocks to playarea buffer
STA bufferaddactive
RTS
; this routine is called when the game is over
GameOver:
LDA #song_index_Mission_Failed
STA sound_param_byte_0
JSR play_song
JSR WaitFrame
JSR ClearScreen
JSR HideAllSprites
JSR CheckHighScore
LDA newhighscore
CMP #1
BNE go1
JSR SetHighScore
JSR PrintNewHighScore
go1:
LDA #<gameoverlogo
STA logoaddr
LDA #>gameoverlogo
STA logoaddr + 1
JSR PrintWordsWithBlocks
LDX #0
goloop1:
TXA
PHA
JSR SmallDelay
PLA
TAX
INX
CPX #20
BNE goloop1
JMP TitleScreen
; this routine is called when the game has been won - well done player!
YouWin:
JSR CheckHighScore
LDA newhighscore
CMP #1
BEQ yw1
LDA #song_index_Mission_Complete_1
JMP yw2
yw1:
LDA #song_index_Mission_Complete_2
yw2:
STA sound_param_byte_0
JSR play_song
JSR WaitFrame
JSR ClearScreen
JSR HideAllSprites
JSR CheckHighScore
LDA newhighscore
CMP #1
BNE yw3
JSR SetHighScore
JSR PrintNewHighScore
yw3:
LDA #<youwinlogo
STA logoaddr
LDA #>youwinlogo
STA logoaddr + 1
JSR PrintWordsWithBlocks
LDX #0
ywloop1:
TXA
PHA
JSR SmallDelay
PLA
TAX
INX
CPX #20
BNE ywloop1
JMP TitleScreen
; if there is a new high score, this routine prints the info on-screen
; this is used when game over (either lost or won)
PrintNewHighScore:
LDA #<congratulations_str
STA textprintaddr
LDA #>congratulations_str
STA textprintaddr + 1
JSR WriteTextToScreen
LDA #<new_high_score_str
STA textprintaddr
LDA #>new_high_score_str
STA textprintaddr + 1
JSR WriteTextToScreen
TXA
PHA
TYA
PHA
; the high score is 6 chars in length
LDX #0
LDA #6
STA bgbuf, x
INX
STX bgbufidx
; now write the PPU address
LDX #NEWHIGHSCOREY
LDA ppu_lookup1, x
LDX bgbufidx
STA bgbuf, x
INX
STX bgbufidx
LDX #NEWHIGHSCOREY
LDA ppu_lookup2, x ; this gives us the value for the start if the row
CLC
ADC #NEWHIGHSCOREX
LDX bgbufidx
STA bgbuf, x
INX
LDA #<highscore
STA textprintaddr
LDA #>highscore
STA textprintaddr + 1
LDY #0
pnhs1:
LDA (textprintaddr), y
STA bgbuf, x
INX
INY
CPY #6
BNE pnhs1
; terminate the buffer
LDA #0
STA bgbuf, x
PLA
TAY
PLA
TAX
JSR CommitChange
RTS
; this routine detects a winning line in the playarea. It checks the line defined in tmpy
; winningline will be set to 1 in the case of a winning line, otherwise 0
; Passes in line to check via Y register
CheckWinningLine:
LDA #0
STA winningline ; winningline reset to 0
; tmpy is already set, but set initial x value
LDA #LEFTWALLX
STA tmpx
INC tmpx
LDX #10 ;10 squares in width of play area
cwl1:
TXA
PHA ; push the loop counter x to the stack
LDX tmpx
JSR AtAdd
CMP #BLANKSPACE ; check is it is an empty square
BEQ cwl2 ;square is empty, can return with winningline set to 0, not winning line
INC tmpx
PLA ;pull back the loop counter from the stack
TAX
DEX
CPX #0
BNE cwl1
; if get this far then winning line
LDA #1
STA winningline
RTS
cwl2:
; not a winning line, but need to tidy the stack, then exit
PLA
RTS
; this is the routine that checks the playarea for all winning lines, adding to
; the players score, flash the lines temporarily and then deleting them and moving
; the playarea down
CheckPlayArea:
LDA #0
STA rowscompleted
; we check all rows between (TOPYWHENUPSIDEDOWN + 1) and (BOTTOMY - 1)
LDY #BOTTOMY
DEY ; start one up from very bottom of screen
cpa1:
JSR CheckWinningLine
LDA winningline
CMP #0
BEQ cpa2
; call flashwinningline
TYA
PHA ; push Y to the stack as we are going to overwrite it
LDA #<score
STA updatecountaddr
LDA #>score
STA updatecountaddr + 1
LDY #4 ; the 10's column
LDA #5
STA increaseamount ; 5 tens, increase score by 50
JSR UpdateCount
LDY #3 ; the 100's column
LDA #2
STA increaseamount ; 2 hundreds, increase score by 200, so overall by 250
JSR UpdateCount
PLA
TAY ; restore Y from the stack
JSR PrintScore ;print this new score
INC rowscompleted
LDA rowscompleted
CMP #4 ; bonus points for 4 rows together (+1000 score)
BNE cpa2
TYA
PHA ; push Y to the stack as we are going to overwrite it
LDA #<score
STA updatecountaddr
LDA #>score
STA updatecountaddr + 1
LDY #2 ; the 1000's column
LDA #1
STA increaseamount ; 1 thousand, increase score by 1000, bonus for 4 lines together
JSR UpdateCount
PLA
TAY ; restore Y from the stack
JSR PrintScore ;print this new score
cpa2:
DEY
CPY #TOPYWHENUPSIDEDOWN
BNE cpa1
; now update the lines or bombs completed
LDA currentlevel
CMP #6
BEQ cpa2a ; we skip adding the total as level 6 works differently
LDA totalrowscompletednum
CLC
ADC rowscompleted
STA totalrowscompletednum
cpa2a:
; now print the new lines completed number
JSR PrintLinesOrBombsCompleted
; if any winning lines need to now remove
LDA rowscompleted
CMP #0
BEQ cpa10 ; if no rows completed we can exit this routine
; There are winning rows, we need to remove them and drop the play area as appropriate
; First we save the value of tilenum as its value will be overwritten
LDA tilenum
PHA ; save it to the stack
LDA upsidedown
CMP #1
BEQ cpa6
LDY #BOTTOMY
DEY ; start one up from very bottom of screen
cpa4:
JSR CheckWinningLine
LDA winningline
CMP #0
BEQ cpa5 ; if not a winning line then skip EraseLine
JSR EraseLine
JSR DropPlayArea
; we now need to add 1 to Y to ensure we check/delete all winning lines. Effectively the
; DEY at the end of the loop means we will recheck this Y value as possibly a winning line
; has dropped down to here
INY
cpa5:
DEY
CPY #TOPYWHENUPSIDEDOWN
BNE cpa4
; all the winning lines have been removed from our playarea buffer
; now we redraw the playarea based on this buffer
JSR ClearedLineNoise
JSR DrawPlayAreaFromBuffer
; we can now retrieve the value of tilenum from the stack
PLA
STA tilenum
; if this is level 6 then we need to calculate number of bombs remaining
LDA currentlevel
CMP #6
BNE cpa5a
JSR CalculateNumBombsFound
JSR PrintLinesOrBombsCompleted
cpa5a:
RTS
cpa6:
LDY #TOPYWHENUPSIDEDOWN
INY ; start one up from very bottom of screen
cpa7:
JSR CheckWinningLine
LDA winningline
CMP #0
BEQ cpa8 ; if not a winning line then skip EraseLine
JSR EraseLine
JSR UpsideDownDropPlayArea
; we now need to decrement 1 from Y to ensure we check/delete all winning lines. Effectively the
; INY in the below loop means we will recheck this Y value as possibly a winning line
; has dropped down to here
DEY
cpa8:
INY
CPY #BOTTOMY
BNE cpa7
; all the winning lines have been removed from our playarea buffer
; now we redraw the playarea based on this buffer
JSR ClearedLineNoise
JSR DrawPlayAreaFromBuffer
; we can now retrieve the value of tilenum from the stack
PLA
STA tilenum
cpa10:
RTS
; this calculates the number of bombs found. It does this by checking every square in
; the playarea and counting the number of bombs in the playarea, it then subtracts this
; from BOMBSONLEVEL6 and puts the result in bombsfound
CalculateNumBombsFound:
LDA #0
STA activebombs
LDX #0
cnbfloop:
LDA playareabuf,x
CMP #BOMBTILE
BEQ cnbf1
JMP cnbf2
cnbf1:
INC activebombs
cnbf2:
INX
CPX #240
BNE cnbfloop
; at this stage we know the number of bombs left (activebombs)
LDA #BOMBSONLEVEL6
SEC
SBC activebombs
STA bombsfound
CMP bombsfoundpreviouscount
BEQ cnbf3
; bombsfound does not equal bombsfoundpreviouscount, therefore a bomb has been found, play sound effect
; LDA #sfx_index_sfx_GoodClear_or_Defuse
; JSR PlaySoundEffect
cnbf3:
; now sync bombsfoundpreviouscount before returning
LDA bombsfound
STA bombsfoundpreviouscount
RTS
; this makes the sound when a line or lines are being removed
ClearedLineNoise:
LDA rowscompleted
CMP #1
BEQ cln1
CMP #2
BEQ cln2
CMP #3
BEQ cln3
CMP #4
BEQ cln4
RTS ; should be one of the values, but return if not
cln1:
LDA #sfx_index_sfx_Clearx1
JMP cln5
cln2:
LDA #sfx_index_sfx_Clearx2
JMP cln5
cln3:
LDA #sfx_index_sfx_Clearx3
JMP cln5
cln4:
LDA #sfx_index_sfx_NotTetris
cln5:
JMP PlaySoundEffect
; this plays a sound effect - requires A to have been set with the sound effect to play
PlaySoundEffect:
STA sound_param_byte_0
LDA #soundeffect_two
STA sound_param_byte_1
JSR play_sfx
RTS
; drawplayareafrombuffer is used when we wish to redraw the entire playarea. The playarea buffer
; contains the (new) playarea we wish to draw
DrawPlayAreaFromBuffer:
LDA #$00 ; reset the index into the background buffer
STA bgbufidx
LDA upsidedown
CMP #1
BEQ dpafb1
LDY #BOTTOMY
DEY ; start one up from very bottom of screen
JMP dpafb2
dpafb1:
LDY #TOPYWHENUPSIDEDOWN
INY ; start one down from very top of screen (as we are upside down)
dpafb2:
LDX #LEFTWALLX
INX
STX tmpx
STY tmpy
LDX bgbufidx
LDA #10 ; adding 10 blocks
STA bgbuf, x
; there are 32 bytes per row, and a max of 30 rows
LDX tmpy
LDA ppu_lookup1, x
INC bgbufidx
LDX bgbufidx
STA bgbuf, x
LDX tmpy
LDA ppu_lookup2, x ; this gives us the value for the start if the row
CLC
ADC tmpx
INC bgbufidx
LDX bgbufidx
STA bgbuf, x
dpafb3:
LDX tmpx
LDY tmpy
JSR AtAdd
INC bgbufidx
LDX bgbufidx
STA bgbuf, x
INC tmpx
LDX tmpx
CPX #RIGHTWALLX
BNE dpafb3
; write 0 at end of bgbuf so write routine knows this is end of data to be written
INC bgbufidx
LDX bgbufidx
LDA #0
STA bgbuf, x
JSR CommitChange ; writes the changes and resets bgbufidx to 0
LDA upsidedown
CMP #1
BEQ dpafb4
DEC tmpy
LDY tmpy
CPY #TOPYWHENUPSIDEDOWN-1
BNE dpafb2
JMP dpafb5
dpafb4:
INC tmpy
LDY tmpy
CPY #BOTTOMY+1
BNE dpafb2
dpafb5:
RTS
; after we build up a buffer of background changes to write we commit those changes
CommitChange:
LDA #$01
STA bgupdaterequired
; wait for background change to be done by NMI
cc1:
LDA bgupdaterequired
CMP #$00
BNE cc1
LDA #$00 ; reset the index into the background buffer
STA bgbufidx
RTS
; eraseline is used for clearing the playarea at the start of every level and is used
; during process for handling winning lines. Register Y is passed in (line to erase)
; Note that this routine overwrites the value in tilenum
EraseLine:
; we first need to push X and Y to the stack so we can safely use them
TXA
PHA
TYA
PHA
LDA #BLANKSPACE
STA tilenum
LDX #LEFTWALLX
INX
el1:
JSR AddBlockToPlayAreaBuffer
INX
CPX #RIGHTWALLX
BNE el1
PLA ; now pull back X and Y from the stack
TAY
PLA
TAX
RTS
; move playarea down. When we get a winning line, we remove the winning line and this routine
; drops the playarea above that line down
; we pass in Y register which is the winning line (drop everything above this)
DropPlayArea:
; we first need to push X and Y to the stack so we can safely use them
TXA
PHA
TYA
PHA
DEY
dpa1:
LDX #LEFTWALLX
INX
dpa2:
JSR AtAdd
STA tilenum
INY
JSR AddBlockToPlayAreaBuffer
DEY
INX
CPX #RIGHTWALLX
BNE dpa2
DEY
CPY #TOPYWHENUPSIDEDOWN-1
BNE dpa1
; at this stage we have dropped everything, now just need to erase the top line
JSR EraseTopLine
PLA ; now pull back X and Y from the stack
TAY
PLA
TAX
RTS
; move playarea up (as we are upside down). When we get a winning line, we remove the
; winning line and this routine drops the playarea below that line up
; we pass in Y register which is the winning line (drop everything below this)
UpsideDownDropPlayArea:
; we first need to push X and Y to the stack so we can safely use them
TXA
PHA
TYA
PHA
INY
udpa1:
LDX #LEFTWALLX
INX
udpa2:
JSR AtAdd
STA tilenum
DEY
JSR AddBlockToPlayAreaBuffer
INY
INX
CPX #RIGHTWALLX
BNE udpa2
INY
CPY #BOTTOMY+1
BNE udpa1
; at this stage we have dropped everything, now just need to erase the top line
JSR EraseTopLine
PLA ; now pull back X and Y from the stack
TAY
PLA
TAX
RTS
; this routine is used to erase the top line of the play area. We need this code
; as when we move everything down a line after a winning line, we need to clear the top line
EraseTopLine:
LDA upsidedown
CMP #1
BEQ etl2
LDY #TOPYWHENUPSIDEDOWN
JSR EraseLine
RTS
etl2:
LDY #BOTTOMY
JSR EraseLine
RTS
; routine used to update a count. Used to update the score
; Y is passed in as the digit to update
; The increaseamount variable is the amount to increase it by (value between 0 and 9)
UpdateCount:
LDA (updatecountaddr), y ; current value of digit.
CLC
ADC increaseamount
STA (updatecountaddr), y ; place new digit back in string.
CMP #58 ; compare to 58 >= than ASCII value '9'?
BCS uc1
RTS ; was not >= 58 so can return
uc1:
SEC
SBC #10 ; subtract 10
STA (updatecountaddr), y ; put new character back in string
uc2:
DEY ; decrement y, go one left
LDA (updatecountaddr), y
CLC
ADC #1
STA (updatecountaddr), y
CMP #58
BCS uc1
RTS
; moves the block right if allowed.
MoveRight:
LDA ply
STA tmpy
LDA plx
STA tmpx ; we are trying to move right
INC tmpx
JSR CheckMove
LDA allowedmove
CMP #$01
BNE mr1
INC plx
JSR ShowAllShapes
mr1:
RTS
; moves the block left if allowed.
MoveLeft:
LDA ply
STA tmpy
LDA plx
STA tmpx ; we are trying to move left
DEC tmpx
JSR CheckMove
LDA allowedmove
CMP #$01
BNE ml1
DEC plx
JSR ShowAllShapes
ml1:
RTS
; rotates the shape anticlockwise if allowed.
MoveAntiClockwise:
INC currentorientation
LDA currentorientation
CMP #$04 ;if 4 then need to set to 0 (as max value for currentorientation is 3)
BNE mac1
LDA #$00
STA currentorientation
mac1:
JSR SetBlockShapes
LDA ply
STA tmpy
LDA plx
STA tmpx
JSR CheckMove
LDA allowedmove
CMP #$01
BEQ mac4
; move is not valid so need to reset blockpointer and blockshapes
LDA currentorientation
CMP #$00
BNE mac2
LDA #$03
STA currentorientation
JMP mac3
mac2:
DEC currentorientation
mac3:
JSR SetBlockShapes
JMP mac5
mac4:
JSR ShowAllShapes
mac5:
RTS
; rotates the shape clockwise if allowed.
MoveClockwise:
LDA currentorientation
CMP #$00 ;if 0 then need to set to 3 (as max value for currentorientation is 3)
BNE mc1
LDA #$04 ; we set to 4 instead of 3 as the first action in mc1 is to decrement
STA currentorientation
mc1:
DEC currentorientation
JSR SetBlockShapes
LDA ply
STA tmpy
LDA plx
STA tmpx
JSR CheckMove
LDA allowedmove
CMP #$01
BEQ mc4
; move is not valid so need to reset blockpointer and blockshapes
LDA currentorientation
CMP #$03
BNE mc2
LDA #$00
STA currentorientation
JMP mc3
mc2:
INC currentorientation
mc3:
JSR SetBlockShapes
JMP mc5
mc4:
JSR ShowAllShapes
mc5:
RTS
; this swaps the ghost setting from active to inactive (and vice versa)
ChangeGhostSetting:
LDA #sfx_index_sfx_Ghost
JSR PlaySoundEffect
LDA ghostactive
CMP #0
BNE cgs1
; ghost is currently off, switch it on
LDA #1
STA ghostactive
JSR ShowAllShapes
JSR PrintGhostSetting
RTS
cgs1:
; ghost is currently on, switch it off
LDA #0
STA ghostactive
JSR ShowAllShapes
JSR PrintGhostSetting
RTS
; this prints the current ghost setting (on or off)
PrintGhostSetting:
LDA ghostactive
CMP #1
BEQ pgs1
; ghost is currently off
LDA #<ghost_off_str
STA textprintaddr
LDA #>ghost_off_str
STA textprintaddr + 1
JMP pgs2
pgs1:
; ghost is currently on
LDA #<ghost_on_str
STA textprintaddr
LDA #>ghost_on_str
STA textprintaddr + 1
pgs2:
JSR WriteTextToScreen
RTS
; this drops the piece when in mixture drop mode and drop key has been tapped
; this routine is called if no buttons have been pressed
; so will only do a full drop if dropmethod is 2, last button pressed was down (drop key)
; and dropbuttonpresscount is 1 (so only a quick tap)
DropPieceIfTapped:
; check dropmethod and lastbuttonspressed and dropbuttonpresscount
LDA dropmethod
CMP #2
BNE dpit4 ; if not mixture drop method quit here immediately
; now we check if the button corresponding to drop was the last button pressed
LDA controlleroption
CMP #1
BEQ dpit1
LDA lastbuttonspressed
AND #%00000100 ; check if down button was last button pressed
CMP #$00
BEQ dpit4 ; if 0 then down button was not last pressed, so out of here
JMP dpit2
dpit1:
; this is the check we do if using the alternate controls, where A button corresponds to drop
LDA lastbuttonspressed
AND #%10000000 ; check if A button was last button pressed
CMP #$00
BEQ dpit4 ; if 0 then down button was not last pressed, so out of here
dpit2:
LDA dropbuttonpresscount
CMP #1
BNE dpit4
dpit3:
LDA #1
STA fulldropactive
JSR DropPiece
JSR SmallDelay
dpit4:
RTS
; moves the block down one square if allowed.
DropPieceOneSquare:
LDA ply
STA tmpy
LDA plx
STA tmpx
LDA upsidedown
CMP #1
BEQ dpo1
INC tmpy ; going down one square
JMP dpo2
dpo1:
DEC tmpy ; going up one square (we are upside down)
dpo2:
JSR CheckMove
LDA allowedmove
CMP #$01
BNE dpo5 ; that move is not valid
; if here then the move is valid, so do it now
LDA upsidedown
CMP #1
BEQ dpo3
INC ply
JMP dpo4
dpo3:
DEC ply
dpo4:
JSR ShowAllShapes
; reset the automatic drop timing - we do this as otherwise we would get occasional piece dropping
; down 2 spaces
LDA frameTimer
STA pretim
dpo5:
RTS
;this drops the piece, either by 1 square or till it cannot go any further
DropPiece:
LDA dropmethod
CMP #0
BEQ DropPieceFull
CMP #1
BEQ DropPieceOneSquare
; we are not 0 or 1 so using a mixture - check for fulldropactive
LDA fulldropactive
CMP #0
BEQ DropPieceOneSquare
; if here then using mixture dropmethod and full drop has been requested
LDA #0
STA fulldropactive
JMP DropPieceFull
; drop the piece till it cannot go any further
; this is a loop, the exit being when no more moves are available
DropPieceFull:
LDA ply
STA tmpy
LDA plx
STA tmpx
LDA upsidedown
CMP #1
BEQ dpf1
INC tmpy ; going down one square
JMP dpf2
dpf1:
DEC tmpy ; we are trying to move up (as upside down)
dpf2:
JSR CheckMove
LDA allowedmove
CMP #$01
BNE dpf5 ; that move is not valid
; if here then the move is valid, so do it now
LDA upsidedown
CMP #1
BEQ dpf3
INC ply
JMP dpf4
dpf3:
DEC ply
dpf4:
JSR ShowAllShapes
;call delay loop with small value to make the drop seem less sudden, but still a very fast drop
LDX #$8
JSR ActualDelay
; we get bonus points for dropping, 5 points per square dropped
TYA
PHA ; push Y to the stack as we are going to overwrite it
LDA #<score
STA updatecountaddr
LDA #>score
STA updatecountaddr + 1
LDY #5 ; the 1's column
LDA #5
STA increaseamount ; 5 ones, increase score by 5
JSR UpdateCount
PLA
TAY ; restore Y from the stack
JSR PrintScore ;print this new score
JMP DropPieceFull ; we are jumping to ourselves as we keep going till not possible to drop anymore
dpf5:
RTS
;setblockshapes uses the currentorientation and currentshape to set the
; value of blockshapes i.e. the exact block to draw
SetBlockShapes:
LDA #$00
STA blockpointer
LDX currentshape
CPX #$00
BEQ sbs1
LDA blocklookuptable,x
STA blockpointer
sbs1:
LDX currentorientation
; for each orientation possibility we have to skip 2 bytes
CPX #$00
BEQ sbs2
sbsloop1:
INC blockpointer
INC blockpointer
DEX
CPX #$00
BNE sbsloop1
sbs2:
LDX blockpointer
LDA shapedata, x
STA blockshapes
INX
LDA shapedata, x
STA blockshapes + 1
RTS
; this activates the relevant sprite on-screen
ActivateSprite:
PHA ; push A to the stack
LDA spriteindex
CMP #$00
BNE as1
LDA #$01
STA spriteindex
JSR ConvertToPixels
LDA tmpy
STA $0200
LDA tilenum
STA $0201
LDA tmpx
STA $0203
JMP as5
as1:
CMP #$01
BNE as2
LDA #$02
STA spriteindex
JSR ConvertToPixels
LDA tmpy
STA $0204
LDA tilenum
STA $0205
LDA tmpx
STA $0207
JMP as5
as2:
CMP #$02
BNE as3
LDA #$03
STA spriteindex
LDA #$01
STA sprite3active
JSR ConvertToPixels
LDA tmpy
STA $0208
LDA tilenum
STA $0209
LDA tmpx
STA $020B
JMP as5
as3:
CMP #$03
BNE as4
LDA #$04
STA spriteindex
LDA #$01
STA sprite4active
JSR ConvertToPixels
LDA tmpy
STA $020C
LDA tilenum
STA $020D
LDA tmpx
STA $020F
JMP as5
as4:
CMP #$04
BNE as5
LDA #$05
STA spriteindex
LDA #$01
STA sprite5active
JSR ConvertToPixels
LDA tmpy
STA $0210
LDA tilenum
STA $0211
LDA tmpx
STA $0213
JMP as5
as5:
PLA ; pop A from the stack
RTS
; this activates the relevant ghost sprite on-screen
ActivateGhostSprite:
PHA ; push A to the stack
LDA ghostspriteindex
CMP #$00
BNE ags1
LDA #$01
STA ghostspriteindex
LDA #$01
STA ghostsprite1active
JSR ConvertToPixels
LDA tmpy
STA $0214
LDA #$03
STA $0215
LDA tmpx
STA $0217
JMP ags5
ags1:
CMP #$01
BNE ags2
LDA #$02
STA ghostspriteindex
LDA #$01
STA ghostsprite2active
JSR ConvertToPixels
LDA tmpy
STA $0218
LDA #$03
STA $0219
LDA tmpx
STA $021B
JMP ags5
ags2:
CMP #$02
BNE ags3
LDA #$03
STA ghostspriteindex
LDA #$01
STA ghostsprite3active
JSR ConvertToPixels
LDA tmpy
STA $021C
LDA #$03
STA $021D
LDA tmpx
STA $021F
JMP ags5
ags3:
CMP #$03
BNE ags4
LDA #$04
STA ghostspriteindex
LDA #$01
STA ghostsprite4active
JSR ConvertToPixels
LDA tmpy
STA $0220
LDA #$03
STA $0221
LDA tmpx
STA $0223
JMP ags5
ags4:
CMP #$04
BNE ags5
LDA #$05
STA ghostspriteindex
LDA #$01
STA ghostsprite5active
JSR ConvertToPixels
LDA tmpy
STA $0224
LDA #$03
STA $0225
LDA tmpx
STA $0227
JMP ags5
ags5:
PLA ; pop A from the stack
RTS
; this converts the location on screen to the pixel location
; it assumes registers x and y have been set and puts the result in
; tmpx and tmpy
ConvertToPixels:
; convert tmpx to pixel position by multiplying by 8
TXA
ASL A
ASL A
ASL A
STA tmpx
TYA
ASL A
ASL A
ASL A
STA tmpy
; according to technical documentation, sprite data is delayed by one scanline
; therefore I need to subtract 1 from the sprite's Y coordinate
DEC tmpy
RTS
; we set up to 5 sprites, but it is possible that depending on the shape
; that not all the sprites are being used. In this case we deactivate the sprite
; by setting its coordinates to x = 0, y = F0
HideUnusedSprites:
LDA sprite3active
CMP #$01
BEQ hus1
; if here then sprite 3 is not active
LDA #$F0
STA $0208
LDA #$00
STA $020B
hus1:
LDA sprite4active
CMP #$01
BEQ hus2
; if here then sprite 4 is not active
LDA #$F0
STA $020C
LDA #$00
STA $020F
hus2:
LDA sprite5active
CMP #$01
BEQ hus3
; if here then sprite 5 is not active
LDA #$F0
STA $0210
LDA #$00
STA $0213
hus3:
LDA ghostsprite1active
CMP #$01
BEQ hus4
; if here then ghost sprite 1 (sprite 6) is not active
LDA #$F0
STA $0214
LDA #$00
STA $0217
hus4:
LDA ghostsprite2active
CMP #$01
BEQ hus5
; if here then ghost sprite 2 (sprite 7) is not active
LDA #$F0
STA $0218
LDA #$00
STA $021B
hus5:
LDA ghostsprite3active
CMP #$01
BEQ hus6
; if here then ghost sprite 3 (sprite 8) is not active
LDA #$F0
STA $021C
LDA #$00
STA $021F
hus6:
LDA ghostsprite4active
CMP #$01
BEQ hus7
; if here then ghost sprite 4 (sprite 9) is not active
LDA #$F0
STA $0220
LDA #$00
STA $0223
hus7:
LDA ghostsprite5active
CMP #$01
BEQ hus8
; if here then ghost sprite 5 (sprite 10) is not active
LDA #$F0
STA $0224
LDA #$00
STA $0227
hus8:
RTS
; this is where we calculate the ghost x and y position
; we do this by first offsetting till no collision (against the actual current shape)
; then dropping down till we hit the top of the already placed pieces
CalculateGhostPosition:
; copy the player x and y to the tmp x and y
LDA plx
STA tmpx
LDA ply
STA tmpy
; the currentshape works as an offset into the ghostlookuptable
LDX currentshape
LDA ghostlookuptable, x
STA ghostpointer
CLC
ADC currentorientation
STA ghostpointer ; ghostpointer now has correct index to ghostoffset
LDX ghostpointer
LDA ghostoffset,x
TAX
LDA upsidedown
CMP #$01
BEQ cgp5
; we add the minimum offset required for the ghost to tmpy (current player y position)
; if equal to or more than BOTTOMY then we exit (cannot show ghost)
TXA
CLC
ADC tmpy
CMP #BOTTOMY
BEQ cgp2
CMP #BOTTOMY + 1
BEQ cgp2
CMP #BOTTOMY + 2
BEQ cgp2
CMP #BOTTOMY + 3
BEQ cgp2
; looks ok, store value in tmpy so we are checking from correct start position
STA tmpy
JMP cgp1
cgp5:
; this is if we are upside down. Basic sanity check that our y is not equal to or less than
; TOPYWHENUPSIDEDOWN
STX calcghosttemp ; store the offset in our temp variable
LDA tmpy
SEC
SBC calcghosttemp
CMP #TOPYWHENUPSIDEDOWN
BEQ cgp2
CMP #TOPYWHENUPSIDEDOWN - 1
BEQ cgp2
CMP #TOPYWHENUPSIDEDOWN - 2
BEQ cgp2
CMP #$FF
BEQ cgp2
; looks ok, store value in tmpy so we are checking from correct start position
STA tmpy
cgp1:
; we have gone the minimum distance required by the ghost offset
; we check if there is an immediate collision, if there is, we exit
JSR CheckMove
LDA allowedmove
CMP #$00
BNE cgp3 ; if no collision then determine ghost location
cgp2:
; if in here this not possible to determine ghost x and y, set the ghostshowing to 0
LDA #$00
STA ghostshowing
RTS
cgp3:
; if here then found empty space, now keep dropping, this will be where the ghost shape will be shown
LDA upsidedown
CMP #$01
BEQ cgp6
INC tmpy
JMP cgp7
cgp6:
DEC tmpy ; as we are upside down
cgp7:
JSR CheckMove
LDA allowedmove
CMP #$00
BNE cgp3
cgp4:
; if we are here then have found the top of the place pieces, allocate ghost x and y
LDA upsidedown
CMP #$01
BEQ cgp8
DEC tmpy ; we decrement one as we had gone one too far with previous loop
LDA tmpy
STA ghosty
JMP cgp9
cgp8:
INC tmpy ; we increment one as we had gone one too far with previous loop
LDA tmpy
STA ghosty
cgp9:
LDA tmpx
STA ghostx
LDA #$01
STA ghostshowing
RTS
; this draws the ghost shape. It only draws if ghost is active
; and if calculateghostposition determines it is possible/safe to draw
ShowGhostShape:
LDA ghostactive
CMP #$00
BEQ sgs2 ; if equal to 0 (ghost not active) then exit
sgs1:
JSR CalculateGhostPosition
; now determine if possible to show ghost
LDA ghostshowing
CMP #$00
BEQ sgs2 ; jump to sgs2 (returns) if not possible to show ghost
LDA ghostx
STA tmpx
LDA ghosty
STA tmpy
; need to pass/set ghost colour as well
LDA #$01
STA drawingghost ; so showshape knows we are drawing the ghost
JSR ShowShape
sgs2:
RTS
; showallshapes shows both the main shape in play and the ghost if that is active ( and if it can be shown)
; when called plx and ply have the correct position for the piece
ShowAllShapes:
; first we reset any variables used
LDA #$00
STA sprite3active
STA sprite4active
STA sprite5active
STA spriteindex
STA ghostsprite1active
STA ghostsprite2active
STA ghostsprite3active
STA ghostsprite4active
STA ghostsprite5active
STA ghostspriteindex
STA drawingghost
LDA plx
STA tmpx
LDA ply
STA tmpy
JSR ShowShape ; draw main player sprite
JSR ShowGhostShape
JMP HideUnusedSprites ; hideunusedsprites has an RTS so just use JMP here
; showshape draws a shape on screen, it is passed a tmpx and tmpy
; The colour used is passed in as drawcolour
; It draws the shape pointed to in blockshapes
ShowShape:
LDX tmpx
LDY tmpy ; instead of referring to tmpx and tmpy through this routine, we copy the values to x and y registers and use those
LDA blockshapes
AND #%10000000
BEQ ss1
JSR DrawBlock
ss1:
INX
LDA blockshapes
AND #%01000000
BEQ ss2
JSR DrawBlock
ss2:
INX
LDA blockshapes
AND #%00100000
BEQ ss3
JSR DrawBlock
ss3:
INX
LDA blockshapes
AND #%00010000
BEQ ss4
JSR DrawBlock
ss4:
INY
LDA blockshapes
AND #%00000001
BEQ ss5
JSR DrawBlock
ss5:
DEX
LDA blockshapes
AND #%00000010
BEQ ss6
JSR DrawBlock
ss6:
DEX
LDA blockshapes
AND #%00000100
BEQ ss7
JSR DrawBlock
ss7:
DEX
LDA blockshapes
AND #%00001000
BEQ ss8
JSR DrawBlock
ss8:
INY
LDA blockshapes+1
AND #%10000000
BEQ ss9
JSR DrawBlock
ss9:
INX
LDA blockshapes+1
AND #%01000000
BEQ ss10
JSR DrawBlock
ss10:
INX
LDA blockshapes+1
AND #%00100000
BEQ ss11
JSR DrawBlock
ss11:
INX
LDA blockshapes+1
AND #%00010000
BEQ ss12
JSR DrawBlock
ss12:
INY
LDA blockshapes+1
AND #%00000001
BEQ ss13
JSR DrawBlock
ss13:
DEX
LDA blockshapes+1
AND #%00000010
BEQ ss14
JSR DrawBlock
ss14:
DEX
LDA blockshapes+1
AND #%00000100
BEQ ss15
JSR DrawBlock
ss15:
DEX
LDA blockshapes+1
AND #%00001000
BEQ ss16
JSR DrawBlock
ss16:
RTS
; drawblock
; this calls the relevant routine, either activatesprite or activateghostsprite
DrawBlock:
LDA drawingghost
CMP #$01
BEQ db1
JSR ActivateSprite
RTS
db1:
JSR ActivateGhostSprite
RTS
; this prints the score
PrintScore:
TXA
PHA
TYA
PHA
; the score is 6 chars in length
LDX #0
LDA #6
STA bgbuf, x
INX
STX bgbufidx
; now write the PPU address
LDX #SCOREY
LDA ppu_lookup1, x
LDX bgbufidx
STA bgbuf, x
INX
STX bgbufidx
LDX #SCOREY
LDA ppu_lookup2, x ; this gives us the value for the start if the row
CLC
ADC #SCOREX
LDX bgbufidx
STA bgbuf, x
INX
LDA #<score
STA textprintaddr
LDA #>score
STA textprintaddr + 1
LDY #0
ps1:
LDA (textprintaddr), y
STA bgbuf, x
INX
INY
CPY #6
BNE ps1
; terminate the buffer
LDA #0
STA bgbuf, x
PLA
TAY
PLA
TAX
JSR CommitChange
RTS
; this prints the high score
PrintHighScore:
TXA
PHA
TYA
PHA
; the high score is 6 chars in length
LDX #0
LDA #6
STA bgbuf, x
INX
STX bgbufidx
; now write the PPU address
LDX #HIGHSCOREY
LDA ppu_lookup1, x
LDX bgbufidx
STA bgbuf, x
INX
STX bgbufidx
LDX #HIGHSCOREY
LDA ppu_lookup2, x ; this gives us the value for the start if the row
CLC
ADC #HIGHSCOREX
LDX bgbufidx
STA bgbuf, x
INX
LDA #<highscore
STA textprintaddr
LDA #>highscore
STA textprintaddr + 1
LDY #0
phs1:
LDA (textprintaddr), y
STA bgbuf, x
INX
INY
CPY #6
BNE phs1
; terminate the buffer
LDA #0
STA bgbuf, x
PLA
TAY
PLA
TAX
JSR CommitChange
RTS
; this prints the 2 digits on-screen that have been generated by print2digit
; the co-ords to print them are set using printnumbersx and printnumbersy
PrintNumbers:
TXA
PHA
TYA
PHA
; the digits to print are 2 chars length
LDX #0
LDA #2
STA bgbuf, x
INX
STX bgbufidx
; now write the PPU address
LDX printnumbersy
LDA ppu_lookup1, x
LDX bgbufidx
STA bgbuf, x
INX
STX bgbufidx
LDX printnumbersy
LDA ppu_lookup2, x ; this gives us the value for the start if the row
CLC
ADC printnumbersx
LDX bgbufidx
STA bgbuf, x
INX
LDA digitprint
CLC
ADC #48 ; to convert it to ascii
STA bgbuf, x
INX
LDA digitprint + 1
CLC
ADC #48
STA bgbuf, x
INX
; terminate the buffer
LDA #0
STA bgbuf, x
PLA
TAY
PLA
TAX
JSR CommitChange
RTS
; this routine writes text on screen
WriteTextToScreen:
; we first need to push X and Y to the stack so we can safely use them
TXA
PHA
TYA
PHA
; first we calculate the number of chars being printed
LDA #0
CLC
ADC textoffset
TAY
wtts1:
LDA (textprintaddr), y
BEQ wtts2
INY
BNE wtts1
wtts2:
; at this stage Y holds the number of chars in the string, save this value to printnumchars
; subtract textoffset if necessary
TYA
SEC
SBC textoffset
STA printnumchars
TAY
; the next 2 values are the x value and the y value
INY
LDA (textprintaddr), y
STA printxpos
INY
LDA (textprintaddr), y
STA printypos
wtts3:
LDX #0
LDA printnumchars
STA bgbuf, x
INX
STX bgbufidx
; now write the PPU address
LDX printypos
LDA ppu_lookup1, x
LDX bgbufidx
STA bgbuf, x
INX
STX bgbufidx
LDX printypos
LDA ppu_lookup2, x ; this gives us the value for the start if the row
CLC
ADC printxpos
LDX bgbufidx
STA bgbuf, x
INX
LDA #0
CLC
ADC textoffset
TAY
wtts4:
LDA (textprintaddr), y
BEQ wtts5
STA bgbuf, x
INX
INY
BNE wtts4
wtts5:
; terminate the buffer
LDA #0
STA bgbuf, x
PLA
TAY
PLA
TAX
JSR CommitChange
RTS
; this draws on-screen any background changes that have been requested.
; this should only be called by the NMI routine
MakeBackgroundChanges:
LDX #$00
mbcloop:
LDA bgbuf, x
CMP #$00
BEQ mbcend ; if length read is 0 then we are finished
TAY ; store this length in Y
INX
LDA bgbuf, x
STA $2006
INX
LDA bgbuf, x
STA $2006
INX
mbcloop1:
LDA bgbuf, x
STA $2007
INX
DEY
CPY #$00
BNE mbcloop1
JMP mbcloop
mbcend:
LDA #$00
STA bgupdaterequired
RTS
; checkmove. tmpx and tmpy will be set to the desired location
; This checks if there are any existing blocks at the new location.
; Sets allowedmove to 1 if move allowed
; The first few block checks do not immediately jump to the end if allowedmove is set to 0
; this is because the branches would be out of range. Later blocks do this
CheckMove:
LDA #$01
STA allowedmove ; default is move allowed
LDX tmpx
LDY tmpy ; instead of referring to tmpx and tmpy through this routine, we copy the values to x and y registers and use those
LDA blockshapes
AND #%10000000
BEQ cm1
; block here, check walls first
JSR CheckAllForBlock
cm1:
INX
LDA blockshapes
AND #%01000000
BEQ cm2
JSR CheckAllForBlock
cm2:
INX
LDA blockshapes
AND #%00100000
BEQ cm3
JSR CheckAllForBlock
cm3:
INX
LDA blockshapes
AND #%00010000
BEQ cm4
JSR CheckAllForBlock
cm4:
INY
LDA blockshapes
AND #%00000001
BEQ cm5
JSR CheckAllForBlock
cm5:
DEX
LDA blockshapes
AND #%00000010
BEQ cm6
JSR CheckAllForBlock
cm6:
DEX
LDA blockshapes
AND #%00000100
BEQ cm7
JSR CheckAllForBlock
cm7:
DEX
LDA blockshapes
AND #%00001000
BEQ cm8
JSR CheckAllForBlock
cm8:
INY
LDA blockshapes+1
AND #%10000000
BEQ cm9
JSR CheckAllForBlock
LDA allowedmove
CMP #$00
BEQ cmend
cm9:
INX
LDA blockshapes+1
AND #%01000000
BEQ cm10
JSR CheckAllForBlock
LDA allowedmove
CMP #$00
BEQ cmend
cm10:
INX
LDA blockshapes+1
AND #%00100000
BEQ cm11
JSR CheckAllForBlock
LDA allowedmove
CMP #$00
BEQ cmend
cm11:
INX
LDA blockshapes+1
AND #%00010000
BEQ cm12
JSR CheckAllForBlock
LDA allowedmove
CMP #$00
BEQ cmend
cm12:
INY
LDA blockshapes+1
AND #%00000001
BEQ cm13
JSR CheckAllForBlock
LDA allowedmove
CMP #$00
BEQ cmend
cm13:
DEX
LDA blockshapes+1
AND #%00000010
BEQ cm14
JSR CheckAllForBlock
LDA allowedmove
CMP #$00
BEQ cmend
cm14:
DEX
LDA blockshapes+1
AND #%00000100
BEQ cm15
JSR CheckAllForBlock
LDA allowedmove
CMP #$00
BEQ cmend
cm15:
DEX
LDA blockshapes+1
AND #%00001000
BEQ cmend
JSR CheckAllForBlock
cmend:
RTS
; checks walls and checks playarea buffer for a passed X and Y
CheckAllForBlock:
JSR CheckWalls
LDA allowedmove
CMP #$00
BEQ ca1 ; hitting wall, skip to end
JSR AtAdd
CMP #BLANKSPACE
BEQ ca1
; there was something at the square, set allowedmove to 00
LDA #$00
STA allowedmove
ca1:
RTS
; using a given x and y, determines if there is a block already there based on the value
; stored in playareabuf corresponding to that location
; Modifies A and X register, result in A
AtAdd:
TXA
PHA ; we push to the stack as we overwrite X later in this routine
; we calculate the playarea buffer index by (10 * y) + (x - LEFTWALLX - 1)
; A holds the X value, need to subtract LEFTWALLX and 1
SEC ; apparently you do a SEC before a SBC
SBC #LEFTWALLX
SEC
SBC #$01
STA ataddtemp
TYA
JSR Mult10 ; A now holds 10 * Y
CLC
ADC ataddtemp ; add ataddtemp (which holds (x - LEFTWALLX - 1) value)
TAX ; transfer index to X
LDA playareabuf, x
STA ataddtemp ; now re- use ataddtemp to hold the value in the play area buffer
PLA
TAX
LDA ataddtemp ; A now holds the value in the play area buffer for this X,Y
RTS
; to determine if we are hitting against another block (used by checkmove) we store
; each block as a byte in dedicated storage. The playarea is 10 bytes across and 24
; rows high. To calculate the index we use a routine that quickly multiplies by 10
; Number to be multiplied is passed in A
; routine adds 8X + 2X to give 10X
Mult10:
ASL ; multiply by 2
STA multtemp
ASL
ASL ; at this stage a is 8 times a
CLC ; clear carry flag
ADC multtemp
RTS
; this checks the walls - basically if x has LEFTWALLX or RIGHTWALLX value then
; move not allowed
CheckWalls:
CPX #LEFTWALLX
BEQ cwno
CPX #RIGHTWALLX
BEQ cwno
RTS
cwno:
LDA #$00
STA allowedmove
RTS
; when the shape in play comes to rest, we need to convert the relevant sprite to a
; background image and update the playarea buffer
; The x and y pos are passed in using the X and Y registers respectively
ConvertShapeToBg:
LDA #$00 ; reset the index into the background buffer
STA bgbufidx
LDA blockshapes
AND #%10000000
BEQ csb1
; there is a block at this position, first we update the background
JSR AddBlockToBgBuffer
; then we update the playarea buffer
JSR AddBlockToPlayAreaBuffer
csb1:
INX
LDA blockshapes
AND #%01000000
BEQ csb2
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
csb2:
INX
LDA blockshapes
AND #%00100000
BEQ csb3
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
csb3:
INX
LDA blockshapes
AND #%00010000
BEQ csb4
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
csb4:
INY
LDA blockshapes
AND #%00000001
BEQ csb5
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
csb5:
DEX
LDA blockshapes
AND #%00000010
BEQ csb6
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
csb6:
DEX
LDA blockshapes
AND #%00000100
BEQ csb7
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
csb7:
DEX
LDA blockshapes
AND #%00001000
BEQ csb8
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
csb8:
INY
LDA blockshapes+1
AND #%10000000
BEQ csb9
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
csb9:
INX
LDA blockshapes+1
AND #%01000000
BEQ csb10
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
csb10:
INX
LDA blockshapes+1
AND #%00100000
BEQ csb11
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
csb11:
INX
LDA blockshapes+1
AND #%00010000
BEQ csb12
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
csb12:
INY
LDA blockshapes+1
AND #%00000001
BEQ csb13
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
csb13:
DEX
LDA blockshapes+1
AND #%00000010
BEQ csb14
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
csb14:
DEX
LDA blockshapes+1
AND #%00000100
BEQ csb15
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
csb15:
DEX
LDA blockshapes+1
AND #%00001000
BEQ csb16
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
csb16:
; at this stage we have a buffer with new background information
; we need to finalise the buffer and make it available for the print routine
; which has handled in our NMI section
LDX bgbufidx
LDA #$00
STA bgbuf, x
LDA #$01
STA bgupdaterequired
; wait for background change to be done by NMI
csb17:
LDA bgupdaterequired
CMP #$00
BNE csb17
RTS
; this adds a single block to the playarea buffer. Overwrites values in tmpx and tmpy
AddBlockToPlayAreaBuffer:
; we first check bufferaddactive. If set to 0 we immediately return
LDA bufferaddactive
CMP #0
BEQ abtpab1
; we need to push X and Y to the stack so we can safely use them
TXA
PHA
TYA
PHA
STX tmpx
STY tmpy
; we calculate the playarea buffer index by (10 * y) + (x - LEFTWALLX - 1)
LDA tmpx
SEC ; apparently you do a SEC before a SBC
SBC #LEFTWALLX
SEC
SBC #$01
STA tmpx
LDA tmpy
JSR Mult10
CLC
ADC tmpx
TAX
LDA tilenum
STA playareabuf, x
PLA
TAY
PLA
TAX
abtpab1:
RTS
; this adds a single block to the background buffer. Overwrites values in tmpx and tmpy
AddBlockToBgBuffer:
; we first need to push X and Y to the stack so we can safely use them
TXA
PHA
TYA
PHA
STX tmpx
STY tmpy
LDX bgbufidx
LDA #$01 ; only adding a single block
STA bgbuf, x
INX
STX bgbufidx
; there are 32 bytes per row, and a max of 30 rows
LDX tmpy
LDA ppu_lookup1, x
LDX bgbufidx
STA bgbuf, x
INX
STX bgbufidx
LDX tmpy
LDA ppu_lookup2, x ; this gives us the value for the start if the row
CLC
ADC tmpx
LDX bgbufidx
STA bgbuf, x
INX
LDA tilenum
STA bgbuf, x
INX
STX bgbufidx ; finished, we increment the index
PLA
TAY
PLA
TAX
RTS
; very small delay, used when dropping the piece
VerySmallDelay:
LDX #$24
JMP ActualDelay
; small delay loop used by main loop
SmallDelay:
LDA sensitivity
CMP #$00
BEQ sd2
CMP #$01
BEQ sd3
; else its slow
LDX #$FF
JMP sd1
sd2:
; fast
LDX #$32
JMP sd1
sd3:
; normal
LDX #$80
sd1:
JMP ActualDelay
ActualDelay:
LDY #$00
adloop1:
adloop2:
LDA #$34 ; just a number, really just something that takes time
INY ; inside loop counter
CPY #$00
BNE adloop2 ; run the inside loop 256 times before continuing down
DEX
CPX #$00
BNE adloop1
RTS
; this does the level special action
; for example put a random square on the screen or slide a floor level or
; rise the entire board.
LevelSpecialAction:
LDA currentlevel
CMP #4
BEQ lsa1
CMP #5
BEQ lsa2
CMP #7
BEQ lsa3
CMP #8
BEQ lsa4
CMP #9
BEQ lsa5
CMP #10
BEQ lsa7
RTS
lsa1:
; level 4, same as level 5, but level 4 uses standard blocks while level 5 uses extended set
lsa2:
; level 5, needs shooting stars every 5 pieces
LDA piecesplayedthislevel
TAX
LDY #5
JSR GetModulo
; register A will be 0 if evenly divisible by 5
CMP #0
BNE lsa8
JSR ShootingStar
JMP CheckPlayArea
lsa3:
; level 7, we just need to update the counter showing number of pieces played
JSR CalculateNumberOfPiecesLeft
JMP PrintNumberOfPiecesLeft
lsa4:
; level 8, sliding floor
; a random level is moved either left or right every 4 pieces
LDA piecesplayedthislevel
TAX
LDY #4
JSR GetModulo
; register A will be 0 if evenly divisible by 4
CMP #0
BNE lsa8
JMP SlidingFloor
lsa5:
; level 9, needs shooting stars every 5 pieces and sliding floor every 4 pieces
LDA piecesplayedthislevel
TAX
LDY #5
JSR GetModulo
; register A will be 0 if evenly divisible by 5
CMP #0
BNE lsa6
JSR ShootingStar
JSR CheckPlayArea
lsa6:
LDA piecesplayedthislevel
TAX
LDY #4
JSR GetModulo
; register A will be 0 if evenly divisible by 4
CMP #0
BNE lsa8
JMP SlidingFloor
lsa7:
; level 10 - rising fall
; the floor rises 1 row and that row is filled with random blocks
LDA piecesplayedthislevel
TAX
LDY #10
JSR GetModulo
; register A will be 0 if evenly divisible by 10
CMP #0
BNE lsa8
JMP RisingFloor
lsa8:
RTS
; routine for calculating modulo - result will be in A
; registers X and Y are also used
GetModulo:
TXA
STY getmodtemp
SEC
gm1:
SBC getmodtemp
BCS gm1
CLC
ADC getmodtemp
RTS
; shooting star. This puts a random square somewhere on the playarea. It puts it at least 4
; squares down from the top of the screen to give the player a chance
ShootingStar:
LDA #sfx_index_sfx_Appear
JSR PlaySoundEffect
JSR rnd
AND #%00001111 ;bitmask bits 0, 1, 2 and 3 (so we pick number between 0 and 15)
CLC
ADC #7 ; to ensure we do not put a block directly in starting position
TAY ; register Y now holds the row we will place our star
; now that we have picked the row, need to pick the column
; there are 10 possible positions in the row, so pick number between 0 and 9 inclusive
sst1:
JSR rnd
AND #%00001111 ; bitmask 4 bits, if greater than 9 we pick again
CMP #10
BEQ sst1
CMP #11
BEQ sst1
CMP #12
BEQ sst1
CMP #13
BEQ sst1
CMP #14
BEQ sst1
CMP #15
BEQ sst1
sst2:
; we now have a value between 0 and 9
CLC
ADC #LEFTWALLX
CLC
ADC #1
; now we have a position on the playarea
TAX ; transfer this value to the X register
JSR AtAdd
CMP #BLANKSPACE
BNE sst1 ; if not blank space then pick again
; at this stage we have picked a square and it is blank
; lets draw our random tile on-screen
LDA #$00 ; reset the index into the background buffer
STA bgbufidx
; save the current tilenum
LDA tilenum
PHA ; save it to the stack
LDA #RANDOMTILE
STA tilenum
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
LDX bgbufidx
LDA #0
STA bgbuf, x
JSR CommitChange
; retrieve tilenum from the stack
PLA
STA tilenum
RTS
; finds a row (that has a square already on that row) and slides it one square left or right
SlidingFloor:
LDA #sfx_index_sfx_Lock_or_Move
JSR PlaySoundEffect
LDA #0
STA slidingcounter
STA bgbufidx ; reset the index into the background buffer
sf1:
JSR rnd
AND #%00001111 ;bitmask bits 0, 1, 2 and 3 (so we pick number between 0 and 15)
CLC
ADC #7 ; to ensure we are picking a row further down the screen (more likely to be row with square)
STA tmpy ; we store the row in tmpy
LDA #LEFTWALLX
STA tmpx
INC tmpx
LDX #10 ;10 squares in width of play area
sf2:
TXA
PHA ; push the loop counter x to the stack
LDY tmpy
LDX tmpx
JSR AtAdd
CMP #BLANKSPACE ; check is it is an empty square
BNE sf4 ;square is not empty
INC tmpx
PLA ;pull back the loop counter from the stack
TAX
DEX
CPX #0
BNE sf2
; if here then we found a row that has just blank spaces, so pick a new row, unless slidingcounter
; has reached 20, in which case we have been quite unlucky finding a row, or the player has just
; cleared the playarea and there are no squares currently to move
INC slidingcounter
LDA slidingcounter
CMP #20
BEQ sf3
JMP sf1
sf3:
RTS
sf4:
; found a row with at least one non blank space
; first need to tidy up the stack
PLA
; save the current tilenum
LDA tilenum
PHA ; save it to the stack
;pick whether to go left (0) or right (1)
JSR rnd
AND #%00001111
TAX
LDY #2
JSR GetModulo
CMP #1
BEQ sf6
; going left, so first we draw arrows on this row showing going left and have a short pause
LDX #1
STX showarrow
JSR DrawArrow
;we are going left so get value at column LEFTWALLX + 1
LDY tmpy
LDX #LEFTWALLX
INX
STX tmpx
JSR AtAdd
STA slidingwraparoundtilenum
INC tmpx
LDX #9 ;10 squares in width of play area, minus 1 due to wraparound
sf5:
TXA
PHA
LDY tmpy
LDX tmpx
JSR AtAdd
STA tilenum
LDX tmpx
DEX ; subtract 1 as we are adding block to the left
;addblocktobgbuffer overwrites values in tmpx and tmpy so we need to save to stack
LDA tmpx
PHA
LDA tmpy
PHA
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
PLA
STA tmpy
PLA
STA tmpx
INC tmpx
PLA ;pull back the loop counter from the stack
TAX
DEX
CPX #0
BNE sf5
; now we place the wraparound tilenum at this position
LDY tmpy
LDX tmpx
DEX ; as we have gone one too far
LDA slidingwraparoundtilenum
STA tilenum
LDA tmpy
PHA
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
PLA
STA tmpy
LDX bgbufidx
LDA #0
STA bgbuf, x
JSR CommitChange
; now hide the arrows we previously drew
LDX #0
STX showarrow
JSR DrawArrow
; retrieve the current tilenum
PLA
STA tilenum
RTS
sf6:
; first draw the arrows showing we are going right
LDX #1
STX showarrow
JSR DrawArrow
;we are going right so get value at column RIGHTWALLX - 1
LDY tmpy
LDX #RIGHTWALLX
DEX
STX tmpx
JSR AtAdd
STA slidingwraparoundtilenum
DEC tmpx
LDX #9 ;10 squares in width of play area, minus 1 due to wraparound
sf7:
TXA
PHA
LDY tmpy
LDX tmpx
JSR AtAdd
STA tilenum
LDX tmpx
INX ; add 1 as we are adding block to the right
;addblocktobgbuffer overwrites values in tmpx and tmpy so we need to save to stack
LDA tmpx
PHA
LDA tmpy
PHA
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
PLA
STA tmpy
PLA
STA tmpx
DEC tmpx
PLA ;pull back the loop counter from the stack
TAX
DEX
CPX #0
BNE sf7
; now we place the wraparound tilenum at this position
LDY tmpy
LDX tmpx
INX ; as we have gone one too far
LDA slidingwraparoundtilenum
STA tilenum
; at this stage we only care about saving tmpy
LDA tmpy
PHA
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
PLA
STA tmpy
LDX bgbufidx
LDA #0
STA bgbuf, x
JSR CommitChange
; now hide the arrows we previously drew
LDX #0
STX showarrow
JSR DrawArrow
; retrieve the current tilenum
PLA
STA tilenum
sf8:
RTS
; this calls placebomb BOMBSONLEVEL6 number of times
populatebombs:
LDX #1
popb1:
JSR PlaceBomb
CPX #BOMBSONLEVEL6
BEQ popb2
INX
JMP popb1
popb2:
RTS
; place bomb. This puts a bomb randomly on the playarea. It puts each
; bomb at least 7 squares down from the top of the screen to give the player a chance
PlaceBomb:
TXA
PHA ; push X to the stack as populatebombs uses X as a loop counter
pb1:
JSR rnd
AND #%00001111 ;bitmask bits 0, 1, 2 and 3 (so we pick number between 0 and 15)
CLC
ADC #12 ; to ensure we do not put a block directly in starting position
CMP #BOTTOMY
BCS pb1 ; if equal or greater than BOTTOMY pick again
TAY ; register Y now holds the row we will place our star
; now that we have picked the row, need to pick the column
; there are 10 possible positions in the row, so pick number between 0 and 9 inclusive
pb2:
JSR rnd
AND #%00001111 ; bitmask 4 bits, if greater than 9 we pick again
CMP #10
BEQ pb2
CMP #11
BEQ pb2
CMP #12
BEQ pb2
CMP #13
BEQ pb2
CMP #14
BEQ pb2
CMP #15
BEQ pb2
pb3:
; we now have a value between 0 and 9
CLC
ADC #LEFTWALLX
CLC
ADC #1
; now we have a position on the playarea
TAX ; transfer this value to the X register
JSR AtAdd
CMP #BLANKSPACE
BNE pb1 ; if not blank space then pick again
; at this stage we have picked a square and it is blank
; lets draw our bomb tile on-screen
LDA #$00 ; reset the index into the background buffer
STA bgbufidx
; save the current tilenum
LDA tilenum
PHA ; save it to the stack
LDA #BOMBTILE
STA tilenum
JSR AddBlockToBgBuffer
JSR AddBlockToPlayAreaBuffer
LDX bgbufidx
LDA #0
STA bgbuf, x
JSR CommitChange
; retrieve tilenum from the stack
PLA
STA tilenum
PLA
TAX ; retrieve X from the stack
RTS
; this draws arrows on the appropriate row, then pauses
; it can also remove those arrows
; it is passed a row to draw on in tmpy
; value in A register show if going left (0) or right (1)
; it uses showarrow to determine if to hide or show the arrows
; overwrites value of tilenum
DrawArrow:
; A already set
CMP #0
BEQ da1
; not going left, so assume going right
LDA #RIGHTARROWTILE
STA tilenum
JMP da2
da1:
; going left
LDA #LEFTARROWTILE
STA tilenum
da2:
; now we check if we are actually drawing arrows - may be erasing them!
LDA showarrow
CMP #1
BEQ da3
;asked not to show the arrows (remove them)
LDA #BLANKSPACE
STA tilenum
da3:
LDY tmpy
LDX #LEFTWALLX
DEX ; one to left of left wall
;addblocktobgbuffer overwrites values in tmpx and tmpy so we need to save to stack
LDA tmpx
PHA
LDA tmpy
PHA
JSR AddBlockToBgBuffer
PLA
STA tmpy
PLA
STA tmpx
LDY tmpy
LDX #RIGHTWALLX
INX ; one to right of right wall
;addblocktobgbuffer overwrites values in tmpx and tmpy so we need to save to stack
LDA tmpx
PHA
LDA tmpy
PHA
JSR AddBlockToBgBuffer
PLA
STA tmpy
PLA
STA tmpx
LDX bgbufidx
LDA #0
STA bgbuf, x
JSR CommitChange
; if we are drawing the arrows (not hiding them) then we put in a short pause so
; the player can definitely see the row impacted
LDA showarrow
CMP #0
BEQ da4
LDX #0
daloop1:
TXA
PHA
JSR SmallDelay
PLA
TAX
INX
CPX #2
BNE daloop1
da4:
; now reset bgbufidx so tidied up for next call
LDA #0
STA bgbufidx
RTS
; lifts the whole playarea by 1 row and fills the newly created row with
; randomly placed blocks
RisingFloor:
LDA #sfx_index_sfx_Lock_or_Move
JSR PlaySoundEffect
; save the current tilenum
LDA tilenum
PHA ; save it to the stack
LDA #0
STA bgbufidx ; reset the index into the background buffer
LDY #TOPYWHENUPSIDEDOWN ; top of the playarea
rf1:
LDX #LEFTWALLX
INX
rf2:
JSR AtAdd
STA tilenum
DEY
JSR AddBlockToPlayAreaBuffer
INY
INX
CPX #RIGHTWALLX
BNE rf2
INY
CPY #BOTTOMY
BNE rf1
; at this stage we have raised everything, now just need to create our new line
LDY #BOTTOMY
DEY
rf3:
LDX #LEFTWALLX
INX
rf4:
TXA
PHA
TYA
PHA
;pick whether to draw blank (0) or block (1)
JSR rnd
AND #%00001111
TAX
LDY #2
JSR GetModulo
CMP #0
BEQ rf5
LDA #RANDOMTILE
STA tilenum
JMP rf6
rf5:
LDA #BLANKSPACE
STA tilenum
rf6:
; retrieve X and Y from stack so we add to the correct location
PLA
TAY
PLA
TAX
JSR AddBlockToPlayAreaBuffer
INX
CPX #RIGHTWALLX
BNE rf4
; now we redraw the playarea
JSR DrawPlayAreaFromBuffer
; retrieve the current tilenum
PLA
STA tilenum
RTS
; prints a 2 digit number, number to be converted is in digittemp
Print2Digit:
LDY #1
LDX #8
LDA #0
p2d1:
ASL digittemp
ROL
CMP #10
BCC p2d2
SBC #10
INC digittemp
p2d2:
DEX
BNE p2d1
STA digitprint,y
p2d3:
LDY #0
LDA digittemp
STA digitprint,y
RTS
; this checks if we have completed the level or won the game
CheckLevelComplete:
LDA currentlevel
CMP #6
BEQ clc1
LDA targetlinesforthislevelnum
CMP totalrowscompletednum
BEQ clc2
BCC clc2 ;Accumulator (targetlinesforthislevelnum) less than totalrowscompletednum at this location
BCS clc4 ;Accumulator (targetlinesforthislevelnum) greater than totalrowscompletednum at this location
clc1:
; this is used for checking time left and bombs defused
LDA leveltimer
CMP #0
BEQ clc5 ; game over, time ran out
BCC clc5
LDA #BOMBSONLEVEL6
CMP bombsfound
BEQ clc2
BCC clc2 ; should not happen but include for completeness
BCS clc4
clc2:
; level is complete, increment the currentlevel and see if game is over
INC currentlevel
LDA currentlevel
CMP #TOTALNUMLEVELS
BEQ clc2a
BCS clc3
; we are going to a new level, hide all sprites, they will be reactivated when new level starts
clc2a:
JSR HideAllSprites
JMP NewLevel
clc3:
; game is over - yay!
JMP YouWin
clc4:
; normally this would just continue the loop, but in level 7 you can run out of pieces
; this checks for that scenario
LDA currentlevel
CMP #7
BNE clc4a
; this is level 7 we are playing on, have we run out of pieces?
LDA piecesleftthislevel
CMP #255
BEQ clc5
clc4a:
JMP MainGameLoop
clc5:
JMP GameOver ; sorry, you lost
; this clears a 4x3 section of the screen (sets it to blank graphic)
; This is used when showing the next shape and the saved shape. The location
; starting position is passed in using tmpx and tmpy
ClearInfoArea:
LDA #0
STA bgbufidx
LDX bgbufidx
LDY #0
cialoop1:
LDA #4 ; adding 4 blocks
STA bgbuf, x
; there are 32 bytes per row, and a max of 30 rows
LDX tmpy
LDA ppu_lookup1, x
INC bgbufidx
LDX bgbufidx
STA bgbuf, x
LDX tmpy
LDA ppu_lookup2, x ; this gives us the value for the start if the row
CLC
ADC tmpx
INC bgbufidx
LDX bgbufidx
STA bgbuf, x
LDA #BLANKSPACE
INX
STA bgbuf, x
INX
STA bgbuf, x
INX
STA bgbuf, x
INX
STA bgbuf, x
INX
STX bgbufidx
INY
CPY #3
BEQ cia1
; not finished our loop yet, so increment tmpy and continue the loop
INC tmpy
JMP cialoop1:
; so we have written our 3 rows of 4 blank spaces, place a 0 at the end of bgbuf
cia1:
LDA #0
STA bgbuf, x
JSR CommitChange
RTS
; random number generator. Thanks to Drag for this code
rnd
TXA
PHA
LDA rnd4 ;3
TAX ;2 5
EOR rnd2 ;3 8
STA rnd2 ;3 11
LSR rnd4 ;5 16
ROR ;2 18
LSR rnd4 ;5 23
ROR ;2 25
PHA ;3 28
TXA ;2 30
EOR rnd4 ;3 33
STA rnd4 ;3 36
PLA ;4 40
LSR rnd4 ;5 45
ROR ;2 47
AND #$e0 ;2 49
EOR rnd2 ;3 52
PHA ;3 55
LDA rnd4 ;3 58
EOR rnd3 ;3 61
STA rnd4 ;3 64
PLA ;4 68
STA rnd3 ;3 71
LDA random ;3 74
STA rnd2 ;3 77
TXA ;2 79
STA random ;3 82
PLA
TAX
LDA random
RTS
; this loads the splash screen for Teuthida (music creator)
LoadTeuthidaScreen:
; load background/ nametable
JSR TurnScreenOff
LDA #$00
LDA $2002 ; read PPU status to reset the high/low latch
LDA #$20
STA $2006
LDA #$00
STA $2006
;; load nametable
LDA #<teuthida
STA addrLo
LDA #>teuthida
STA addrHi
JSR LoadRLEBkg
; we do not use the normal turn screen on as this uses a different pattern table
BIT $2002 ; read from PPUSTATUS
LDA #$00
STA $2005
STA $2005
LDA #%10010000 ; re-enable NMI, use background table 1
STA $2000
LDA #%00011110
STA $2001
LDA #1
STA backgroundmode
; end section load background/ nametable
RTS
; this loads a nametable that is encoded with RLE - this is my ASM6 port of RLE decompressor by Shiru
LoadRLEBkg:
LDX addrLo
STX RLE_LOW
LDY addrHi
STY RLE_HIGH
LDY #0
JSR rle_byte
STA RLE_TAG
lrb1:
JSR rle_byte
CMP RLE_TAG
BEQ lrb2
STA $2007
STA RLE_BYTE
BNE lrb1
lrb2:
JSR rle_byte
CMP #0
BEQ lrb4
TAX
LDA RLE_BYTE
lrb3:
STA $2007
DEX
BNE lrb3
BEQ lrb1
lrb4:
RTS
rle_byte:
LDA (RLE_LOW),y
INC RLE_LOW
BNE rb1
INC RLE_HIGH
rb1:
rts
; this loads the main game screen graphics (name table and attributes)
LoadMainGameGraphics:
; load background/ nametable
JSR TurnScreenOff
LDA #$00
LDA $2002 ; read PPU status to reset the high/low latch
LDA #$20
STA $2006
LDA #$00
STA $2006
;; load nametable
LDA #<background
STA addrLo
LDA #>background
STA addrHi
JSR LoadRLEBkg
JSR TurnScreenOn
; end section load background/ nametable
RTS
; this loads the attributes
LoadAttributes:
LDA $2002 ; read PPU status to reset the high/low latch
LDA #$23
STA $2006 ; write the high byte of $23C0 address
LDA #$C0
STA $2006 ; write the low byte of $23C0 address
LDX #$00 ; start out at 0
loadattributeLoop:
LDA attribute, x ; load data from address (attribute + the value in x)
STA $2007 ; write to PPU
INX ; X = X + 1
CPX #64 ; Compare X to 64 - copying 64 bytes
BNE loadattributeLoop ; Branch to loadattributeLoop if compare was Not Equal to zero
RTS
; this clears the screen
ClearScreen:
JSR TurnScreenOff
LDA $2002 ; read PPU status to reset the high/low latch
LDA #$20
STA $2006
LDA #$00
STA $2006
LDX #$04
LDY #$00
clearscreenLoop:
; JSR TurnScreenOff
LDA #BLANKSPACE
STA $2007
INY
BNE clearscreenLoop
DEX
BNE clearscreenLoop
JSR LoadAttributes
JSR TurnScreenOn
RTS
TurnScreenOn: ; Enable screen rendering
BIT $2002 ; read from PPUSTATUS
LDA #$00
STA $2005
STA $2005
LDA #%10000000 ; re-enable NMI, use background table 0
STA $2000
LDA #%00011110
STA $2001
RTS
TurnScreenOff: ; Disable screen rendering
LDA #$00
STA $2000 ; disables the NMI
STA $2001 ; disables rendering
RTS
; WaitFrame - waits for VBlank, returns after NMI handler is done
WaitFrame:
INC sleeping
wfloop1:
LDA sleeping
BNE wfloop1
RTS
;hide all sprites. If we do not do this, then on PAL displays we will see the 0 graphic
;in the top left corner (at pos 0,0). The following sets the y pos to be F0 (off screen)
;for all the sprites
HideAllSprites:
LDX #$00
hsloop1:
LDA #$F0
STA $0200,x
INX
LDA #$0
STA $0200,x
INX
STA $0200,x
INX
STA $0200,x
INX
BNE hsloop1
RTS
; this resets all the variables that need to be reset for the start of a new game
NewGameInitialisation:
LDA #$0
STA upsidedown
LDA #$01
STA allowedswap
STA currentlevel ; set the current level to 1 (starting)
STA bufferaddactive
LDA #1
STA currentlevel
LDA #$00
STA currentorientation
STA blockpointer
STA currentshape
STA totalrowscompletednum
STA ghostactive ; ghost is set to off
STA savedshape ; reset the saved shape to 0 (long bar)
STA dropbuttonpresscount
JSR ResetScore
RTS
; this resets the score back to 000000
ResetScore:
LDX #0
LDA #48 ; ASCII 0
rsloop:
STA score,x
INX
CPX #6
BNE rsloop
RTS
; this compares the score against the high score. If the score is higher it
; sets the variable newhighscore to have a value of 1
; For each digit check we first check the equal comparison as both BCC and BCS
; also check this and we do not want invalid triggers
CheckHighScore:
LDA #0
STA newhighscore
LDA highscore
CMP score
BEQ chs1
BCC chs7 ;Accumulator (high score) less than score at this location
BCS chs6 ;Accumulator (high score) greater than score at this location
chs1:
LDA score + 1
STA checkhighscoretemp
LDA highscore + 1
CMP checkhighscoretemp
BEQ chs2
BCC chs7
BCS chs6
chs2:
LDA score + 2
STA checkhighscoretemp
LDA highscore + 2
CMP checkhighscoretemp
BEQ chs3
BCC chs7
BCS chs6
chs3:
LDA score + 3
STA checkhighscoretemp
LDA highscore + 3
CMP checkhighscoretemp
BEQ chs4
BCC chs7
BCS chs6
chs4:
LDA score + 4
STA checkhighscoretemp
LDA highscore + 4
CMP checkhighscoretemp
BEQ chs5
BCC chs7
BCS chs6
chs5:
LDA score + 5
STA checkhighscoretemp
LDA highscore + 5
CMP checkhighscoretemp
BEQ chs6
BCC chs7
chs6:
RTS ; if here then score is not bigger than highscore
chs7:
LDA #1 ; score is larger than high score
STA newhighscore
RTS
; this sets the highscore to be the value of score. This would be called if
; newhighscore had a value of 1
SetHighScore:
LDX #0
shsloop:
LDA score,x
STA highscore,x
INX
CPX #6
BNE shsloop
RTS
; NES TV system detection code
; Copyright 2011 Damian Yerrick
;
; Copying and distribution of this file, with or without
; modification, are permitted in any medium without royalty provided
; the copyright notice and this notice are preserved in all source
; code copies. This file is offered as-is, without any warranty.
;
; @return A: TV system (0: NTSC, 1: PAL, 2: Dendy; 3: unknown
; Y: high byte of iterations used (1 iteration = 11 cycles)
; X: low byte of iterations used
GetTVSystem:
LDX #0
LDY #0
LDA frameTimer
gtvs1:
CMP frameTimer
BEQ gtvs1:
LDA frameTimer
gtvs2:
; Each iteration takes 11 cycles.
; NTSC NES: 29780 cycles or 2707 = $A93 iterations
; PAL NES: 33247 cycles or 3022 = $BCE iterations
; Dendy: 35464 cycles or 3224 = $C98 iterations
; so we can divide by $100 (rounding down), subtract ten,
; and end up with 0=ntsc, 1=pal, 2=dendy, 3=unknown
INX
BNE gtvs3
INY
gtvs3:
CMP frameTimer
BEQ gtvs2
TYA
SEC
SBC #10
CMP #3
BCC gtvs4
LDA #3
gtvs4:
RTS
; this prints the number of lines that need to completed this level
PrintLevelTarget:
LDX currentlevel
DEX
LDA linesneededperlevel,x
STA digittemp
JSR Print2Digit
LDA #LINESTOCOMPLETEX
STA printnumbersx
LDA #LINESTOCOMPLETEY
STA printnumbersy
JSR PrintNumbers
RTS
; this prints the lines completed so far
PrintLinesOrBombsCompleted:
LDA currentlevel
CMP #6
BEQ plobc1
LDA totalrowscompletednum
JMP plobc2
plobc1:
LDA bombsfound
plobc2:
STA digittemp
JSR Print2Digit
LDA #LINESCOMPLETEDX
STA printnumbersx
LDA #LINESCOMPLETEDY
STA printnumbersy
JSR PrintNumbers
RTS
; this writes the name of the level at the bottom of the screen, max of 12 levels using this code
WriteNameOfLevel:
; each level piece of data is 20 bytes long
; to calculate the offset, we subtract one from the currentlevel, call mult10
; then double - this gives the correct offset
LDA currentlevel
SEC
SBC #1
JSR Mult10
ASL ; multiply by 2
STA textoffset
LDA #<levelnames
STA textprintaddr
LDA #>levelnames
STA textprintaddr + 1
JSR WriteTextToScreen
LDA #0
STA textoffset
RTS
; this prints the upcoming level with a short pause
PrintUpcomingLevel:
LDA #<level_str
STA textprintaddr
LDA #>level_str
STA textprintaddr + 1
JSR WriteTextToScreen
LDA currentlevel
STA digittemp
JSR Print2Digit
LDA #LEVELINFOPRINTX
STA printnumbersx
LDA #LEVELINFOPRINTY
STA printnumbersy
JSR PrintNumbers
LDA currentlevel
CMP #6
BEQ pucl1
CMP #7
BEQ pucl2
JMP pucl3
pucl1:
; show specific message for level 6
LDA #<defuse_info1_str
STA textprintaddr
LDA #>defuse_info1_str
STA textprintaddr + 1
JSR WriteTextToScreen
LDA #<defuse_info2_str
STA textprintaddr
LDA #>defuse_info2_str
STA textprintaddr + 1
JSR WriteTextToScreen
JMP pucl3
pucl2:
; show specific message for level 7
LDA #<limitedpieces_info1_str
STA textprintaddr
LDA #>limitedpieces_info1_str
STA textprintaddr + 1
JSR WriteTextToScreen
LDA #<limitedpieces_info2_str
STA textprintaddr
LDA #>limitedpieces_info2_str
STA textprintaddr + 1
JSR WriteTextToScreen
pucl3:
JSR LargePause
RTS
; this waits a couple of seconds
LargePause:
JSR SmallDelay
JSR SmallDelay
JSR SmallDelay
JSR SmallDelay
JSR SmallDelay
JSR SmallDelay
JSR SmallDelay
JSR SmallDelay
JSR SmallDelay
JSR SmallDelay
JSR SmallDelay
JSR SmallDelay
JSR SmallDelay
JSR SmallDelay
JSR SmallDelay
JSR SmallDelay
RTS
; This draws words onscreen using blocks to make up the parts of the letters
; Each byte represents the tile number of the block to draw
; 254 means end of line and 255 means end of data (stop drawing)
PrintWordsWithBlocks:
; we first need to push X and Y to the stack so we can safely use them
TXA
PHA
TYA
PHA
LDA #0
STA bgbufidx
; X and Y hold the x and y pos to print on screen
LDY #0
LDA (logoaddr),y
STA printxpos
INY
LDA (logoaddr),y
STA printypos
LDA #2
STA logoidx ; we skip the first two bytes as these are the X and Y pos
pwwbmain:
LDX #0
LDY logoidx
pwwb1:
LDA (logoaddr),y
CMP #255 ; end of logo
BEQ pwwb6
CMP #254 ; end of line
BEQ pwwb2
INY
INX
JMP pwwb1
pwwb2:
; x now holds the length of the line to print, if x is zero then just skip to new line to print
CPX #0
BEQ pwwb5
TXA
LDX #0
STA bgbuf, x
INX
INC bgbufidx
; now write the PPU address
LDX printypos
LDA ppu_lookup1, x
LDX bgbufidx
STA bgbuf, x
INX
INC bgbufidx
LDX printypos
LDA ppu_lookup2, x ; this gives us the value for the start if the row
CLC
ADC printxpos
LDX bgbufidx
STA bgbuf, x
INX
LDY logoidx
pwwb3:
LDA (logoaddr),y
CMP #254 ; end of line
BEQ pwwb4
STA bgbuf, x
INX
INY
JMP pwwb3
pwwb4:
; terminate the buffer
LDA #0
STA bgbuf, x
JSR CommitChange
pwwb5:
LDA #0
STA bgbufidx
INY
STY logoidx
INC printypos ; so we start printing on next line
JMP pwwbmain
pwwb6:
; restore stack
PLA
TAY
PLA
TAX
RTS
;; Includes and data tables
include "titleroutines.asm"
include "initroutines.asm"
include "ggsound.asm"
include "BGM.asm"
.align 64
include "BGM_dpcm.asm"
include "data.inc"
;; The Vectors
.org $fffa ; sets us up at the very end of the code.
.dw NMI ; now the NMI points to our label NMI
.dw RESET ; now the Reset points to our label RESET
.dw 00
.incbin "graphics.chr" ;; this includes the graphics for
;; the sprites in the
;; assembly of the game
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 5,953
|
Posted: February 4, 2014 in Uncategorized
Featuring tracks from The Glitch Mob, Gardens & Villa, Future Islands, Active Child, Francis Lung (ex-WU LYF), Darkside, Au Palais, The War On Drugs and Made In Heights.
Stream it here: https://thebreakdownwithben.files.wordpress.com/2014/02/the-breakdown-with-ben-episode-66.mp3
To download the mp3 file, right click and "save link as" here: The Breakdown with Ben Episode 66
Hello music lovers and welcome to another fantastic edition of The Breakdown. This episode is super awesome (as I always tend to say, but hell, its never a lie!). Some big names return with new material and some brilliant newer acts are killing it as well. This one is just all round very strong.
This episode contains an unusually high number of songs from bands represented in the pointy end of The Breakdown's top album lists of previous years. Three of the four bands that topped The Breakdown's albums list in 2012, and the bands responsible for the top two albums of 2011 are represented in this episode.
Number 2 album of 2012 holders Gardens & Villa are about to drop their second LP, Dunes. Colony Glen is the second song lifted from it; packing that familiar G&V sound, but moving into a bit more of an electro feel, which at this very early stage, I sense the entire album has done. To be honest, moving from a guitar based sound to an electro based sound across two albums, while maintaining the same overall flavour is a pretty difficult and very clever thing to have achieved. I'm only two listens in, but it has me very excited and you will definitely be hearing more from it over coming episodes.
The band that took out The Breakdown's number 1 album in 2012, WU LYF, was a crying shame of a story. After releasing the stunning album Go Tell Fire To The Mountain, the enigmatic frontman and once in a generation vocalist, Ellery James Roberts, broke the band up in a very public manner, without even telling the other members. Aside from it being a massive loss to the music world, I can imagine the humiliation felt by the other band members. It seems this indignation has been harnessed in a very clever and mature way from WU LYF bassist Tom McClung, who has released a single under the pseudonym Francis Lung. In his song A Selfish Man, he pens the lyrics "When everything becomes too much, You have to leave the band, And it was not the plan, But I don't wanna know you, Or wanna understand, I can let you go, 'cause I'm a selfish man". This is possibly the most accurate depiction of the bands reaction to the unfortunate wayward ways and bitter departure of their frontman.
Number 4 of 2012 holder Future Islands is also back with brand new material, bringing back that unmistakable, highly unconventional and highly entertaining vocal sound.
Another former number 1 album holder, 2011's The Glitch Mob, is about to release their second studio album, Love, Death, Immortality. The lead single from it, Can't Kill Us, brings back that incredibly hard hitting, heavy, dark and sonically all-encompassing sound that they and they alone own. This song is slightly on the heavier side of anything on Drink The Sea, but their trademark sound has not changed. This album promises to be one of the highlights of this year.
Rounding out the previous years' top album holders is number 2 from 2011, Active Child. His trademark sound is apparent in this beautiful song from his recently released EP, Rapor.
Other notable highlights in this episode include Made In Heights, who have released a spine tingling song entitled Murakami, which I find has originality on par with Alt-J and Yeasayer. Brooklyn duo Darkside has penned possibly the best blues based song I have ever laid ears on with Paper Trails. It is dark, deep, dripping with intrigue and almost impossible to stop listening to. London-via-Toronto brother-sister duo Au Palais have brought back their beautiful, swirling, ethereal, electro sound with a new song, and hopefully soon an album. Swedish indie group Last Lynx have also been busy, and will hopefully have an album for us soon. A new solo producer out of the UK, Koloto, has also raised eyebrows with the awesome tune Cedar Sheds, invoking comparisons to Beats Antique and Tor.
Philadelphia band The War On Drugs is back with their second album Lost In The Dream due for release next month, and the lead single from it, Red Eyes, invoking memories of Bruce Springsteen.
Fantastic albums still on high rotation that are represented in this episode include RÜFÜS's Atlas, July Talk and The 1975's self-titled releases, and Darkside's Psychic.
Lastly another big thumbs up to Vienna based duo Chronic City, who have been personally sending me their music for quite a while now. They never disappoint, and their latest release, a beautiful song titled Ocean Of Luxury has not let us down again. Well done guys.
Have fun with this one. Good luck getting tired of it before the next Breakdown episode is upon us!
Peace x
Artist – Title (Start Time)
1. The War On Drugs – Red Eyes (00:00)
2. Bad Suns – Salt (04:59)
3. RÜFÜS – Unforgiven (08:44)
4. Made In Heights – Murakami (13:16)
5. Darkside – Paper Trails (17:34)
6. July Talk – The Come Down Champion (22:20)
7. Francis Lung – A Selfish Man (25:20)
8. J'mapelle Bob Waddle – We Be Well Prepared (31:47)
9. Yellow Ostrich – Shades (35:30)
10. Future Islands – Seasons (Waiting On) (39:19)
11. Crystal Fighters – Separator (43:09)
12. Gardens & Villa – Colony Glen (47:15)
13. Everything Everything – Cough Cough (51:35)
14. Chronic City – Ocean Of Luxury (ft. Sleep Sleep) (55:18)
15. Koloto – Cedar Shed (59:18)
16. Last Lynx – Killing Switch (1:02:28)
17. Au Palais – Blue Lights (1:05:45)
18. Germany Germany – All Of Your Love (Ft. Kotomi) (1:09:30)
19. RÜFÜS – Take Me (1:13:17)
20. Peer Kusiv – I Can't stop (ft. Lenny) (1:17:18)
21. Streets Of Laredo – Lonsdale Line (1:23:45)
22. The 1975 – Settle Down (1:27:24)
23. Active Child – She Cut Me (1:31:23)
24. July Talk – Paper Girl (1:33:39)
25. The Glitch Mob – Can't Kill Us (1:37:00)
26. Wax Beach – Circles (1:41:53)
The Breakdown's Top 100 Songs of 2013
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,537
|
\section{Introduction}
\label{sec:introduction}
Social programs, whether developmental, humanitarian or public health related, rely on knowledge of where vulnerable populations are located. People travel nationally and internationally for a variety of purposes including regular commuting, seasonal work, tourism or coerced migration. Data describing these movements allow for the development of statistical models and analyses and significant universal patterns have been found in human mobility patterns \cite{Gonzalez:2008ul}.
Consider a few illustrative examples. In public health, epidemiological models of disease spread can forecast the course of an outbreak,allowing health workers to head-off infection transmission.
These models rely on travel data to project disease transmission between geographic
areas \cite{balcan2009multiscale,bajardi2011human,parker2011distributed,Viboud447,sadilek2012predicting}. Human migration, whether caused by economic hardship or resulting from physical danger to a population, follows both geographically advantageous routes, as well as previously established transit patterns resulting from existing connections between populations. Tracking current and predicting future migrations, which allows governments and NGOs to respond to migrations and refugee crises, depends on global mobility patterns \cite{JORS:JORS521,simini2012universal}.
A sudden change in established travel patterns may provide early-warning of crisis onset \cite{sonmez1998tourism,prideaux2003events}.
Researchers have utilized a diverse range of data resources for estimating global mobility patterns, each with distinct tradeoffs. These data sources can provide local travel patterns (within a metropolitan area) domestic patterns (travel within a country), and global patterns (international travel.) Airline travel dominates as a means for measuring
long distance travel \cite{colizza2006role,khan2009spread}. However, public air travel data is not timely, has poor coverage of local and domestic travel and may not accurately capture flights with connections\cite{iata}. Anonymized mobile phone meta-data can provide coverage of travel at multiple levels \cite{sagl2012social,krings2009urban,deville2014dynamic}
especially throughout urban areas \cite{calabrese2013understanding}.
As a result, mobile data has been used increasingly in epidemiological models of disease spread \cite{wesolowski2014commentary,bengtsson2015using}.
However, mobile data is proprietary and can be privacy sensitive. Diverse providers throughout
the world prevent the construction of a large, global dataset. Tourist statistics, available for many locations, do not typically
reflect traveler origin and tourism reflects only one type of travel. Finally, travel diaries, where people manually log
travel, are a traditional way of obtaining travel data \cite{axhausen1994travel}. But such methods simply cannot scale beyond specialized purposes motivating new approaches.
Social media provides a new and mostly untapped resource for obtaining travel patterns. Many social media platforms allow users to geotag their content. For example, Twitter allows users to geotag a tweet
with a specific set of coordinates -- using a GPS enabled device -- or tag a location as being associated with the message.
Additionally, local search and discovery services, such as Foursquare, allows users to {\em check-in} from different locations, creating
geotagged tweets.
The overall rate of geotagged tweets in Twitter remains low, roughly 2-3\%, but continues to grow. Even at this relatively low rate, with
roughly 500 million tweets per day, Twitter provides millions of geolocated data points on a daily basis.
Since most tweets are publicly available, the result is a large, public geotagged corpus.
There have been numerous uses of geotagged Twitter data, such as in public health \cite{Paul:2013lm,sadilek2012predicting}, political science \cite{o2010tweets}, linguistics \cite{eisenstein2010latent,eisenstein2014diffusion},
disaster response \cite{tapia2011seeking}, event detection \cite{watanabe2011jasmine}, topic discovery \cite{hong2012discovering} and location recommendation \cite{noulas2012random,liu2013point}. The importance of geotagged data has led to the task of geolocation,
in which a system automatically infers the location of a user
\cite{han2014text,rout2013s,compton2014geotagging,cha2015twitter,jurgens2015geolocation,osborne2014real,Dredze:2013a} or a specific tweet \cite{osborne2014real,Dredze:2016rm}.
Compared to the extensive literature on inferring and using geolocated Twitter data, there has been less work on understanding
aggregate location patterns. \cite{mocanu2013twitter} used location data to understand the languages of Twitter. \cite{leetaru2013mapping} used geotagged tweets to describe the geography of Twitter. Some have studied check-in data, such as that from Foursquare, which provided
an early map of the emerging landscape of this type of data on Twitter \cite{cheng2011exploring,bauer2012talking}.
The most relevant work to ours is that of \cite{hawelka2014geo}, who also derived
global mobility patterns from Twitter. We contrast our work with theirs below.
This paper describes preliminary results from our investigation into Twitter as a data source of global mobility patterns for social good.
We consider a massive dataset: over 8.5 billion tweets that represent almost four years of all publicly available geotagged Twitter data.
We construct a global travel network for both cities and countries, which includes more than 87,856 cities and 248 countries, that reflects
travel patterns over four years.
We describe the construction of this travel network from Twitter data and a preliminary analysis of the resulting network.
\section{Data Resources}
\label{sec:data}
\myparagraph{Twitter} We use a collection of every publicly available geotagged tweet from January 1, 2012 to September 30, 2015. The collection contains 8.578 billion tweets from over 50 million users. Users had a median of 10 tweets each, with a mean of 168.98 and standard deviation of 962.5. Each tweet contains text, a time the tweet was posted, the user id and a location. These tweets include those authored directly by the user, or those created by an automated service, such as FourSquare. No private tweets were captured.
There are two methods by which users can share location information with their tweet. First, a user can author a message from a GPS enabled device, such as a smart phone. If geotagging is enabled, then the device will attach the current latitude and longitude to the tweet. Second, a user can choose to tag their tweet with a location. For example, a user may identify their location as ``Starbucks'' or ``Johns Hopkins University.'' In this case, Twitter associates a known location with the tweet. Locations can be countries, administrative areas (e.g. US States), cities, neighborhoods and points of interest (e.g. stores, parks, buildings, etc.). These locations contain several fields, including a name, location type and bounding box. Tweets may have both a set of coordinates and an associated known location. We note that users can also attach a location to their profile, which indicates their primary location, but we did not use this information on account of ambiguities e.g. `NYC/LA` or humorous locations `The World`.
\myparagraph{Geonames} While Twitter includes information about each location, we sought to map our data to an external knowledge resource. This will allow for future comparisons to other data sources, as well as inclusion of additional information about locations (e.g. populations, geographic administrative hierarchies, etc.) We use Geonames \cite{wick2012geonames}, a geographical database that covers all countries and contains over eight million named locations.
We used the datafile {\sc allCountries.zip}\footnote{Accessed April 25, 2016} which contains 11,005,123 locations. Each location comes with a set of coordinates and associated metadata (e.g. population).
\section{Computing Travel Statistics}
\label{sec:methods}
For each user in the Twitter collection, we organized all of their tweets from the entire time period chronologically. We then examined successive tweets to identify possible travel events as indicated by different locations between two adjacent tweets. A travel event is defined using the following guidelines:
\squishlisttwo
\item The successive tweets must occur within 72 hours of each other.
\item Both tweets must have a location as either a tagged location or specific coordinates.
\item The locations associated with each tweet are different, and one location does not contain the other. For example, a user may tweet first from Midtown Manhattan, and then from New York City. We would identify this as the same location.
\item The tweets must have been authored more than 50km apart. Tweets closer than 50km are not recognized as a travel event as they likely indicate local travel, even when they are in different locations. When specific coordinates are not available, distance is measured from the centroid of the bounding box of the associated location.
\squishend
Resulting travel events are associated with a timestamp (the time of the second tweet), a user, an origin and a destination location. Overall, we identified over 300 million travel events,
with the number of travel events per user having a median of 0, mean of 3.6 and standard deviation of 250.7.
Some user accounts falsify location information for a variety of reasons. For example, a news aggregation account may list as its location the place most relevant to a tweeted story, or a spam account may attach false location information. We remove these accounts using several methods. First, we exclude travel events that require travel in excess of 1000km/hour (following \cite{hawelka2014geo,compton2014geotagging}). Second, as can be seen from the distribution of tweets per user (Figure (\ref{fig:tweet_dist})) there is a large skew in user activity. Therefore we remove users with more than 1000 geolocated tweets, roughly the top 4\% of all users in our data. Finally, we remove users who have more than 100 travel events, roughly the top 0.4\% of all users.
\begin{figure}[!tb]
\centering
\includegraphics[width=.4\textwidth]{histogram.pdf}
\caption{\label{fig:tweet_dist} A histogram of the number of tweets (black) and events (blue) per user (y-axes in millions).}
\vspace{-.5cm}
\end{figure}
\myparagraph{Geonames Matching} We match every Twitter location to a Geonames location. We proceed in two passes. First, we attempt to match each location to a city with a population of at least 1,000 people (145,343 possible cities). Second, for unmatched places, we consider all possible locations in the database, which include administrative areas, roads, buildings, and other types of locations
(11,005,123 unique options). We match a Twitter location to a Geonames location by measuring the distance of the centroid of the Twitter
location, as computed from the provided bounding box, to the closest possible Geonames location, which is defined by a single set
of coordinates. We only consider matches closer than 50 km. Of the 1,128,662 unique Twitter locations 521 did not
match to Geonames; these locations were dropped from the data.
Table \ref{tab:geonames} shows statistics on the number and types of matches of Twitter locations to Geonames locations. We provide
statistics on the number of matches of unique Twitter location, as well as their coverage of the total dataset.
\begin{table}[t]
\begin{center}
\small
\begin{tabular}{|l|c|c|}
\hline
\bf Geonames Type & \bf Twitter Locations & \bf Travel Events \\
\hline
Admin area (A) & 672 & 115,163\\
Water (H) & 887 & 324,039 \\
Park (L) & 221 & 18,387 \\
City (P)& 84,982 & 156,273,217 \\
Road (R) & 12 & 33,012 \\
Point of interest (S) & 606 & 64,123 \\
Mountain (T) & 405 & 121,416 \\
Undersea (U) & 30 & 85,781 \\
Forest (V) & 4 & 339 \\
None & 26 & 352\\
\hline
\end{tabular}
\end{center}
\caption{ \label{tab:geonames} The types of Geonames locations used. Travel events include the type of each vertex on the edge in the count. Parenthesis indicate the Geonames feature type code.}
\vspace{-.5cm}
\end{table}
\myparagraph{Travel Network Construction}
The final step is to construct the travel network from the individual travel events.
We construct a graph, in which vertices are locations and weighted edges indicate the total number of travels between the two locations. We generate both a directed and undirected graph, where the undirected graph sums the weights of the two edges between a pair of vertices.
We construct two travel networks, where each has a directed and undirected version.
First, we use the Geonames locations to construct a full global network between cities and other types of Geonames locations. This network contains 7,688,854 edges between 87,856 vertices.
Second, we construct a global network between countries. This network contains 12,449 edges between 248 vertices. For this network, we rely on the country associated with each Twitter provided location, allowing for the inclusion of those few locations not successfully mapped to Geonames locations.
Statistics on each network are shown in Table \ref{tab:network_stats}.
\begin{table}[t]
\begin{center}
\small
\begin{tabular}{|l|c|c|}
\hline
\bf & \bf Full Network & \bf Country Network \\
\hline
Locations & 87,856 & 248 \\
Edges & 7,688,854 & 12,449 \\
Edge density & 9.96$\times 10^{-4}$ & 1.6$\times 10^{-6}$ \\
Travel events & \multicolumn{2}{|c|}{309,253,447} \\
Total users & \multicolumn{2}{|c|}{50,766,672} \\
Total tweets & \multicolumn{2}{|c|}{8,578,399,048} \\
\hline
\multicolumn{3}{|c|}{Only travel events} \\
\hline
Users &\multicolumn{2}{|c|}{11,581,990}\\
Total tweets & \multicolumn{2}{|c|}{2,145,810,039}\\
\hline
\end{tabular}
\end{center}
\caption{ \label{tab:network_stats} Statistics of the two travel networks.}
\vspace{-.3cm}
\end{table}
\begin{figure*}[!tb]
\begin{minipage}{0.49\textwidth}
\centering
\includegraphics[width=1\textwidth]{country_cropped_new.png}
\end{minipage}
\hspace{.3cm}
\begin{minipage}{0.49\textwidth}
\centering
\includegraphics[width=1\textwidth]{city_in_same_country_cropped_new.png}
\end{minipage}
\caption{\label{fig:maps} Mobility as observed in the travel network between countries (left) and between cities within the same country (right).}
\vspace{-.5cm}
\end{figure*}
\begin{table}[t]
\begin{center}
\scriptsize
\begin{tabular}{|c|c|c|c|}
\hline
\bf Continent & \bf Top edge &\bf Top penetration (penetration)\\
\hline
Europe & UK-Spain & United Kingdom (4.4\%) \\
Africa & Botswana-Africa & South Africa (2.9\%) \\
North America & US-Canada & US (3.7\%) \\
South America & Argentina-Brazil & Chile (3.6\%) \\
Asia & Indonesia-Malaysia & Qatar (4.1\%) \\
\hline
\end{tabular}
\end{center}
\caption{ \label{tab:penetration} Most common edge and country with the highest Twitter penetration per continent (with at least 5000 users).}
\vspace{-.5cm}
\end{table}
\subsection{Comparison to Prior Work}
The work of \cite{hawelka2014geo} also derived global mobility patterns from Twitter. We follow their approach with some modifications,
such as mapping to an external reference (Geonames), the criteria for identifying travel events, and the spam removal method.
The major difference from our work is the amount of data considered. They use one year worth of geotagged tweets from 2012, which
encompasses 944 million tweets. In contrast, our dataset is roughly nine times larger, and covers four years worth of data.
The most immediate benefit of the increase in data size is our ability to consider cities, whereas their analysis only included countries.
Additionally, their work presents methods for normalizing data by Twitter penetration. Our development of normalization methods is ongoing
and the results in this paper do not yet reflect those efforts. Finally, they include extensive evaluations of their data, and we intend
to replicate several of their analyses.
\section{Analysis}
Figure \ref{fig:maps} shows the number of travel events between locations on a world map, where edge intensity denotes weight.
For clarity, we filter the edges to show just country links (left) and links of cities within the same country (right).
Next, we compute statistics on user penetration: the country with the highest Twitter penetration (number of Twitter users normalized by population) for each continent (Table \ref{tab:penetration}.)
We also include the most heavily travelled country to country link in each continent. While these initial results are promising, they highlight the need for careful normalization of the data based on Twitter
penetration (as in \cite{hawelka2014geo}.) Additionally, we may consider merging locations in the same metropolitan area
to smooth out local travel effects \cite{han2014text}.
\section{Discussion}
Our preliminary results suggest that Twitter may be a promising new data source for global mobility patterns and we plan to evaluate the suitability of this dataset for several applications. The most pressing consideration is the representativity of Twitter as determined by relatively low adoption of the service within low income countries. Careful calibration of movements aggregated from Twitter relative to the user base is required.
The benefits of Twitter as a mobility data source are clear. Firstly, data can be collected in real-time and are easily accessible through public APIs. Twitter can also capture movements on smaller spatial scales i.e. intra-urban, that are not captured by long distance travel records.
In this work we do not consider the content of tweets. While this content has been shown to be of great value in monitoring the opinions and topics of interest of vulnerable populations, further development of taxonomies and tools are required to analyze non-European languages and so provide insight in lower income countries. Analyzing these messages would allow us to
consider the relationship between topic and travel. For example, do users who discuss climate change take fewer long distance trips, or
are users who tweet about political activism less likely to travel to certain countries? We look forward to developing these ideas further
in future work.
{\bf Acknowledgements} We thank Adela Quinones and Mark Dimont for their insights and comments.
\begin{scriptsize}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 3,942
|
Q: How to automatically select solutions from a set of solutions given by Solve? I have a function of trigonometric functions which must be equated to zero in order to obtain the appropriate results. This is done in the following fashion:
Solve[G[a,b,y,x]==0,x},
which returns several results, all of which only one has significance to me. I know I can select this result by using, for example,
Solve[G[a,b,y,x]==0,x}[[1]][[2]]
but I need to plot such results, so I used the Solve command in a Table command
data = Table[{y,Solve[G[a,b,y,x]==0, {x, -90, 90}];
The problem is that this gives me, sometimes 4 results sometimes 2, but I'm always interested in the smallest real result. How can I select automatically only the result that interests me?
Here is the function I'm using:
G[ni_, ki_, nt_, kt_, y_, x_] :=
Sqrt[(ni^2 - ki^2) + Sqrt[((ni^2 - ki^2)^2 +
4 ((ni ki)/Cos[y])^2)]] Sin[y] -
Sqrt[(nt^2 - kt^2) +
Sqrt[((nt^2 - kt^2)^2 + 4 ((nt kt)/Cos[x])^2)]]Sin[x]
and parameters:
data = Table[{y,Solve[G[1.391, 1.19, 2.6, 1.3, y Pi/180, x Pi/180] == 0, x]}, {y, -90, 90}];
Thank you very much.
A: I will give a solution for the minimum real root
G[ni_, ki_, nt_, kt_, y_, x_] :=
Sqrt[(ni^2 - ki^2) +
Sqrt[((ni^2 - ki^2)^2 + 4 ((ni ki)/Cos[y])^2)]] Sin[y] -
Sqrt[(nt^2 - kt^2) +
Sqrt[((nt^2 - kt^2)^2 + 4 ((nt kt)/Cos[x])^2)]] Sin[x]
Table[{y,
x /. (First[
NSolve[G[1391/1000, 119/100, 26/10, 13/10, y Pi/180,
x Pi/180] == 0, x, Reals]] /. C[1] -> 0)}, {y, -80, 80, 10}]
Out[]= {{-80, -66.3258}, {-70, -47.9345}, {-60, -36.8608}, {-50, \
-28.9019}, {-40, -22.3127}, {-30, -16.3845}, {-20, -10.7898}, {-10, \
-5.36059}, {0, 0.}, {10, 5.36059}, {20, 10.7898}, {30, 16.3845}, {40,
22.3127}, {50, 28.9019}, {60, 36.8608}, {70, 47.9345}, {80,
66.3258}}
ListPlot[%]
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,835
|
Robyn April 9, 2014
Review: A Werewolf! – Because Why Not?
Because Why Not? is a very apt name for the debut EP from Worcestershire mathrock duo A Werewolf! The entire record is a whistle-stop tour through genres and musical styles to complicated rhythms with crazy, crazy film quotes thrown in. I'd like to say that if you've got a record in front of you with a song called 'Chop Yourself Off at the Knees and Pretend You're Tom Cruise', you kind of know what you're getting into but with Because Why Not?, you totally don't. And that is not a bad thing at all.
The record starts off intense. 'Hellbent on Duck Slaughter' is the mathiest track of them all, and if you're not into crazy riffs bordering on the wrong side of jazz, then this will probably put you off for life. However, listen closely and you'll find that there's an incredibly full sound coming from these guys, despite the fact that they're a duo. It's all completely instrumental, and in most cases, this works. In tracks like 'Come At Me Bro', which are less complex, vocals are missed somewhat, but that punk edge instils a great sense of fun anyway.
Where A Werewolf! truly shine though is in their more post-rock sounding tunes – 'Psycho Scientist vs Super Massive Giant Swan' and 'Sanka Ya Dead?' both feature jangly guitars and incredibly tight drums with a more laidback feel than the rest of the record – slowing down slightly truly enables their talent to shine through. However, they're still highly exciting when they're playing more frenetic stuff – 'I Have To Return Some Videotapes' effortlessly mixes funk and metal with those complex time signatures with awe-inspiring effect. It's probably not the kind of stuff you'd just stick on in the background, and nor should it be – Because Why Not? deserves to be dissected and digested and to be appreciated fully.
Because Why Not? is ambitious and it's completely mental, but most of all, it's great fun. It's not for the faint-hearted, but if you're willing to try something a little different, you'll have struck gold with A Werewolf!
A Werewolf!
Previous Post Review: Dearist – Get What You Want [7″]
Next Post Review: Red Seas Fire – Confrontation [EP]
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 761
|
Q: how to update a product in database i am trying to update a product in mysql DB
here is my product table structure :
[table product structure]
it has a foreign key id_category that references to the table category's id :
[table category structure]
and this my code :
if(isset($_POST['submit'])){
$id=htmlspecialchars($_POST['id']);
$name=htmlspecialchars($_POST['name']);
$photo=htmlspecialchars($_POST['photo']);
$quantity=htmlspecialchars($_POST['quantity']);
$price=htmlspecialchars($_POST['price']);
$description=htmlspecialchars($_POST['description']);
$category=htmlspecialchars($_POST['category']);
$brand=htmlspecialchars($_POST['brand']);
$obj=new Connexion();
$cnx=$obj->getconnexion();
//sql statement
$sql="update product set id=$id,name='$name',photo='$photo',quantity=$quantity,price=$price,description='$description',category=(select id_category from category where category_name='$category'),brand='$brand' where id=1";
$res=$cnx->exec($sql);
if($res)
{ header("location:findall.html.php");}
else echo "modification problem!!";
when i try it, it states
modification problem!!
the POST method works fine but i can't figure out where's the error in the sql statement.
A: you should change "category" to "id_category" in your query
id_category=(select id_category from category where category_name='$category')
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 5,798
|
Q: Highlight (change background) / of the content in a web page dynamically Is there any way to change the background-color of text in a web page dynamically, while select the particular text.
Ex :
Sample text display in the html page. I want to high light the particular text in that page, while selecting from mouse pointer.
My Ground Work :
Add the class "CSS Style" for particular selected text. But how to take the selected text from a web page dynamically.
A: You could style the selected text dynamically using the CSS selector ::selection.
#content::selection {
background-color: plum;
color: white;
}
#content::-moz-selection {
background-color: plum;
color: white;
}
<div id="content">Sample text display in the html page. I want to high light the particular text in that page, while selecting from mouse pointer.</div>
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 8,892
|
{"url":"https:\/\/www.getshifting.com\/wiki\/q\/q89?rev=1466584482&do=diff","text":"# SHIFT\n\n--- Sjoerd Hooft's InFormation Technology ---\n\n### Site Tools\n\nq:q89\n##### Differences\n\nThis shows you the differences between two versions of the page.\n\n \u2014 q:q89 [2016\/06\/22 10:34] (current) Line 1: Line 1: + = Question 89 = + This page is part of Q, the IT exam trainer. \\\\ See https:\/\/\u200bwww.getshifting.com\/\u200bq for more info \\\\ \\\\ **Question:\u200b** \\\\ How can you manage an newly installed Windows Server 2012 R2 core from a another Windows Server 2012 R2 with computer manager?\u00a0\u200b \\\\ **Description:\u200b** \\\\ NA \\\\ \\\\ **Correct Answer:** \\\\ Through Network Settings \\\\ {{tag>\u200bqq}} \\\\\nq\/q89.txt \u00b7 Last modified: 2016\/06\/22 10:34 (external edit)","date":"2019-11-22 07:39:49","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 1.0000100135803223, \"perplexity\": 12994.377914434455}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-47\/segments\/1573496671245.92\/warc\/CC-MAIN-20191122065327-20191122093327-00120.warc.gz\"}"}
| null | null |
Bernardino Baldi (Urbino, Italia, 5 de junio de 1553 - ídem, 12 de octubre de 1617) fue un escritor, historiador y matemático italiano, descendiente de una familia noble.
Baldi realizó sus estudios en Padua, y es reconocido por sus amplias habilidades relacionadas con la geografía, pintura, teología, poesía y traducción pues hablaba al menos 12 idiomas.
Referencias
Matemáticos de Italia del siglo XVI
Matemáticos de Italia del siglo XVII
Nacidos en Urbino
Fallecidos en Urbino
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 9,528
|
Q: Google Maps ambiguous use of a GMSMapViewType I just upgraded to Xcode 7.1. When I try to set the mapType of a GMSMapView I get the error Ambiguous use of 'kGMSTypeNormal', Ambiguous use of 'kGMSTypeTerrain', and Ambiguous use of 'kGMSTypeHybrid'.
@IBOutlet weak var mapView: GMSMapView!
func myfunc() {
if let myMapType = NSUserDefaults.standardUserDefaults().stringForKey(SettingsTableViewController.History.MapType) {
switch myMapType {
case "kGMSTypeNormal":
mapView.mapType = kGMSTypeNormal
case "kGMSTypeTerrain":
mapView.mapType = kGMSTypeTerrain
case "kGMSTypeHybrid":
mapView.mapType = kGMSTypeHybrid
default: break
mapView.mapType = kGMSTypeNormal
}
} else {
mapView.mapType = kGMSTypeNormal
}
}
A: mapView.mapType = GMSMapViewType(rawValue: 1)!
*
*kGMSTypeNormal = 1
*kGMSTypeSatellite = 2
*kGMSTypeTerrain = 3
*kGMSTypeHybrid = 4
*kGMSTypeNone = 5
A: here is the updated version
import UIKit
import GoogleMaps
class ViewController: UIViewController, GMSMapViewDelegate {
var mapView: GMSMapView!
override func viewDidLoad() {
super.viewDidLoad()
mapView = GMSMapView(frame: self.view.bounds)
mapView.animate(toViewingAngle: 45)
mapView.mapType = GMSMapViewType.satellite
self.view = mapView
}
A: I'm not sure why but putting "GoogleMaps." in front of all the kGMSTypes (i.e. GoogleMaps.kGMSTypeNormal) fixed the problem.
A: In Swift 3 use as bellow:
.normal
.hybrid
.satellite
.terrain
A: If you open GMSMapViewType, you will see it defined as enum. In your switch statement, you're comparing it with strings which is wrong. You should better compare them with integers.
kGMSTypeNormal = 1
kGMSTypeSatellite = 2
kGMSTypeTerrain = 3
kGMSTypeHybrid = 4
kGMSTypeNone = 5
A: You need to use like this
mapView.mapType = GoogleMaps.kGMSTypeSatellite
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,036
|
{"url":"https:\/\/www.physicsforums.com\/threads\/gauss-law-and-magnitude-of-the-electric-field.89932\/","text":"# Gauss' Law and magnitude of the electric field\n\nA long, nonconducting, solid cylinder of radius 4.5 cm has a nonuniform volume charge density that is a function of the radial distance r from the axis of the cylinder, as given by $$\\rho = A r^2$$, with $$A = 3.0 \\mbox{ }\\mu C\/\\mbox{m}^5$$.\n\n(a) What is the magnitude of the electric field at a radial distance of 3.5 cm from the axis of the cylinder?\n\nGauss' Law:\n\n$$\\Phi _{\\mbox{Net}} = \\oint \\vec{E} \\cdot d\\vec{S} = \\int _{\\mbox{Sides}} \\vec{E} \\cdot d\\vec{S} = ES =\\frac{Q_{\\mbox{Enc}}}{\\epsilon _0}$$\n\nLet a = 3.5 cm. Then:\n\n$$E\\left( 2\\pi a L \\right)=\\frac{\\rho \\left( \\pi a^ 2 L \\right)}{\\epsilon _0} \\Longrightarrow E = \\frac{\\rho a}{2\\epsilon _0} = \\frac{Aa^ 3}{2\\epsilon _0} \\approx 7.3 \\mbox{ } \\frac{N}{C}$$\n\nThis is wrong, but I don't know where.\n\n(b) What is the magnitude of the electric field at a radial distance of 5.5 cm from the axis of the cylinder?\n\nGauss' Law:\n\nLet b = 5.5 cm. Then:\n\n$$\\Phi _{\\mbox{Net}} = \\oint \\vec{E} \\cdot d\\vec{S} = \\int _{\\mbox{Sides}} \\vec{E} \\cdot d\\vec{S} = ES =\\frac{Q_{\\mbox{Enc}}}{\\epsilon _0}$$\n\n$$E\\left( 2\\pi b L \\right)=\\frac{\\rho \\left( \\pi R^ 2 L \\right)}{\\epsilon _0} \\Longrightarrow E = \\frac{\\rho R^2}{2b\\epsilon _0} = \\frac{AR^ 4}{2b\\epsilon _0} \\approx 1.3 \\times 10 \\mbox{ } \\frac{N}{C}$$\n\nThis is wrong, but I don't know where.\n\nAny help is highly appreciated\n\nDear thiago_j\n\nI think the way you apply Gauss' Law in general is correct. The one thing that is wrong for sure is your calculation of the enclosed charge.\nAs you mentioned the charge density is a function of the radius. In your calculations you ignore this. You just take the volume (with radius a) and act as if the whole cylinder had the density it has at radius a, which is not the case (as you stated).\nSo, in order to calculate the charge enclosed you need to integrate!\nSome hints on how to do this: In general, proceed as you always do with integration. Take a certain radius r, calculate the volume of the hollow cylinder with radii r and r+dr and calculate the charge on this infinitesimal hollow cylinder. Then do the integration over the whole volume needed.\n\nI hope it was useful.\nBest regards...Cliowa\n\nmukundpa\nHomework Helper\nthiago_j said:\n$$E\\left( 2\\pi a L \\right)=\\frac{\\rho \\left( \\pi a^ 2 L \\right)}{\\epsilon _0} \\Longrightarrow E = \\frac{\\rho a}{2\\epsilon _0} = \\frac{Aa^ 3}{2\\epsilon _0} \\approx 7.3 \\mbox{ } \\frac{N}{C}$$\n$$Q_{\\mbox{Enc}}$$ is not $$\\rho \\left( \\pi a^ 2 L \\right)$$\n\nit is\n\n$$\\int_0^r \\ ( Ar^2 )2 \\pi r dr L$$\n\n(a) What is the magnitude of the electric field at a radial distance of 3.5 cm from the axis of the cylinder?\n\nGauss' Law:\n\n$$\\Phi _{\\mbox{Net}} = \\oint \\vec{E} \\cdot d\\vec{S} = \\int _{\\mbox{Sides}} \\vec{E} \\cdot d\\vec{S} = ES =\\frac{Q_{\\mbox{Enc}}}{\\epsilon _0}$$\n\nLet a = 3.5 cm. Then:\n\n$${Q_{\\mbox{Enc}} = \\int _0 ^a \\left( Ar^2 \\right) 2\\pi r L \\: dr = 2\\pi LA \\int _0 ^a r^3 \\: dr = \\frac{\\pi LA a^ 4}{2}$$\n\nand so\n\n$$E\\left( 2\\pi a L \\right)= \\frac{\\pi LA a^ 4}{2\\epsilon _0} \\Longrightarrow E = \\frac{A a^3}{4\\epsilon _0} \\approx 3.6 \\mbox{ } \\frac{N}{C}$$\n\n(b) What is the magnitude of the electric field at a radial distance of 5.5 cm from the axis of the cylinder?\n\nGauss' Law:\n\n$$\\Phi _{\\mbox{Net}} = \\oint \\vec{E} \\cdot d\\vec{S} = \\int _{\\mbox{Sides}} \\vec{E} \\cdot d\\vec{S} = ES =\\frac{Q_{\\mbox{Enc}}}{\\epsilon _0}$$\n\nLet b = 5.5 cm and R = 4.5 cm. Then:\n\n$${Q_{\\mbox{Enc}} = \\int _0 ^R \\left( Ar^2 \\right) 2\\pi r L \\: dr = 2\\pi LA \\int _0 ^R r^3 \\: dr = \\frac{\\pi LA R^ 4}{2}$$\n\nand so\n\n$$E\\left( 2\\pi b L \\right)= \\frac{\\pi LA R^ 4}{2\\epsilon _0} \\Longrightarrow E = \\frac{A R^4}{4b\\epsilon _0} \\approx 6.3 \\mbox{ } \\frac{N}{C}$$\n\nmukundpa\nHomework Helper\nAppears correct.","date":"2021-01-22 04:23:14","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8738062381744385, \"perplexity\": 313.22994682636914}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-04\/segments\/1610703529080.43\/warc\/CC-MAIN-20210122020254-20210122050254-00554.warc.gz\"}"}
| null | null |
{"url":"https:\/\/swampthingecology.org\/blog\/too-much-outside-the-box-outliers-and-boxplots\/","text":"# Paul Julian II, PhD\n\nEcologist, Wetland Biogeochemist, Data-scientist, lover of Rstats.\n\n# Too much outside the box - Outliers and Boxplots\n\nWritten on January 24, 2020\n\nKeywords: boxplots, outlier, data analysis\n\nIn a recent commentary due out in Marine Biology soon (hopefully) I argue against the use of boxplots as a method of outlier detection. Also seems that boxplots are very popular with people having strong opinons \u2026\n\nBefore we get too into the weeds lets present the classical definition of what an outlier is, here I use Gotelli and Ellison (2013) but across statistical literature outliers are generally defined\/described similarly.\n\n\u201c\u2026extreme data points that are not characteristic of the distribution they were sampled\u2026\u201d (Gotelli and Ellison 2013).\n\nWhat would a classic example of this definition look like in \u201creal data\u201d (below is generated data\u2026technically not real data)?\n\nHere is how the data was generated for demonstration purposes\n\nClearly, based on the example above it seems like the red point in the plot to the left looks like it doesn\u2019t really belong. A quick density plot of the data with and without the point (use plot(density(...))) gives you a sense of if the extreme data point is outside of the data distribution. The plot to the right demonstrates the data distribution and mean (dashed) without the extreme value relative to the extreme value (red line).\n\nThe next step to really determine if its an outlier would be to conduct an outlier test on your data. Outliers in data can distort the data distribution, affect predictions (if used in a model) and affect the overall accuracy of estimates if they are not detected and handled, especially in bi-variate analysis (such as linear modeling). Most of the information you will see on the internet and in some textbooks is that boxplots are good way to identify outliers. I fully endorse using boxplots as a first looks at the data, just to get a sense of things as they were intended by Tukey (1977). Thats right Dr.\u00a0John W Tukey was the mastermind behind the boxplot\u2026you may remember him from such statistical analyses as Tukey\u2019s range test\/HSD or Tukey lambda distribution.\n\nOverall, boxplots are extremely helpful in quickly visualization of the central tendency and spread of the data. Don\u2019t confuse the central tendency and spread for mean and standard deviation, as these values are not usually displayed in boxplots.\n\nAt its root, boxplots providing no information on the underlying data distribution and provide a somewhat arbitrary detection of extreme values especially for non-normal data distributions (Kampstra 2008; Krzywinski and Altman 2014). Extreme values are identified using a univariate boxplot simply identifies values that fall outside of 1.5 time the inter-quartile range (IQR) of the first or third quartile (Tukey 1977). As discussed above, outliers are extreme values outside the distribution of the data. Since IQR (i.e.\u00a0median, 25th quantile, 75th quantile, etc.) calculations are distributionless calculations, values outside the IQR therefore are not based on any distribution. Below are four examples of data pulled from different distributions with a mean of zero ($$\\mu = 0$$) and standard deviation of one ($$\\sigma = 1$$). In these cases, especially for normally and skewed normal distributions, median, 25th quantile and 75th quantile values do not differ greatly, but the number of outliers do differ.\n\nThe boxplot examples above show the span of over 10,000 values pulled from uniform, normal and skewed normal distribtuions. A directly obvious observations is that the uniform distribition does not generate any extreme values while the others generate some depending on the skewness of the distributions. Kampstra (2008) suggests that even for normal distributions the number of extreme values identified will increase concurrently with sample size. This is demonstrated below where as sample size increases, the number of extreme values identified also increases. Furthermore, as sample size increases the IQR estimates narrows which you would expect given the central limit theorem. This sample size dependance ultimately makes individual \u201coutlier\u201d detection problematic.\n\nBottom line, a boxplot is not a suitable outlier detection test but rather an exploratory data analysis to understand the data. While boxplots do identify extreme values, these extreme values are not truely outliers, they are just values that outside a distribution-less metric on the near extremes of the IQR. Outlier tests such as the Grubbs test, Cochran test or even the Dixon test all can be used to idenify outliers. These tests and more can be found in the outlier R package. Outlier identification and culling is a tricky situtation and requires a strong and rigirous justification and validation that data points identified as an outlier is truely an outlier otherwise you can run afoul of type I and\/or type II errors.\n\n## References\n\nGotelli, Nicholas J., and Aaron M. Ellison. 2013. A Primer of Ecological Statistics. Sunderland, MA: Sinauer Associates, Inc.\n\nKampstra, Peter. 2008. \u201cBeanplot: A Boxplot Alternative for Visual Comparison of Distributions.\u201d Journal of Statistical Software 28 (Code Snippet 1). https:\/\/doi.org\/10.18637\/jss.v028.c01.\n\nKrzywinski, Martin, and Naomi Altman. 2014. \u201cVisualizing Samples with Box Plots.\u201d Nature Methods 11 (2): 119\u201320. https:\/\/doi.org\/10.1038\/nmeth.2813.\n\nTukey, John Wilder. 1977. \u201cExploratory Data Analysis.\u201d In Statistics and Public Policy, edited by Frederick Mosteller, 1st ed. Addison-Wesley Series in Behavioral Science. Quantitative Methods. Addison-Wesley.","date":"2020-02-28 01:46:54","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7263927459716797, \"perplexity\": 1889.2745520164383}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-10\/segments\/1581875146940.95\/warc\/CC-MAIN-20200228012313-20200228042313-00289.warc.gz\"}"}
| null | null |
\section{Introduction} \label{sec:intro}
Mechanism Design has found important applications in the design of offline and online markets. One of its main applications is the design of auctions, where a common goal is to maximize the seller's revenue from the sale of one or multiple items to one or multiple bidders. This is challenging because bidders are strategic and interact with the auction in a way that benefits themselves rather than the seller. It is well-understood that, without any information about the bidders' willingness to pay for different bundles of items, there is no meaningful way to optimize revenue. As such, a classical approach in Economics is to assume that bidders' {\em types} -- which determine their values for different bundles and thus their willingness to pay for different bundles -- are not arbitrary but randomly drawn from a joint distribution $D$ that is common knowledge, i.e.~known to all bidders and the auctioneer. With such a Bayesian prior, the revenue of different mechanisms is compared on the basis of what revenue they achieve in expectation with respect to bidder type vectors drawn from $D$, and assuming that bidders play according to some (Bayesian) Nash equilibrium strategies, or some other type of (boundedly) rational behavior, e.g.~no-regret learning.
Even with a Bayesian prior, however, revenue maximization is quite a challenging task. While Myerson's celebrated work showed that a relatively simple mechanism is optimal in single-item settings~\cite{Myerson81}, characterizing the structure of optimal multi-item mechanisms has been notoriously difficult both analytically and computationally. Indeed, it is known that (even approximately) optimal multi-item mechanisms may require description complexity that scales exponentially in the number of items, even when there is a single buyer~\cite{hart2013menu,dughmiLN14,Daskalakis2017,babaioff2021menu}, they might be computationally intractable, even in simple settings~\cite{CaiDW12b,DaskalakisDT14,chen2015complexity}, and they may exhibit several counter-intuitive properties which do not arise in single-item settings; see survey~\cite{Daskalakis2015}. Nevertheless, recent years have seen substantial progress on various fronts: analytical characterizations of optimal multi-item mechanisms~\cite{DaskalakisDT13,giannakopoulos2014duality,kash2016optimal,Daskalakis2017}; computational frameworks for computing near-optimal multi-item mechanisms~\cite{AlaeiFHHM12,CaiDW12a,CaiDW12b,CaiDW13a,CaiDW13b}; approximate multi-item revenue optimization via simple mechanisms~\cite{ChawlaHK07,ChawlaHMS10,Alaei11,HartN12,KleinbergW12,CaiH13,BILW14,Yao15,RubinsteinW15,CaiDW16,ChawlaM16,CaiZ17,DaskalakisFLSV20}; and (approximate) multi-item revenue optimization using sample access to the type distribution~\cite{morgenstern2016learning, goldner2016prior, CaiD17,Syrgkanis17,GonczarowskiW18,brustle2020multi}, including via the use of deep learning~\cite{feng2018deep,shen2019automated,dutting2019optimal}.
The afore-described progress on multi-item revenue optimization provides a diversity of tools that can be combined to alleviate the analytical and computational intractability of optimal mechanisms. Yet, there still remains an important challenge in applying those tools, which is that they typically require that the type distribution $D$ is either known or can be sampled. However, this is too strong an assumption. It is common that $D$ is {\em estimated} through market research or econometric analysis in related settings, involving similar items or a subset of the items. In this case, we would only hope to know some approximate distribution $\hat D$ that is close to $D$. In
other settings, we may have sample access to the true distribution $D$ but there might be errors in measuring
or recording those samples. Again, we might hope to {\em estimate} an approximate distribution $\hat D$ that is close
to $D$. Unfortunately, it is well understood that designing a mechanism for $\hat D$ and using it for $D$ might be a bad idea, as optimal mechanisms tend to overfit the details of the type distribution. This has motivated a strand of recent literature to study how to robustify mechanisms to errors in the distribution~\cite{BergemannS11,CaiD17,Brustle2019}.
There is, in fact, another important reason why one might want to design mechanisms for some approximate type distribution. Multi-dimensional data is complex and one would want to leverage the extensive statistical and machine learning toolkit that allows approximating such high-dimensional distributions with more structured models. Indeed, while the true type distribution $D$ might not conform to a simple model, it might be close to a distribution $\hat D$ that does. We would like to leverage the simple structure in $\hat D$ to (i) alleviate the computational intractability of multi-item mechanisms, and (ii) reduce the amount of communication that the bidders and the auctioneer need to exchange. While the structured model $\hat D$ might allow (i) and (ii), we need the guarantee that the revenue of our mechanism be robust when we apply it to the true distribution~$D$.
Motivated by the discussion above, in this work we build a multi-item mechanism design framework that combines matrix factorization models developed for recommendation systems with mechanism design, targeting two issues: (1) the intractability of Mechanism Design with respect to the number of items (arising from the exponential dependence of the number of types on the number of items if no further assumptions are placed); (2) the lack of exact access to the Bayesian priors. In particular, we assume that each bidder draws their type -- specifying their values for a very large universe of $N$ items (think all restaurants in a city or all items on Amazon) -- from a distribution $D_i$ that is close to a Matrix Factorized model $\hat{D}_i$, whose latent dimension is $k << N$. Targeting these approximate distributions $\hat{D}_i$ allows us to reduce the effective dimensionality of bidder types to $k$, which has huge advantages in terms of the computational/representation/communication/sample complexity of mechanism design. We develop tools that allow us to (a) use the mechanism constructed for the approximate $\hat{D}_i$'s under the true ${D}_i$'s without sacrificing much revenue; and (b) interact with the bidders who are unaware of the latent codes (they only understand their values for the $N$ items and are oblivious to the matrix factorized model) yet exploit the factorized model for efficiently communicating with them without the impractical burden of having them communicate their $N$-dimensional type to the mechanism. In sum, our results are as follows:
\begin{itemize}
\item With a query protocol $\mathcal{Q}$ that learns an approximate latent representation of a bidder's type, Theorem~\ref{thm:main} shows how to combine it with any mechanism $\widehat{M}$ that is designed only for the Matrix Factorization model to produce a mechanism that generates comparable revenue but with respect to the true distribution. The result is obtained via a refinement of the robustification result in~\cite{brustle2020multi}, where the loss in revenue, as well as the violation in incentive compatibility now only depend on the effective dimension of the Matrix Factorization model, $k$, but not the total number of items, $N$ (Lemma~\ref{lem:robustness}).
\item We show that if the valuations are constrained-additive (Definition~\ref{def:constrained additive}), we can obtain communication-efficient query protocols in several natural settings (Theorem~\ref{thm:query protocol}). The queries we consider ask a bidder whether they are willing to purchase an item at a given price. In the first setting, the design matrix of the Matrix Factorization model contains a diagonally dominant matrix -- a generalization of the well-known separability assumption by Donoho and Stodden~\cite{DonohoS03}. In two other settings, we assume that the design matrix is generated from a probablistic model and show that a simple query protocol succeeds with high probability.
\item Combining Theorems~\ref{thm:main} and~\ref{thm:query protocol}, we show that, given any mechanism $\widehat{M}$ that is designed only for the Matrix Factorization model, we can design a mechanism that achieves comparable revenue and only requires the bidders to answer a small number of simple queries. In particular, for several natural settings, we show that the number of queries scales \yangnote{quasi-linearly} in the effective dimension of the Matrix Factorization model and independent of the total number of items (Proposition~\ref{prop:1+2 deterministic}).
\end{itemize}
\section{Preliminaries}
\subsection{Brief Introduction to Mechanism Design}
We provide a brief introduction to mechanism design. To avoid a very long introduction, we only define the concepts in the context of multi-item auctions, which will be the focus of this paper. See Chapter 9 of~\cite{AGTbook} and the references therein for a more detailed introduction to mechanism design.
\paragraph{Multi-item Auctions.} The seller is selling \textbf{$N$ heterogenous items} to \textbf{$m$ bidders}. Each bidder $i$ is assumed to have a \textbf{private type} $t_i$ that encodes their preference over the items and bundles of items. We assume that $t_i$ lives in the $N$-dimensional Euclidean space. For each bidder, there is a publicly known valuation function $v_i(\cdot,\cdot)$, where $v_i(t_i,S)\in \mathbb{R}$ is bidder $i$'s value for bundle $S\subseteq [N]$ when $i$'s private type is $t_i$. In this paper, we consider the \emph{Bayesian setting with private types}, that is, each bidder's type $t_i$ is drawn \emph{privately} and \emph{independently} from a publicly known distribution $D_i$.
\vspace{-.1in}
\paragraph{Mechanism.} The seller designs a mechanism to sell the items to bidders. A mechanism consists of an allocation rule and a payment rule, where the allocation rule decides a way to allocate the items to the bidders, and the payment rule decides how much to charge each bidder.
\vspace{-.1in}
\paragraph{Direct Mechanism:} In a {direct mechanism}, the mechanism directly solicits types from the bidders and apply the allocation and payment rules on the reported types. More specifically, for any reported type profile $b=(b_1,\ldots, b_m)$, a direct mechanism $M:=(x(\cdot),p(\cdot))$ selects $x(b)\in\{0,1\}^{m\times N}$ as the allocation and charges each bidder $i$ payment $p_i(b)$.\footnote{Note that $p(b)=(p_1(b),\ldots, p_m(b))$.} We slightly abuse notation to allow the allocation rule to be randomized, so $x(b)\in \Delta\left(\{0,1\}^{m\times N}\right)$. We assume that bidders have quasi-linear utilities. If bidder $i$'s private type is $t_i$, her utility under reported bid profile $b$ is $u_i\left(t_i, M(b)\right)=\mathbb{E}\left[v_i\left(t_i,x(b)\right)-p_i(b)\right]$, where the expectation is over the randomness of the allocation and payment~rule.
\vspace{-.1in}
\paragraph{Expected Revenue:} In this paper, our goal is to design mechanisms with high expected revenue. For a direct mechanism $M$, we use $\textsc{Rev}(M,D)$ to denote $\mathbb{E}_{t\sim D}[\sum_{i\in[m]} p_i(t)]$, where $t=(t_1,\ldots, t_m)$ is the type profile and is drawn from $D=\bigtimes_{i\in[m]} D_i$.
\vspace{-.1in}
\paragraph{Incentive Compatibility and Individual Rationality}
Since the bidders' types are private, unless the mechanism \emph{incentivizes} the bidders to report truthfully, there is no reason to expect that the reported types correspond to the true types. The notion of incentive compatibility is defined to capture this.
\begin{itemize}
\item {\bf $\varepsilon$-Bayesian Incentive Compatible ($\varepsilon$-BIC):} if bidders draw their types from some distribution $D=\bigtimes_{i=1}^m D_i$, then a direct mechanism $M$ is \emph{$\varepsilon$-BIC with respect to $D$} if for each bidder $i\in[m]$
$$\mathbb{E}_{t_{-i} \sim D_{-i}}[u_i(t_i,M(t_i,t_{-i}))] \geq \mathbb{E}_{t_{-i} \sim D_{-i}}[u_i(t_i,M(t'_i,t_{-i}))] -\varepsilon,$$ for all potential misreports $t'_i$, in expectation over all other bidders bid $t_{-i}$. A mechanism is BIC if it is $0$-BIC.
\item \yangnote{{\bf $(\varepsilon,\delta)$-Bayesian Incentive Compatible ($(\varepsilon,\delta)$-BIC):} if bidders draw their types from some distribution $D=\bigtimes_{i=1}^m D_i$, then a direct mechanism $M$ is \emph{$(\varepsilon,\delta)$-BIC with respect to $D$} if for each bidder $i\in[m]$:
$$\Pr_{t_i\sim D_i}\left[\mathbb{E}_{t_{-i} \sim D_{-i}}[u_i(t_i,M(t_i,t_{-i}))] \geq \mathbb{E}_{t_{-i} \sim D_{-i}}[u_i(t_i,M(t'_i,t_{-i}))] -\varepsilon\right]\geq 1-\delta.$$
}
\item {\bf Individually Rational (IR):} A direct mechanism $M$ is \emph{IR} if for all type profiles $t=(t_1,\ldots, t_m)$, $$u_i(t_i,M(t_i,t_{-i})) \geq 0$$ for all bidders $i\in [m]$.
\end{itemize}
\vspace{-.1in}
\paragraph{Indirect Mechanism:} An {\em indirect mechanism} does not directly solicit the bidders' types. After interacting with the bidders, the mechanism selects an allocation and payments. The notions of $\varepsilon$-Bayesian Incentive Compatibility and Individual Rationality can be extended to indirect mechanisms using the solution concept of $\varepsilon$-Bayes Nash equilibrium. \yangnote{The notion of $(\varepsilon,\delta)$-Bayesian Incentive Compatibility can be extended to indirect mechanisms using the new solution concept, which we call {\em $(\varepsilon,\delta)$-weak approximate Bayes Nash equilibrium}. In an incomplete information game, a strategy profile is an $(\varepsilon,\delta)$-weak approximate Bayes Nash equilibrium if for every bidder, with probability no more than $\delta$ (over the randomness of their own type), unilateral deviation from the Bayesian Nash strategy can increase the deviating bidder's expected utility (with respect to the randomness of the other bidders' types and assuming those follow their Bayesian Nash equilibrium strategies) by more than $\varepsilon$.}
\begin{remark}\label{rmk:revenue and IC estimate}
For a $(\varepsilon,\delta)$-weak approximate Bayes Nash equilibrium, its expected revenue computation is made in this paper using the convention that all bidders follow their $(\varepsilon,\delta)$-weak approximate Bayes Nash equilibrium strategies. At a cost of an additive $m^2\delta H$ loss in revenue (where $H$ is the highest possible value of any bidder), we can assume that only the $(1-\delta)$-fraction of types of each bidder who have no more than $\varepsilon$ incentive to deviate from the weak approximate Bayes Nash equilibrium strategies follow these strategies while the remaining $\delta$ fraction use arbitrary strategies. Similarly, we can interpret the $(\varepsilon,\delta)$-weak approximate Bayes Nash equilibrium definition as requiring that at least $(1-\delta)$-fraction of the types of each bidder have at most $O(\varepsilon+m\delta H)$ incentive to deviate from the Bayes Nash strategies assuming that for every other bidder at most $\delta$ fraction of their types deviate from their Bayes Nash strategies.
\end{remark}
\subsection{Further Preliminaries}
\begin{definition}\label{def:prokhorov}
Let $(U,d)$ be a metric space and $\mathcal{B}$ be a $\sigma$-algebra on $U$. For $A \in \mathcal{B}$, let $A^{\varepsilon} = \{x : \exists y \in A \ \ s.t \ \ d(x,y)<\varepsilon \}$. Two probability measure
$P$ and $Q$ on $\mathcal{B}$ have \emph{Prokhorov distance}
$$ \inf \left \{\varepsilon>0 : P(A) \leq Q(A^{\varepsilon}) + \varepsilon \text{ and } \ Q(A)\leq P(A^{\varepsilon})+\varepsilon ,~ \forall A \in \mathcal{B}\right \}.$$
We consider distributions supported on some Euclidean Space, and we choose {$d$ to be the $\ell_\infty$-distance}. We denote the $\ell_\infty$-Prokhorov distance between distributions $F$, $\widehat{F}$ by $d_P(F,\widehat{F})$.
\end{definition}
We will also make use of the following characterization of the Prokhorov metric by~\cite{Strassen65}.
\begin{lemma}[Characterization of the Prokhorov Metric \cite{Strassen65}]\label{lem:prokhorov characterization}
Let $F$ and $\widehat{F}$ be two distributions supported on $\mathbb{R}^n$. $d_P(F,\widehat{F})\leq \varepsilon$ if and only if there exists a coupling $\gamma$ of $F$ and $\widehat{F}$, such that $\Pr_{(x,y)\sim \gamma}\left[\normI{x-y}>\varepsilon \right]\leq~\varepsilon$.
\end{lemma}
\begin{definition}[Influence Matrix and Weak Dependence]
For any $d$-dimensional random vector ${X}=(X_1,\ldots, X_d)$, we define the influence of variable $j$ on variable $i$ as $$\alpha_{i,j}:=\sup_{\substack{x_{-i-j} \\x_j\neq x'_j}} d_{TV}\left(F_{X_i\mid X_j=x_j, X_{-i-j}=x_{-i-j}},F_{X_i\mid X_j=x'_j, X_{-i-j}= x_{-i-j}}\right), $$ where $F_{X_i\mid X_{-i}=x_{-i}}$ denotes the conditional distribution of $X_i$ given $X_{-i}=x_{-i}$, and $d_{TV}(D,D')$ denotes the total variational distance between distribution $D$ and $D'$.
Also, let $\alpha_{i,i}:=0$ for each $i$, and we use $\Influ{X}$ to denote the $d\times d$ matrix $(\alpha_{i,j})_{i\in[d],j\in[d]}$. In this paper, we consider the coordinates of $X$ to be \textbf{weakly dependent} if $\norm{\Influ{X}}<1$.
\end{definition}
\section{Our Model and Main Results}
\paragraph{Setting and Goal:} We consider a classical mechanism design problem, wherein a seller is selling $N$ items to $m$ buyers, where buyer $i$'s type $t_i$ is drawn from a distribution $D_i$ over $\mathbb{R}^N$ independently. The goal is to design a mechanism that maximizes the seller's revenue. In this paper, we operate in a setting where $D_i$ is unknown, but we are given access to the following components: (I) For each bidder~$i$, we are given a machine learning model $\widehat{D}_i$ --- of the matrix factorization type as described below, which approximates $D_i$. (II) We are given a good mechanism $\widehat{M}$ for the approximate type distributions; in its design this mechanism can exploit the low effective dimensionality, $k$, of types in the approximate model. Our goal is (III) to use (I) and (II) to obtain a good mechanism for the true type distributions.
\paragraph{(I) The Machine Learning Component:} We assume that each bidder's type distribution~$D_i$ can be well-approximated by a known \emph
Matrix Factorization
(MF)} model $\widehat{D}_i$. In particular:
\begin{itemize}
\item We use $A\in \mathbb{R}^{N\times k}$ to denote the design matrix of the model, where each column can be viewed as the type (over $N$ items) of an ``archetype.'' As described in the following two bullets, types are sampled by each $\widehat{D}_i$ as linear combinations over archetypes.
\item We use $\widehat{D}_{z,i}$ to denote a distribution over $[0,1]^k$. The subscript $z$ is not a parameter of the distribution --- it serves to remind us that this distribution samples in the latent space $[0,1]^k$ and distinguish it from the distribution $\widehat{D}_i$ defined next.
\item If $F$ is a distribution over $\mathbb{R}^k$, we use $A\circ F$ to denote the distribution of the random variable $Az$, where $z\sim F$. With this notation, we use $\widehat{D}_i$ to denote $A\circ \widehat{D}_{z,i}$.
\item We assume that, for each bidder, the matrix factorization model is not far away from the true type distribution, that is, for some $\varepsilon_1 >0$ we have that $d_P(D_i,\widehat{D}_i) \le \varepsilon_1$ for all $i\in [m]$.
\end{itemize}
\begin{remark}
In the above description we assumed that all $\widehat{D}_i$'s share the same design matrix $A$. This is done to avoid overloading notation but all our results would hold if each $\widehat{D}_i$ had its own design matrix $A_i$.
\end{remark}
\paragraph{(II) The Mechanism Design Component:} We assume that we are given a direct mechanism $\widehat{M}$ for types drawn from the Machine Learning model. In particular, we assume that this mechanism makes use of the effective dimension $k$ of the Machine Learning model, accepting ``latent types'' (of dimension $k$) as input from the bidders. Specifically:
\begin{itemize}
\item Recall that, for each bidder $i$, their valuation function $v_i(\cdot,\cdot): \mathbb{R}^N\times 2^{[N]}\rightarrow \mathbb{R}$ is common knowledge. (Recall that $v_i$ takes as input the bidder's type and a subset of items so how the bidder values different subsets of items depends on their private type.)
\item\label{itm:induced value} The designer is given $A$ and $\widehat{D}_{z,i}$ for each bidder $i$, and treats bidder $i$'s type as drawn from $\widehat{D}_{z,i}$, i.e.~in the latent space $[0,1]^k$. With respect to such ``latent types,'' there is an induced valuation function. In particular, for each bidder $i$, we use $v^A_i:\mathbb{R}^k\times 2^{[N]} \rightarrow \mathbb{R}$ to denote the valuation function defined as follows ${v}^A_i(z_i,S):=v_i(Az_i,S)$, where $z_i\in\mathbb{R}^k$.
\item With the above as setup, we assume that the designer designs a mechanism $\widehat{M}$ that is BIC and IR w.r.t. $\widehat{D}_z=\bigtimes_{i=1}^m \widehat{D}_{z,i}$ and valuation functions $\{v^A_i(\cdot,\cdot)\}_{i\in[m]}$.
\end{itemize}
\paragraph{(III) The New Component:} We consider the regime where $N \gg k$, and our goal is to combine the Machine Learning component with the Mechanism Design component to produce a mechanism which generates revenue comparable to $\textsc{Rev}(\widehat{M},\widehat{D}_z)$ when used for bidders whose types are drawn from $D=\bigtimes_{i=1}^m D_i$. There are two challenges: (i) $\widehat{M}$ takes as input the latent representation of a bidder's type under $\widehat{D}_z$, however under $D$ a bidder is simply ignorant about any latent representation of their type so they cannot be asked about it;
(ii) $\widehat{M}$'s revenue is evaluated with respect to $\widehat{D}_z$ and valuation functions $\{v^A_i(\cdot,\cdot)\}_{i\in[m]}$ and our goal is to obtain a mechanism whose revenue is similar under $D$ and valuation functions $\{v_i(\cdot,\cdot)\}_{i\in[m]}$. We show how to use a communication efficient query protocol together with a robustification procedure to combine the Machine Learning and Mechanism Design components.
To state our results, we first need to formally define query protocols and some of their properties.
\begin{definition}[$(\varepsilon,\delta)$-query protocol]\label{def:query protocol}
Let $\mathcal{Q}$ be a \textbf{query protocol}, i.e., some communication protocol that exchanges messages with a bidder over possibly several rounds and outputs a vector in $\mathbb{R}^k$. We say that a bidder interacts with the query protocol truthfully, if whenever the protocol asks the bidder to evaluate some function on their type the bidder evaluates the function and returns the result truthfully. We use $\mathcal{Q}(t)\in \mathbb{R}^k$ to denote the output of $\mathcal{Q}$ when interacting with a {truthful bidder} whose type is $t\in\mathbb{R}^N$. $\mathcal{Q}$ is called a $(\varepsilon,\delta)$-query protocol, if for any $t\in\mathbb{R}^N$ and $z\in \mathbb{R}^k$ satisfying $\normI{t-Az}\leq \varepsilon$, we have that $\normI{z-\mathcal{Q}(t)} \le \delta$.
\end{definition}
We also need the notion of Lipschitz valuations to formally state our result.
\begin{definition}[Lipschitz Valuations]\label{def:Lipschitz}
$v(\cdot,\cdot):\mathbb{R}^N\times 2^{[N]}\rightarrow \mathbb{R}$ is a $\mathcal{L}$-Lipschitz valuation, if for any two types $t,t'\in\mathbb{R}^N$ and any bundle $S\subseteq [N]$, $|v(t,S)-v(t',S)|\leq \mathcal{L}\normI{t-t'}$.
\end{definition}
\noindent This includes familiar settings, for example if the bidder is $c$-demand, the Lipschitz constant $\mathcal{L}=c$.\footnote{A bidder is $c$-demand if for any set $S$ of items, the bidder picks their favorite bundle with size no more than $c$ in $S$ evaluating the value of each such bundle additively, with values as determined by the bidder's type $t$. Formally, $v(t,S)=\max_{B\subseteq S, |B|\leq c} \sum_{j\in B} t_j$.}
We are now ready to state our first main result.
\begin{theorem}\label{thm:main}
Let $D=\bigtimes_{i=1}^m D_i$ be the bidders' type distributions and $v_i:\mathbb{R}^N\times 2^{[N]}\rightarrow \mathbb{R}$ be a $\mathcal{L}$-Lipschitz valuation for each bidder $i\in[m]$. Also, let $A\in \mathbb{R}^{N\times k}$ be a design matrix and $\widehat{D}_{z,i}$ be a distribution over $\mathbb{R}^k$
for each $i\in[m]$.
Suppose we are given query access to a mechanism $\widehat{M}$ that is BIC and IR w.r.t. $\widehat{D}_z=\bigtimes_{i=1}^m \widehat{D}_{z,i}$ and valuations $\{{v}^A_i\}_{i\in[m]}$ (as defined in the second bullet of the Mechanism Design component above), and there exists $\varepsilon_1>0$ such that $d_P(D_i,A\circ \widehat{D}_{z,i})\leq \varepsilon_1$ for all $i\in[m]$. Given any $(\varepsilon_1,\varepsilon)$-query protocol with $\varepsilon\geq \varepsilon_1$, we can construct mechanism $M$ using only query access to $\widehat{M}$ and
obliviously with respect to $D$, such that for any possible $D$ that satisfies the above conditions of Prokhorov distance closeness the following hold:
\begin{enumerate}
\item $M$ only interacts with every bidder using $\mathcal{Q}$ once;
\item $M$ is \yangnote{ $(\kappa,\varepsilon_1)$-BIC} w.r.t. $D$ and IR, where \yangnote{$\kappa=O\left( \mathcal{L} \varepsilon_1 +\normI{A}\mathcal{L} m \varepsilon+ \normI{A}\mathcal{L} \sqrt{m\varepsilon}\right)$};
\item The expected revenue of $M$ is at least $ \textsc{Rev}(\widehat{M},\widehat{D}_z)-O\left(m\kappa\right).$
\end{enumerate}
\end{theorem}
\begin{remark}
The mechanism $M$ will be an indirect mechanism. We are slightly imprecise here to call the mechanism $(\kappa,\varepsilon_1)$-BIC. Formally what we mean is that interacting with $\mathcal{Q}$ \emph{truthfully} is a $(\kappa,\varepsilon_1)$-weak approximate Bayes Nash equilibrium. We compute the expected revenue assuming all bidders interacting with $\mathcal{Q}$ \emph{truthfully}. As we discussed in~\Cref{rmk:revenue and IC estimate}, with an additional additive $\normI{A} \mathcal{L} m^2 \varepsilon_1$ loss in revenue, we can assume that only the $(1-\delta)$-fraction of types of each bidder who have no more than $\varepsilon$ incentive to deviate from the Bayes Nash strategies interact with $\mathcal{Q}$ truthfully while the remaining $\delta$ fraction uses arbitrary strategies.
\end{remark}
\paragraph{\textbf{Why isn't ~\cite{brustle2020multi} sufficient?}} One may be tempted to prove Theorem~\ref{thm:main} using~\cite{brustle2020multi}. However, there are two subtle issues with this approach: (i) The violation of the incentive compatibility constraints and the revenue loss of the robustification process in~\cite{brustle2020multi} depend linearly in $N$, rather than in $\normI{A}$ as in Theorem~\ref{thm:main}. Note that $\normI{A}=\max_{i\in[N]} \sum_{j=1}^k |A_{ij}|$, which only depends on $k$ and the largest value an archetype can have for a single item and thus could be significantly smaller than $N$. (ii) The robustification process involves sampling from the conditional distribution of $A\circ \widehat{D}_{z,i}$ on an $N$-dimensional cube, which is equivalent to sampling from the conditional distribution of $\widehat{D}_{z,i}$ on a set $S$ whose image after the linear transformation $A$ is the $N$-dimensional cube. However, $S$ may be difficult to sample from if $A$ is not a well-conditioned.
In the following lemma, we refine the robustification result in~\cite{brustle2020multi} (Theorem 3 in that paper) and show that given an approximate distribution $\widehat{F}$ in the latent space and a BIC and IR mechanism $\widehat{M}$ w.r.t. $\widehat{F}$, we can \emph{robustify} $\widehat{M}$ with \emph{negligible revenue loss} so that it is an approximately BIC and exactly IR mechanism w.r.t. $F$ for any distribution $F$ that is within the $\varepsilon$-Prokhorov ball around $\widehat{F}$. Importantly, we exploit the effective dimension of the matrix factorization model to replace the dependence on $N$ with $\normI{A}$ in both the violation of the incentive compatibility constraints and the revenue loss. Additionally, we only need to be able to sample from the conditional distribution of $\widehat{D}_{z,i}$ on a $k$-dimensional cube. We postpone the proof of Lemma~\ref{lem:robustness} to the Appendix~\ref{sec:robustness proof}.
\begin{lemma}\label{lem:robustness}
Let $A\in \mathbb{R}^{N\times k}$ be the design matrix. Suppose we are given a collection of distributions over latent types $\{\widehat{F}_{z,i}\}_{i\in[m]}$, where the support of each $\widehat{F}_{z,i}$ lies in $[0,1]^k$, and a BIC and IR mechanism $\widehat{M}$ w.r.t.~$\widehat{F}=\bigtimes_{i=1}^m
\widehat{F}_{z,i}$ and valuations $\{v^A_i\}_{i\in [m]}$, where each $v_i$ is an $\mathcal{L}$-Lipschitz valuation. Let $F=\bigtimes_{i=1}^m
F_{z,i}$ be any distribution such that $d_P(F_{z,i},\widehat{F}_{z,i})\leq \varepsilon$ for all $i\in[m]$. Given access to a \textbf{sampling algorithm $\mathcal{S}_i$} for each $i\in[m]$, where $\mathcal{S}_i(x,\delta)$ draws a sample from the conditional distribution of $\widehat{F}_{z,i}$ on the $k$-dimensional cube $\bigtimes_{j\in [k]}[x_j,x_j+\delta)$, we can construct a randomized mechanism $\widetilde{M}$ using only query access to $\widehat{M}$ and
obliviously with respect to $F$, such that for any $F$ satisfying the above conditions of Prokhorov distance closeness the following hold:
\begin{enumerate}
\item $M$ is
$\kappa$-BIC and IR w.r.t.~ $F$ and valuations $\{v^A_i\}_{i\in [m]}$, where $\kappa=O\left( \normI{A}\mathcal{L} m \varepsilon+\normI{A}\mathcal{L} \left(\delta+ \frac{m\varepsilon}{\delta} \right)\right)$;
\item The expected revenue of $\widetilde{M}$ is $\textsc{Rev}\left(\widetilde{M},F\right)\geq \textsc{Rev}(\widehat{M},\widehat{F})-O\left(m\kappa\right).$
\end{enumerate}
\end{lemma}
Equipped with Lemma~\ref{lem:robustness}, we proceed to prove Theorem~\ref{thm:main}.
\begin{prevproof}{Theorem}{thm:main}
Consider the following mechanism:
\begin{algorithm}[h]
\begin{algorithmic}[1]
\STATE Construct mechanism $\widetilde{M}$ using Lemma~\ref{lem:robustness} by choosing $\widehat{F}_{z,i}$ to be $\widehat{D}_{z,i}$ for each $i\in [m]$
and $\delta$ to be $\sqrt{m\varepsilon}$.
\STATE Query each agent $i$ using $\mathcal{Q}$. Let $\mathcal{Q}(b_i)$ be the output after interacting with bidder $i$.~(For any possible output produced by $\mathcal{Q}$, there exists a type $b\in \mathbb{R}^N$, so this is w.l.o.g..)
\STATE Execute mechanism $\widetilde{M}$ on bid profile $\left(\mathcal{Q}(b_1),\ldots, \mathcal{Q}(b_m)\right)$.
\end{algorithmic}
\caption{Query-based Indirect Mechanism $M$}
\label{mechanism}
\end{algorithm}
Let $t_i$ be bidder $i$'s type and $z_i$ be a random variable distributed according to $\widehat{D}_{z,i}$. Since $d_P(D_i,\widehat{D}_i)\leq \varepsilon_1$, Lemma~\ref{lem:prokhorov characterization} guarantees a coupling between $t_i$ and $Az_i$ such that their $\ell_\infty$ distance is more than $\varepsilon_1$ with probability no more than $\varepsilon_1$. As $\mathcal{Q}$ is a $(\varepsilon_1,\varepsilon)$-query protocol, when $t_i$ and $Az_i$ are not $\varepsilon_1$ away, we have $\normI{\mathcal{Q}(t_i)-z_i}\leq \varepsilon$. Hence, there exists a coupling between $\mathcal{Q}(t_i)$ and $z_i$ so that their $\ell_\infty$ distance is more than $\varepsilon$ with probability no more than $\varepsilon$ (recall $\varepsilon_1\leq \varepsilon$). If we choose $F_{z,i}$ to be the distribution of $\mathcal{Q}(t_i)$, $\widehat{F}_{z,i}$ to be $\widehat{D}_{z,i}$, and $\delta$ to be $\sqrt{m\varepsilon}$,~\Cref{lem:robustness} states that $\widetilde{M}$ is a $O\left( \normI{A}\mathcal{L} m \varepsilon+ \normI{A}\mathcal{L} \sqrt{m\varepsilon}\right)$-BIC mechanism if bidder $i$ has valuation $v_i^A(\cdot)$ and type $\mathcal{Q}(t_i)$. \yangnote{Consider two cases: (a) When $\normI{t_i-Az_i}\leq \varepsilon_1$, then $\normI{t_i-A\mathcal{Q}(t_i)}\leq \varepsilon_1+\normI{A} \varepsilon$. Since $v_i(\cdot)$ is $\mathcal{L}$-Lipschitz, deviating from interacting with $\mathcal{Q}$ truthfully can increase the expected utility by at most $O\left(\mathcal{L}\varepsilon_1+\normI{A}\mathcal{L} m \varepsilon+ \normI{A}\mathcal{L} \sqrt{m\varepsilon}\right)$. (b) When $\normI{t_i-Az_i}>\varepsilon_1$, the bidder may substantially improve their expected utility by deviating. Luckily, such case happens with probability no more than $\varepsilon_1$. }
\end{prevproof}
In Theorem~\ref{thm:query protocol}, we show how to obtain $(\varepsilon,\delta)$-queries under various settings. We further assume that the bidders' valuations are all constrained-additive.
\begin{definition}[Constrained-Additive valuation]\label{def:constrained additive}
A valuation function $v:\mathbb{R}^N\times2^{[N]}\rightarrow \mathbb{R}$ is constrained additive if $v(t,S)=\max_{T\in \mathcal{I}\cap 2^S} \sum_{j\in T} (\mu_j+t_j)$, where $\mathcal{I}$ is a downward-closed set system, and $\mu=(\mu_1,\ldots,\mu_N)$ is a fixed vector.\footnote{One can interpret $\mu$ as the common based values for the items that are shared among all types.} For example, unit-demand valuation is when $\mathcal{I}$ includes all subsets with size no more than $1$. If all elements of $\mathcal{I}$ have size no more than $\mathcal{L}$, then $v$ is a $\mathcal{L}$-Lipschitz valuation.
\end{definition}
\begin{theorem}\label{thm:query protocol}
Let all bidders' valuations be constrained-additive. We consider queries of the form: $e_j^T t\overset{?}{\geq} p$, where $e_j$ is the $j$-th standard unit vector in $\mathbb{R}^N$. The query simply asks whether the bidder is willing to pay at least $p+\mu_j$ for winning item $j$. The bidder provides a \emph{Yes/No} answer. We obtain communicationally efficient protocols in the following settings:
\begin{itemize}
\item \textbf{Deterministic Structure:} If $A^T$ can be expressed as $[C^T H^T]\Pi_N$, where $\Pi_N\in \mathbb{R}^N$ is a permutation matrix, $H$ is an arbitrary $(N-k)\times k$ matrix, and $C\in \mathbb{R}^{k\times k}$ is diagonally dominant both by rows and by columns. This is a relaxation of the well-known \textbf{separability assumption} by Donoho and Stodden~\cite{DonohoS03}, that is, $A^T$ can be expressed as $[I_k H^T]\Pi_N$, where $I_k$ is the $k$-dimensional identity matrix. Let $\alpha=\min_{i\in[k]} \left(|C_{ii}|-\sum_{j\neq i} |C_{ij}|\right)$ and $\beta = \min_{j\in[k]} \left(|C_{jj}|-\sum_{i\neq j} |C_{ij}|\right)$. We have a $\left(\varepsilon,\frac{4 \cdot \max_{j\in[k]} C_{jj} }{\alpha\beta}\cdot \varepsilon\right)$-query protocol using $O\left(k\cdot\log\left(\frac{\normI{A}}{\varepsilon} \right)\right)$ queries for any $\varepsilon>0$.
\item \textbf{Ex-ante Analysis:} If $A$ is generated from a distribution, where each archetype is an independent copy of a $N$-dimensional random vector $\theta$.
\begin{itemize}
\item \textbf{Multivariate Gaussian Distributions:} $\theta$ is distributed according to a multivariate Gaussian distribution $\mathcal{N}(0,\Sigma)$. If there exists a subset $S\subseteq [N]$ such that $\frac{\Tr{\Sigma_S}}{\rho(\Sigma_S)}> 64k$, where $\Sigma_S=\mathbb{E}[\theta_S\theta_S^T]$ is the covariance matrix for items in $S$ and $\rho(\Sigma_S)$ is the largest eigenvalue of $\Sigma_S$,\footnote{$\theta_S$ is the $|S|$-dimensional vector that contains all $\theta_i$ with $i\in S$.} then with probability at least $1-2\exp\left(-\frac{\Tr{\Sigma_S}}{16\cdot \rho(\Sigma_S)}\right)$, we have a $\left(\varepsilon,\frac{64\sqrt{|S| k}}{\sqrt{\Tr{\Sigma_S}}} \cdot \varepsilon\right)$-query protocol using $O\left(|S|\cdot\log\left(\frac{\normI{A}}{\varepsilon} \right)\right)$ queries for any $\varepsilon>0$. Note that when the entries of $\theta$ are i.i.d., any $S$ with size at least $64k$ satisfies the condition.
\item \textbf{Bounded Distributions with Weak Dependence:} Let $\theta_i$ be supported on $[-c,c]$ and has mean $0$ for each $i\in[N]$. If there exists a subset $S\subseteq [N]$ such that $\norm{\Influ{\theta_S}}<1$, and $\sum_{i\in S}v_i^2>\frac{16c^2 k\sqrt{|S|}}{1-\norm{\Influ{\theta_S}}}$, where $v_i^2:=\mathrm{Var}[\theta_i]$, then with probability at least \\ $1-2\exp\left(-\frac{\left(1-\norm{\Influ{\theta_S}}\right)\cdot (\sum_{i\in S}v_i^2)^2}{64c^4 k|S|}\right)$, we have a $\left(\varepsilon,\frac{64\sqrt{|S| k}}{\sqrt{\sum_{i\in S}v_i^2}} \cdot \varepsilon\right)$-query protocol using \\ $O\left(|S|\cdot\log\left(\frac{\normI{A}}{\varepsilon} \right)\right)$ queries for any $\varepsilon>0$. Note that when the entries of $\theta$ are independent, $\norm{\Influ{\theta_S}}=0$ for any set $S$. If each $\theta_i$ has variance $\Omega(c^2)$, then any set with size at least $\alpha k^2$ suffices for some absolute constant $\alpha$.
\end{itemize}
\end{itemize}
\begin{remark}
In the ex-ante analysis, the success probabilities depend on the parameters of the distributions, but note that they are both at least $1-2\exp(-4k)$.
\end{remark}
\end{theorem}
Before we prove Theorem~\ref{thm:query protocol}, we combine it with Theorem~\ref{thm:main} to derive results for a few concrete settings.
\begin{proposition}\label{prop:1+2 deterministic}
Under the same setting as in Theorem~\ref{thm:main} with the extra assumption that every valuation $v_i$ is constrained-additive,
we can construct mechanism $M$ using only query access to the given mechanism $\widehat{M}$ and
oblivious to the true type distribution $D$, such that for any possible $D$, \yangnote{$M$ is
$\left(\eta,\varepsilon_1\right)$-BIC and IR, where $\eta =O\left(\mathcal{L}\varepsilon_1+ \normI{A}\mathcal{L} m f(\varepsilon_1)+ \normI{A}\mathcal{L} \sqrt{m f(\varepsilon_1)}\right)$,} and has revenue at least $\textsc{Rev}(\widehat{M},\widehat{D}_z)-O\left(\normI{A}\mathcal{L} m^2 f(\varepsilon_1)+ \normI{A}\mathcal{L} m^{3/2}f(\varepsilon_1)^{1/2}\right)$. Recall that $\varepsilon_1$ satisfies $d_P(D_i,A\circ \widehat{D}_{z,i})\leq \varepsilon_1$ for all $i\in [m]$. We compute the function $f(\cdot)$ and the number of queries for the following three concrete settings (one for each of the three assumptions in Theorem~\ref{thm:query protocol}).
\begin{enumerate}
\item \textbf{Deterministic Structure: Separability.} If the design matrix $A$ satisfies the \textbf{separability assumption} by Donoho and Stodden~\cite{DonohoS03}, that is, $A^T$ can be expressed as $[I_k H^T]\Pi_N$, where $\Pi_N\in \mathbb{R}^N$ is a permutation matrix, $f(\varepsilon_1)=4\varepsilon_1$ for all $\varepsilon>0$. The number of queries each bidder needs to answer is $O\left(k\cdot\log\left(\frac{\normI{A}}{\varepsilon_1} \right)\right)$ .
\item \textbf{Multivariate Gaussian Distributions: Well-Conditioned Covariance Matrix.} Let $A$ be generated from a distribution, where each archetype is an independent draw from a $N$-dimensional normal distribution $\mathcal{N}(0,\Sigma)$. Let $\kappa(\Sigma)$ be the condition number of $\Sigma$.\footnote{$\Sigma$ is well-conditioned if $\kappa(\Sigma)$ is small. When $\Sigma=I_N$, $\kappa(\Sigma)=1$.} For any set $S$ with size $64\kappa(\Sigma)k$, if we query each bidder about items in $S$, with probability at least $1-2\exp(-4k)$, $f(\varepsilon_1)=O\left(\frac{k\sqrt{\kappa(\Sigma)}}{\sqrt{\Tr{\Sigma_S}}}\cdot \varepsilon_1 \right)$, and each bidder needs to answer $O\left(\kappa(\Sigma)k\cdot\log\left(\frac{\normI{A}}{\varepsilon_1} \right)\right)$ queries.
\item \textbf{Weak Dependence: Sufficient Variance per Item.} Let $A$ be generated from a distribution, where each archetype is an independent copy of an $N$-dimensional random vector $\theta$. Assuming (i) $\norm{\Influ{\theta}}<1$, (ii) $\theta_i$ lies in $[-c,c]$, and (iii) $\mathrm{Var}[\theta_i]\geq a^2$ for each $i\in[N]$, then for any set $S$ with size $\frac{256 c^4 k^2}{a^4\left(1-\norm{INF(\theta)}\right)^2}$, if we query each bidder about items in $S$, with probability at least $1-2\exp(-4k)$, $f(\varepsilon_1)=O\left(\frac{\sqrt{k}}{a}\cdot \varepsilon_1\right)$ and each bidder needs to answer $O\left( \frac{c^4 k^2}{a^4\left(1-\norm{INF(\theta)}\right)^2}\cdot \log\left(\frac{\normI{A}}{\varepsilon_1} \right)\right)$ queries.\footnote{Clearly, we can weaken condition (i),(ii) and (iii). The result still holds if we can find a set $S$, so that for vector $\theta_S$, condition (i), (ii), and (iii) hold, and $|S|$ is at least $\frac{256 c^4 k^2}{a^4\left(1-\norm{INF(\theta_S)}\right)^2}$.}
\end{enumerate}
\end{proposition}
\begin{proof}
The results in the first and last setting follows directly from Theorem~\ref{thm:query protocol}. For the second setting, notice that by the eigenvalue interlacing theorem, $\kappa(\Sigma_S)\leq \kappa(\Sigma)$, as $\Sigma_S$ is a principal submatrix of $\Sigma$. Therefore, $\frac{\Tr{\Sigma_S}}{\rho(\Sigma_S)}\geq \frac{|S|}{\kappa(\Sigma_S)}\geq 64 k$. Now, the result follows from Theorem~\ref{thm:query protocol}.
\end{proof}
\begin{prevproof}{Theorem}{thm:query protocol}
Instead of directly studying the query complexity under our query model. We first consider the query complexity under a seemingly stronger query model, where we directly query the bidder about their value of $e_j^T t$, and their answer will be within $e_j^T t\pm \eta$ for some $\eta>0$. We refer to this type of queries as noisy value queries. Since for each item $j$, $|e_j^T Az|\leq \normI{A}$ for all $z\in [0,1]^k$ and we only care about types in $\mathbb{R}^N$ that are close to some $Az$, we can use our queries to perform binary search on $p$ to simulate noisy value queries. In particular, we only need $\log{\normI{A}}+\log{1/\eta}+\log{1/\varepsilon}$ many queries to simulate one noisy value queries. From now on, the plan is to first investigate the query complexity for noisy value queries, then convert the result to query complexity in the original model.
We first fix the notation. Let $\ell$ be the number of noisy value queries, and $Q\in \mathbb{R}^{\ell\times N}$ be the query matrix, where, each row of $Q$ is a standard unit vector. We use $\hat{y}\in \mathbb{R}^\ell$ to denote the bidder's answers to the queries and $y\in\mathbb{R}^\ell$ to true answers to the queries. Note that $\normI{\hat{y}-y}\leq \eta$. Given $\hat{y}$, we solve the following least squares problem: $\min_{z\in\mathbb{R}^k}\norm{QAz-\hat{y}}^2$.
The problem has a closed form solution: $\hat{z}=\left(A^TQ^TQA\right)^{-1}A^TQ^T\hat{y}$. Let $B:=QA$, and $z(t)\in \mathbb{R}^k$ be a vector that satisfies $\normI{t-Az(t)}\leq \varepsilon$. We are interested in upper bounding $\normI{\hat{z}-z(t)}$. Note that
\begin{align*}
\hat{z}-z(t) =& (B^TB)^{-1}B^T (\hat{y}-Bz(t))\\
=& (B^TB)^{-1} B^T \left((\hat{y}-y)+(y-Bz(t))\right)\\
=& (B^TB)^{-1} B^T (\hat{y}-y) + (B^TB)^{-1} B^T Q(t-Az(t))
\end{align*}
Since the rows of $Q$ are all standard unit vectors, $\normI{Q}=1$.
\begin{align*}
\normI{\hat{z}-z(t)}\leq &\normI{(B^TB)^{-1} B^T (\hat{y}-y)} +\normI{(B^TB)^{-1} B^T Q(t-Az(t))}\\
\leq &\normI{(B^TB)^{-1}}\normI{B^T}\left(\eta+\normI{Q(t-Az(t))}\right)\\
\leq &\normI{(B^TB)^{-1}}\normI{B^T}(\eta+\varepsilon).
\end{align*} Next, we bound $\normI{(B^TB)^{-1}}\normI{B^T}$ under the different assumptions.
\paragraph{Deterministic Structure:} We choose $\ell=k$ and $Q$ so that $QA=B=C$. Since $C$ is diagonally dominant, $C$ is non-singular, and $(C^T C)^{-1} = C^{-1}(C^{T})^{-1}$.
\begin{lemma}[Adapted from Theorem 1 and Corollary 1 of~\cite{varah1975lower}]\label{lem:diagonally dominant l-infinity}
If a matrix $U\in \mathbb{R}^{n\times n}$ is diagonally dominant both by rows and by columns, and $\alpha=\min_{i\in[n]} \left(|U_{ii}|-\sum_{j\neq i} |U_{ij}|\right)$ and $\beta = \min_{j\in[n]} \left(|U_{jj}|-\sum_{i\neq j} |U_{ij}|\right)$, then $\normI{U^{-1}}\leq 1/\alpha$ and $\normI{(U^T)^{-1}}\leq 1/\beta$.
\end{lemma}
By Lemma~\ref{lem:diagonally dominant l-infinity}, $\normI{(C^TC)^{-1}}\normI{ C^T} \leq \frac{\normI{C^T}}{\alpha\beta}$. Note that $\normI{C^T}=\max_{j\in[k]} \sum_{i\in[k]} |C_{ij}|\leq 2\max_{j\in[k]} C_{jj}$. The last inequality is because $C$ is diagonally dominant by columns. To sum up, if we choose $Q$ so that $QA=C$, $$\normI{\hat{z}-z(t)}\leq \frac{ (\varepsilon+\eta)\cdot\normI{C^T}}{\alpha\beta}\leq \frac{2 (\varepsilon+\eta)\cdot \max_{j\in[k]} C_{jj} }{\alpha\beta}.$$
\paragraph{Ex-ante Analysis:}
Since $\normI{(B^TB)^{-1}}\leq \sqrt{k}\norm{(B^TB)^{-1}}$ and $\normI{B^T}\leq \sqrt{\ell}\norm{B}$, $$\normI{\hat{z}-z(t)}\leq \frac{\sqrt{\ell k}\cdot \sigma_{max}(B)}{\sigma_{min}(B)^2}\cdot(\eta+\varepsilon),$$ where $\sigma_{max}(B)$ (or $\sigma_{min}(B)$) is $B$'s largest (or smallest) singular value.
\paragraph{Multivariate Gaussian distribution:} When $\theta$ is distributed according to a multivariate Gaussian distribution, we choose $\ell=|S|$ and $Q$ so that each row corresponding to an $e_j$ with $j\in S$. Now, $B$ is a $\ell\times k$ random matrix where each column is an independent copy of $\theta_S$. We use Lemma~\ref{lem:GGM singular values} to bound $B$'s largest singular value $\lsv{B}$ and smallest singular value $\ssv{B}$. The proof of Lemma~\ref{lem:GGM singular values} is postponed to Section~\ref{sec:proof of concentration Gaussian}.
\begin{lemma}\label{lem:GGM singular values}[Concentration of Singular Values under multivariate Gaussian distributions]\\
Let $U=[X^{(1)},\ldots, X^{(n)}]$ be a $m\times n$ random matrix, where each column of $U$ is an independent copy of a $m$-dimensional random vector $X$ distributed according to a multivariate Gaussian distribution $\mathcal{N}(0,\Lambda^T D\Lambda)$. In particular, $\Lambda\in \mathbb{R}^{m\times m}$ is an orthonormal matrix, and $D\in \mathbb{R}^{m\times m}$ is a diagonal matrix. We have $\sigma_{max}(U)\leq 2\sqrt{\Tr{D}} \text{ and }\sigma_{min}(U)\geq \frac{\sqrt{\Tr{D}}}{4},$ with probability at least $1-2\exp\left(-\frac{\Tr{D}}{8\cdot d_{max}}+4n
\right)$, where $d_{max}$ is the largest entry in $D$.
\end{lemma}
Since $\frac{\Tr{\Sigma_S}}{\rho(\Sigma_S)}>64 k$, by Lemma~\ref{lem:GGM singular values}, $\lsv{B}\leq 2\sqrt{\Tr{\Sigma_S}}$ and $\ssv{B}\geq \sqrt{\Tr{\Sigma_S}}/4$ with probability at least $1-2\exp\left(-\frac{\Tr{\Sigma_S}}{16\cdot \rho(\Sigma_S)}\right)\geq 1-2\exp(-4k)$. Hence, $\normI{\hat{z}-z(t)}\leq \frac{32\sqrt{|S| k}}{\sqrt{\Tr{\Sigma_S}}}\cdot (\eta+\varepsilon)$ with probability at least $1-2\exp\left(-\frac{\Tr{\Sigma_S}}{16\cdot \rho(\Sigma_S)}\right)$.
\paragraph{Weakly Dependent Distributions:} When the coordinates of $\theta_S$ are weakly dependent, i.e., $\norm{\Influ{\theta_S}}<1$, we choose $\ell=|S|$ and $Q$ so that each row corresponding to an $e_j$ with $j\in S$. Now, $B$ is a $\ell\times k$ random matrix where each column is an independent copy of $\theta_S$. We use Lemma~\ref{lem:singular values under Dobrushin} to bound $B$'s largest singular value $\lsv{B}$ and smallest singular value $\ssv{B}$. The proof of Lemma~\ref{lem:singular values under Dobrushin} is postponed to Section~\ref{sec:proof of concentration Dobrushin}.
\begin{lemma}\label{lem:singular values under Dobrushin}[Concentration of Singular Values under Weak Dependence]\\
Let $U=[X^{(1)},\ldots, X^{(n)}]$ be a $m\times n$ random matrix, where each column of $U$ is an independent copy of a $m$-dimensional random vector $X$. We assume that the coordinates of $X$ are weakly dependent, i.e., $\norm{\Influ{X}}<1$, and each coordinate of $X$ lies in $[-c,c]$ and has mean $0$ and variance $v_i^2$. Let $v=\sqrt{\sum_{i\in[m]} v_i^2}$.
We have $\sigma_{max}(U)\leq 2v \text{ and }\sigma_{min}(U)\geq \frac{v}{4},$ with probability at least $1-2\exp\left(-\frac{\left(1-\norm{\Influ{X}}\right)v^4}{32c^4 nm}+4
\right)$.
\end{lemma}
Since $\sum_{i\in S}v_i^2>\frac{16 c^2 k\sqrt{|S|}}{1-\norm{\Influ{\theta_S}}}$, by Lemma~\ref{lem:singular values under Dobrushin}, we have $\lsv{B}\leq 2\sqrt{\sum_{i\in S}v_i^2}$ and $\ssv{B}\geq \sqrt{\sum_{i\in S}v_i^2}/4$ with probability at least $1-2\exp\left(-\frac{\left(1-\norm{\Influ{\theta_S}}\right)\cdot (\sum_{i\in S}v_i^2)^2}{64c^4 k|S|}\right)\geq 1-2\exp(-4k)$. Therefore,
$\normI{\hat{z}-z(t)}\leq \frac{32\sqrt{|S|k}}{\sqrt{\sum_{i\in S}v_i^2}}\cdot (\eta+\varepsilon)$ with probability at least $1-2\exp\left(-\frac{\left(1-\norm{\Influ{\theta_S}}\right)\cdot (\sum_{i\in S}v_i^2)^2}{64c^4 k|S|}\right)$.
\paragraph{Query Complexity in Different Models:} We set $\eta$ to be $\varepsilon$.
\begin{itemize}
\item \textbf{Deterministic structure:} we have a $\left(\varepsilon,\frac{4 \cdot \max_{j\in[k]} C_{jj} }{\alpha\beta}\cdot \varepsilon\right)$-query protocol using $k(\log{\normI{A}}+2\log (1/\varepsilon))$ queries.
\item \textbf{Multivariate Gaussian distributions:} with probability at least $1-2\exp\left(-\frac{\Tr{\Sigma_S}}{16\cdot \rho(\Sigma_S)}\right)$ (no less than $1-2\exp(-4k)$ by our choice of $S$), we have a $\left(\varepsilon,\frac{64\sqrt{|S| k}}{\sqrt{\Tr{\Sigma_S}}} \cdot \varepsilon\right)$-query protocol using $|S|(\log{\normI{A}}+2\log (1/\varepsilon))$ queries.
\item \textbf{Weakly dependent distributions:} with probability at least $1-2\exp\left(-\frac{\left(1-\norm{\Influ{\theta_S}}\right)\cdot (\sum_{i\in S}v_i^2)^2}{64c^4 k|S|}\right)$ (no less than $1-2\exp(-4k)$ by our choice of $S$), we have a $\left(\varepsilon,\frac{64\sqrt{|S| k}}{\sqrt{\sum_{i\in S}v_i^2}} \cdot \varepsilon\right)$-query protocol using $|S|(\log{\normI{A}}+2\log (1/\varepsilon))$ queries.
\end{itemize}
\end{prevproof}
\section{Bounding the Largest and Smallest Singular Values }
We prove both Lemma~\ref{lem:GGM singular values} and~\ref{lem:singular values under Dobrushin} using an $\varepsilon$-net argument. We first state a lemma that says that for any matrix $M$, if we can bound the maximum value of $\norm{Mx}$ over all points $x$ in the $\varepsilon$-net, then we also bound the largest and smallest singular values of $M$.
\begin{lemma}[Adapted from~\cite{rudelson2014recent}]\label{lem:eps-net}
For any $\varepsilon<1$, there exists an $\varepsilon$-net $\mathcal{K}\subseteq S^{n-1}$, i.e., $\forall x\in S^{n-1}~\exists y\in \mathcal{K}~ \norm{x-y}<\varepsilon$, such that $|\mathcal{K}|\leq (3/\varepsilon)^n$. For any matrix $M\in \mathbb{R}^{m\times n}$, let $a = max_{x\in \mathcal{K}} \norm{Mx}$ and $b=min_{x\in \mathcal{K}} \norm{Mx}$, then $\lsv{M}\leq \frac{a}{1-\varepsilon}$ and $\ssv{M}\geq b-\frac{\varepsilon}{1-\varepsilon}\cdot a$.
\end{lemma}
\begin{prevproof}{Lemma}{lem:eps-net}
Let $x^*\in S^{n-1}$ be a vector that satisfies $\norm{Mx^*}=\lsv{M}$. Let $x$ be a vector in $\mathcal{K}$ such that $\norm{x-x^*}\leq \varepsilon$. Then $\lsv{M}=\norm{Mx^*}\leq \norm{Mx}+\norm{M(x-x^*)}\leq a+\varepsilon \lsv{M}$, which implies that $\lsv{M}\leq \frac{a}{1-\varepsilon}$. On the other hand, for any $y\in S^{n-1}$, let $y'\in \mathcal{K}$ satisfies $\norm{y-y'}\leq \varepsilon$, then $\norm{My}\geq \norm{My'}-\norm{M(y-y')}\geq b- \varepsilon\cdot \lsv{M}\geq b- \frac{\varepsilon}{1-\varepsilon}\cdot a$.
\end{prevproof}
\subsection{Multivariate Gaussian Distributions}\label{sec:proof of concentration Gaussian}
In this section, we prove the case where the columns of the random matrix are drawn from a multivariate Gaussian distribution. The key is again to prove that for every unit-vector, $\norm{Ux}$ lies between $[c_1\cdot\mathbb{E}[\norm{Ux}], c_2\cdot\mathbb{E}[\norm{Ux}]]$ with high probability for some absolute constant $c_1$ and $c_2$ (Lemma~\ref{lem:GGM concentration for every unit-vector}). Lemma~\ref{lem:GGM singular values} follows from the combination of Lemma~\ref{lem:GGM concentration for every unit-vector},~\ref{lem:eps-net}, and the union bound.
\begin{prevproof}{Lemma}{lem:GGM singular values}
Let $Y^{(1)},\ldots, Y^{(n)}$ be $n$ i.i.d. samples from the distribution $\mathcal{N}(0,I_m)$, and $V:=D^{1/2} [Y^{(1)},\ldots, Y^{(s)}]$.
\begin{proposition}\label{prop:change of variable}
$\mathcal{N}(0,\Sigma)\overset{d}{=} \Lambda^T\circ \mathcal{N}(0,D)$ and $U\overset{d}{=} \Lambda^T V$.
\end{proposition}
\begin{proof}
$\mathbb{E}[\Lambda^T D^{1/2} Y^{(i)} (Y^{(i)})^T D^{1/2}\Lambda] = \Lambda^T D^{1/2}\mathbb{E}[Y^{(i)} (Y^{(i)})^T ]D^{1/2} \Lambda= \Lambda^T D\Lambda= \Sigma$.
\end{proof}
Since $\Lambda$ is an orthonormal matrix, $\lsv{U}=\lsv{V}$ and $\ssv{U}=\ssv{V}$. We will proceed to show that both $\lsv{V}$ and $\lsv{V}$ concentrate around their means. We do so via an $\varepsilon$-net argument.
\begin{lemma}\label{lem:GGM concentration for every unit-vector}
For any fix $x\in S^{n-1}$, $\mathbb{E}[\norm{Vx}^2]=\Tr{D}$. Moreover,
$$\Pr\left[\norm{Vx}^2 \leq \frac{\Tr{D}}{4} \right]\leq \exp\left(-\frac{\Tr{D}}{8\cdot d_{max}}\right),$$ and
$$\Pr\left[\norm{Vx}^2\geq 2 \Tr{D} \right]\leq \exp\left(-\frac{\Tr{D}}{4\cdot d_{max}}\right).$$
\end{lemma}
\begin{prevproof}{Lemma}{lem:GGM concentration for every unit-vector}
Let $g_1,\ldots, g_n$ to be $n$ i.i.d. samples from $\mathcal{N}(0,1)$. It is not hard to see that $Vx\overset{d}{=} (\sqrt{d_1}g_1,\ldots,\sqrt{d_n}g_n)^T$, so we need to prove that $\sum_{i\in[n]} d_i g_i^2$ concentrates around its mean $\Tr{D}$.
\begin{align*}
&\Pr\left[\sum_{i\in[n]} d_i g_i^2\leq \Tr{D}-t\right]\\
=& \Pr\left[\exp\left(\lambda\cdot (\Tr{D}-\sum_{i\in[n]} d_i g_i^2)\right)\geq \exp(\lambda t)\right]~\quad(\text{$\lambda>0$ and will be specified later})\\
\leq & \frac{\exp(\lambda \Tr{D}
)\mathbb{E}\left[ \exp\left(-\lambda\cdot \sum_{i\in[n]} d_i g_i^2\right)\right]}{\exp(\lambda t)}= \frac{\exp(\lambda \Tr{D}
)\prod_{i\in[n]}\mathbb{E}\left[ \exp\left(-\lambda\cdot d_i g_i^2\right)\right]}{\exp(\lambda t)}
\end{align*}
Since $g_i^2$ distributes according to a chi-square distribution, its moment generating function $$\mathbb{E}\left[ \exp\left(-\lambda\cdot d_i g_i^2\right)\right]=\frac{1}{\sqrt{1+2\lambda d_i}}.$$ If we choose $\lambda$ to be no more than $1/2d_{max}$, since for any $a\in[0,1]$, $1+2a\geq e^a$, we have that $$\frac{1}{\sqrt{1+2\lambda d_i}}\leq \exp(-\lambda d_i/2).$$
Putting everything together, we have that $$\Pr\left[\sum_{i\in[n]} d_i g_i^2\leq \Tr{D}-t\right]\leq \exp\left (-\lambda\cdot (t-\Tr{D}/2)\right).$$ When we choose $\lambda=1/2d_{max}$ and $t=3/4\cdot \Tr{D}$, the RHS of the inequality becomes $\exp\left(-\frac{\Tr{D}}{8\cdot d_{max}}\right)$.
Next, we upper bound $\Pr\left[\sum_{i\in[n]} d_i g_i^2\geq \Tr{D}+t\right]$ via a similar approach.
\begin{align*}
&\Pr\left[\sum_{i\in[n]} d_i g_i^2\geq \Tr{D}+t\right]\\
=& \Pr\left[\exp\left(\lambda\cdot (\sum_{i\in[n]} d_i g_i^2-\Tr{D})\right)\geq \exp(\lambda t)\right]~\quad(\text{$\lambda>0$ and will be specified later})\\
\leq & \frac{\prod_{i\in[n]}\mathbb{E}\left[ \exp\left(\lambda\cdot (d_i g_i^2-d_i)\right)\right]}{\exp(\lambda t)}
\end{align*}
Note that $\mathbb{E}\left[ \exp\left(\lambda\cdot (d_i g_i^2-d_i)\right)\right]=\frac{\exp(-\lambda d_i)}{\sqrt{1-2\lambda d_i}}$.
\begin{proposition}\label{prop:approx}
For any $x\in [0, 1/4]$, $\frac{\exp(-x)}{\sqrt{1-2x}}\leq \sqrt{1+2x}$.
\end{proposition}
\begin{prevproof}{Proposition}{prop:approx}
We first state a few inequalities that are not hard to verify. First, for all $x>0$, $e^{-x}\leq 1-x+x^2$. Second, $\sqrt{1-4x^2}\geq 1-2x^2-8x^4$ if $x\in [0,1/2)$. Finally, $1-2x^2-8x^4\geq 1-x+x^2$ if $x\in[0,1/4]$. Combining all three inequalities, we have that $$e^{-x}\leq \sqrt{1-4x^2}=\sqrt{1-2x}\sqrt{1+2x},~\text{for all $x\in[0,1/4]$}.$$
\end{prevproof}
If we choose $\lambda$ to be no more than $1/4d_{max}$, then by Proposition~\ref{prop:approx}, $\frac{\exp(-\lambda d_i)}{\sqrt{1-2\lambda d_i}}\leq \sqrt{1+2\lambda d_i}$, which is upper bounded by $\exp(\lambda d_i)$. Putting everything together, we have that
$$\Pr\left[\sum_{i\in[n]} d_i g_i^2\geq \Tr{D}+t\right]\leq \exp\left(-\lambda(t-\Tr{D})\right).$$
When we choose $\lambda=1/4d_{max}$ and $t=2 \Tr{D}$, the RHS of the inequality becomes $\exp\left(-\frac{\Tr{D}}{4\cdot d_{max}}\right)$.
\end{prevproof}
Next, we only consider when the good event happens, that is, for all points $x$ in the $\varepsilon$-net, $\norm{Vx}\in \left[\frac{\sqrt{\Tr{D}}}{2},\sqrt{2\Tr{D}}\right]$. Combining Lemma~\ref{lem:GGM concentration for every unit-vector} and the union bound, we know that the good event happens with probability at least $1-2\exp\left(-\frac{\Tr{D}}{8\cdot d_{max}}+\ln(3/\varepsilon)\cdot n\right)$. According to Lemma~\ref{lem:eps-net}, $\lsv{V}\leq \frac{\sqrt{2\Tr{D}}}{1-\varepsilon}$ and $\ssv{V}\geq \frac{\sqrt{\Tr{D}}}{2}-\frac{\varepsilon}{1-\varepsilon}\cdot \sqrt{2\Tr{D}}$. If we choose $\varepsilon=1/7$, then $\lsv{V}\leq 2\sqrt{\Tr{D}}$ and $\ssv{V}\geq \frac{\sqrt{\Tr{D}}}{4}$.
\end{prevproof}
\subsection{Bounded Distributions with Weak Dependence}\label{sec:proof of concentration Dobrushin}
In this section, we prove the case where the columns of the random matrix are drawn from a $m$-dimensional distribution that satisfies weak dependence. The overall plan is similar to the one for multivariate Gaussian distributions. The key is again to prove that for every unit-vector, $\norm{Ux}$ lies between $\left[c_1\cdot\mathbb{E}[\norm{Ux}], c_2\cdot\mathbb{E}[\norm{Ux}]\right]$ with high probability for some absolute constant $c_1$ and $c_2$ (Lemma~\ref{lem:Dobrushin concentration for every unit-vector}). Lemma~\ref{lem:singular values under Dobrushin} then follows from the combination of Lemma~\ref{lem:Dobrushin concentration for every unit-vector},~\ref{lem:eps-net}, and the union bound.
\begin{prevproof}{Lemma}{lem:singular values under Dobrushin}
We first show that for each fix $x\in S^{n-1}$, $\norm{Ux}$ is concentrates around its mean. Then, we apply Lemma~\ref{lem:eps-net} to bound $\lsv{U}$ and $\ssv{U}$.
\begin{lemma}\label{lem:Dobrushin concentration for every unit-vector}
Let $U=[X^{(1)},\ldots, X^{(n)}]$ be a $m\times n$ random matrix, where each column of $U$ is an independent copy of a $m$-dimensional random vector $X$. We assume that the coordinates of $X$ are weakly dependent, i.e., $\norm{\Influ{X}}<1$, and each coordinate of $X$ lies in $[-c,c]$ and has mean $0$ and variance $v_i^2$. Let $v=\sqrt{\sum_{i\in[m]} v_i^2}$. For any fix $x\in S^{n-1}$, $\mathbb{E}[\norm{Ux}^2]= v^2$ and
$$\Pr\left[|\norm{Ux}^2-v^2|>t\right]\leq 2 \exp\left(-\frac{\left(1-\norm{\Influ{X}}\right)t^2}{16c^4 nm}\right)$$
\end{lemma}
\begin{prevproof}{Lemma}{lem:Dobrushin concentration for every unit-vector}
We first expand $\norm{Ux}^2$. \begin{align*}
\norm{Ux}^2
=\sum_{i\in[m]}\left(\sum_{j\in[n]} u_{ij}x_j\right)^2
=\sum_{i\in[m]}\left(\sum_{j\in[n]} u_{ij}^2x_j^2+2\sum_{k\neq j} u_{ij}u_{ik}x_jx_k\right).
\end{align*}
Therefore, $\mathbb{E}\left[\norm{Ux}^2\right]=\sum_{i\in[m]} v_i^2=v^2$. To prove that $\norm{Ux}^2$ concentrates, we first need a result by Chatterjee~\cite{Chatterjee2005a}.
\begin{lemma}[Adapted from Theorem 4.3 in~\cite{Chatterjee2005a}]\label{lem:concentration weak dependence}
Let $X$ be a $d$-dimensional random vector. Suppose function $f$ satisfies the following generalized Lipschitz condition: $$|f(x)-f(y)|\leq \sum_{i\in[d]} c_i \mathds{1}[x_i\neq y_i],$$ for any $x$ and $y$ in the support of $X$. If $\Influ{X}<1$, we have $$\Pr\left[ |f(X)-\mathbb{E}[f(X)]|\geq t\right]\leq 2\exp\left(-\frac{\left(1-\norm{\Influ{X}}\right)t^2}{\sum_{i\in[d]}c_i^2}\right).$$
\end{lemma}
The function we care about is $\norm{Ux}^2$, where the variables are $\{u_{ij}\}_{i\in[m],j\in[n]}$. If $U$ and $U'$ only differs at the $(i,j)$ entry, then
\begin{align*}
&|\norm{Ux}^2-\norm{U'x}^2|\\
=&| u_{ij}^2 x_j^2+2\sum_{k\neq j} u_{ij}u_{ik}x_j x_k-(u'_{ij})^{2} x_j^2-2\sum_{k\neq j} u'_{ij}u_{ik}x_jx_k|\\
\leq & c^2 x_j^2+4c^2|x_j||x_k|\leq 4c^2 |x_j|\left(\sum_{k\in[n]}|x_k|\right)\leq 4c^2\sqrt{n} |x_j|
\end{align*}
We denote $4c^2\sqrt{n} |x_j|$ by $c_{ij}$. Clearly, for any $U$ and $U'$, $|\norm{Ux}^2-\norm{U'x}^2|\leq \sum_{i,j\in[d]} c_{ij}\mathds{1}[u_{ij}\neq u'_{ij}]$. Also, notice that $\Influ{U}=I_n\otimes \Influ{X}$, and therefore $\norm{\Influ{U}}=\norm{\Influ{X}}$.~\footnote{$\otimes$ denotes the Kronecker product of the two matrices.} We apply Lemma~\ref{lem:concentration weak dependence} to $\norm{Ux}^2$ and derive the following inequality:
$$\Pr\left[|\norm{Ux}^2-v^2|>t\right]\leq 2 \exp\left(-\frac{\left(1-\norm{\Influ{X}}\right)t^2}{\sum_{i\in[m],j\in[n]}c_{ij}^2}\right)=2 \exp\left(-\frac{\left(1-\norm{\Influ{X}}\right)t^2}{16c^4 nm}\right).$$
\end{prevproof}
Next, we only consider when the good event happens, that is, for all points $x$ in the $\varepsilon$-net, $\norm{Ux}\in \left[\frac{v}{2},\sqrt{2}v\right]$. Combining Lemma~\ref{lem:Dobrushin concentration for every unit-vector} (setting $t=3/4 v^2$) and the union bound, we know that the good event happens with probability at least $1-2\exp\left(-\frac{\left(1-\norm{\Influ{X}}\right)9v^4}{256c^4 nm}+\ln(3/\varepsilon)\cdot n\right)$. According to Lemma~\ref{lem:eps-net}, $\lsv{U}\leq \frac{\sqrt{2}v}{1-\varepsilon}$ and $\ssv{U}\geq \frac{v}{2}-\frac{\varepsilon}{1-\varepsilon}\cdot \sqrt{2}v$. If we choose $\varepsilon=1/7$, then $\lsv{U}\leq 2v$ and $\ssv{U}\geq \frac{v}{4}$.
\end{prevproof}
\bibliographystyle{plain}
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"redpajama_set_name": "RedPajamaArXiv"
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<?php
// Fonctions
// Vérifie si la chaîne ressemble à une adresse IP
function IPValidate($IPtoValidate) {
//if (preg_match('#^([0-9]{1,3}\.){3}[0-9]{1,3}$#', $IPtoValidate)) {
if (filter_var($IPtoValidate, FILTER_VALIDATE_IP)) {
return TRUE;
} else {
return FALSE;
}
}
// show ifconfig
$str_ifconfig2 = shell_exec("/sbin/ifconfig");
// lecture fichier /etc/network/interfaces et affichage
$str_ifconfig = @file_get_contents("/etc/network/interfaces");
$modif = FALSE;
$str_ifconfig_tmp = strstr($str_ifconfig, 'eth0');
$conf_str = strstr($str_ifconfig_tmp, 'dhcp', TRUE); // Cherche la première occurence de 'dhcp' et renvoie ce qu'il y a avant
if (strstr($conf_str, 'eth0')) { // Si 'eth0 est dans la chaîne
$str_ifconfig_tmp = 'DHCP';
} else {
$conf_str = strstr($str_ifconfig_tmp, 'static', TRUE); // Cherche la première occurence de 'static' et renvoie ce qu'il y a avant
if (strstr($conf_str, 'eth0')) { // Si 'eth0 est dans la chaîne
$conf_str = strstr($str_ifconfig_tmp, 'static'); // Cherche la première occurence de 'static' et renvoie ce qu'il y a après
if (strstr($conf_str, 'address')) {
$address = strstr($conf_str, 'address');
preg_match("/\d{1,3}\.\d{1,3}\.\d{1,3}\.\d{1,3}/", $address, $matches);
$address = $matches[0];
if(isset($_POST['address'])) {
if ((IPValidate($_POST['address'])==TRUE)) {
if ($address != $_POST['address']) { //Verifie si l'adresse est différente
$prefix = 'address ';
$str_ifconfig = str_replace($prefix.$address, $prefix.$_POST['address'],$str_ifconfig);
$modif = TRUE;
$address = $_POST['address'];
}
} else {
$display_network .= '<div class="alert alert-error">Error in address</div>';
}
}
}
if (strstr($conf_str, 'netmask')) {
$netmask = strstr($conf_str, 'netmask');
preg_match("/\d{1,3}\.\d{1,3}\.\d{1,3}\.\d{1,3}/", $netmask, $matches);
$netmask = $matches[0];
if(isset($_POST['netmask'])) {
if ((IPValidate($_POST['netmask'])==TRUE)) {
if ($netmask != $_POST['netmask']) { //Verifie si l'adresse est différente
$prefix = 'netmask ';
$str_ifconfig = str_replace($prefix.$netmask, $prefix.$_POST['netmask'],$str_ifconfig);
$modif = TRUE;
$netmask = $_POST['netmask'];
}
} else {
$display_network .= '<div class="alert alert-error">Error in netmask</div>';
}
}
}
if (strstr($conf_str, 'network')) {
$network = strstr($conf_str, 'network');
preg_match("/\d{1,3}\.\d{1,3}\.\d{1,3}\.\d{1,3}/", $network, $matches);
$network = $matches[0];
if(isset($_POST['network'])) {
if (IPValidate($_POST['network'])==TRUE) {
if ($network != $_POST['network']) { //Verifie si l'adresse est différente
$prefix = 'network ';
$str_ifconfig = str_replace($prefix.$network, $prefix.$_POST['network'],$str_ifconfig);
$modif = TRUE;
$network = $_POST['network'];
}
} else {
$display_network .= '<div class="alert alert-error">Error in network</div>';
}
}
}
if (strstr($conf_str, 'gateway')) {
$gateway = strstr($conf_str, 'gateway');
preg_match("/\d{1,3}\.\d{1,3}\.\d{1,3}\.\d{1,3}/", $gateway, $matches);
$gateway = $matches[0];
if(isset($_POST['gateway'])) {
if (IPValidate($_POST['gateway'])==TRUE) {
if ($gateway != $_POST['gateway']) { //Verifie si l'adresse est différente
$prefix = 'gateway ';
$str_ifconfig = str_replace($prefix.$gateway, $prefix.$_POST['gateway'],$str_ifconfig);
$modif = TRUE;
$gateway = $_POST['gateway'];
}
} else {
$display_network .= '<div class="alert alert-error">Error in gateway</div>';
}
}
}
if (strstr($conf_str, 'broadcast')) {
$broadcast = strstr($conf_str, 'broadcast');
preg_match("/\d{1,3}\.\d{1,3}\.\d{1,3}\.\d{1,3}/", $broadcast, $matches);
$broadcast = $matches[0];
if(isset($_POST['broadcast'])) {
if (IPValidate($_POST['broadcast'])==TRUE) {
if ($broadcast != $_POST['broadcast']) { //Verifie si l'adresse est différente
$prefix = 'broadcast ';
$str_ifconfig = str_replace($prefix.$broadcast, $prefix.$_POST['broadcast'],$str_ifconfig);
$modif = TRUE;
$broadcast = $_POST['broadcast'];
}
} else {
$display_network .= '<div class="alert alert-error">Error in broadcast</div>';
}
}
}
} else {
$display_network = '<div class="alert alert-error">ERROR: not a static configuration and/or an eth0 device</div>';
}
if ($modif == TRUE) {
file_put_contents("/etc/network/interfaces", $str_ifconfig);
$display_network = '<div class="alert alert-success">File "/etc/network/interfaces" updated successfully</div>';
}
}
?>
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1">
<!-- The above 3 meta tags *must* come first in the head; any other head content must come *after* these tags -->
<title>OPENSTRIATO</title>
<meta name="description" content="">
<meta name="author" content="Samuel Salas">
<!-- Latest compiled and minified CSS -->
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/css/bootstrap.min.css">
<!-- Optional theme -->
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/css/bootstrap-theme.min.css">
<style>
body {
padding-top: 60px; }
</style>
</head>
<body>
<div class="container">
<?php
include('menu.php');
showMenu(4);
if (isset($display_network)) {
echo $display_network;
}
?>
<form id="networkFileUpdate" action="network.php" method="post">
<table><tr>
<td><h3>Network interfaces</h3></td>
<td><button id="validateReboot" type="submit" class="btn btn-primary">Modify all infos</button></td>
</tr></table>
<div class="container" class="alert alert-success">
<table>
<?php
echo '<tr><td><h4>IP Address</h4></td><td><input type="text" value="'.$address.'" name="address" id="address"></td></tr>';
echo '<tr><td><h4>Mask</h4></td><td><input type="text" value="'.$netmask.'" name="netmask" id="netmask"></td></tr>';
echo '<tr><td><h4>Network</h4></td><td><input type="text" value="'.$network.'" name="network" id="network"></td></tr>';
echo '<tr><td><h4>Gateway</h4></td><td><input type="text" value="'.$gateway.'" name="gateway" id="gateway"></td></tr>';
echo '<tr><td><h4>Broadcast</h4></td><td><input type="text" value="'.$broadcast.'" name="broadcast" id="broadcast"></td></tr>';
?>
</table>
</div> <!-- /container -->
</form>
</div>
<div class="container">
<h3>ifconfig</h3>
<div class="container" class="alert alert-success">
<pre>
<?php echo $str_ifconfig2;?>
</pre>
</div> <!-- /container -->
</div>
<div class="container">
<h3>/etc/network/interfaces</h3>
<div class="container" class="alert alert-success">
<pre>
<?php echo $str_ifconfig;?>
</pre>
</div> <!-- /container -->
</div>
<div class="container">
<form id="rebootNetwork" action="network.php" method="post">
<table><tr>
<td><h3>Validate and reboot</h3></td>
<td><button id="validateReboot" type="submit" class="btn btn-primary">Validate File and Reboot</button></td>
</tr></table>
<input type="hidden" value="OK" name="reboot" id="reboot">
<div class="container" class="alert alert-success">
<?php
if ((isset($_POST['reboot']))&&($_POST['reboot']=='OK')) {
exec("reboot");
}
echo '';
?>
</div> <!-- /container -->
</form>
</div>
<!-- Le javascript
================================================== -->
<!-- Placed at the end of the document so the pages load faster -->
<script src="js/jquery.min.js"></script>
<script src="js/bootstrap.min.js"></script>
</body>
</html>
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,825
|
is a railway station in the city of Kashiwazaki, Niigata, Japan, operated by East Japan Railway Company (JR East).
Lines
Nishiyama Station is served by the Echigo Line and is 12.8 kilometers from the terminus of the line at Kashiwazaki Station.
Station layout
The station consists of a two opposed ground-level side platforms connected to the station building by a footbridge.
The station is unattended. Suica farecard cannot be used at this station.
Platforms
History
Nishiyama Station opened on 11 November 1912. With the privatization of Japanese National Railways (JNR) on 1 April 1987, the station came under the control of JR East. A new station building was completed in 1992.
Surrounding area
Nishiyama Post Office
See also
List of railway stations in Japan
References
External links
JR East station information
Railway stations in Niigata Prefecture
Railway stations in Japan opened in 1912
Echigo Line
Stations of East Japan Railway Company
Kashiwazaki, Niigata
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 1,543
|
Q: Django - Model id in Detail View URL, 1st id not working I have a model, Position, which I have created a detail view to view each individual position.
views.py
def position_detail_view(request, id=None):
position = get_object_or_404(Position, id=id)
context= {
'object': position,
}
return render(request, 'positions/position_detail.html', context)
positions/urls.py
from django.urls import path, include
from .views import position_list_view, position_detail_view
urlpatterns = [
path('', position_list_view),
path('<int:id>', position_detail_view, name='detail')
]
When I go to http://localhost:8000/apply/1/, where the id=1, I get a Page Not Found 404 Error. However, with any other id, the page loads just fine. Any ideas on why the first id in the model gives a 404 error?
Edit 1: Traceback Error
Page not found (404) Request Method: GET Request
URL: http://localhost:8000/apply/1/ Using the URLconf defined in
bta_website.urls, Django tried these URL patterns, in this order:
admin/ [name='home'] apply/application/ apply/ apply/
[name='detail'] The current path, apply/1/, didn't match any of these.
You're seeing this error because you have DEBUG = True in your Django
settings file. Change that to False, and Django will display a
standard 404 page.
A: Django get_object_or_404 works like below.
get_object_or_404(klass, *args, **kwargs)
Calls get() on a given model manager, but it raises Http404 instead of the model's DoesNotExist exception.
In your case,
your URL path is not properly configured.
Try to make changes this:
path('/<int:id>/', position_detail_view, name='detail')
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,496
|
resume and template ~ Free Sample Resumeplates Pdf Download For Windows Examples Banking Writing Letter Format Cover Easy 64 Fabulous Sample Resume Templates Pdf. Sample Resume Templates Pdf Format Word Document. Sample Resume Templates Pdf Format Example Word. Free Sample Resume Template.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 761
|
{"url":"https:\/\/uk.mathworks.com\/help\/robust\/ug\/robust-controller-design-using-mu-synthesis.html","text":"## Robust Controller Design Using Mu Synthesis\n\nThe technique of \u03bc synthesis extends the methods of H synthesis to design a robust controller for an uncertain plant. You can perform \u03bc synthesis on plants with parameter uncertainty, dynamic uncertainty, or both using the `musyn` command.\n\n`musyn` seeks a controller that minimizes the robust H performance of the closed-loop system. The robust H performance, also called \u03bc, quantifies how modeled uncertainty affects the performance of a feedback loop. For details about \u03bc and how it is computed, see Robust Performance Measure for Mu Synthesis.\n\n### Basic \u03bc Synthesis Workflow\n\nYou can use `musyn` to:\n\n\u2022 Synthesize \"black box\" unstructured robust controllers.\n\n\u2022 Robustly tune a fixed-order or fixed-structure controller made up of tunable components such as PID controllers, state-space models, and static gains.\n\n#### \u03bc Synthesis of Unstructured Controllers\n\n\u03bc synthesis of unstructured controllers is analogous to controller synthesis with `hinfsyn`, except that the plant includes uncertainty. As with `hinfsyn`, you set up your problem as the feedback system `CL = lft(P,K)`, where `P` is the plant and `K` is the controller to design.\n\nIn the diagram:\n\n\u2022 w represents the disturbance inputs.\n\n\u2022 u represents the control inputs.\n\n\u2022 z represents the error outputs to be kept small.\n\n\u2022 y represents the measurement outputs provided to the controller.\n\nYou construct the uncertain plant P by building a state-space model with uncertain coefficients (`ureal` or `ucomplex`) blocks, uncertain dynamics (`ultidyn` blocks), or both. Construct the plant such that the measurement outputs y are the last outputs, and the control inputs u are the last inputs. As with `hinfsyn`, you can optionally augment the plant inputs and outputs with weighting functions (loop-shaping filters) that represent control objectives.\n\nYou then pass this plant to `musyn`, which seeks a controller K that minimizes the robust H performance. The controller is returned as a state-space model. For a simple example, see Unstructured Robust Controller Synthesis on the `musyn` reference page.\n\n#### \u03bc Synthesis of Fixed-Structure Controllers\n\nInstead of obtaining a controller that is a free-form state-space model, you can specify a fixed controller structure with tunable parameters. `musyn` then adjusts those parameters to minimize the robust H performance of the system. \u03bc synthesis of fixed-structure controllers is analogous to controller tuning with `hinfstruct`, except that the plant includes uncertainty.\n\nTo set up your problem for fixed-structure \u03bc synthesis, you construct a generalized state-space (`genss`) model of the uncertain closed-loop system with tunable controller elements. To do so, you create and interconnect:\n\n\u2022 Numeric LTI models representing the fixed components of the control system\n\n\u2022 Uncertain control design blocks such as `ureal` and `ultidyn` blocks representing the uncertain components of the plant\n\n\u2022 Optional LTI weighting functions (loop-shaping filters) that represent control objectives\n\n\u2022 Tunable control design blocks such as `tunablePID`, `tunableSS`, and `tunableGain` to represent tunable components of the system\n\nFor an example that shows how to build such a model, see Build Tunable Control System Model With Uncertain Parameters.\n\nYou pass the tunable, uncertain closed-loop model to `musyn`, which seeks values of the tunable parameters that optimize the robust H performance from the model inputs to its outputs. For a simple example, see Robust Tuning of Fixed-Structure Controller on the `musyn` reference page.\n\nIf you have a Simulink\u00ae model of your control system, you can use `slTuner` to linearize the model with specified uncertain parameters and tunable blocks. You then use `getIOTransfer` to extract a `genss` model for controller design with `musyn`. For an example, see Model Uncertainty in Simulink for Robust Tuning.\n\n### Interpret the Results of \u03bc Synthesis\n\n`musyn` returns a robust controller `K` (for unstructured controller tuning) or a tuned version of the control system `CL` (for fixed-structure controller tuning). It also returns the best achieved robust H performance as the `CLperf` output argument. This value tells you that with the controller returned by `musyn`, the peak gain of the closed-loop system remains below `CLperf` for uncertainty up to 1\/`CLperf` in normalized units. For example:\n\n\u2022 `CLperf` = 0.5 means that the closed-loop gain remains below 0.5 for uncertainty up to twice the uncertainty specified in the input model. The worst-case gain for the specified uncertainty is typically smaller.\n\n\u2022 `CLperf` = 2 means that the closed-loop gain remains below 2 for uncertainty up to half the uncertainty specified in CL. For this value, the worst-case gain for the full specified uncertainty can be much larger. It can even be infinite, meaning that the system does not remain stable over the full range of the specified uncertainty.\n\nFor more detailed information about this quantity and how it is computed, see Robust Performance Measure for Mu Synthesis.\n\nTo find `K`, `musyn` uses an iterative process called D-K iteration. This process solves a sequence of scaled H problems. The frequency-dependent scalings, called D and G scalings, take advantage of the uncertainty structure. To perform D-K iteration, `musyn`:\n\n1. Uses H synthesis to find a controller that minimizes the closed-loop gain of the nominal system.\n\n2. Performs a robustness analysis to estimate the robust H performance of the closed-loop system. This quantity is expressed as a scaled H norm involving the D and G scalings (the D step).\n\n3. Finds a new controller to minimize the H norm obtained in step 2 (the K step).\n\n4. Repeats steps 2 and 3 until the robust performance stops improving.\n\nFor mathematical details about how this algorithm works, see D-K Iteration Process.\n\n`musyn` gives you two ways to monitor and interpret the progress of the algorithm: the default display and the full display.\n\n### Default `musyn` Display\n\nBy default, `musyn` provides a brief display of algorithm progress in the MATLAB\u00ae command window. For instance:\n\n```DG-K ITERATION SUMMARY: ------------------------------------------------------------------- Robust performance Fit order ------------------------------------------------------------------- Iter K Step Peak MU DG Fit D G 1 100 5.747 6.394 10 4 2 5.221 3.433 4.607 10 6 3 2.682 2.263 2.627 10 4 4 1.987 1.687 2.18 10 6 5 1.287 1.192 1.377 10 8 6 1.079 1.087 1.09 10 8 7 1.076 1.046 1.055 8 6 8 1.049 1.024 1.044 10 6 9 1.045 1.022 1.039 8 6 10 1.04 1.023 1.033 8 6 Best achieved robust performance: 1.02 ```\n\nThe display includes information about each D-K iteration.\n\n\u2022 `K Step` column \u2014 For the first iteration, this value is the H performance of the closed-loop nominal system after controller synthesis. For remaining iterations, this column shows the scaled H norm after controller synthesis.\n\n\u2022 `Peak MU` column \u2014 Robust performance ($\\overline{\\mu }$, an upper bound on \u03bc) for the controller designed in the `K Step`.\n\n\u2022 `DG fit` column \u2014 Scaled H performance after fitting the D and G scalings with rational functions.\n\n\u2022 `Fit order` columns \u2014 Orders of the rational function used to fit the scalings in that iteration. If the system has only complex uncertainty, or when the `'MixedMU'` option of `musynOptions` is set to `'off'`, then `musyn` does not apply G scaling. In that case, only the D fit order is listed.\n\nIf you see a large difference between the `Peak MU` and ```DG Fit``` values in a given iteration, it is a sign that `musyn` cannot find a good fit for the scalings. In that case, you can try increasing the maximum fit order using the `'FitOrder'` option of `musynOptions`.\n\nFor other ways to improve the results, see Improve Results of Mu Synthesis.\n\n### Full `musyn` Display\n\nYou can obtain a more detailed view into the progress of D-K iteration by setting the `'Display'` option of `musynOptions` to `'full'`. If you turn on the full display, then `musyn` pauses after each D-K iteration so that you can view the detailed results of the iteration. In addition to the information described in Default musyn Display, the full display:\n\n\u2022 Shows detailed computation information for the controller synthesis (K step) of the current iteration. For unstructured controllers, see `hinfsyn` for information about this display. For fixed-structure controllers, see `hinfstructOptions`.\n\n\u2022 Shows information about the fits for the D scalings and the G scalings (if any) of the current iteration. The information includes the fit order of the scalings for each uncertain block. It also includes a goodness-of-fit score. A score less than or equal to 1 indicates adequate fit for \u03bc synthesis.\n\n\u2022 Generates plots that let you visualize the D and G fits, the robust performance before fitting, and the scaled H performance after fitting. Examining these plots can help you determine if the maximum fit order is high enough to capture all the frequency-dependent variation in the scalings (see the `FitOrder` option of `musynOptions` for more information).\n\nThe `D Fit` or `D,G Fit` plot shows the scaling data and the corresponding rational fits.\n\nUse the radio buttons to select which scalings to inspect:\n\n\u2022 `D (diagonal)` shows the magnitude of the diagonal elements of the D scalings.\n\n\u2022 `D (offdiagonal)` shows the magnitude and phase of the off-diagonal elements of the D scalings. This plot is available when your system has repeated uncertain blocks. (See the `'FullDG'` option of `musynOptions` for more information.)\n\n\u2022 `jG` shows the magnitude and phase of the G-scalings. G scalings are present only when there is real uncertainty and the `MixedMU` option of `musynOptions` is `'on'`. See Improve Results of Mu Synthesis.\n\nThe `Robust Performance` plot shows the performance of the closed-loop system before and after fitting.\n\nThe traces on this plot are:\n\n\u2022 `Mu upper bound` \u2014 Robust performance, the upper bound $\\overline{\\mu }$ as a function of frequency\n\n\u2022 `Scaled CL for D,G data` \u2014 Scaled H performance before fitting the D and G scaling data with rational functions\n\n\u2022 `Scaled CL for fitted D,G` \u2014 Scaled H performance after fitting\n\n\u2022 `Scaled CL for fitted D only` \u2014 Shows what behavior would not be captured if G were omitted\n\nFor detailed information about the D-K iteration algorithm and the meaning of all the quantities in the full display, see D-K Iteration Process.","date":"2022-01-16 09:51:08","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 2, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8415229916572571, \"perplexity\": 1486.6919494243778}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-05\/segments\/1642320299852.23\/warc\/CC-MAIN-20220116093137-20220116123137-00058.warc.gz\"}"}
| null | null |
Egerton es una parroquia civil del distrito de Ashford, en el condado de Kent (Inglaterra), y uno de los pueblos que se ubican dentro de su límite.
Geografía
Según la Oficina Nacional de Estadística británica, Egerton tiene una superficie de 12,38 km².
Demografía
Según el censo de 2001, Egerton tenía 1104 habitantes (48,19% varones, 51,81% mujeres) y una densidad de población de 89,18 hab/km². El 17,93% eran menores de 16 años, el 74,82% tenían entre 16 y 74 y el 7,25% eran mayores de 74. La media de edad era de 41,95 años. Del total de habitantes con 16 o más años, el 21,85% estaban solteros, el 62,03% casados y el 16,11% divorciados o viudos.
El 97,09% de los habitantes eran originarios del Reino Unido. El resto de países europeos englobaban al 0,45% de la población, mientras que el 2,45% había nacido en cualquier otro lugar. Según su grupo étnico, el 98,82% eran blancos, el 0,36% mestizos, el 0,27% asiáticos, el 0,27% negros y el 0,27% de cualquier otro salvo chinos. El cristianismo era profesado por el 80,15%, el budismo por el 0,27% y cualquier otra religión, salvo el hinduismo, el judaísmo, el islam y el sijismo, por el 0,63%. El 10,88% no eran religiosos y el 8,07% no marcaron ninguna opción en el censo.
556 habitantes eran económicamente activos, 543 de ellos (97,66%) empleados y 13 (2,34%) desempleados. Había 445 hogares con residentes, ninguno vacío y 6 eran alojamientos vacacionales o segundas residencias.
Referencias
Enlaces externos
Localidades de Kent
Parroquias civiles de Kent
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 2,149
|
Welcome to the Winner's Circle where we celebrate the success of our ICL students. Today we are cheering for Kitty Griffin!
Little Mouse is the story of a young mouse taking the first lone venture out of the nest to get food for the family. The journey is dangerous, but the reward—so sweet.
Children love stories about small animals, and mice are perfect. I struggle with poetry so this was a challenge to myself to work with a small animal in a small structure.
It came at a time when I needed a boost. What a delight to see that phrase, "Grand Prize Winner!" Writing can be lonely and suddenly feeling like a winner in a writer's community gave me a dose of, "Keep Going!"
I'm in that stage of life where I've pulled back from teaching so writing is my focus, although I'm a new grandmother and now there are some little people who need me (and I need them). There's nothing like sitting at the computer with a baby in your arms as you sing a revised chapter out loud, gently rocking them. If the baby throws up, well, maybe I need to read that section out loud to my group! Ha ha.
I've been creating stories all my life.
Give it to my agent!
My problem isn't blockage, it's distraction. Look at that lovely problem over there! It's much more interesting than my character's. Oh! Look at that incident floating by. Let me grab it. I've learned to put my stories on a stovetop. Two burners up front each have a big stewpot with my works in progress. There can be other burners with pots on them, but I'm only allowed to lift the lid, drop a tidbit in, and the lid goes back on and I focus on the front two burners. Focus was my challenge as a writer. Ideas flow over, under, around, and through me constantly. Finding the story I love and the one that loves me—that is what works for me.
I would like to go to Max's house and buy his private boat so I could sailor through night and day and in and out of weeks so I could go where the wild things are.
Everyone was so kind. I'm humbled and appreciative and want to thank those who read my story and found it grand.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 513
|
{"url":"https:\/\/gmatclub.com\/forum\/m60-267727.html","text":"GMAT Question of the Day - Daily to your Mailbox; hard ones only\n\n It is currently 24 May 2019, 22:14\n\n### GMAT Club Daily Prep\n\n#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.\n\nCustomized\nfor You\n\nwe will pick new questions that match your level based on your Timer History\n\nTrack\n\nevery week, we\u2019ll send you an estimated GMAT score based on your performance\n\nPractice\nPays\n\nwe will pick new questions that match your level based on your Timer History\n\n# M60-16\n\nAuthor Message\nTAGS:\n\n### Hide Tags\n\nMath Revolution GMAT Instructor\nJoined: 16 Aug 2015\nPosts: 7372\nGMAT 1: 760 Q51 V42\nGPA: 3.82\n\n### Show Tags\n\n11 Jun 2018, 06:31\n00:00\n\nDifficulty:\n\n45% (medium)\n\nQuestion Stats:\n\n50% (01:33) correct 50% (01:58) wrong based on 6 sessions\n\n### HideShow timer Statistics\n\nIs $$n < 0$$?\n\n1) $$n - 1 < 0$$\n\n2) $$|3 - n| > |n + 5|$$\n\n_________________\nMathRevolution: Finish GMAT Quant Section with 10 minutes to spare\nThe one-and-only World\u2019s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.\n\"Only $149 for 3 month Online Course\" \"Free Resources-30 day online access & Diagnostic Test\" \"Unlimited Access to over 120 free video lessons - try it yourself\" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7372 GMAT 1: 760 Q51 V42 GPA: 3.82 Re M60-16 [#permalink] ### Show Tags 11 Jun 2018, 06:31 Official Solution: Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first. Condition 1) :$$n - 1 < 0$$ \u21d4 $$n < 1$$ Since the range of the question, $$n < 0$$ does not include that of the condition 1), $$n < 1$$, the condition 1) is not sufficient. Condition 2) : $$|3-n| > |n+5|$$ \u21d4 $$|3-n|^2 > |n+5|^2$$ \u21d4 $$(3-n)^2 > (n+5)^2$$ \u21d4 $$n^2 -6n + 9 > n^2+10n + 25$$ \u21d4 $$-16 > 16n$$ \u21d4 $$n < -1$$ Since the range of the question includes that of the condition 2), the condition 2) is sufficient. Therefore, B is the answer. If the original condition includes \"1 variable\", or \"2 variables and 1 equation\", or \"3 variables and 2 equations\" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World\u2019s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. \"Only$149 for 3 month Online Course\"\n\"Free Resources-30 day online access & Diagnostic Test\"\n\"Unlimited Access to over 120 free video lessons - try it yourself\"\nIntern\nJoined: 08 Jul 2018\nPosts: 3\n\n### Show Tags\n\n08 Aug 2018, 01:20\nIn this question and the next, why is it that similar method or solving is giving contradictory results for statement 1?\nManager\nJoined: 07 Apr 2018\nPosts: 104\nLocation: United States\nConcentration: General Management, Marketing\nGPA: 3.8\n\n### Show Tags\n\n26 Mar 2019, 18:00\nMathRevolution wrote:\nOfficial Solution:\n\nForget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.\n\nSince we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.\n\nCondition 1) :$$n - 1 < 0$$ \u21d4 $$n < 1$$\n\nSince the range of the question, $$n < 0$$ does not include that of the condition 1), $$n < 1$$, the condition 1) is not sufficient.\n\nCondition 2) :\n\n$$|3-n| > |n+5|$$\n\n\u21d4 $$|3-n|^2 > |n+5|^2$$\n\n\u21d4 $$(3-n)^2 > (n+5)^2$$\n\n\u21d4 $$n^2 -6n + 9 > n^2+10n + 25$$\n\n\u21d4 $$-16 > 16n$$\n\n\u21d4 $$n < -1$$\n\nSince the range of the question includes that of the condition 2), the condition 2) is sufficient.\n\nIf the original condition includes \"1 variable\", or \"2 variables and 1 equation\", or \"3 variables and 2 equations\" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.\n\nshould we always take the square of the mod on both side of an inequality? if the value of the mod is less than 1 and greater than 0\nM60-16 \u00a0 [#permalink] 26 Mar 2019, 18:00\nDisplay posts from previous: Sort by\n\n# M60-16\n\nModerators: chetan2u, Bunuel\n\n Powered by phpBB \u00a9 phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT\u00ae test is a registered trademark of the Graduate Management Admission Council\u00ae, and this site has neither been reviewed nor endorsed by GMAC\u00ae.","date":"2019-05-25 05:14:57","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6390093564987183, \"perplexity\": 3697.3728518870357}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-22\/segments\/1558232257889.72\/warc\/CC-MAIN-20190525044705-20190525070705-00127.warc.gz\"}"}
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Превентор (от — предупреждаю) — рабочий элемент комплекта противовыбросового оборудования, устанавливаемый на устье скважины. Основная функция превентора — герметизация устья нефтегазовой скважины в чрезвычайных ситуациях при строительстве или ремонтных работах на скважине. Герметизация скважины предотвращает открытое фонтанирование нефти и, как следствие, предотвращает возникновение пожара или загрязнение окружающей среды. В настоящее время установка противовыбросового оборудования является обязательным условием при ведении буровых работ .
Разновидности
Оборудование противовыбросовое предназначено для герметизации устья нефтяных и газовых скважин в процессе их строительства и ремонта с целью безопасного ведения работ, предупреждения выбросов и открытых фонтанов, охраны окружающей среды.
В состав оборудования входят колонные фланцы, крестовины, надпревенторные катушки, система гидроуправления превенторами и задвижками, манифольд и трубопроводы, соединяющие гидроуправление, гидроуправляемые элементы.
По способу герметизации устья скважины противовыбросовое оборудование различается на:
плашечные превенторы (делятся на трубные и глухие), также к ним можно отнести превентора со срезающими плашками (у которых в случае ЧП (ГНВП или ОФ) буровая труба перекусывается и зажимается мощными гидравлическими плашками).
превенторы универсальные (кольцевые) предназначены для перекрытия отверстия в скважине, если в ней находится любая часть бурильной колонны (замок, труба, ведущая труба)
превенторы вращающиеся (герметизаторы роторные) предназначены для уплотнения устья скважины с вращающейся в ней трубой или ведущей трубой
Маркировка
Маркировка состоит из букв ОП, после чего идёт номер схемы, по которой выполнен превентор, далее условный проход превентора в мм, потом условный проход манифольда, и расчётное рабочее давление при выбросе в мегапаскалях.
Пример:
ОП5 230/80х35
ОП5 230/80-35
ОП5 230/80х350
ОП5 350/80х35
ОП5 350/80-35
ОП5 350/80х350
Технические условия эксплуатации противовыбросового оборудования и порядок его освидетельствования
Противовыбросовое оборудование работает в диапазоне температур от +55 °C до −40 °C. Превенторы подлежат обязательному техническому освидетельствованию: раз в 8 лет — Ростехнадзором (при сроке эксплуатации более 10 лет), раз в квартал — техническими службами буровой эксплуатирующей компании.
Ссылки
Буровое оборудование
Нефтедобыча
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\section{Introduction}
The problem of quantum thermalization can be stated as:
\begin{itemize}\label{question}
\item Given microscopic unitarity, how do Gibbs ensembles emerge?
\end{itemize}
If a many body quantum system is set in an initial pure state $\vert\psi (0)\rangle$, the evolved state $\vert\psi (t)\rangle=U(t)\vert\psi (0)\rangle$ is pure and time dependent, so it can never become a time independent mixed density matrix, such as Gibbs ensembles:
\begin{equation}\label{iloss}
U(t)\,\vert \psi (0)\rangle\langle\psi (0)\vert \,U^{\dagger}(t) \neq \rho^{\textrm{Gibbs}}\;,
\end{equation}
where $\rho^{\textrm{Gibbs}}$ is any Gibbs distribution. The dynamical emergence of Gibbs ensembles from unitary dynamics will be termed the problem of quantum thermalization. This problem is almost as old as quantum mechanics itself. For a selfcontained recent review, with an excellent account of references and historical rigor, see \cite{eisertreview}.
Although exact thermality cannot be attained within unitary evolution, we might still expect approximate thermality for the actual measurements done in experiments, the correlation functions of the theory. Given an observable $\mathcal{O}$ of the theory, it is written mathematically as:
\begin{equation}\label{thermalityt}
\langle\psi (t)\vert\,\mathcal{O}\,\vert\psi (t)\rangle = \textrm{Tr}(\rho^{\textrm{Gibbs}}\,\mathcal{O})\pm \textrm{error}\;.
\end{equation}
stating that the correct expectation value, as measured by the evolving quantum state is equal to a Gibbs ensemble average, up to some error. This error has to be negligible in the thermodynamic limit for the previous relation to be non trivial, and for the thermal expectation value to be a good approximation of the correct one.
To understand such behavior it was proposed in \cite{srednickisub} that the typical energy eigenstate $\vert E_{a}\rangle$ of the quantum system satisfy themselves the previous property:
\begin{equation}\label{thermalityE}
\langle E_{a}\vert\,\mathcal{O}\,\vert E_{a}\rangle = \textrm{Tr}(\rho^{\textrm{Gibbs}}\,\mathcal{O})\pm \textrm{error}\;,
\end{equation}
stating that the expectation value in the energy basis is well approximated by the thermal correlator. The previous phenomenom was coined Eigenstate Themalization in \cite{srednickisub}, but was earlier noticed in \cite{ETH}, in the context of quantum spin systems. At any rate, as argued in \cite{eisertreview}, both previous equations can be seen as more precise formulations of the original question~(\ref{question}), and as such they are hypothesis about the nature of quantum systems. Indeed, the second equation~(\ref{thermalityE}) is commonly known as the Eigenstate Thermalzation Hypothesis (ETH).
Relations~(\ref{thermalityt}) and~(\ref{thermalityE}) suggest various obvious questions:
\begin{itemize}
\item What type of systems display such behavior? Over which range of initial states and eigenstates do they display it?
\item What is $\rho^{\textrm{Gibbs}}$? Can we find the effective temperature $T=1/\beta$ from the pure state scenario?
\item What is the `error'?
\end{itemize}
Although we have a great deal of intuition about these questions through the connection between ETH and random matrices, to the author knowledge, see \cite{eisertreview}, no time independent Hamiltonian containing only few body interactions has been proven to satisfy relations~(\ref{thermalityt}) and~(\ref{thermalityE}). The difficulty to prove such behavior is related to the belief that non-linear interactions are fundamental to the quantum thermalization mechanism.
The objective of this article is to study a family of quantum systems displaying ETH, satisfying relation~(\ref{thermalityE}). Contrary to common belief, these systems are `gaussian', containing only two-body interactions, see~(\ref{H}). We further compute the errors, both in correlations and entanglement entropies. These errors differ from the random matrix approximation, providing a physically motivated measure of `randomness' of the quantum state.
We want to remark that although these systems might seem unnatural from several points of view, they indeed serve as microscopic toy models of black physics. The underlying reason is that they are examples of systems with no locality structure whatsoever. The Hamiltonian connects every oscillator with every other democratically, a characteristic feature of black hole physics \cite{matrixpol,susskind,lashkari,sahakian2,sekino,subir,uswalks,usrandomfree}.
From a different perspective, since these systems display ETH, entanglement entropy is extensive across all bipartitions, even for `vacuum states' in the sectors with a large number of particles. This could be of interest for the type of questions raised in \cite{simone}.
\section{Random free fermions, entanglement entropy and ETH}
The family of Hamiltonians we wish to study is the following:
\begin{equation}\label{H}
H=\alpha \sum\limits_{i=1}^{N}c_{i}^{\dagger}\,c_{i}+\eta\sum\limits_{i,j=1}^{N}c_{i}^{\dagger}\,V_{ij}\,c_{j}\;,
\end{equation}
where $\alpha$ and $\eta$ are parameters with energy dimensions, $c_{i}^{\dagger}$ and $c_{i}$ are creation and annihilation operators of spinless free fermions, with usual anticommutator relations, and the couplings $V_{ij}$ are independent random gaussian real numbers with zero mean and unit variance. The matrix $(\eta V)_{ij}\equiv\eta V_{ij}$ is therefore a random matrix taken from the GOE ensemble with deviation $\sigma_{V}=\eta$ (see \cite{tao} for a beautiful and modern treatment of random matrices).
The `free' nature of the model allows an exact solution via diagonalization of the matrix $V$. If $\psi^{a}$, for $a=1,\cdots , N$, are the eigenvectors of $V$ with eigenvalues $\epsilon_{a}$:
\begin{equation}
\sum\limits_{j=1}^{N}V_{ij}\,\psi^{a}_{j} = \epsilon_{a}\,\psi^{a}_{i}\;,
\end{equation}
then the Hamiltonian can be written as:
\begin{equation}
H = \sum\limits_{a=1}^{N}(\alpha +\epsilon_{a})\, d_{a}^{\dagger}\,d_{a}= \sum\limits_{a=1}^{N}E_{a}\, d_{a}^{\dagger}\,d_{a}\;,
\end{equation}
where $d_{a}^{\dagger}$ and $d_{a}$ are new creation and annihilation operators defined by:
\begin{equation}
d_{a}=\sum\limits_{i=1}^{N}\psi^{a}_{i}\,c_{i}\;.
\end{equation}
All eigenstates are constructed by choosing a set $\mathcal{A}$ of particles, and associate to it the following eigenstate:
\begin{equation}\label{eigenstate}
|\Psi^{N_{p}}\rangle =\prod\limits_{a\in \mathcal{A}}d_{a}^{\dagger}\,|0\rangle\;,
\end{equation}
where $|0\rangle$ is the state annihilated by all $d_{a}$, and $N_{p}$ is the number of particles in the state, a number which will play a key role below. Notice that there are $\binom{N}{N_{p}}$ independent states for a given $N_{p}$.
The objective of this article is to study the structure of these eigenstates, associated with~(\ref{H}). We will focus on the number operator, the two point correlation functions and entanglement entropies. Since the correlations and entanglement structure of the eigenstates are symmetrical under $N_{p}\rightarrow N-N_{p}$, a manifestation of particle-hole symmetry in this model, we will only focus on $N_{p}\leq N/2$.
To compute the correlations and entanglement entropies, we will make use of the theory of random matrices, which deals with the statistical properties of eigenvalues and eigenvectors of matrices such as $\eta V$ (see \cite{taovectors},\cite{tao} and \cite{haake} for an extense treatment of random matrices). In relation to the eigenvectors, the main assertion is that the orthogonal matrix of eigenvectors $(\psi^{1},\cdots ,\psi^{N} )$ is distributed according to the Haar measure on the orthogonal group $O(N)$. For our purposes, this means that the eigenvectors have independent and random gaussian entries, up to normalization. Matemathically:
\begin{equation}\label{statvec}
[\psi^{a}_{i}]=0 \,\,\,\,\,\,\,\, [\psi^{a}_{i}\,\psi^{b}_{j}]=\frac{1}{N}\,\delta_{ab}\,\delta_{ij}\;,
\end{equation}
where $[p]$ denotes the average of the random variable $p$ over the matrix ensemble.
For the eigenvalues we will only need Wigner's semicircle law, accounting for the probability of having an eigenvalue equal to $\lambda$:
\begin{equation}\label{wigner}
P(\lambda)=\frac{2}{\pi^{2}R^{2}}\,\sqrt{R^{2}-\lambda^{2}}\;,
\end{equation}
where $R^{2}\equiv 4N\eta^{2}$, and where we remind that this law concerns the eigenvalues of $\eta\, V$, a matrix with deviation equal to $\eta$, see the Hamiltonian~(\ref{H}). To ensure a zero energy vacuum eigenstate of $H$ we assume $R=2\sqrt{N}\eta<\alpha$. Given~(\ref{wigner}), the first two moments for the eigenenergies $E_{a}$ are:
\begin{equation}\label{E}
[\sum\limits_{a\in \mathcal{A}}E_{a}]=N_{p}\,\alpha \,\,\,\,\,\,\,\, [(\sum\limits_{a\in \mathcal{A}}E_{a})^{2}]-[\sum\limits_{a\in \mathcal{A}}E_{a}]^{2}=N_{p}\,N\,\eta^{2}\;.
\end{equation}
With the previous statistical information about eigenvalues and eigenvectors we can now compute the correlation functions for the state~(\ref{eigenstate}) with $N_{p}$ particles:
\begin{eqnarray}
C_{ij}^{\Psi}&=&\langle\Psi^{N_{p}}|c_{i}^{\dagger}c_{j}|\Psi^{N_{p}}\rangle =\sum\limits_{a,b\,=\,1}^{N}\psi^{a}_{i}\psi^{b}_{j}\,\langle\Psi^{N_{p}}|d_{a}^{\dagger}d_{b}|\Psi^{N_{p}}\rangle= \nonumber \\ &=&\sum\limits_{a\in \mathcal{A}}\psi^{a}_{i}\psi^{a}_{j}\;,
\end{eqnarray}
where the last sum just runs over the subset $\mathcal{A}$ of particles chosen. The previous correlator is itself a random variable, a functional of the random eigenvectors $\psi^{a}$. By using~(\ref{statvec}) we obtain:
\begin{equation}\label{purec}
[C_{ij}^{\Psi}]=\frac{N_{p}}{N}\,\delta_{ij} \,\,\,\,\,\,\,\, [C_{ij}^{\Psi}C_{kl}^{\Psi}]-[C_{ij}^{\Psi}]\,[C_{kl}^{\Psi}]=\frac{N_{p}}{N^{2}}\,\delta_{ik}\,\delta_{jl}\;.
\end{equation}
We thus can see the correlation matrix as the sum of a `thermal' part and an error, the error being a random matrix taken from the GOE ensemble with deviation $\sigma_{C}^{2}=\frac{N_{p}}{N^{2}}$. Notice that the `thermal' part just depends on the `macroscopic' parameter $N_{p}$, and cannot distinguish between the $\binom{N}{N_{p}}$ independent states in the corresponding $N_{p}$ sector. Also notice that the `thermal' part is a good approximation in the window $N_{p}\gg 1$. As might have been expected, and anticipating results, $N_{p}=N/2$ will correspond to the high temperature sector.
To proof ETH for this system, relation~(\ref{thermalityE}) described in the introduction, we need to compute the corresponding correlation matrix in the thermal ensemble. This is given by:
\begin{eqnarray}
C_{ij}^{\beta}&=&\frac{1}{Z}\textrm{Tr}(e^{-\beta H}\,c_{i}^{\dagger}\,c_{j})=\frac{1}{Z}\sum\limits_{a,b\,=\,1}^{N}\psi^{a}_{i}\,\psi^{b}_{j}\,\textrm{Tr}(e^{-\beta H}\,d_{a}^{\dagger}\,d_{b})=\nonumber \\ &=&\sum\limits_{a=1}^{N}\psi^{a}_{i}\,\psi^{a}_{j}\, n^{E_{a}}_{\beta}\;,
\end{eqnarray}
where $n^{E_{a}}_{\beta}=1/(e^{\beta E_{a}}+1)$ is the average number operator for a fermionic oscillator at temperature $T=1/\beta$, and $Z=\textrm{Tr}(e^{-\beta H})$ is the usual partition function. The thermal correlation matrix is again a random variable, due to the randomness of $H$. Since there is no correlation between eigenstates and eigenvalues, the mean and variance are given by:
\begin{equation}\label{thermalc}
[C_{ij}^{\beta}]=[n_{\beta}]\,\delta_{ij} \,\,\,\,\,\,\,\, [C_{ij}^{\beta}C_{kl}^{\beta}]-[C_{ij}^{\beta}]\,[C_{kl}^{\beta}]=\frac{[(n_{\beta})^{2}]}{N}\,\delta_{ik}\,\delta_{jl}\;.
\end{equation}
where:
\begin{equation}
[n_{\beta}]=\int\limits_{-R}^{R}\,P(\lambda)\,n^{\lambda}_{\beta}\,d\lambda \,\,\,\,\,\,\,\,\,\, [(n_{\beta})^{2}]=\int\limits_{-R}^{R}\,P(\lambda)\,(n^{\lambda}_{\beta})^{2}\,d\lambda\;.
\end{equation}
We did not succeed in analytically computing the averages for all $\beta$. In the large temperature limit, $\beta\alpha\rightarrow 0$, they read:
\begin{equation}
[n_{\beta}]=\frac{1}{2}-\frac{\alpha\beta}{4} \,\,\,\,\,\,\,\, [(n_{\beta})^{2}]=\frac{1}{4}-\frac{\alpha\beta}{4}\;,
\end{equation}
whereas in the low temperature limit, $\beta R\rightarrow\infty$, we have slightly more complicated expressions:
\begin{equation}\label{n}
[n_{\beta}]=\frac{2e^{-\alpha\beta}\,I_{1}(\beta R)}{\beta R}\rightarrow \sqrt{\frac{2}{\pi\beta R}}\frac{e^{-\beta \,(\alpha-R)}}{\beta R}\;,
\end{equation}
and
\begin{equation}\label{nn}
[(n_{\beta})^{2}]=\frac{e^{-2\beta\alpha}\,I_{1}(2\beta R)}{\beta R}\rightarrow\frac{e^{-2\beta \,(\alpha-R)}}{\beta R\sqrt{4\pi\beta R}}\;,
\end{equation}
where $I_{1}(x)$ is the modified Bessel function of the first kind. Since to ensure a zero energy vacuum eigenstate of $H$ we assumed $R=2\sqrt{N}\eta<\alpha$, from~(\ref{thermalc}),~(\ref{n}) and~(\ref{nn}) we conclude that the leading diagonal approximation of the thermal correlation matrix is valid at all temperatures.
Now we are ready to compare both correlation matrices, the exact eigenstate correlations~(\ref{purec}) versus the thermal~(\ref{thermalc}) ones, allowing us to arrive to the following conclusions:
\begin{itemize}
\item For $N_{p}\gg 1$, a pure eigenstate with $N_{p}$ particles can be effectively approximated by a Gibbs distribution at temperature $\beta$ satisfying $\frac{N_{p}}{N}=[n_{\beta}]$, the difference being subleading in the thermodynamic limit. Random free fermions then constitute an explicit analytical example of ETH~(\ref{thermalityE}), an example in which we know the effective temperature and the error size in terms of the microscopic parameters of the theory.
\item For $N_{p}\sim \mathcal{O}(1)$, approximating pure states by thermal ensembles is not a valid approximation.
\end{itemize}
These features can be made clearer by studying entanglement entropy. For gaussian systems, as shown in \cite{peschel}, one can compute the entanglement entropy of a given subsystem $A$ directly from the correlation matrix. More concretely, given a subsystem $A$ with $m$ degrees of freedom, knowledge of $C_{ij}^{\Psi}=\langle\Psi|c_{i}^{\dagger}c_{j}|\Psi\rangle$, where $i,j\in A$, allows for the computation of the entanglement entropy. It is given by:
\begin{equation}\label{ent}
S_{A}=-\sum\limits_{i=1}^{m}(\lambda_{i}\log \lambda_{i}+(1-\lambda_{i})\log (1-\lambda_{i}))\;,
\end{equation}
where $\lambda_{i}$, with $i=1,\cdots ,m$ are the $m$ eigenvalues of the matrix $C^{\Psi}$ in the given subsystem $A$. The proof relies only on the fact that the correlation matrix and the reduced density matrix share the same set of eigenvectors.
Although formula~(\ref{ent}) is fairly simple, one still need to compute the eigenvalues of $C^{\Psi}$, and this is not always possible analytically, even for one-dimensional systems, see \cite{peschel}. Indeed we were not able to compute the entanglement entropy for all $N_{p}$. We will compute it in the two standard limiting cases: the thermal regime, specified by $N_{p}\gg 1$, and for $N_{p}=1$, corresponding to the non-thermal phase.
Let us begin with the simpler case of having just one particle. The wave function is then given by:
\begin{equation}\label{single}
|\Psi_{a}^{1}\rangle =d^{\dagger}_{a}\,|0\rangle =\sum\limits_{i=1}^{N}\psi^{a}_{i}\,c_{i}^{\dagger}\,|0\rangle =\sum\limits_{i=1}^{N}\psi^{a}_{i}\,|i\rangle\;,
\end{equation}
where $|i\rangle\equiv c_{i}^{\dagger}\,|0\rangle$. This state is considered in \cite{usloc}, in relation to the Many-Body-Localized phase transition. Because the state is fully supported in the single particle sector, the entanglement of any subsystem $A$ can be expressed as:
\begin{equation}\label{entsingle}
S_{A}=-p_{A}\log p_{A}-(1-p_{A})\log (1-p_{A})\;,
\end{equation}
where $p_{A}=\sum\limits_{i\in A}|\psi_{i}|^{2}$, see \cite{usloc} for an explicit derivation of the previous formula. The average and variance of $p_{A}$ are $[p_{A}]=m/N$ and $\sigma_{p_{A}}^{2}=m/N^{2}$. Because the variance of the probabilities $p_{A}$ is small in comparison to the mean value, we Taylor expand to compute the average entanglement entropy, following \cite{usrandom} for the case of random QFT states. For the case at hand, the entanglement entropy of a subsystem $A$ of $m\leq N/2$ degrees of freedom in the state~(\ref{single}) is given by:
\begin{equation}\label{ent1}
[S_{m}^{\Psi^{1}}]=-\frac{m}{N}\log\frac{m}{N}-(1-\frac{m}{N})\log(1-\frac{m}{N})-\frac{1}{2(N-m)}\;,
\end{equation}
where we remark that on average does not depend on the particle type chosen, labeled by $a$, and that the last term in the previous equation is alway subleading in the thermodynamic limit. The previous formula for entanglement entropy is a monotonic growing function for $1\leq m\leq N/2$, with $S_{1}^{\Psi^{1}}\simeq \frac{\log N}{N}$ and $S_{N/2}^{\Psi^{1}}\simeq \log 2$. This is a very small amount of entanglement, and certainly not extensive with the number of sites $m$. Therefore it cannot be faithfully represented as a thermal entropy, signalling that the small $N_{p}$ sector does not satisfy ETH.
For the high $N_{p}$ sector we follow a novel approximate method developed in \cite{usrandom}, Appendix A. The key aspect to observe is that for $N_{p}\gg 1$ the correlator matrix~(\ref{purec}) is a diagonal matrix plus a random matrix with parametrically smaller entries. Writing $C^{\Psi}=\bar{C}^{\Psi}+\delta C^{\Psi}$, to first order the eigenvalues of $C^{\Psi}$ are given by $\lambda_{i}\simeq \bar{\lambda}_{i}+\delta\lambda_{i} $, where $\bar{\lambda}_{i}=N_{p}/N$ and $\delta\lambda_{i}$ are the eigenvalues of a random matrix of size $m$ with deviation $\sigma_{C^{\Psi}}^{2}=\frac{N_{p}}{N^{2}}\,$, see~(\ref{purec}). Using Wigner's semicircle law~(\ref{wigner}), for a matrix of size $m$ with such variance, these eigenvalues satisfy $[\delta\lambda_{i}]=0$ and $[(\delta\lambda_{i})^{2}]=m\frac{N_{p}}{N^{2}}\,$. Therefore, for $m\lesssim N_{p}$, plugging these eigenvalues into~(\ref{ent}), Taylor expanding in $\delta\lambda_{i}$ and finally taking the average, we obtain the following formula for the average entanglement entropy of a subsystem of size $m\lesssim N_{p}$ in the multiparticle state $|\Psi^{{N_{p}}}\rangle$:
\begin{equation}\label{entmany}
[S_{m}^{\Psi^{N_{p}}}]= m\, S^{N_{p}}_{1}-\frac{m^{2}}{2(N-N_{p})}\;,
\end{equation}
where we have defined:
\begin{equation}
S^{N_{p}}_{1}=-\frac{N_{p}}{N}\log \frac{N_{p}}{N}-(1-\frac{N_{p}}{N})\log (1-\frac{N_{p}}{N})\;,
\end{equation}
corresponding to the thermal entropy per degree of freedom for a state with $N_{p}\gg 1$ particles. Notice that to change from $N_{p}$ to the effective temperature $T=1/\beta$ we just need to use $\frac{N_{p}}{N}=[n_{\beta}]$.
Given the explicit expressions~(\ref{ent1}) and~(\ref{entmany}) we conclude:
\begin{itemize}
\item Entanglement entropy is well approximated by the thermal entropy for subsystems with sizes smaller than the number of particles in the given eigenstate. For bigger subsystems we cannot state anything with certainty, but it is tempting to speculate a slower growth of entanglement entropy for $m\gtrsim N_{p}$. For $N_{p}\simeq N/2$ the thermal approximation is valid for every subsystem.
\item The random nature of the state seems to increase with the number of particles.
\end{itemize}
\section{Error scalings as randomness measures}\label{secIII}
Until now we have focused in the structural properties of the eigenstates of the Hamiltonian~(\ref{H}), in particular on their thermal nature. It is now fruitful to check the differences between traditional approaches to quantum chaos and ETH based on fully random Hamiltonians, and the exact solution we found. This will provide a physically motivated quantification of the `randomness' of the quantum state.
Although this section is self-contained, for extensive reviews about the traditional approach to ETH and quantum thermalization based on `typicality' arguments and random matrices in the contexts of quantum information theory, condensed matter and black hole physics see \cite{eisertreview,vijayreview,harlowreview}. To proceed we first write the Hamiltonian~(\ref{H}) as:
\begin{equation}\label{Hchaotic}
H=H_{\textrm{free}}+\bar{\eta} \,H_{\textrm{int}}\;.
\end{equation}
In most cases in which $H_{\textrm{int}}$ contains non-linear interactions we cannot diagonalize $H$ exactly. The traditional approximation assumes that the Hamiltonian can be taken from one of the random matrix ensembles, see \cite{haake}. The approximation implies the famous chaotic spectra, and more concretely Wigner's semicircle law~(\ref{wigner}). More interestingly for the concerns of this article, it also implies ETH as we show below, see \cite{jain1,jain2,eisertreview,vijayreview,harlowreview,usrandom}.
Let us begin with the spectrum. Since the dimension of the subspace with $N_{p}$ particles is $\binom{N}{N_{p}}$, and assuming the entries of $H_{\textrm{int}}$ to be random gaussian variables with zero mean and unit variance, the eigenenergies satisfy:
\begin{equation}\label{ranener}
E_{a}^{\textrm{random}}=N_{p}\,\alpha\pm 2\,\sqrt{\binom{N}{N_{p}}}\,\bar{\eta}\;,
\end{equation}
where $a=1,\cdots , \binom{N}{N_{p}}$. The first two moments of the random approximation can be computed from Wigner's semicircle law:
\begin{equation}\label{ranE}
[E_{a}^{\textrm{random}}]=N_{p}\,\alpha \,\,\,\,\,\,\,\, [(E_{a}^{\textrm{random}})^{2}]-[E_{a}^{\textrm{random}}]^{2}=\binom{N}{N_{p}} \,\bar{\eta}^{2}\;.
\end{equation}
On the eigenvectors side, the assumption of a random Hamiltonian implies that the eigenvectors are random vectors in the corresponding subspace:
\begin{equation}
\vert E_{a}^{\textrm{random}}\rangle=\sum\limits_{i=1}^{\binom{N}{N_{p}}}\psi^{a}_{i}\,\vert i\rangle\;,
\end{equation}
where $\vert i\rangle$ is a basis in the $N_{p}$ subspace and:
\begin{equation}\label{ranvec}
[\psi^{a}_{i}]=0 \,\,\,\,\,\,\,\, [\psi^{a}_{i}\,\psi^{b}_{j}]=\frac{1}{\binom{N}{N_{p}}}\,\delta_{ab}\,\delta_{ij}\;.
\end{equation}
See \cite{usrandom} for a recent detailed treatment of these type of vectors. Using~(\ref{ranvec}), the statistical properties of $C_{ij}^{\textrm{r}}= \langle E_{a}^{\textrm{random}}\vert \,c_{i}^{\dagger}c_{j}\,\vert E_{a}^{\textrm{random}}\rangle$ are:
\begin{equation}\label{ranC}
[C_{ij}^{\textrm{r}}]=\frac{N_{p}}{N}\delta_{ij} \,\,\,\,\,\,\,\, [(C_{ij}^{\textrm{r}})^{2}]-[C_{ij}^{\textrm{r}}]^{2}=\frac{\binom{N-2}{N_{p}-1}}{\binom{N}{N_{p}}^{2}}\sim \mathcal{O}(\frac{1}{\binom{N}{N_{p}}})\;.
\end{equation}
Comparing formulas~(\ref{ranE}) and~(\ref{ranC}), corresponding to the random Hamiltonian approximation, with the exact solutions~(\ref{E}) and~(\ref{purec}), and with the thermal result~(\ref{thermalc}), we conclude that:
\begin{itemize}
\item Appropriately fixing $\bar{\eta}$ in terms of $\eta$, $N_{p}$ and $N$, the mean and variance of the eigenvalues is the same for the exact Hamiltonian~(\ref{H}) than for its random approximation.
\item The average correlation matrix $[C_{ij}]$ coincides for all cases, the differences lying on variances. These variances furnish good quantifiers of randomness in the quantum state. They subtly distinguish between macroscopically equal phases, such as eigenstates of fully random hamiltonians and eigenstates of random free fermions. The scaling properties of the errors in typical eigenstates seem a fruitful field to explore in the context of quantum thermalization.
\item The random Hamiltonian approximation seems valid for all subsystem sizes $m$ (notice that in the one particle sector is exact for all subsystems), while the Gibbs distribution seems to hold only for $m\lesssim N_{p}$.
\end{itemize}
\section{Conclusions}
In this article we studied aspects of the Hamiltonian~(\ref{H}), such as the spectral properties~(\ref{E}), correlation matrix~(\ref{purec}) and entanglement entropies,~(\ref{ent}) and~(\ref{entmany}). They can be expanded in $1/N$, where $N$ is the number of spinless fermions of the model. The leading term in this expansion is always the thermal result, given by~(\ref{thermalc}), the effective temperature being found in terms of the macroscopic parameter $N_{p}$ characterizing the sector. The family of Hamiltonians~(\ref{H}) thus satisfy~(\ref{thermalityE}), furnishing explicit examples of the Eigenstate Thermalization Hypothesis (ETH). The conclusion is remarkable, since it implies that ETH is \emph{typical} within the space of gaussian Hamiltonians. Since it is also typical in the full space of Hamiltonians \cite{eisertreview}, as proved by relation~(\ref{ranC}), it is tempting to conclude that it is typical for Hamiltonians with random $2,3\cdots N$ body interactions, such as the model presented in \cite{subir}.
We found that the entanglement properties of big subsystems in these eigenstates are different from the thermal result. For a sector with $N_{p}\gg 1$ particles, we were able to prove thermality of entanglement entropies until subsystems of size of $\mathcal{O}(N_{p})$. For bigger subsytems we speculated with a slower growth of entanglement entropy, but otherwise further study is needed to unravelled its nature. These results might have impact in black hole physics, in which the present picture is that given by Page in \cite{page}, a picture in which thermality holds for every subsystem, and in which deviations from thermality are assumed to be those given by the random Hamiltonian approximation.
The last section was devoted to study the differences between the approach to quantum chaos and ETH based on random matrices, see the reviews \cite{eisertreview,vijayreview,harlowreview}, and the exact solution of the Hamiltonian~(\ref{H}). These differences lie in the deviations from the thermal result. The `errors' in equations~(\ref{thermalityt}) and~(\ref{thermalityE}) are good quantifiers of the `randomness' of the quantum state. Their scaling properties seem an exciting new route to explore in the context of quantum thermalization.
\section*{Acknowledgements}
It is a pleasure to thank Jose Barb\' on, Marcos Crichigno, Simone Paganelli and Stefan Vandoren for interesting discussions in closely related subjects, Hrachya Babujian for useful comments on the manuscript and the constructive criticisms of an anonymous referee regarding section~(\ref{secIII}). The author also wishes to thank all the participants of the workshop `Strongly coupled field theories for condensed matter and quantum information', held in Natal, Brasil, in which this work was presented, and in special the hospitality of the International Institute of Physics, located in Natal, in which part of this work has been developed. This work was supported by the Delta-Institute for Theoretical Physics (D-ITP) that is funded by the Dutch Ministry of Education, Culture and Science (OCW).
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\section{Introduction}
\par
Type-I and Type-II censoring schemes are two most popular censoring schemes which are used in practice. They can be briefly described as follows. Suppose $n$ units are put on a life test. In Type-I censoring, the test is terminated when a pre-determined time, $T$, on test has been reached, and failures after time
$T$ are not observed. In Type-II censoring, the test is terminated when a pre-chosen number, $R$, out of $n$ items has failed. It is also assumed that the failed items are not replaced. So, in Type-I censoring scheme, the number of failures is random and in Type-II censoring scheme, the experimental time is random.\par
A hybrid censoring scheme is a mixture of Type-I and Type-II censoring schemes and it can be described as follows. Suppose $n$ identical units are put to test. The test is finished when a pre-selected number $R$ out of $n$ items are failed, or when a pre-determined time $T$ on the test has been obtained. From
now on, we call this Type-I hybrid censoring scheme and this scheme has been used as a reliability acceptance test
in \cite{mil}. This censoring scheme was introduced by Epstin \cite{eps}, he also studied the life testing data under the assumption of exponential distribution with mean life $\theta$. Epstein \cite{eps} proposed two-sided confidence intervals for $\theta$ without any formal proof. Fairbanks et al. \cite{fai} moderated partly the proposition of Epstein \cite{eps} and suggested a simple set of confidence intervals. Chen and Bhattacharya \cite{che} earned the exact distribution of the conditional maximum likelihood estimator (MLE) of $\theta$ and implied a one-sided confidence interval. Childs et al. \cite{chil} proposed some simplifications of the exact distribution. From the Bayesian point of view, Drapper and Guttmann \cite{dra} studied the same problem, and reached a two-sided credible interval of the mean lifetime based on the gamma prior. Comparison of the different methods using Monte Carlo simulations, can be found in Gupta and Kundu \cite{gup3}. For some related work, one may refer to Ebrahimi \cite{ebra1,ebra2}, Jeong et al. \cite{jeo}, Childs et al. \cite{chil}, Kundu \cite{kun1}, Banerjee and Kundu \cite{ban}, Kundu and Pradhan \cite{kun2}, Dube et al. \cite{dub} and the references cited there.
\par
One of the disadvantages of Type-I hybrid censoring scheme is that there may be very few failures occurring up to the pre-fixed time $T$. Because of this, Childs et al. \cite{chil} proposed a new hybrid censoring scheme known as Type-II hybrid censoring scheme which can be described as follows. Put $n$ identical items on test, and then stop the experiment at the random time $T^*=\mbox{max}\{x_{R:n},T\}$ , where $R$, and $T$ are prefixed numbers and $x_{R:n}$ indicates the time of $R$th failure in a sample of size $n$. Under the Type-II hybrid censoring scheme, we have one of the following three types of observations:\\
Case I: $\{x_{1:n}<\cdots<x_{R:n}\}$ if $x_{R:n}>T.$\\
Case II: $\{x_{1:n}<\cdots<x_{d:n}<T<x_{d+1:n}\}$ if $R\leq d<n$ and $x_{d:n}<T<x_{d+1:n}.$\\
Case III: $\{x_{1:n}<\cdots<x_{n:n}<T\},$ \\
where $x_{1:n}<\cdots<x_{R:n}$ denote the observed ordered failure times of the experimental units. A schematic illustration of the hybrid censoring scheme is presented in Figure \ref{fig1}.
\vspace{1.5cm}
\hspace{1cm}
\small
\begin{picture}(10,30)(10,15)
\put(25,25){\vector(1,0){220}}
\put(35,25){\vector(1,1){20}}
\put(70,25){\vector(1,1){20}}
\put(200,25){\vector(1,1){20}}
\put(25,15){\scriptsize $X_{1:n}$}
\put(35,50){\scriptsize 1-st Failure}
\put(60,15){\scriptsize $X_{2:n}$}
\put(90,50){\scriptsize 2-nd Failure}
\put(190,15){\scriptsize $X_{R:n}$}
\put(180,50){\scriptsize R-th Failure (Experiment Stops)}
\put(165,15){\scriptsize $T$}
\put(122,20){\scriptsize $...$}
\put(300,25){\scriptsize Case I}
\put(35,25){\circle*{1}}
\put(70,25){\circle*{1}}
\put(170,25){\circle*{1}}
\end{picture}
\vspace{1.5cm}
\hspace{1cm}
\small
\begin{picture}(10,30)(10,15)
\put(25,25){\vector(1,0){220}}
\put(35,25){\vector(1,1){20}}
\put(70,25){\vector(1,1){20}}
\put(155,25){\vector(1,1){20}}
\put(200,25){\vector(1,1){20}}
\put(25,15){\scriptsize $X_{1:n}$}
\put(35,50){\scriptsize 1-st Failure}
\put(60,15){\scriptsize $X_{2:n}$}
\put(90,50){\scriptsize 2-nd Failure}
\put(110,20){\scriptsize $...$}
\put(145,15){\scriptsize $X_{d:n}$}
\put(150,50){\scriptsize d-th Failure }
\put(195,15){\scriptsize $T$}
\put(215,50){\scriptsize Experiment Stops}
\put(300,25){\scriptsize Case II}
\put(35,25){\circle*{1}}
\put(70,25){\circle*{1}}
\put(200,25){\circle*{1}}
\end{picture}
\vspace{1.5cm}
\hspace{1cm}
\small
\begin{picture}(10,30)(10,15)
\put(25,25){\vector(1,0){220}}
\put(35,25){\vector(1,1){20}}
\put(70,25){\vector(1,1){20}}
\put(155,25){\vector(1,1){20}}
\put(25,15){\scriptsize $X_{1:n}$}
\put(35,50){\scriptsize 1-st Failure}
\put(60,15){\scriptsize $X_{2:n}$}
\put(90,50){\scriptsize 2-nd Failure}
\put(110,20){\scriptsize $...$}
\put(145,15){\scriptsize $X_{n:n}$}
\put(150,50){\scriptsize n-th Failure (Experiment Stops) }
\put(195,15){\scriptsize $T$}
\put(300,25){\scriptsize Case III}
\put(35,25){\circle*{1}}
\put(70,25){\circle*{1}}
\put(200,25){\circle*{1}}
\put(10,-5){\scriptsize \label{fig1}Figure 1: A schematic presentation for Type-II hybrid censored scheme.}
\end{picture}
\vspace{0.5in}
\par
In this article, we consider the analysis of Type-II hybrid censored lifetime data when the lifetime of each experimental unit follows a two-parameter weighted exponential (WE) distribution. This distribution was originally proposed by Gupta and Kundu \cite{gup1}. The two-parameter WE distribution with the shape and scale parameters $\alpha>0$ and $\lambda>0$, respectively, has the probability density function (pdf) as:
\begin{equation}\label{we}
f_{WE}(x;\alpha,\lambda)=\frac{\alpha+1}{\alpha}\lambda e^{-\lambda x}(1-e^{-\alpha\lambda x});~~~~~~x>0.
\end{equation}
We denote a two-parameter WE distribution with the pdf (\ref{we}) by $WE(\alpha,\lambda)$ and the corresponding cumulative distribution function (cdf) by $F_{WE}(x;\alpha,\lambda)$.
\par
The aim of this article is two fold. First, we try to earn the MLE's of the unknown parameters. It is observed that the maximum likelihood
estimators can be obtained implicitly by solving two nonlinear equations, but they cannot be obtained in closed form. So MLE's of parameters are derived numerically. Newton-Raphson algorithm is one of the standard methods to determine the MLE's of the parameters. To employ the algorithm, second derivatives of the log-likelihood are required for all iterations. The EM algorithm is a very powerful tool in handling the incomplete data problem see Dempster et al. \cite{dem} and McLachlan and Krishnan \cite{mcl}. Then we use the EM algorithm to compute the MLE's. We also evaluate the observed Fisher information matrix using the missing information principle which have been used to obtained asymptotic confidence intervals of the unknown parameters. The second aim of this article is to provide the Bayes inference for the unknown parameters for Type-II hybrid censored data. It is observed that Bayes estimators can not be obtained explicitly, we provide two approximations namely Lindley's approximation and Gibbs sampling procedure. So we use the Gibbs sampling procedure to compute the Bayes estimators, and the HPD confidence intervals. We compare the performances of the different methods by Monte Carlo simulations, and for illustrative purposes we have analyzed one real data set.
\par
The rest of the article is arranged as follows. In Section 2, we provide The MLE's of the unknown parameters. Fisher information matrix is evaluated in Section 3. Using Lindley's approximation and Gibbs sampling we obtain Bayes estimators and HPD confidence intervals for the parametes in Section 4. Simulation results are presented in section 5. We verify our theoretical results via analyzing data set in Section 6.
\section{Maximum likelihood estimators}
In this section, we study MLEs of the model parameters $\alpha$ and $\lambda$ for $\mbox{WE}(\alpha,\lambda)$ distribution with density function:
$$f(x)=\frac{\alpha+1}{\alpha}\lambda e^{-\lambda x}(1-e^{-\alpha\lambda x}):~\alpha,\lambda,x>0.$$
For simplicity, we apply a re-parametrization as $\alpha$ and $\beta=\alpha \lambda$. By this, the $\mbox{WE}(\alpha,\lambda)$ distribution can be written as:
\begin{equation}
\label{bl}f(x)=\frac{\alpha+1}{\alpha^2}\beta e^{-\frac{\beta}{\alpha}x}(1-e^{-\beta x}):~\alpha,\beta,x>0.
\end{equation}
The likelihood function in Case I is given by
\begin{equation}
\label{a}\hspace{-1.7in}L(\alpha,\lambda)=\frac{n!}{(n-R)!}\Pi_{i=1}^Rf(x_i)(1-F(x_{(R)}))^{(n-R)},
\end{equation}
for Case II,
\begin{equation}
\label{b}\hspace{-1.9in}L(\alpha,\lambda)=\frac{n!}{(n-d)!}\Pi_{i=1}^df(x_i)(1-F(T))^{(n-d)},
\end{equation}
and for case III,
\begin{equation}
\label{III}\hspace{-1.9in}L(\alpha,\lambda)=\Pi_{i=1}^nf(x_i),
\end{equation}
where $f(x)$ is presented by (\ref{bl}), so
$$\hspace{-2.2in}F(x)=1-\frac{1}{\alpha}e^{-\frac{\beta}{\alpha}x}(\alpha+1-e^{-\beta x}).$$
We present likelihood functions (\ref{a}), (\ref{b}) and (\ref{III}) by:
\begin{equation}
\label{c}\hspace{-1.9in}L(\alpha,\lambda)=\frac{n!}{(n-r)!}\Pi_{i=1}^rf(x_i)(1-F(c))^{(n-r)},
\end{equation}
where
\begin{equation}
r=\left\{
\begin{array}{rl}
R & \text{for Case I}\\
d & \text{for Case II}\\
n & \text{for Case III},
\end{array}
\right.
\end{equation}
\mbox{and}
\begin{equation}
c=\left\{
\begin{array}{rl}
x_{R:n} & \text{for Case I}\\
T & \text{for Cases II and III.}
\end{array}
\right.
\end{equation}
Taking the logarithm of Equation \ref{c}, we obtain
$$l(\alpha,\lambda)=r\ln(\alpha+1)-(n+r)\ln(\alpha)+r\ln(\beta)-\frac{\beta}{\alpha}\sum_{i=1}^rx_i+\sum_{i=1}^r{\ln(1-e^{-\beta x_i})}$$
\begin{equation}
\label{1}+(n-r)(-\frac{\beta}{\alpha})c+(n-r)\ln(\alpha+1-e^{-\beta c}),
\end{equation}
then the normal equations are
\begin{equation}
\displaystyle
\left\{
\begin{array}c
\hspace{-.85 in}\frac{\partial l}{\partial\alpha}=\frac{r}{\alpha+1}-\frac{n+r}{\alpha}+\frac{\beta}{\alpha^2}(\sum_{i=1}^rx_i+(n-r)c)+\frac{(n-r)}{\alpha+1-e^{-\beta c}}\\
\frac{\partial l}{\partial\beta}=\frac{r}{\beta}-\frac{1}{\alpha}(\sum_{i=1}^rx_i+(n-r)c)+\sum_{i=1}^r\frac{x_ie^{-\beta x_i}}{1-e^{-\beta x_i}}+(n-r)\frac{ce^{-\beta c}}{\alpha+1-e^{-\beta c}}
.\end{array}
\right.
\end{equation}
Maximum likelihood estimators can be secured by solving these equations, but they cannot be expressed explicitly. So we use EM algorithm to compute them. The advantage of this method is that it is convergence for any initial value fast enough.\\
\subsection{EM algorithm}
The EM algorithm, originally proposed by Dempster et al. \cite{dem}, is a very powerful tool for handling
the incomplete data problem.\\
Let us symbolize the observed and
the censored data by $X=(X_{1:n},\cdots,X_{r:n})$ and $Z=(Z_1,\cdots,Z_{n-r})$, respectively. Here
for a given r, $(Z_1,\cdots,Z_{n-r})$ are not observable. The censored data vector $Z$ can
be thought of as missing data. The combination of $W=(X,Z)$ forms the whole
data set.
In next we follow the method Kundu and Pradhan \cite{kun2} for missing data introducing. \\ If we denote the log-likelihood function of the uncensored data set by
$$l_c(\alpha,\beta)=n\ln(\alpha+1)-2n\ln(\alpha)+n\ln(\beta)-\frac{\beta}{\alpha}\left(\sum_{i=1}^rX_i+\sum_{i=1}^{n-r}Z_i\right)$$
\begin{equation}
\label{2}+\left(\sum_{i=1}^r{\ln(1-e^{-\beta x_i})}+\sum_{i=1}^r{\ln(1-e^{-\beta z_i})}\right).
\end{equation}
For the E-step of the EM algorithm, one needs to compute the pseudo log-likelihood function as $l_s(\alpha,\beta)=E(l_c(\alpha,\beta|X)).$
Therefor,
$$l_s(\alpha,\beta)=n\ln(\alpha+1)-2n\ln(\alpha)+n\ln(\beta)-\frac{\beta}{\alpha}\left(\sum_{i=1}^rX_i\right)+
\sum_{i=1}^r{\ln(1-e^{-\beta x_i})}$$
$$-\frac{\beta}{\alpha}(n-r)A(c;\alpha,\beta)+(n-r)B(c;\alpha,\beta),$$
where
$$A[c;\alpha,\beta]=E(Z_i|Z_i>c)
~~\mbox{and}~~
B(c;\alpha,\beta)=E[\ln(1-e^{-\beta Z_i})|Z_i>c],$$
and they are obtained in Appendix A.
Now the M-step includes the maximization of the pseudo log-likelihood
function \ref{2}. Therefore, if at the kth stage, the estimation of $(\alpha,\beta)$ is $(\hat{\alpha}_k,\hat{\beta}_k)$, then $(\hat{\alpha}_{k+1},\hat{\beta}_{k+1})$
can be obtained by maximizing
$$g(\alpha,\beta)=n\ln(\alpha+1)-2n\ln(\alpha)+n\ln(\beta)-\frac{\beta}{\alpha}\left(\sum_{i=1}^rX_i\right)+
\sum_{i=1}^r{\ln(1-e^{-\beta x_i})}$$
\begin{equation}
\label{3}-\frac{\beta}{\alpha}(n-r)A(c;\hat{\alpha}_k,\hat{\beta}_k)+(n-r)B(c;\hat{\alpha}_k,\hat{\beta}_k)
\end{equation}
Note that the maximization of \ref{3} can be earned quite effectively by the similar method proposed by Gupta and Kundu \cite{gup2}. First, $\hat{\beta}_{k+1}$ can be obtain by solving a fixed-point type equation
$$h(\beta)=\beta.$$
The function $h(\beta)$ is defined
$$h(\beta)=n\left[\frac{B}{\hat{\alpha}(\beta)}-\sum_{i=1}^r\frac{x_ie^{-\beta x_i}}{1-e^{-\beta x_i}}\right]^{-1}$$
where
$$B=\sum_{i=1}^rx_i+(n-r)A(c,\hat{\alpha}_k,\hat{\beta}_k)$$ and
$$\hat{\alpha}(\beta)=\frac{\sqrt{(\beta B-2n)^2+4n\beta B}+(\beta B-2n)}{2n}.$$
One can follow iteration method.
Once $\hat{\beta}_{k+1}$ is determined, $\hat{\alpha}_{k+1}$ can be evaluated as $\hat{\alpha}_{k+1}=\hat{\alpha}(\hat{\beta}_{k+1})$.
\par For the estimation of $\lambda$, we can use the invariance property maximum likelihood estimators and obtain $\hat{\lambda}$ as follow:
$$\hat{\lambda}=\frac{\hat{\beta}}{\hat{\alpha}}.$$
\section{Fisher Information matrices}
One of the advantages of using EM algorithm is that presents a measure of information in censored data through the missing information principle. Louis \cite{lou} improved a procedure for extracting the observed information matrix. In this section, we display the observed Fisher information matrix by using the missing value principles of Louis \cite{lou}. The observed Fisher information matrix can be used to build the asymptotic confidence intervals.
\\
Using the notations: $\theta=(\alpha,\beta)$, X=observed data, W=complete data, $I_X(\theta)$=observed information, $I_W(\theta)$=complete information and
$I_{W|X}(\theta)$=missing information, follow the relation to
\begin{equation}
\label{Ix}I_X(\theta)=I_W(\theta)-I_{W|X}(\theta),
\end{equation}
to evaluate $I_X(\theta).$\\
Complete information and the missing information are given respectively as:
$$I_W(\theta)=-E\left[\frac{\partial^2L_c(W;\theta)}{\partial\theta^2}\right]$$
\mbox{and}
\begin{equation}
\label{IWX}I_{W|X}(\theta)=-(n-r)E\left[\frac{\partial^2\ln f_Z(z|y,\theta)}{\partial\theta^2}\right].
\end{equation}
As the dimension of $\theta$ is 2, $I_X(\theta)$ and $I_{W|X}(\theta)$ are both of the order $2\times2$.\par
The elements of matrix $I_W(\theta)$ for complete data set are presented in Gupta and Kundu \cite{gup1}. They re-parametrized $\mbox{WE}(\alpha,\lambda)$ distribution as $\lambda$ and $\beta=\alpha\lambda$.\\ We report $I_W(\theta)$ which have been evaluated by them here as:
\begin{equation*}
I_W(\theta)=\left[
\begin{array} {cc}
a_{11} & a_{12}\\
a_{21} & a_{22}
\end{array}
\right]
\end{equation*}
where
$$\hspace{-3.3in}\displaystyle a_{11}=\frac{n}{(\beta+\lambda)^2}+\frac{n}{\lambda^2}.$$
$$\hspace{-3.4in}\displaystyle a_{12}=a_{21}=\frac{n}{(\beta+\lambda)^2}.$$
$$\hspace{-2.4in} \displaystyle a_{22}=\frac{n}{(\beta+\lambda)^2}-\frac{n}{\beta^2}+\frac{n\lambda(\beta+\lambda)A}{\beta^4},$$
in which $\displaystyle A=\int_0^1\frac{(\ln (1-y))^2(1-y)^{\frac{\lambda}{\beta}}}{y}dy.$\\
On the other hand, with the above re-parametrization and by using (\ref{IWX}), one can easily verify
\begin{equation*}
I_{W|X}(\theta)=(n-r)\left[
\begin{array} {cc}
b_{11}(c;\alpha,\beta) & b_{12}(c;\alpha,\beta)\\
b_{21}(c;\alpha,\beta) & b_{22}(c;\alpha,\beta)
\end{array}
\right],
\end{equation*}
where
$$\hspace{-1.in}\displaystyle b_{11}(c;\alpha,\beta)=\frac{1}{(\beta+\lambda)^2}+\frac{2\beta}{\lambda^3(\frac{\beta}{\lambda}+1-e^{-\beta c})}-\frac{\beta^2}{\lambda^4(\frac{\beta}{\lambda}+1-e^{-\beta c})^2}.$$
$$\hspace{-0.2in}\displaystyle b_{12}(c;\alpha,\beta)=b_{21}(c;\alpha,\beta)=\frac{1}{(\beta+\lambda)^2}-\frac{1}{\lambda^2(\frac{\beta}{\lambda}+1-e^{-\beta c})}+\frac{\beta(\frac{1}{\lambda}+ce^{-\beta c})}{\lambda^2(\frac{\beta}{\lambda}+1-e^{-\beta c})^2}.$$
$$\hspace{0in}\displaystyle b_{22}(c;\alpha,\beta)=\frac{1}{(\beta+\lambda)^2}-\frac{c^2e^{-\beta c}}{\frac{\beta}{\lambda}+1-e^{-\beta c}}-\frac{(\frac{1}{\lambda}+c-e^{-\beta c})^2}{(\frac{\beta}{\lambda}+1-e^{-\beta c})^2}+\frac{(\beta+\lambda)B}{\beta^3e^{-\lambda c}(\frac{\beta}{\lambda}+1-e^{-\beta c})},$$
in which $B=\int_{1-e^{-\beta c}}^1\frac{(\ln (1-y))^2(1-y)^{\frac{\lambda}{\beta}}}{y}dy.$
\par Now, $I_X(\theta)$ can be computed by (\ref{Ix}). The asymptotic variance-covariance matrix of $\hat{\theta}$ can be obtained by inverting $I_X(\theta)$. We use this matrix to secure the asymptotic confidence intervals for $\lambda$ and $\beta$. To obtain the asymptotic confidence interval for $\alpha$, we use the non-parametric bootstrap method \cite{zog}.
\section{Bayes Estimators and Confidence Intervals}
In this section, we study Bayes estimators for parameters $\alpha$ and $\lambda$ under symmetric loss functions. A very well known symmetric loss function is the squared error which is defined as:
$L(f(\mu),\hat{f}(\mu))=(\hat{f}(\mu)-f(\mu))^2,$ with $\hat{f}(\mu)$ being an estimate of $f(\mu)$. Here $f(\mu)$ denotes
some function of $\mu$. Bayes estimators, say $\hat{f}_{Bayes}(\mu)$, is evaluated by the
posterior mean of $f(\mu)$.\par
Let $x=(x_{1:n},\cdots,x_{r:n})$ be an observed sample from the hybrid censoring scheme, drawn from a $\mbox{WE}(\alpha,\lambda)$ distribution. We apply re-parametrization as $\alpha$ and $\beta=\alpha\lambda$. So the likelihood function becomes
$$L(\alpha,\beta|\b{x})\varpropto\frac{(\alpha+1)^r}{\alpha^{n+r}}\beta^re^{-\frac{\beta}{\alpha}\left(\sum_{i=1}^rx_i+c(n-r)\right)}(\alpha+1-e^{-\beta c})^{n-r}\Pi_{i=1}^r(1-e^{-\beta x_i}),$$
and $\log$-likelihood function:
\begin{equation*}
l(\alpha,\beta|\b{x})=r\log(\alpha+1)-(n+r)\log\alpha+r\log(\beta)-\frac{\beta}{\alpha}\left(\sum_{i=1}^rx_i+c(n-r)\right)
\end{equation*}
\begin{equation}\label{log}
+(n-r)\log(\alpha+1-e^{-\beta c})+\sum_{i=1}^r\log(1-e^{-\beta x_i}).
\end{equation}
It is assumed that $\beta$ and $\alpha$ have the following independent
gamma priors:
$$\pi_1(\beta)\varpropto\beta^{w_2-1}e^{-\beta w_1},~~~~~~\beta>0,$$
$$\pi_2(\alpha)\varpropto\alpha^{w_4-1}e^{-\alpha w_3},~~~~~~\alpha>0.$$
So, the joint prior distribution of $\alpha$ and $\beta$ is of the form
$$\pi(\alpha,\beta)\varpropto\alpha^{w_4-1}e^{-\alpha w_3}\beta^{w_2-1}e^{-\beta w_1},~~~~~~~\alpha>0,~\beta>0,~w_1>0,~w_2>0,~w_3>0,~w_4>0.$$
Then the posterior distribution $\alpha$ and $\beta$ can be written as
$$\pi(\alpha,\beta|\b{x})=\frac{1}{k}\alpha^{w_4-n-r-1}\beta^{w_2+r-1}(\alpha+1)^re^{-\alpha w_3}e^{-\beta w_1}e^{-\frac{\beta}{\alpha}\left(\sum_{i=1}^rx_i+c(n-r)\right)}$$
\begin{equation}
\times(\alpha+1-e^{-\beta c})^{n-r}\Pi_{i=1}^r(1-e^{-\beta x_i})\label{pos}
\end{equation}
where
$$k=\int_0^\infty\int_0^\infty\alpha^{w_4-n-r-1}\beta^{w_2+r-1}(\alpha+1)^re^{-\alpha w_3}e^{-\beta w_1}e^{-\frac{\beta}{\alpha}\left(\sum_{i=1}^rx_i+c(n-r)\right)}$$
$$\times(\alpha+1-e^{-\beta c})^{n-r}\Pi_{i=1}^r(1-e^{-\beta x_i})d\alpha d\beta.$$
Now the Bayes estimators of $\alpha$ and $\beta$ under the squared error loss function L are respectively obtained as:
$$\hat{\alpha}_{Bayes}=E[\alpha|\b{x}]=\frac{1}{k}\int_0^\infty\int_0^\infty\alpha^{w_4-n-r}\beta^{w_2+r-1}(\alpha+1)^re^{-\alpha w_3}e^{-\beta w_1}$$$$\times e^{-\frac{\beta}{\alpha}\left(\sum_{i=1}^rx_i+c(n-r)\right)}(\alpha+1-e^{-\beta c})^{n-r}\Pi_{i=1}^r(1-e^{-\beta x_i})d\alpha d\beta,$$
and
$$\hat{\beta}_{Bayes}=E[\beta|\b{x}]=\frac{1}{k}\int_0^\infty\int_0^\infty\alpha^{w_4-n-r-1}\beta^{w_2+r}(\alpha+1)^re^{-\alpha w_3}e^{-\beta w_1}$$$$\times e^{-\frac{\beta}{\alpha}\left(\sum_{i=1}^rx_i+c(n-r)\right)}(\alpha+1-e^{-\beta c})^{n-r}\Pi_{i=1}^r(1-e^{-\beta x_i})d\alpha d\beta.$$
Since $\lambda$ is a function of $\alpha$ and $\beta$, then one can obtain the posterior density function of $\lambda$ and so the Bayes estimator of $\lambda$ under the squared error loss function $L$ as:
$$\hat{\lambda}_{Bayes}=E[\lambda|\b{x}]=\frac{1}{k}\int_0^\infty\int_0^\infty u^{w_4+w_2-n-1}\lambda^{w_2+r-1}(1+u)^{r}e^{-u(w_3+\lambda w_1)}$$$$
\times e^{-\lambda\left(\sum_{i=1}^rx_i+c(n-r)\right)}(u+1-e^{-\lambda u c})^{n-r}\Pi_{i=1}^r(1-e^{-\lambda u x_i})du d\lambda.$$
As these estimators can not be evaluated explicitly, so we adopt two different procedures to approximate them:
\begin{itemize}
\item{ Lindley approximation,}
\item{ MCMC method}.
\end{itemize}
\subsection{Lindley approximation method}
\par
In previous section, based on Type-II hybrid censored scheme we obtained the Bayes estimators of $\alpha$, $\beta$ and $\lambda$ against squared error loss function $L$. It is easily observed that theses estimators have not explicit closed forms. For these evaluation, numerical techniques are required. One of the most numerical techniques is Lindley's method (see \cite{lin}), that for these estimators can be describe as follows.
In general, Bayes estimator of $u(\alpha,\beta)$ as a function of $\alpha$ and $\beta$ is identified:
$$I(\b{x})=\frac{\int_0^\infty\int_0^\infty u(\alpha,\beta)e^{l(\alpha,\beta|\b{x})+\rho(\alpha,\beta)}d\alpha d\beta}{\int_0^\infty\int_0^\infty e^{l(\alpha,\beta|\b{x})+\rho(\alpha,\beta)}d\alpha d\beta},$$
where $l(\alpha,\beta|\b{x})$ is $\log$-likelihood function (defined by \ref{log}) and $\rho(\alpha,\beta)=\log\pi(\alpha,\beta)$.
\\ By the Lindley's method $I(\b{x})$ can be approximated as:
$$I(\b{x})=u(\hat{\alpha},\hat{\beta})+\frac{1}{2}[(\hat{u}_{\alpha\alpha}+2\hat{u}_{\alpha}\hat{\rho}_{\alpha})\hat{\sigma}_{\alpha\alpha}+
(\hat{u}_{\beta\alpha}+2\hat{u}_{\beta}\hat{\rho}_{\alpha})\hat{\sigma}_{\beta\alpha}+
(\hat{u}_{\alpha\beta}+2\hat{u}_{\alpha}\hat{\rho}_{\beta})\hat{\sigma}_{\alpha\beta}$$$$
+(\hat{u}_{\beta\beta}+2\hat{u}_{\beta}\hat{\rho}_{\beta})\hat{\sigma}_{\beta\beta}]+\frac{1}{2}[(\hat{u}_{\alpha}\hat{\sigma}_{\alpha\alpha}+
\hat{u}_{\beta}\hat{\sigma}_{\alpha\beta})(\hat{l}_{\alpha\alpha\alpha}\hat{\sigma}_{\alpha\alpha}+
\hat{l}_{\alpha\beta\alpha}\hat{\sigma}_{\alpha\beta}+\hat{l}_{\beta\alpha\alpha}\hat{\sigma}_{\beta\alpha}$$$$
+\hat{l}_{\beta\beta\alpha}\hat{\sigma}_{\beta\beta})+(\hat{u}_{\alpha}\hat{\sigma}_{\beta\alpha}+
\hat{u}_{\beta}\hat{\sigma}_{\beta\beta})(\hat{l}_{\beta\alpha\alpha}\hat{\sigma}_{\alpha\alpha}
+\hat{l}_{\alpha\beta\beta}\hat{\sigma}_{\alpha\beta}+\hat{l}_{\beta\alpha\beta}\hat{\sigma}_{\beta\alpha}
+\hat{l}_{\beta\beta\beta}\hat{\sigma}_{\beta\beta})],$$
where $\hat{\alpha}$ and $\hat{\beta}$ are the MLE's of $\alpha$ and $\beta$ respectively. Also, $u_{\alpha\alpha}$ is the second derivative of the function $u(\alpha,\beta)$ with the respect to $\alpha$ and $\hat{u}_{\alpha\alpha}$ valued of $u_{\alpha\alpha}$ at $(\hat{\alpha},\hat{\beta}).$ Other expressions can be calculated with following definitions:
$$\hspace{-1in}\hat{l}_{\alpha\alpha}=\frac{\partial^2l}{\partial\alpha^2}\left|_{\alpha=\hat{\alpha},\beta=\hat{\beta}}=\frac{-r}{(\hat{\alpha}+1)^2}+\frac{n+r}{\hat{\alpha}^2}-\frac{2\hat{\beta} A}{\hat{\alpha}^3}-\frac{n-r}{(\hat{\alpha}+1-e^{-\hat{\beta} c})^2}\right.,$$
$$\hspace{-2in}\hat{l}_{\alpha\beta}=\frac{\partial^2l}{\partial\alpha\partial\beta}\left|_{\alpha=\hat{\alpha},\beta=\hat{\beta}}=\hat{l}_{\beta\alpha}=\frac{A}{\hat{\alpha}^2}-\frac{c(n-r)e^{-\hat{\beta} c}}{(\hat{\alpha}+1-e^{-\hat{\beta} c})^2}\right.,$$
$$\hspace{-.2in}\hat{l}_{\alpha\beta\alpha}=\frac{\partial^3l}{\partial\alpha\partial\beta\partial\alpha}\left|_{\alpha=\hat{\alpha},\beta=\hat{\beta}}=\hat{l}_{\beta\alpha\alpha}=\frac{\partial^3l}{\partial\beta\partial\alpha^2}\left|_{\alpha=\hat{\alpha},\beta=\hat{\beta}}=\frac{-2A}{\hat{\alpha}^3}+\frac{2c(n-r)e^{-\hat{\beta} c}}{(\hat{\alpha}+1-e^{-\hat{\beta} c})^3}\right.\right.,$$
$$\hspace{-0.8in}\hat{l}_{\alpha\alpha\alpha}=\frac{\partial^3l}{\partial\alpha^3}\left|_{\alpha=\hat{\alpha},\beta=\hat{\beta}}=\frac{2r}{(\hat{\alpha}+1)^3}-\frac{2(n+r)}{\hat{\alpha}^3}+\frac{6\hat{\beta} A}{\hat{\alpha}^4}+\frac{2(n-r)}{(\hat{\alpha}+1-e^{-\hat{\beta} c})^3}\right.,$$
where $A=\sum_{i=1}^rx_i+(n-r)c,$
$$\hspace{0in}\hat{l}_{\alpha\beta\beta}=\frac{\partial^3l}{\partial\alpha\partial\beta^2}\left|_{\alpha=\hat{\alpha},\beta=\hat{\beta}}=\hat{l}_{\beta\alpha\beta}=\frac{\partial^3l}{\partial\beta\partial\alpha\partial\beta}\left|_{\alpha=\hat{\alpha},\beta=\hat{\beta}}=\frac{c^2(n-r)e^{-\hat{\beta} c}(\hat{\alpha}+1+e^{-\hat{\beta}c})}{(\hat{\alpha}+1-e^{-\hat{\beta} c})^3}\right.\right.,$$
$$\hspace{-.9in}\hat{l}_{\beta\beta}=\frac{\partial^2l}{\partial\beta^2}\left|_{\alpha=\hat{\alpha},\beta=\hat{\beta}}=\frac{-r}{\hat{\beta}^2}-\frac{c^2(n-r)(\hat{\alpha}+1)e^{-\hat{\beta} c}}{(\hat{\alpha}+1-e^{-\hat{\beta} c})^2}-\sum_{i=1}^r\frac{x_i^2e^{-\hat{\beta} x_i}}{(1-e^{-\hat{\beta} x_i})^2}\right.,$$
$$\hspace{-1.9in}\hat{l}_{\beta\beta\alpha}=\frac{\partial^3l}{\partial\beta^2\partial\alpha}\left|_{\alpha=\hat{\alpha},\beta=\hat{\beta}}=\frac{c^2(n-r)e^{-\hat{\beta} c}(\hat{\alpha}+1+e^{-\hat{\beta}c})}{(\hat{\alpha}+1-e^{-\hat{\beta} c})^3}\right.,$$
$$\hspace{0.05in}\hat{l}_{\beta\beta\beta}=\frac{\partial^3l}{\partial\beta^3}\left|_{\alpha=\hat{\alpha},\beta=\hat{\beta}}=\frac{2r}{\hat{\beta}^3}+\frac{c^3(n-r)(\hat{\alpha}+1)e^{-\hat{\beta} c}(\hat{\alpha}+1+e^{-\hat{\beta}c})}{(\hat{\alpha}+1-e^{-\hat{\beta} c})^3}+\sum_{i=1}^r\frac{x_i^3e^{-\hat{\beta} x_i}(1+e^{-\hat{\beta}x_i})}{(1-e^{-\hat{\beta} x_i})^3}\right.,$$
$$\hspace{-3.6in}\hat{\rho}_{\beta}=\frac{\partial\rho}{\partial\beta}\left|_{\beta=\hat{\beta}}=\frac{w_2-1}{\hat{\beta}}-w_1\right.,$$
$$\hspace{-3.6in}\hat{\rho}_{\alpha}=\frac{\partial\rho}{\partial\alpha}\left|_{\alpha=\hat{\alpha}}=\frac{w_4-1}{\hat{\alpha}}-w_3\right.,$$
and we have:
\[ \left( \begin{array}{cc}
\hat{\sigma}_{\alpha\alpha} & \hat{\sigma}_{\alpha\beta} \\
\hat{\sigma}_{\beta\alpha} & \hat{\sigma}_{\beta\beta} \end{array} \right) = \left( \begin{array}{cc}
-\hat{l}_{\alpha\alpha} & -\hat{l}_{\alpha\beta} \\
-\hat{l}_{\beta\alpha} & -\hat{l}_{\beta\beta} \end{array} \right)^{-1}.\]
With the above defined expressions, we obtain the approximation Bayes estimators.\\
Also we have:
$$u(\alpha,\beta)=\alpha,~~~~u_{\alpha}=1,~~~~u_{\alpha\alpha}=u_{\beta}=u_{\beta\beta}=u_{\alpha\beta}=u_{\beta\alpha}=0,$$
the Bayes estimator of $\alpha$ under the squared error loss function $L$ becomes
$$\hat{\alpha}_{Bayes}=\hat{\alpha}+\frac{1}{2}[2\hat{\rho}_{\alpha}\hat{\sigma}_{\alpha\alpha}+
2\hat{\rho}_{\beta}\hat{\sigma}_{\alpha\beta}+\hat{\sigma}^2_{\alpha\alpha}\hat{l}_{\alpha\alpha\alpha}+
3\hat{\sigma}_{\alpha\alpha}\hat{\sigma}_{\alpha\beta}\hat{l}_{\beta\alpha\alpha}+2\hat{\sigma}^2_{\alpha\beta}\hat{l}_{\alpha\beta\beta}$$$$
+\hat{\sigma}_{\alpha\alpha}\hat{\sigma}_{\beta\beta}\hat{l}_{\beta\beta\alpha}+
\hat{\sigma}_{\alpha\beta}\hat{\sigma}_{\beta\beta}\hat{l}_{\beta\beta\beta}].$$
Proceeding similarly, the Bayes estimator of $\beta$ under $L$ is given by
$$(u(\alpha,\beta)=\beta,~~~~u_{\beta}=1,~~~~u_{\alpha\alpha}=u_{\alpha}=u_{\beta\beta}=u_{\alpha\beta}=u_{\beta\alpha}=0),$$
$$\hat{\beta}_{Bayes}=\hat{\beta}+\frac{1}{2}[2\hat{\rho}_{\alpha}\hat{\sigma}_{\alpha\beta}+
2\hat{\rho}_{\beta}\hat{\sigma}_{\beta\beta}+2\hat{\sigma}^2_{\alpha\beta}\hat{l}_{\beta\alpha\alpha}+
2\hat{\sigma}_{\alpha\beta}\hat{\sigma}_{\beta\beta}\hat{l}_{\alpha\beta\beta}$$
$$+\hat{\sigma}^2_{\beta\beta}\hat{l}_{\beta\beta\beta}+
\hat{\sigma}_{\alpha\alpha}\hat{\sigma}_{\alpha\beta}\hat{l}_{\alpha\alpha\alpha}+
\hat{\sigma}_{\beta\beta}\hat{\sigma}_{\alpha\alpha}\hat{l}_{\beta\alpha\alpha}+
\hat{\sigma}_{\alpha\beta}\hat{\sigma}_{\beta\beta}\hat{l}_{\beta\beta\alpha}].$$
Finally the Bayes estimator of $\lambda$ under $L$ is given by
$$(u(\alpha,\beta)=\frac{\beta}{\alpha},~~u_{\beta}=\frac{1}{\alpha},~~u_{\alpha}=\frac{-\beta}{\alpha^2},~~u_{\alpha\alpha}=\frac{2\beta}{\alpha^3},
~~u_{\beta\beta}=0,~~u_{\alpha\beta}=u_{\beta\alpha}=\frac{-1}{\alpha^2}),$$
$$\hat{\lambda}_{Bayes}=\frac{\hat{\beta}}{\hat{\alpha}}+\frac{1}{2}[(\hat{u}_{\alpha\alpha}+2\hat{u}_{\alpha}\hat{\rho}_{\alpha})\hat{\sigma}_{\alpha\alpha}+
(\hat{u}_{\beta\alpha}+2\hat{u}_{\beta}\hat{\rho}_{\alpha})\hat{\sigma}_{\beta\alpha}+
(\hat{u}_{\alpha\beta}+2\hat{u}_{\alpha}\hat{\rho}_{\beta})\hat{\sigma}_{\alpha\beta}$$$$
+2\hat{u}_{\beta}\hat{\rho}_{\beta}\hat{\sigma}_{\beta\beta}]+\frac{1}{2}[(\hat{u}_{\alpha}\hat{\sigma}_{\alpha\alpha}+
\hat{u}_{\beta}\hat{\sigma}_{\alpha\beta})(\hat{l}_{\alpha\alpha\alpha}\hat{\sigma}_{\alpha\alpha}+
\hat{l}_{\alpha\beta\alpha}\hat{\sigma}_{\alpha\beta}+\hat{l}_{\beta\alpha\alpha}\hat{\sigma}_{\beta\alpha}$$$$
\hspace{0.5in}+\hat{l}_{\beta\beta\alpha}\hat{\sigma}_{\beta\beta})+(\hat{u}_{\alpha}\hat{\sigma}_{\beta\alpha}+
\hat{u}_{\beta}\hat{\sigma}_{\beta\beta})(\hat{l}_{\beta\alpha\alpha}\hat{\sigma}_{\alpha\alpha}
+\hat{l}_{\alpha\beta\beta}\hat{\sigma}_{\alpha\beta}+\hat{l}_{\beta\alpha\beta}\hat{\sigma}_{\beta\alpha}
+\hat{l}_{\beta\beta\beta}\hat{\sigma}_{\beta\beta})].$$
\par
The approximate Bayes estimators of $\alpha$, $\beta$ and $\lambda$ can be obtained using Lindley approximation, but it is not possible to construct highest posterior density (HPD) confidence intervals using this method. Therefore, we suggest the following Markov Chain Monte Carlo (MCMC) method to generate samples from the posterior density function, and in turn to obtain the Bayes estimators, and HPD confidence intervals.
\subsection{Gibbs sampling}
\par
\par
Here we study the Gibbs sampling method to draw samples from the posterior density function and then compute the Bayes estimators and HPD confidence intervals of $\alpha$, $\beta$ and $\lambda$ under the squared errors loss function.
\par
Let $\b{x}=(x_{1:n},\cdots,x_{r:n})$ be an observed sample from the hybrid censoring scheme, drawn from a $\mbox{WE}(\alpha,\lambda)$ distribution.
From (\ref{pos}), we can write the joint posterior density function of $\alpha$ and $\beta$ given $\b{x}$ as:
$$\pi(\alpha,\beta|\b{x})\propto\alpha^{w_4-n-r-1}\beta^{w_2+r-1}(\alpha+1)^re^{-\alpha w_3}e^{-\beta w_1}\left\{e^{-\frac{\beta}{\alpha}\left(\sum_{i=1}^rx_i+c(n-r)\right)}\right.$$
\begin{equation}
\left.\times(\alpha+1-e^{-\beta c})^{n-r}\Pi_{i=1}^r(1-e^{-\beta x_i})\right\}\label{pos2},
\end{equation}
by this, the posterior density function of $\beta$ given $\alpha$ and $\b{x}$ is
$$\pi(\beta|\alpha,\b{x})\propto\beta^{w_2+r-1}e^{-\beta \left(w_1+\frac{\beta}{\alpha}\sum_{i=1}^rx_i+c(n-r)\right)}
(\alpha+1-e^{-\beta c})^{n-r}\Pi_{i=1}^r(1-e^{-\beta x_i}).$$
{\label{the1}\theorem The conditional distribution of $\beta$ given $\alpha$ and $\b{x}$ is log-concave.}
{\proof See Appendix, part B.}\\
By (\ref{pos2}), the posterior density function of $\alpha$ given $\beta$ and $\b{x}$ is
\begin{equation}
\pi(\alpha|\beta,\b{x})\propto\alpha^{w_4-n-r-1}(\alpha+1)^re^{-\alpha w_3}e^{-\frac{\beta}{\alpha}\left(\sum_{i=1}^rx_i+c(n-r)\right)}(\alpha+1-e^{-\beta c})^{n-r}.\label{albe}
\end{equation}
{\label{th2}\theorem The conditional distribution of $\alpha$ given $\beta$ and $\b{x}$ has a finite maximum point.}
{\proof See Appendix, part C.}
{\corollary With the help of the acceptance rejection principle (see Devroye \cite{dev} for details) and the previous theorem, the generation from (\ref{albe}) can be performed using the WE generator.}\\ \par
Now we use theorems \ref{the1} and \ref{th2} and pursue the idea of Geman and Geman \cite{gem}, and suggest the following scheme.
\\
\begin{itemize}
{\item Step 1) Take some initial value of $\alpha$ and $\beta$, such as $\alpha_0$ and $\beta_0$.}
{\item Step 2) Generate $\alpha_{i+1}$ and $\beta_{i+1}$ from $\pi(\alpha|\beta_i,\b{x})$ and $\pi(\beta|\alpha_i,\b{x})$.}
{\item Step 3) Repeat Step 2, $N$ times.}
{\item Step 4) Obtain Bayes estimators of $\alpha$ and $\beta$ with respect to a squared error loss function:
$$\hat{\alpha}_{Bayes}=\frac{1}{N-M_1}\sum_{i=M_1+1}^{N}{\alpha_i}~~~~\mbox{and}
~~~~\hat{\beta}_{Bayes}=\frac{1}{N-M_2}\sum_{i=M_2+1}^{N}{\beta_i}$$
where $M_1$ and $M_2$ are the burn-in periods in generating of $\alpha_i$ and $\beta_i$ respectively.}
{\item Step 5) Obtain the HPD confidence interval of $\alpha$: Order $\alpha_1,\cdots,\alpha_{M_1}$ as $\alpha_{(1)}<\cdots<\alpha_{(M_1)}$ and construct all the $100(1-\eta)\%$ confidence intervals of $\alpha$, as:
$$(\alpha_{(1)},\alpha_{([M_1(1-\eta)])}),\cdots,(\alpha_{([M_1\eta])},\alpha_{(M_1)}),$$
where $[M]$ symbolizes the largest integer less than or equal to $M$. The HPD confidence interval of $\alpha$ is the shortest length interval. Similarly, we can construct a $100(1-\eta)\%$ HPD confidence interval of $\beta$.}
\end{itemize}\par
Finally, using the idea of Chen and Shao \cite{chen}, we can compute the estimation and HPD confidence interval for $\lambda$.
\section{Numerical Experiments}
In this section, we carry out a simulation study to compare the performance of MLE's and Bayes estimators. In all the cases $\alpha=2.5$ and $\lambda=3$ are taken. We estimate the unknown parameters using the MLE, Bayes estimators obtained by Lindley's approximations and also Bayes estimators obtained by using MCMC technique. We compare the performances of different estimators with MSE. We also obtain the average length of the asymptotic confidence intervals and the HPD confidence intervals. \par
For computing the Bayes estimators, it is assumed that $\beta$ and $\alpha$ have $\mbox{Gamma}(w_2,w_1)$ and $\mbox{Gamma}(w_4,w_3)$ priors, respectively. Moreover we use the non-informative priors of both $\beta$ and $\alpha$, by considering $w_1=w_2=w_3=w_4=0$. The Bayes estimators are computed under the squared error loss function and with respect to the above non-informative priors. \par
The simulation is performed for different choices of $n,~R,~T$ values. We replicate the procedure for 1000 times and report the average estimators, the MSE's, the average asymptotic confidence intervals length and the average HPD confidence intervals length from the MCMC technique. The results are reported in Table 1-4. The first and second rows are parameter estimators of $\lambda$ and $\alpha$, respectively.
\begin{table}
\caption{{\small Average estimators, corresponding MSE and average confidence (asymptotic or HPD for Gibbs) length for N=40 , T=1}}
\hspace{0.2in}
{\begin{tabular}{|l|l|l|l|}
\hline
~ & R=25 & R=30 & R=35\\
\hline
{\small\mbox{MLE}} & 2.978(4.623)3.013 & 3.014(1.836)2.993 & 2.909(0.008)2.999 \\
~ & 2.575(0.029)0.945 & 2.574(0.028)0.985 & 2.578(0.027)0.814 \\
\hline
{\small\mbox{Bayes(Lindley)}} & 2.863(0.019) & 2.968(0.019) & 2.863(0.019) \\
~ & 2.573(0.005) & 2.570(0.005) & 2.574(0.005) \\
\hline
{\small\mbox{Bayes(Gibbs)}} & 2.987(0.246)1.829 & 2.979(0.179)1.516 & 2.944(0.159)1.451 \\
~ & 2.472(0.055)0.757 & 2.482(0.053)0.751 & 2.489(0.053)0.759 \\
\hline
\end{tabular}}
\end{table}
\begin{table}
\caption{{\small Average estimators, corresponding MSE and average confidence (asymptotic or HPD for Gibbs) length for N=40 , T=2}}
\hspace{0.2in}
{\begin{tabular}{|l|l|l|l|}
\hline
~ & R=25 & R=30 & R=35\\
\hline
{\small\mbox{MLE}} & 3.192(0.037)2.865 & 3.145(0.021)2.899 & 2.908(0.008)2.889 \\
~ & 2.624(0.046)0.972 & 2.591(0.033)0.891 & 2.585(0.032)0.894 \\
\hline
{\small\mbox{Bayes(Lindley)}} & 2.968(0.001) & 2.968(0.001) & 2.963(0.001) \\
~ & 2.621(0.015) & 2.576(0.006) & 2.581(0.006) \\
\hline
{\small\mbox{Bayes(Gibbs)}} & 3.148(0.216)1.544 & 3.004(0.166)1.217 & 2.956(0.146)1.354 \\
~ & 2.479(0.054)0.0752 & 2.482(0.054)0.748 & 2.481(0.053)0.758 \\
\hline
\end{tabular}}
\end{table}
\begin{table}
\caption{{\small Average estimators, corresponding MSE and average confidence (asymptotic or HPD for Gibbs) length for N=50 , T=1}}
\hspace{0.2in}
{\begin{tabular}{|l|l|l|l|}
\hline
~ & R=35 & R=40 & R=45\\
\hline
{\small\mbox{MLE}} & 3.287(0.083)2.669 & 3.079(0.006)2.667 & 3.041(0.002)2.735 \\
~ & 2.556(0.019)0.731 & 2.555(0.018)0.763 & 2.463(0.018)0.784 \\
\hline
{\small\mbox{Bayes(Lindley)}} & 2.979(0.000) & 2.984(0.000) & 2.981(0.000) \\
~ & 2.554(0.003) & 2.552(0.003) & 2.561(0.003) \\
\hline
{\small\mbox{Bayes(Gibbs)}} & 2.958(0.269)1.661 & 3.066(0.247)1.643 & 2.966(0.234)1.318 \\
~ & 2.484(0.054)0.759 & 2.485(0.054)0.757 & 2.485(0.052)0.757 \\
\hline
\end{tabular}}
\end{table}
\begin{table}
\vspace{-.05in}
\caption{{\small Average estimators, corresponding MSE and average confidence (asymptotic or HPD for Gibbs) length for N=50 , T=2}}
\hspace{0.2in}
{\begin{tabular}{|l|l|l|l|}
\hline
~ & R=35 & R=40 & R=45\\
\hline
{\small\mbox{MLE}} & 3.282(0.079)2.587 & 2.921(0.006)2.579 & 2.930(0.005)2.577 \\
~ & 2.557(0.021)0.751 & 2.558(0.022)0.745 & 2.556(0.018)0.783 \\
\hline
{\small\mbox{Bayes(Lindley)}} & 2.973(0.000) & 2.972(0.000) & 2.964(0.001) \\
~ & 2.556(0.003) & 2.555(0.003) & 2.553(0.002) \\
\hline
{\small\mbox{Bayes(Gibbs)}} & 3.194(0.214)1.418 & 3.083(0.155)1.349 & 3.001(0.045)0.504 \\
~ & 2.483(0.053)0.754 & 2.495(0.053)0.754 & 2.493(0.054)0.759 \\
\hline
\end{tabular}}
\end{table}
From Tables 1-4, it is observed that for fixed N and T as R increases, the MSE decrease. The performances of the MLE's and Bayes estimators are very similar in all aspects. The average HPD confidence lengths are smaller than the average asymptotic lengths in all the cases considered. Finally it should be mentioned that Bayes estimators are most computationally expensive followed by MLE's.
\section{Data Analysis}
In this section, we demonstrate one data set for illustrative purposes. It has been studied by Gupta and Kundu \cite{gup1} that the $\mbox{WE}(\alpha,\lambda)$ distribution can be used quite to analyze them and MLE's of $\alpha$ and $\lambda$ are 1.6232 and 0.0138 respectively. The data set was studied by Bjerkedal \cite{bje} and is given below:\\
12 15 22 24 24 32 32 33 34 38 38 43 44 48 52 53 54 54 55 56 57 58 58 59 60 60 60 60 61 62 63
65 65 67 68 70 70 72 73 75 76 76 81 83 84 85 87 91 95 96 98 99 109 110 121 127 129 131 143
146 146 175 175 211 233 258 258 263 297 341 341 376.
\\
We use them and create the following two sampling schemes:
$$\mbox{Scheme 1:}~ T=300,~R=60,$$
$$\mbox{Scheme 2:}~ T=250,~R=65,$$
Now for scheme 1, MLE of $\beta,~\alpha~\mbox{and}~\lambda$ are $(0.0239,1.7715,0.0135)$ and Bayes estimators with assumed non-informative priors, i.e., $w_1=w_2=w_3=w_4=0$ with Lindley approximation and Gibbs sampling method are $(0.0198,1.5019,0.0147)$ and $(0.0256,2.0372,0.0138)$ respectively. The $95\%$ confidence intervals based on MLE and Bayes estimators of $\beta,~\alpha~\mbox{and}~\lambda$ are $$\{(0,0.0664),(0.0073,4.3224),(0.0075,0.0195)\}$$ and $$\{(0.0161,0.0350),(1.1000,2.9996),(0.0053,0.0256)\}$$ respectively. \\
For scheme 2, MLE of $\beta,~\alpha~\mbox{and}~\lambda$ are $(0.0255,1.9390,0.0132)$ Bayes estimators with assumed non-informative priors, i.e., $w_1=w_2=w_3=w_4=0$ with Lindley approximation and Gibbs sampling method are $(0.0223,1.7395,0.0142)$ and $(0.0254,2.0835,0.0131)$ respectively. The $95\%$ confidence intervals based on MLE and Bayes estimators of $\beta,~\alpha~\mbox{and}~\lambda$ are $$\{(0,0.0677),(0.0024,4.5216),(0.0075,0.0189))\}$$ and $$\{(0.0170,0.0340),(1.2242,2.9353),(0.0085,0.0222)\}$$ respectively.\par
Because we see the effect of the hyper parameters on the Bayes estimators and also on confidence intervals, we take the following informative priors $w_1=3,~w_2=1.5,~w_3=0.01,~w_4=1.$ \\
Based on this, for scheme 1, Bayes estimators of $\beta,~\alpha~\mbox{and}~\lambda$ with Lindley approximation and Gibbs sampling method are $(0.0233,1.8233,0.0142)$ and $(0.0255,1.8205,0.0150)$ respectively. The $95\%$ confidence intervals based on Bayes estimators of $\beta,~\alpha~\mbox{and}~\lambda$ are $$\{(0.0162,0.0350),(1.0042,2.6231),(0.0062,0.0269)\}.$$
For scheme 2, Bayes estimators of $\beta,~\alpha~\mbox{and}~\lambda$ with Lindley approximation and Gibbs sampling method are $(0.0231,1.8162,0.0141)$ and $(0.0246,2.0799,0.0127)$ respectively. The $95\%$ confidence intervals based on Bayes estimators of $\beta,~\alpha~\mbox{and}~\lambda$ are $$\{(0.0170,0.0322),(1.2043,2.9135),(0.0060,0.0217)\}.$$
\par
We plot all the different estimated density functions with non-informative priors and informative priors in Figure 1 and Figure 2. \label{fig3}\input{epsf}
\epsfxsize=3in \epsfysize=2in
\begin{figure}
\centerline{\epsfxsize=5in \epsfysize=2in \epsffile{good.eps}}
\vspace{-0.3in}
\caption{\scriptsize Estimated density functions with informative priors for scheme 1(left) and scheme 2(right). }
\end{figure}
\label{sch}\input{epsf}
\epsfxsize=3in \epsfysize=2in
\begin{figure}
\centerline{\epsfxsize=5in \epsfysize=2in \epsffile{noninformative.eps}}
\vspace{-0.3in}
\caption{\scriptsize Estimated density functions with non-informative priors for scheme 1(left) and scheme 2(right). }
\end{figure}
Comparing the two schemes with informative and non-informative priors, it is observed that for scheme 1, estimators have smaller standard errors than scheme 2, as expected. Also it is clear that the Bayes estimators depend on the hyper parameters. Because the HPD confidence intervals based on informative priors are slightly smaller than corresponding length of HPD confidence intervals based on non-informative priors, therefore the prior informative should be used if they are available.
\section{Conclusion}
\par In this article, we have studied the classical and Bayes inference procedure for the Type-II hybrid censored $\mbox{WE}(\alpha,\lambda)$ distribution. We provide the maximum likelihood estimators and it is observed that the maximum likelihood estimators of the unknown parameters can not be obtained in the closed form and we suggest the EM algorithm to compute them. we also earn the Bayes estimators of the unknown parameters and show that they can not be obtained in explicit forms, and we have proposed two approximation methods to earn them. We have compared the performance of the different methods by Monte Carlo simulations, and it is observed that the performance of quite satisfactory.
\newpage
\begin{center}
{\bf Appendix A}
\end{center}
{{\label{ap}\theorem{Given $X_{(1)}=x_{(1)},\cdots,X_{(r)}=x_{(r)}$, the conditional distribution of $Z_i$ for $i=1,\cdots,n-r$ is
$$f_{Z|X}(z_i|X_{(1)}=x_{(1)},\cdots,X_{(i)}=x_{(i)})=f_{Z|X}(z_i|X_{(i)}=x_{(i)})=
\frac{f_{WE}(z_i)}{1-F_{WE}(x_i)}$$
where\\ $$f_{WE}(x)=\frac{\alpha+1}{\alpha^2}\beta e^{-\frac{\beta}{\alpha}x}(1-e^{-\beta x})$$
and $$F_{WE}(x)=1-\frac{1}{\alpha}e^{-\frac{\beta}{\alpha}x}[\alpha+1-e^{-\beta x}]$$}}}
{\proof The proof can be obtained similarly as in Ng et al. (2002).}\\
Note that using Theorem \ref{ap}, we can write
\begin{equation*}
\displaystyle
\begin{array}{c}
A(c;\alpha,\beta)=E[Z_i|Z_i>c]=\int_c^\infty \frac{\alpha+1}{\alpha}\frac{\beta}{K}xe^{-\frac{\beta}{\alpha}x}(1-e^{-\beta x})dx\;\;\;\;\left(K=e^{-\frac{\beta}{\alpha}c}(\alpha+1-e^{-\beta c})\right)\\ \\
\hspace{1in}=\frac{(\alpha+1)\alpha}{K\beta}\int_{\frac{\beta}{\alpha}c}^\infty ue^{-u}du-\frac{\alpha}{K\beta(\alpha+1)}\int_{\frac{\beta(\alpha+1)}{\alpha}c}^\infty ve^{-v}dv \;\;\;\left(put \;\;u=\frac{\beta}{\alpha}x\;\;\&\;\;v=\frac{\beta(\alpha+1)}{\alpha}x\right)\\ \\
\hspace{-0.5in}=\frac{(\alpha+1)\alpha}{K\beta}(-e^{-u})(u+1)]_{\frac{\beta}{\alpha}c}^\infty-\frac{\alpha}{K\beta(\alpha+1)}(-e^{-v})(v+1)]
_{\frac{\beta(\alpha+1)}{\alpha}c}^\infty\\ \\
\hspace{-0.7in}=\frac{(\alpha+1)\alpha}{K\beta}(\frac{\beta}{\alpha}c+1)e^{-\frac{\beta}{\alpha}c}-\frac{\alpha}{K\beta(\alpha+1)}(\frac{\beta(\alpha+1)}{\alpha}c+1)e^{
-\frac{\beta(\alpha+1)}{\alpha}c}\\ \\
\hspace{-1.25in}=\frac{\alpha e^{-\frac{\beta}{\alpha}c}}{K\beta}\left[(\alpha+1)(\frac{\beta}{\alpha}c+1)-\frac{e^{-\beta c}}{\alpha+1}(\frac{\beta(\alpha+1)c}{\alpha}+1)\right]\\ \\
\hspace{-1.1in}=\frac{e^{-\frac{\beta}{\alpha}c}}{K\beta}\left[(\alpha+1)(\beta c+\alpha)-\frac{e^{-\beta c}}{\alpha+1}\left(\beta(\alpha+1)c+\alpha\right)\right]
\\ \\ \displaystyle
\hspace{-1.9in}=\frac{(\alpha+1)(\beta c+\alpha)-\frac{e^{-\beta c}(\beta c(\alpha+1)+\alpha)}{\alpha+1}}{\beta(\alpha+1-e^{-\frac{\beta}{\alpha}c})}
\end{array}
\end{equation*}
and about $B(c;\alpha,\beta)$, we have:
$$B(c;\alpha,\beta)=E[\ln (1-e^{-\beta Z_i})|Z_i>c]=\int_c^\infty\frac{\alpha+1}{\alpha}\frac{\beta}{K}\ln(1-e^{-\beta x})e^{-\frac{\beta}{\alpha}x}(1-e^{-\beta x})dx$$$$
=-\frac{\alpha+1}{\alpha K}\int_{1-e^{-\beta c}}^1u(1-u)^{\frac{1}{\alpha}-1}\ln(u)$$
$$=\frac{\alpha+1}{\alpha K}\left[\frac{1}{18}(1-e^{-\beta c})^3(-\frac{1}{\alpha}+1)\mbox{hypergeom}_{3,2}([3,3,-\frac{1}{\alpha}+2],[4,4],1-e^{-\beta c})\right.$$$$+\left(-\frac{1}{4}\mbox{hypergeom}_{2,1}([2,-\frac{1}{\alpha}+1],[3],1-e^{-\beta c})\right.$$$$\left.+\frac{1}{2}\ln(x)\mbox{hypergeom}_{2,1}([2,-\frac{1}{\alpha}+1],[3],1-e^{-\beta c})\right)(1-e^{-\beta c})^2$$$$-\frac{1}{18}(-\frac{1}{\alpha}+1)\mbox{hypergeom}_{3,2}([3,3,-\frac{1}{\alpha}+2],[4,4],1)$$$$\left.+\frac{1}{4}
\mbox{hypergeom}_{2,1}([2,-\frac{1}{\alpha}+1],[3],1)\right]$$
where hypergeom(.) is Generalized hypergeometric function. This function is also known as Barnes's extended hypergeometric function. The definition of $F_{p,q}(\mathbf{n},\mathbf{d},\xi)$ is:
$$F_{p,q}(\mathbf{n},\mathbf{d},\xi)=\sum_{k=0}^\infty\frac{\lambda^k\Pi_{i=1}^p\Gamma(n_i+k)\Gamma^{-1}(n_i)}{\Gamma(k+1)
\Pi_{i=1}^q\Gamma(d_i+k)\Gamma^{-1}(d_i)},$$
where $\mathbf{n}=[n_1,\cdots,n_p]$, $p$ is the number of operands of $\mathbf{n}$, $\mathbf{d}=[d_1,\cdots,d_q]$ and $q$ is the number of operands
of $\mathbf{d}$. Generalized hypergeometric function is quickly evaluated and readily available in standard software such as Maple.
\begin{center}
{\bf Appendix B}
\end{center}
The conditional density of $\beta$ given $\alpha$ and $\b{x}$ is
$$\pi(\beta|\alpha,\b{x})\propto\beta^{w_2+r-1}e^{-\beta \left(w_1+\frac{\beta}{\alpha}\sum_{i=1}^rx_i+c(n-r)\right)}
(\alpha+1-e^{-\beta c})^{n-r}\Pi_{i=1}^r(1-e^{-\beta x_i}).$$
This function is log-concave because we have
$$\frac{\partial^2\log(\pi(\beta|\alpha,\b{x}))}{\partial\beta^2}=-\frac{w_2+r-1}{\beta^2}-\frac{(n-r)c^2e^{-\beta c}(\alpha+1)}{(\alpha+1-e^{-\beta c})^2}-\sum_{i=1}^r\frac{x_i^2e^{-\beta x_i}}{(1-e^{-\beta x_i})^2}<0.$$
Therefore, the result follows.
\\ \quad\\
\begin{center}
{\bf Appendix C}
\end{center}
The conditional distribution of $\alpha$ given $\beta$ and $\b{x}$ is
$$\pi(\alpha|\beta,\b{x})\propto\alpha^{w_4-n-r-1}(\alpha+1)^re^{-\alpha w_3}e^{-\frac{\beta}{\alpha}(\sum_{i=1}^rx_i+c(n-r))}
(\alpha+1-e^{-\beta c})^{n-r}.$$
In this function, we have $\pi(\infty|\beta,\b{x})\rightarrow\pi(0|\beta,\b{x})=0$ and $\pi(\alpha|\beta,\b{x})\geq0~~\forall\alpha$, now it is enough that prove $\pi(\alpha|\beta,\b{x})$ is bounded. With simple calculation we see that $\forall\alpha$ this function is less than the gamma function and the gamma function is a bounded function, so this function is bounded. Therefore $\pi(\alpha|\beta,\b{x})$ has a finite maximum point.
\bibliographystyle{plain}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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\section{Introduction}
Past few years have witnessed the rapid development of dialogue systems.
Based on the sequence-to-sequence framework \cite{sutskever2014sequence}, most models are trained in an end-to-end manner with large corpora of human-to-human dialogues and have obtained impressive success \cite{shang2015neural, vinyals2015neural, li2015diversity, serban2016building}.
While there is still a long way for reaching the ultimate goal of dialogue systems, which is to be able to talk like humans.
And one of the essential intelligence to achieve this goal is the ability to make use of knowledge.
There are several works on dialogue systems exploiting knowledge.
The Mem2Seq \cite{madotto2018mem2seq} incorporates structured knowledge into the end-to-end task-oriented dialogue.
~\citeauthor{liu2018knowledge}~\shortcite{liu2018knowledge} introduces fact-matching and knowledge-diffusion to generate meaningful, diverse and natural responses using structured knowledge triplets.
~\citeauthor{ghazvininejad2018knowledge}~\shortcite{ghazvininejad2018knowledge}, ~\citeauthor{parthasarathi2018extending}~\shortcite{parthasarathi2018extending}, ~\citeauthor{yavuzdeepcopy}~\shortcite{yavuzdeepcopy}, ~\citeauthor{dinan2018wizard}~\shortcite{dinan2018wizard} and ~\citeauthor{lo2019knowledge}~\shortcite{lo2019knowledge} apply unstructured text facts in open-domain dialogue systems. These works mainly focus on integrating factoid knowledge into dialogue systems, while factoid knowledge requires a lot of work to build up, and is only limited to expressing precise facts. Documents as a knowledge source provide a wide spectrum of knowledge, including but not limited to factoid, event updates, subjective opinion, etc. Recently, intensive research has been applied on using documents as knowledge sources for Question-Answering \cite{chen2017reading, huang2018flowqa, yu2018qanet, rajpurkar2018know, reddy2018coqa}.
The Document Grounded Conversation is a task to generate natural dialogue responses when chatting about the content of a specific document. This task requires to integrate document knowledge with the multi-turn dialogue history. Different from previous knowledge grounded dialogue systems, Document Grounded Conversations utilize documents as the knowledge source, and hence are able to employ a wide spectrum of knowledge. And the Document Grounded Conversations is also different from document QA since the contextual consistent conversation response should be generated.
To address the Document Grounded Conversation task, it is important to:
1) Exploit document knowledge which are relevant to the conversation;
2) Develop a unified representation combining multi-turn utterances along with the relevant document knowledge.
In this paper, we propose a novel and effective Transformer-based \cite{vaswani2017attention} architecture for Document Grounded Conversations, named Incremental Transformer with Deliberation Decoder. The encoder employs a transformer architecture to incrementally encode multi-turn history utterances, and incorporate document knowledge into the the multi-turn context encoding process. The decoder is a two-pass decoder similar to the Deliberation Network in Neural Machine Translation \cite{xia2017deliberation}, which is designed to improve the context coherence and knowledge correctness of the responses. The first-pass decoder focuses on contextual coherence, while the second-pass decoder refines the result of the first-pass decoder by consulting the relevant document knowledge, and hence increases the knowledge relevance and correctness. This is motivated by human cognition process. In real-world human conversations, people usually first make a draft on how to respond the previous utterance, and then consummate the answer or even raise questions by consulting background knowledge.
We test the effectiveness of our proposed model on Document Grounded Conversations Dataset \cite{zhou2018dataset}. Experiment results show that our model is capable of generating responses of more context coherence and knowledge relevance. Sometimes document knowledge is even well used to guide the following conversations. Both automatic and manual evaluations show that our model substantially outperforms the competitive baselines.
Our contributions are as follows:
\begin{itemize}
\item We build a novel Incremental Transformer to incrementally encode multi-turn utterances with document knowledge together.
\item We are the first to apply a two-pass decoder to generate responses for document grounded conversations. Two decoders focus on context coherence and knowledge correctness respectively.
\end{itemize}
\section{Approach}
\subsection{Problem Statement}
Our goal is to incorporate the relevant document knowledge into multi-turn conversations. Formally, let $\mathbf{U}=\mathbf{u}^{(1)},...,\mathbf{u}^{(k)},...,\mathbf{u}^{(K)}$ be a whole conversation composed of $K$ utterances. We use $\mathbf{u}^{(k)} = u^{(k)}_{1},...,u^{(k)}_{i},...,u^{(k)}_{I}$ to denote the $k$-th utterance containing $I$ words, where $u^{(k)}_{i}$ denotes the $i$-th word in the $k$-th utterance. For each utterance $\mathbf{u}^{(k)}$, likewise, there is a specified relevant document $\mathbf{s}^{(k)} = s^{(k)}_{1},...,s^{(k)}_{j},...,s^{(k)}_{J}$, which represents the document related to the $k$-th utterance containing $J$ words.
We define the document grounded conversations task as generating a response $\mathbf{u}^{(k+1)}$ given its related document $\mathbf{s}^{(k+1)}$ and previous $k$ utterances $\mathbf{U}_{\leq k}$ with related documents $\mathbf{S}_{\leq k}$, where $\mathbf{U}_{\leq k} = \mathbf{u}^{(1)},...,\mathbf{u}^{(k)}$ and $\mathbf{S}_{\leq k} = \mathbf{s}^{(1)},...,\mathbf{s}^{(k)}$. Note that $\mathbf{s}^{(k)}, \mathbf{s}^{(k+1)},...,\mathbf{s}^{(k+n)}$ may be the same.
Therefore, the probability to generate the response $\mathbf{u}^{(k+1)}$ is computed as:
\begin{equation}
\begin{array}{ll}
& P(\mathbf{u}^{(k+1)}|\mathbf{U}_{\leq k}, \mathbf{S}_{\leq k+1}; \theta) \\
& =\prod_{i=1}^{I} P(u^{k+1}_{i}|\mathbf{U}_{\leq k}, \mathbf{S}_{\leq k+1}, u^{(k+1)}_{<i};\theta)
\end{array}
\end{equation}
where $u_{< i}^{(k+1)} = u_{1}^{(k+1)},...,u_{i-1}^{(k+1)}$.
\subsection{Model Description}
\begin{figure}[t]
\centering
\small
\includegraphics[width=0.48\textwidth]{ACL2019-figure3.pdf}
\caption{The framework of Incremental Transformer with Deliberation Decoder for Document Grounded Conversations. } \vspace{-10pt}
\centering
\label{model architecture}
\end{figure}
\begin{figure*}[t]
\centering
\includegraphics[width=0.98\textwidth]{ACL2019-figure2.pdf}
\caption{(1) Detailed architecture of model components. (a) The Self-Attentive Encoder(SA). (b) Incremental Transformer (ITE). (c) Deliberation Decoder (DD). (2) Simplified version of our proposed model used to verify the validity of our proposed Incremental Transformer Encoder and Deliberation Decoder. (d) Knowledge-Attention Transformer(KAT). (e) Context-Knowledge-Attention Decoder (CKAD).} \vspace{-10pt}
\centering
\label{model modules}
\end{figure*}
Figure \ref{model architecture} shows the framework of the proposed Incremental Transformer with Deliberation Decoder. Please refer to Figure \ref{model modules} (1) for more details. It consists of three components:
1) Self-Attentive Encoder (SA) (in orange) is a transformer encoder as described in \cite{vaswani2017attention}, which encodes the document knowledge and the current utterance independently.
2) Incremental Transformer Encoder (ITE) (on the top) is a unified transformer encoder which encodes multi-turn utterances with knowledge representation using an incremental encoding scheme. This module takes previous utterances $\mathbf{u}^{(i)}$ and the document $\mathbf{s}^{(i)}$'s SA representation as input, and use attention mechanism to incrementally build up the representation of relevant context and document knowledge.
3) Deliberation Decoder (DD) (on the bottom) is a two-pass unified transformer decoder for better generating the next response. The first-pass decoder takes current utterance $\mathbf{u}^{(k)}$'s SA representation and ITE output as input, and mainly relies on conversation context for response generation. The second-pass decoder takes the SA representation of the first pass result and the relevant document $\mathbf{s}^{(k+1)}$'s SA representation as input, and uses document knowledge to further refine the response.
\subsubsection*{Self-Attentive Encoder}
As document knowledge often includes several sentences, it's important to capture long-range dependencies and identify relevant information.
We use multi-head self-attention \cite{vaswani2017attention} to compute the representation of document knowledge.
As shown in Figure \ref{model modules} (a), we use a self-attentive encoder to compute the representation of the related document knowledge $\mathbf{s}^{(k)}$. The input ($\mathbf{In}_{s}^{(k)}$) of the encoder is a sequence of document words embedding with positional encoding added.\cite{vaswani2017attention}:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{In}_{s}^{(k)} = [\mathbf{s}^{(k)}_{1},...,\mathbf{s}^{(k)}_{J}]
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{s}^{(k)}_{j} = \mathbf{e}_{s_{j}} + {\rm PE}(j)
\end{equation}
where $\mathbf{e}_{s_{j}}$ is the word embedding of $s_{j}^{(k)}$ and ${\rm PE}(\cdot)$ denotes positional encoding function.
The Self-Attentive encoder contains a stack of $N_{x}$ identical layers. Each layer has two sub-layers. The first sub-layer is a multi-head self-attention ($\rm MultiHead$) \cite{vaswani2017attention}. ${\rm MultiHead}(\mathbf{Q}, \mathbf{K}, \mathbf{V})$ is a multi-head attention function that takes a query matrix $\mathbf{Q}$, a key matrix $\mathbf{K}$, and a value matrix $\mathbf{V}$ as input. In current case, $\mathbf{Q}$ = $\mathbf{K}$ = $\mathbf{V}$. That's why it's called self-attention. And the second sub-layer is a simple, position-wise fully connected feed-forward network ($\rm FFN$). This $\rm FFN$ consists of two linear transformations with a ReLU activation in between. \cite{vaswani2017attention}.
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{A}^{(1)} = {\rm MultiHead}(\mathbf{In}_{s}^{(k)},\mathbf{In}_{s}^{(k)},\mathbf{In}_{s}^{(k)})
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{D}^{(1)} = {\rm FFN}(\mathbf{A}^{(1)})
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
{\rm FFN}(x) = \max (0, xW_{1}+b_{1})W_{2} + b_{2}
\end{equation}
where $\mathbf{A}^{(1)}$ is the hidden state computed by multi-head attention at the first layer, $\mathbf{D}^{(1)}$ denotes the representation of $\mathbf{s}^{(k)}$ after the first layer. Note that residual connection and layer normalization are used in each sub-layer, which are omitted in the presentation for simplicity. Please refer to \cite{vaswani2017attention} for more details.
For each layer, repeat this process:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{A}^{(n)} = {\rm MultiHead}(\mathbf{D}^{(n-1)},\mathbf{D}^{(n-1)},\mathbf{D}^{(n-1)})
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{D}^{(n)} = {\rm FFN}(\mathbf{A}^{(n)})
\end{equation}
where $n=1,...,N_{s}$ and $\mathbf{D}^{(0)} = \mathbf{In}_{s}^{(k)}$.
We use ${\rm SA}_{s}(\cdot)$ to denote this whole process:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{d}^{(k)} = \mathbf{D}^{(N_{x})} = {\rm SA}_{s}(\mathbf{s}^{(k)})
\end{equation}
where $\mathbf{d}^{(k)}$ is the final representation for the document knowledge $\mathbf{s}^{(k)}$.
Similarly, for each utterance $\mathbf{u}^{(k)}$, we use ${\mathbf{In}}_{u}^{(k)} = [\mathbf{u}^{(k)}_{1},...,\mathbf{u}^{(k)}_{I}]$ to represent the sequence of the position-aware word embedding. Then the same Self-Attentive Encoder is used to compute the representation of current utterance $\mathbf{u}^{(k)}$, and we use ${\rm SA}_{u}(\mathbf{u}^{(k)})$ to denote this encoding result. The Self-Attentive Encoder is also used to encode the document ${\mathbf{s}}^{(k+1)}$ and the first pass decoding results in the second pass of the decoder. Note that ${\rm SA}_{s}$ and ${\rm SA}_{u}$ have the same architecture but different parameters. More details about this will be mentioned in the following sections.
\subsubsection*{Incremental Transformer Encoder}
To encode multi-turn document grounded utterances effectively, we design an Incremental Transformer Encoder.
Incremental Transformer uses multi-head attention to incorporate document knowledge and context into the current utterance's encoding process.
This process can be stated recursively as follows:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{c}^{(k)} = {\rm ITE}(\mathbf{c}^{(k-1)}, \mathbf{d}^{(k)}, \mathbf{In}_{u}^{(k)})
\end{equation}
where ${\rm ITE}(\cdot)$ denotes the encoding function, $\mathbf{c}^{(k)}$ denotes the context state after encoding utterance $\mathbf{u}^{(k)}$, $\mathbf{c}^{(k-1)}$ is the context state after encoding last utterance $\mathbf{u}^{(k-1)}$, $\mathbf{d}^{(k)}$ is the representation of document $\mathbf{s}^{(k)}$ and $\mathbf{In}_{u}^{(k)}$ is the embedding of current utterance $\mathbf{u}^{(k)}$.
As shown in Figure \ref{model modules} (b), we use a stack of $N_{u}$ identical layers to encode $\mathbf{u}^{(k)}$. Each layer consists of four sub-layers.
The first sub-layer is a multi-head self-attention:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{B}^{(n)} = {\rm MultiHead}(\mathbf{C}^{(n-1)}, \mathbf{C}^{(n-1)}, \mathbf{C}^{(n-1)})
\end{equation}
where $n = 1,...,N_{u}$, $\mathbf{C}^{(n-1)}$ is the output of the last layer and $\mathbf{C}^{(0)} = \mathbf{In}_{u}^{(k)}$. The second sub-layer is a multi-head knowledge attention:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{E}^{(n)} = {\rm MultiHead}(\mathbf{B}^{(n)}, \mathbf{d}^{(k)}, \mathbf{d}^{(k)})
\end{equation}
The third sub-layer is a multi-head context attention:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{F}^{(n)} = {\rm MultiHead}(\mathbf{E}^{(n)}, \mathbf{c}^{(k-1)}, \mathbf{c}^{(k-1)})
\end{equation}
where $\mathbf{c}^{(k-1)}$ is the representation of the previous utterances. That's why we called the encoder "Incremental Transformer". The fourth sub-layer is a position-wise fully connected feed-forward network:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{C}^{(n)} = {\rm FFN}(\mathbf{F}^{(n)})
\end{equation}
We use $\mathbf{c}^{(k)}$ to denote the final representation at $N_{u}$-th layer:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{c}^{(k)} = \mathbf{C}^{(N_{u})}
\end{equation}
\subsubsection*{Deliberation Decoder}
Motivated by the real-world human cognitive process, we design a Deliberation Decoder containing two decoding passes to improve the knowledge relevance and context coherence. The first-pass decoder takes the representation of current utterance ${\rm SA}_{u}(\mathbf{\mathbf{u}^{(k)}})$ and context $\mathbf{c}^{(k)}$ as input and focuses on how to generate responses contextual coherently. The second-pass decoder takes the representation of the first-pass decoding results and related document $\mathbf{s}^{(k+1)}$ as input and focuses on increasing knowledge usage and guiding the following conversations within the scope of the given document.
When generating the $i$-th response word ${u}^{(k+1)}_{i}$, we have the generated words $\mathbf{u}^{(k+1)}_{<i}$ as input \cite{vaswani2017attention}. We use $\mathbf{In}_{r}^{(k+1)}$ to denote the matrix representation of $\mathbf{u}^{(k+1)}_{<i}$ as following:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{In}_{r}^{(k+1)} = [\mathbf{u}^{(k+1)}_{0}, \mathbf{u}^{(k+1)}_{1},...,\mathbf{u}^{(k+1)}_{i-1}]
\end{equation}
where $\mathbf{u}^{(k+1)}_{0}$ is the vector representation of sentence-start token.
As shown in Figure \ref{model modules} (c), the Deliberation Decoder consists of a first-pass decoder and a second-pass decoder. These two decoders have the same architecture but different input for sub-layers. Both decoders are composed of a stack of $N_{y}$ identical layers. Each layer has four sub-layers.
For the first-pass decoder, the first sub-layer is a multi-head self-attention:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{G}^{(n)}_{1} = {\rm MultiHead}(\mathbf{R}^{(n-1)}_{1}, \mathbf{R}^{(n-1)}_{1}, \mathbf{R}^{(n-1)}_{1})
\end{equation}
where $n = 1,...,N_{y}$, $\mathbf{R}^{(n-1)}_{1}$ is the output of the previous layer, and $\mathbf{R}^{(0)}_{1} = \mathbf{In}_{r}^{(k+1)}$. The second sub-layer is a multi-head context attention:
\begin{equation} \label{eq18}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{H}^{(n)}_{1} = {\rm MultiHead}(\mathbf{G}^{(n)}_{1}, \mathbf{c}^{(k)}, \mathbf{c}^{(k)})
\end{equation}
where $\mathbf{c}^{(k)}$ is the representation of context $\mathbf{u}_{\leq k}$. The third sub-layer is a multi-head utterance attention:
\begin{equation} \label{eq19}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\begin{array}{cc}
\mathbf{M}^{(n)}_{1} = {\rm MultiHead}(\mathbf{H}^{(n)}_{1}, & {\rm SA}_{u}(\mathbf{u}^{(k)}), \\
& {\rm SA}_{u}(\mathbf{u}^{(k)}))
\end{array}
\end{equation}
where $SA_{u}(\cdot)$ is a Self-Attentive Encoder which encodes latest utterance $\mathbf{u}^{(k)}$. Eq. (\ref{eq18}) mainly encodes the context and document knowledge relevant to the latest utterance, while Eq. (\ref{eq19}) encodes the latest utterance directly. We hope optimal performance can be achieved by combining both.
The fourth sub-layer is a position-wise fully connected feed-forward network:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{R}^{(n)}_{1} = {\rm FFN}(\mathbf{M}^{(n)}_{1})
\end{equation}
After $N_{y}$ layers, we use softmax to get the words probabilities decoded by first-pass decoder:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
P(\mathbf{\hat{u}}^{(k+1)}_{(1)})= {\rm softmax}(\mathbf{R}^{(N_{y})}_{1})
\end{equation}
where $\mathbf{\hat{u}}^{(k+1)}_{(1)}$ is the response decoded by the first-pass decoder.
For second-pass decoder:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{G}^{(n)}_{2} = {\rm MultiHead}(\mathbf{R}^{(n-1)}_{2}, \mathbf{R}^{(n-1)}_{2}, \mathbf{R}^{(n-1)}_{2})
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{H}^{(n)}_{2} = {\rm MultiHead}(\mathbf{G}^{(n)}_{2}, \mathbf{d}^{(k+1)}, \mathbf{d}^{(k+1)})
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\begin{array}{cc}
\mathbf{M}^{(n)}_{2} = {\rm MultiHead}(\mathbf{H}^{(n)}_{2}, & {\rm SA}_{u}(\mathbf{\hat{u}}^{(k+1)}_{(1)}), \\
& {\rm SA}_{u}(\mathbf{\hat{u}}^{(k+1)}_{(1)}))
\end{array}
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{R}^{(n)}_{2} = {\rm FFN}(\mathbf{M}^{(n)}_{2})
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
P(\mathbf{\hat{u}}^{(k+1)}_{(2)}) = {\rm softmax}(\mathbf{R}^{(N_{y})}_{2})
\end{equation}
where $\mathbf{R}^{(n-1)}_{2}$ is the counterpart to $\mathbf{R}^{(n-1)}_{1}$ in pass two decoder, referring to the output of the previous layer. $\mathbf{d}^{(k+1)}$ is the representation of document $\mathbf{s}^{(k+1)}$ using Self-Attentive Encoder, $\mathbf{\hat{u}}^{(k+1)}_{(2)}$ is the output words after the second-pass decoder.
\subsubsection*{Training}
In contrast to the original Deliberation Network \cite{xia2017deliberation}, where they propose a complex joint learning framework using Monte Carlo Method,
we minimize the following loss as ~\citeauthor{xiong2018modeling}~\shortcite{xiong2018modeling} do:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
L_{mle} = L_{mle1} + L_{mle2}
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
L_{mle1} = - \sum_{k=1}^{K}\sum_{i=1}^{I}\log P(\mathbf{\hat{u}}^{(k+1)}_{(1)i})
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
L_{mle2} = - \sum_{k=1}^{K}\sum_{i=1}^{I}\log P(\mathbf{\hat{u}}^{(k+1)}_{(2)i})
\end{equation}
\section{Experiments}
\subsection{Dataset}
We evaluate our model using the Document Grounded Conversations Dataset \cite{zhou2018dataset}. There are 72922 utterances for training, 3626 utterances for validation and 11577 utterances for testing. The utterances can be either casual chats or document grounded. Note that we consider consequent utterances of the same person as one utterance. For example, we consider \textit{A: Hello! B: Hi! B: How's it going?} as \textit{A: Hello! B: Hi! How's it going?}.
And there is a related document given for every several consequent utterances, which may contain movie name, casts, introduction, ratings, and some scenes. The average length of documents is about 200.
Please refer to \cite{zhou2018dataset} for more details.
\begin{table*}[!t]
\centering
\scalebox{0.95} {
\begin{tabular}{lccccc}
& & & & Knowledge & Context \\
Model & PPL & BLEU(\%) & Fluency & Relevance & Coherence\\
\hline
Seq2Seq without knowledge & 80.93 & 0.38 & 1.62 & 0.18 & 0.54\\
HRED without knowledge & 80.84 & 0.43 & 1.25 & 0.18 & 0.30\\
Transformer without knowledge & 87.32 & 0.36 & 1.60 & 0.29 & 0.67\\
Seq2Seq (+knowledge) & 78.47 & 0.39 & 1.50 & 0.22 & 0.61\\
HRED (+knowledge) & 79.12 & 0.77 & 1.56 & 0.35 & 0.47\\
Wizard Transformer & 70.30 & 0.66 & 1.62 & 0.47 & 0.56\\
\hline
\textbf{ITE+DD} (ours) & \textbf{15.11} & \textbf{0.95} & 1.67 & \textbf{0.56} & \textbf{0.90}\\
\textbf{ITE+CKAD} (ours) & 64.97 & 0.86 & \textbf{1.68} & 0.50 & 0.82\\
\textbf{KAT} (ours) & 65.36 & 0.58 & 1.58 & 0.33 & 0.78\\
\hline
\end{tabular}
}
\caption{Automatic evaluation and manual evaluation results for baselines and our proposed models.} \vspace{-10pt}
\label{Automatic Evaluation and Munual Evaluation}
\end{table*}
\subsection{Baselines}
We compare our proposed model with the following state-of-the-art baselines:\\
\textbf{Models not using document knowledge}:
\textbf{Seq2Seq}: A simple encoder-decoder model \cite{shang2015neural, vinyals2015neural} with global attention \cite{luong2015effective}. We concatenate utterances context to a long sentence as input.
\textbf{HRED}: A hierarchical encoder-decoder model \cite{serban2016building}, which is composed of a word-level LSTM for each sentence and a sentence-level LSTM connecting utterances.
\textbf{Transformer}: The state-of-the-art NMT model based on multi-head attention \cite{vaswani2017attention}. We concatenate utterances context to a long sentence as its input. \\
\textbf{Models using document knowledge}:
\textbf{Seq2Seq (+knowledge)} and \textbf{HRED (+knowledge)} are based on Seq2Seq and HRED respectively. They both concatenate document knowledge representation and last decoding output embedding as input when decoding. Please refer to \cite{zhou2018dataset} for more details.
\textbf{Wizard Transformer}: A Transformer-based model for multi-turn open-domain dialogue with unstructured text facts \cite{dinan2018wizard}. It concatenates context utterances and text facts to a long sequence as input. We replace the text facts with document knowledge.
Here, we also conduct an ablation study to illustrate the validity of our proposed Incremental Transformer Encoder and Deliberation Decoder.
\textbf{ITE+CKAD}: It uses Incremental Transformer Encoder (ITE) as encoder and Context-Knowledge-Attention Decoder (CKAD) as shown in Figure \ref{model modules} (e). This setup is to test the validity of the deliberation decoder.
\textbf{Knowledge-Attention Transformer (KAT)}: As shown in Figure \ref{model modules} (d), the encoder of this model is a simplified version of Incremental Transformer Encoder (ITE), which doesn't have context-attention sub-layer. We concatenate utterances context to a long sentence as its input. The decoder of the model is a simplified Context-Knowledge-Attention Decoder (CKAD). It doesn't have context-attention sub-layer either. This setup is to test how effective the context has been exploited in the full model.
\begin{table}[t]
\centering
\scalebox{0.95} {
\begin{tabular}{|c|c|c|}
\hline
& Knowledge & Context \\
Model & Relevance(\%) & Coherence(\%)\\ \hline
Wizard & 64/25/11 & 58/28/14\\
\hline
\textbf{ITE+CKAD} & 67/16/17 & 40/37/23 \\ \hline
\textbf{ITE+DD} & 64/16/20 & 38/34/28 \\ \hline
\end{tabular}
}
\caption{The percent(\%) of score (0/1/2) of Knowledge Relevance and Context Coherence for Wizard Transformer, ITE+CKAD and ITE+DD.} \vspace{-10pt}
\label{Score Distribution}
\end{table}
\subsection{Experiment Setup}
We use OpenNMT-py\footnote{\url{https://github.com/OpenNMT/OpenNMT-py}} \cite{opennmt} as the code framework\footnote{The code and models are available at \url{https://github.com/lizekang/ITDD}}. For all models, the hidden size is set to 512. For rnn-based models (Seq2Seq, HRED), 3-layer bidirectional LSTM \cite{hochreiter1997long} and 1-layer LSTM is applied for encoder and decoder respectively. For transformer-based models, the layers of both encoder and decoder are set to 3. The number of attention heads in multi-head attention is 8 and the filter size is 2048. The word embedding is shared by utterances, knowledge and generated responses. The dimension of word embedding is set to 512 empirically. We use Adam \cite{kingma2014adam} for optimization. When decoding, beam size is set to 5. We use the previous three utterances and its related documents as input.
\begin{table*}[!t]
\centering
\scalebox{0.95} {
\begin{tabular}{|rp{13cm}|}
\hline
\multicolumn{2}{|p{15cm}|}{\textbf{Document}} \\ \hline
\multicolumn{2}{|p{15cm}|}{moviename \underline{\textbf{despicable me}} ... \underline{\textbf{cast: steve carell as gru}} ... \underline{\textbf{rotten tomatoes: 81\%}} ... it is the debut film of \underline{\textbf{illumination entertainment}}. ... gru, a \underline{\textbf{supervillain}}, is disheartened when an unknown supervillain steals the great pyramid of giza. gru, with the assistance of his colleague dr. Nefario and his \underline{\textbf{minions}}, resolves to one-up this mystery rival by shrinking and stealing the moon. as it would be costly to steal the moon, \underline{\textbf{gru seeks a loan from the bank of evil}}. ... upon learning that an up-and-coming \underline{\textbf{villain}} named vector was responsible for the pyramid theft ...} \\
\hline
\textbf{Utterance 1} & what do you think about \underline{\textbf{despicable me}}? \\
\hline
\textbf{ITE+DD} & i think it is an awesome movie, \underline{\textbf{what about you?}} \\
\textbf{Wizard} & i think it's a great movie! \\
\hline
\textbf{Utterance 2} & i rather liked it. it wasn't what i was expecting but it was still good. \\
\hline
\textbf{ITE+DD} & yeah, \underline{\textbf{it makes me laugh}}, even when they make a movie about it. \\
\textbf{Wizard} & it's a great movie for kids and adults. \\
\hline
\textbf{Utterance 3} & i like it too. \underline{\textbf{funny and heart warming at the same time}}. \\
\hline
\textbf{ITE+DD} & i think it's interesting that \underline{\textbf{gru decided to take a loan from the bank of evil}}. \\
\textbf{Wizard} & i think they should have made a sequel. \\
\hline
\textbf{Utterance 4} & \underline{\textbf{gru was a really interesting character}}, too. \underline{\textbf{i liked steve carell and the voice he}} \underline{\textbf{used for gru}}. \\
\hline
\textbf{ITE+DD} & yeah, now that you mention it, what did you think of the \underline{\textbf{minions}}? \\
\textbf{Wizard} & i think the entire cast was great. \\
\hline
\textbf{Utterance 5} & yes, he did an excellent job portraying the character. \underline{\textbf{81\% in ratings}} i think is great. \\
\hline
\textbf{ITE+DD} & yes, \underline{\textbf{81\%}} is a great score! \\
\textbf{Wizard} & i also liked the \underline{\textbf{villain}} of the movie. \\
\hline
\end{tabular}
}
\caption{Responses generated by Incremental Transformer with Deliberation Decoder(\textbf{ITE+DD}) and the Wizard Transformer(\textbf{Wizard}). These utterances are from continuous dialogues. \textbf{ITE+DD} and \textbf{Wizard} generate responses using context utterances and a given document. Note that \textbf{Utterance $i+1$} is the gold response of \textbf{Utterance $i$}.} \vspace{-10pt}
\label{Case Study}
\end{table*}
\subsection{Evaluation Metrics}
\textbf{Automatic Evaluation}:
We adopt perplexity (PPL) and BLEU \cite{Papineni02bleu:a} to automatically evaluate the response generation performance.
Models are evaluated using perplexity of the gold response as described in \cite{dinan2018wizard}. Lower perplexity indicates better performance.
BLEU measures n-gram overlap between a generated response and a gold response. However, since there is only one reference for each response and there may exist multiple feasible responses, BLEU scores are extremely low. We compute BLEU score by the \emph{multi-bleu.perl}\footnote{\url{https://github.com/google/seq2seq/blob/master/bin/tools/multi-bleu.perl}} \\
\textbf{Manual Evaluation}:
Manual evaluations are essential for dialogue generation. We randomly sampled 30 conversations containing 606 utterances from the test set and obtained 5454 utterances from the nine models. We have annotators score these utterances given its previous utterances and related documents.
We defined three metrics - \textbf{fluency}, \textbf{knowledge relevance} \cite{liu2018knowledge} and \textbf{context coherence} for manual evaluation. All these metrics are scored 0/1/2.
\textbf{fluency}: Whether the response is natural and fluent. Score 0 represents not fluent and incomprehensible; 1 represents partially fluent but still comprehensible; 2 represents totally fluent.
\textbf{knowledge relevance}: Whether the response uses relevant and correct knowledge. Score 0 represents no relevant knowledge; 1 represents containing relevant knowledge but not correct; 2 represents containing relevant knowledge and correct.
\textbf{context coherence}: Whether the response is coherent with the context and guides the following utterances. Score 0 represents not coherent or leading the dialogue to an end; 1 represents coherent with the utterance history but not guiding the following utterances; 2 represents coherent with utterance history and guiding the next utterance.
\subsection{Experimental Results}
Table \ref{Automatic Evaluation and Munual Evaluation} shows the automatic and manual evaluation results for both the baseline and our models.
In manual evaluation, among baselines, Wizard Transformer and RNN without knowledge have the highest fluency of 1.62 and Wizard obtains the highest knowledge relevance of 0.47 while Transformer without knowledge gets the highest context coherence of 0.67. For all models, ITE+CKAD obtains the highest fluency of 1.68 and ITE+DD has the highest Knowledge Relevance of 0.56 and highest Context Coherence of 0.90.
In automatic evaluation, our proposed model has lower perplexity and higher BLEU scores than baselines. For BLEU, HRED with knowledge obtains the highest BLEU score of 0.77 among the baselines. And ITE+DD gets 0.95 BLEU score, which is the highest among all the models. For perplexity, Wizard Transformer obtains the lowest perplexity of 70.30 among baseline models and ITE+DD has remarkably lower perplexity of 15.11 than all the other models. A detailed analysis is in Section \ref{Analysis}.
\subsection{Analysis and Discussion} \label{Analysis}
To our surprise, ITE+DD reaches an extremely low ground truth perplexity. We find that the ground truth perplexity after the first-pass decoding is only similar to the ITE+CKAD. It shows that the second-pass decoder utilizes the document knowledge well, and dramatically reduced the ground truth perplexity.
As shown in Table \ref{Score Distribution}, ITE+DD has a higher percent of score 2 both on Knowledge Relevance and Context Coherence than ITE+CKAD. This result also demonstrates that Deliberation Decoder can improve the knowledge correctness and guide the following conversations better.
Although the perplexity of ITE+CKAD is only slightly better than KAT, the BLEU score, Fluency, Knowledge Relevance and Context Coherence of ITE+CKAD all significantly outperform those of KAT model, which indicates that Incremental Transformer can deal with multi-turn document grounded conversations better.
Wizard Transformer has a great performance on Knowledge Relevance only second to our proposed Incremental Transformer. However, its score on Context Coherence is lower than some other baselines. As shown in Table \ref{Score Distribution}, Wizard Transformer has Knowledge Relevance score 1 results twice more than score 2 results, which indicates that the model tends to generate responses with related knowledge but not correct. And the poor performance on Context Coherence also shows Wizard Transformer does not respond to the previous utterance well. This shows the limitation of representing context and document knowledge by simple concatenation.
\begin{table}[t]
\small
\centering
\scalebox{0.95} {
\begin{tabular}{|c|p{3cm}|p{3cm}|}
\hline
\textbf{ID} & \textbf{Utterance} & \textbf{Two-pass Responses} \\
\hline
1 & \multirow{2}{3cm}{I think rachel mcadams had an even better role as regina george however! would you agree?} & i'm not a fan of \underline{\textbf{kristen bell}}, but i think \underline{\textbf{she}} did a great job. \\ \cline{3-3}
& & i'm not a huge fan of \underline{\textbf{rachel mcadams}}, but \underline{\textbf{he}} did a great job. \\
\hline
2 & \multirow{2}{3cm}{yeah, I guess that's always worth it, and a truce was made as well.} & yeah, \underline{\textbf{not only}} does she reconcile with the \underline{\textbf{plastics}}. \\ \cline{3-3}
& & yeah, she reconciles with \underline{\textbf{janis}} , \underline{\textbf{damien}} and \underline{\textbf{aaron}}. \\
\hline
3 & \multirow{2}{3cm}{i liked the scene where buzz thinks he's a big shot hero but then the camera reveals him to be a tiny toy.} & i think that's one of the best scenes in the movie. \\ \cline{3-3}
& & oh, i think that is what makes the movie unique as well. \underline{\textbf{have}} \underline{\textbf{you seen any of the}} \underline{\textbf{other pixar movies}}? \\
\hline
\end{tabular}
}
\caption{Examples of the two pass decoding. Underlined texts are the differences between two results. For each case, the first-pass response is on the top.} \vspace{-10pt}
\label{examples}
\end{table}
\subsection{Case Study}
In this section, we list some examples to show the effectiveness of our proposed model.
Table \ref{Case Study} lists some responses generated by our proposed Incremental Transformer with Deliberation Decoder (ITE+DD) and Wizard Transformer (which achieves overall best performance among baseline models). Our proposed model can generate better responses than Wizard Transformer on knowledge relevance and context coherence.
To demonstrate the effectiveness of the two-pass decoder, we compare the results from the first-pass decoding and the second-pass decoding. Table \ref{examples} shows the improvement after the second-pass decoding. For Case 1, the second-pass decoding result revises the knowledge error in the first-pass decoding result. For Case 2, the second-pass decoder uses more detailed knowledge than the first-pass one. For Case 3, the second-pass decoder cannot only respond to the previous utterance but also guide the following conversations by asking some knowledge related questions.
\section{Related Work}
The closest work to ours lies in the area of open-domain dialogue system incorporating unstructured knowledge.
~\citeauthor{ghazvininejad2018knowledge}~\shortcite{ghazvininejad2018knowledge} uses an extended Encoder-Decoder where the decoder is provided with an encoding of both the context and the external knowledge.
~\citeauthor{parthasarathi2018extending}~\shortcite{parthasarathi2018extending} uses an architecture containing a Bag-of-Words Memory Network fact encoder and an RNN decoder.
~\citeauthor{dinan2018wizard}~\shortcite{dinan2018wizard} combines Memory Network architectures to retrieve, read and condition on knowledge, and Transformer architectures to provide text representation and generate outputs.
Different from these works, we greatly enhance the Transformer architectures to handle the document knowledge in multi-turn dialogue from two aspects: 1) using attention mechanism to combine document knowledge and context utterances; and 2) exploiting incremental encoding scheme to encode multi-turn knowledge aware conversations.
Our work is also inspired by several works in other areas.
~\citeauthor{zhang2018improving}~\shortcite{zhang2018improving} introduces document context into Transformer on document-level Neural Machine Translation (NMT) task.
~\citeauthor{guan2018story}~\shortcite{guan2018story} devises the incremental encoding scheme based on rnn for story ending generation task.
In our work, we design an Incremental Transformer to achieve a knowledge-aware context representation using an incremental encoding scheme.
~\citeauthor{xia2017deliberation}~\shortcite{xia2017deliberation} first proposes Deliberation Network based on rnn on NMT task.
Our Deliberation Decoder is different in two aspects:
1) We clearly devise the two decoders targeting context and knowledge respectively; 2) Our second pass decoder directly fine tunes the first pass result, while theirs uses both the hidden states and results from the first pass.
\section{Conclusion and Future Work}
In this paper, we propose an Incremental Transformer with Deliberation Decoder for the task of Document Grounded Conversations. Through an incremental encoding scheme, the model achieves a knowledge-aware and context-aware conversation representation. By imitating the real-world human cognitive process, we propose a Deliberation Decoder to optimize knowledge relevance and context coherence.
Empirical results show that the proposed model can generate responses with much more relevance, correctness, and coherence compared with the state-of-the-art baselines. In the future, we plan to apply reinforcement learning to further improve the performance.
\section{Acknowledgments}
This work is supported by 2018 Tencent Rhino-Bird Elite Training Program, National Natural Science Foundation of China (NO. 61662077, NO.61876174) and National Key R\&D Program of China (NO.YS2017YFGH001428). We sincerely thank the anonymous reviewers for their thorough reviewing and valuable suggestions.
\section{Introduction}
Past few years have witnessed the rapid development of dialogue systems.
Based on the sequence-to-sequence framework \cite{sutskever2014sequence}, most models are trained in an end-to-end manner with large corpora of human-to-human dialogues and have obtained impressive success \cite{shang2015neural, vinyals2015neural, li2015diversity, serban2016building}.
While there is still a long way for reaching the ultimate goal of dialogue systems, which is to be able to talk like humans.
And one of the essential intelligence to achieve this goal is the ability to make use of knowledge.
There are several works on dialogue systems exploiting knowledge.
The Mem2Seq \cite{madotto2018mem2seq} incorporates structured knowledge into the end-to-end task-oriented dialogue.
~\citeauthor{liu2018knowledge}~\shortcite{liu2018knowledge} introduces fact-matching and knowledge-diffusion to generate meaningful, diverse and natural responses using structured knowledge triplets.
~\citeauthor{ghazvininejad2018knowledge}~\shortcite{ghazvininejad2018knowledge}, ~\citeauthor{parthasarathi2018extending}~\shortcite{parthasarathi2018extending}, ~\citeauthor{yavuzdeepcopy}~\shortcite{yavuzdeepcopy}, ~\citeauthor{dinan2018wizard}~\shortcite{dinan2018wizard} and ~\citeauthor{lo2019knowledge}~\shortcite{lo2019knowledge} apply unstructured text facts in open-domain dialogue systems. These works mainly focus on integrating factoid knowledge into dialogue systems, while factoid knowledge requires a lot of work to build up, and is only limited to expressing precise facts. Documents as a knowledge source provide a wide spectrum of knowledge, including but not limited to factoid, event updates, subjective opinion, etc. Recently, intensive research has been applied on using documents as knowledge sources for Question-Answering \cite{chen2017reading, huang2018flowqa, yu2018qanet, rajpurkar2018know, reddy2018coqa}.
The Document Grounded Conversation is a task to generate natural dialogue responses when chatting about the content of a specific document. This task requires to integrate document knowledge with the multi-turn dialogue history. Different from previous knowledge grounded dialogue systems, Document Grounded Conversations utilize documents as the knowledge source, and hence are able to employ a wide spectrum of knowledge. And the Document Grounded Conversations is also different from document QA since the contextual consistent conversation response should be generated.
To address the Document Grounded Conversation task, it is important to:
1) Exploit document knowledge which are relevant to the conversation;
2) Develop a unified representation combining multi-turn utterances along with the relevant document knowledge.
In this paper, we propose a novel and effective Transformer-based \cite{vaswani2017attention} architecture for Document Grounded Conversations, named Incremental Transformer with Deliberation Decoder. The encoder employs a transformer architecture to incrementally encode multi-turn history utterances, and incorporate document knowledge into the the multi-turn context encoding process. The decoder is a two-pass decoder similar to the Deliberation Network in Neural Machine Translation \cite{xia2017deliberation}, which is designed to improve the context coherence and knowledge correctness of the responses. The first-pass decoder focuses on contextual coherence, while the second-pass decoder refines the result of the first-pass decoder by consulting the relevant document knowledge, and hence increases the knowledge relevance and correctness. This is motivated by human cognition process. In real-world human conversations, people usually first make a draft on how to respond the previous utterance, and then consummate the answer or even raise questions by consulting background knowledge.
We test the effectiveness of our proposed model on Document Grounded Conversations Dataset \cite{zhou2018dataset}. Experiment results show that our model is capable of generating responses of more context coherence and knowledge relevance. Sometimes document knowledge is even well used to guide the following conversations. Both automatic and manual evaluations show that our model substantially outperforms the competitive baselines.
Our contributions are as follows:
\begin{itemize}
\item We build a novel Incremental Transformer to incrementally encode multi-turn utterances with document knowledge together.
\item We are the first to apply a two-pass decoder to generate responses for document grounded conversations. Two decoders focus on context coherence and knowledge correctness respectively.
\end{itemize}
\section{Approach}
\subsection{Problem Statement}
Our goal is to incorporate the relevant document knowledge into multi-turn conversations. Formally, let $\mathbf{U}=\mathbf{u}^{(1)},...,\mathbf{u}^{(k)},...,\mathbf{u}^{(K)}$ be a whole conversation composed of $K$ utterances. We use $\mathbf{u}^{(k)} = u^{(k)}_{1},...,u^{(k)}_{i},...,u^{(k)}_{I}$ to denote the $k$-th utterance containing $I$ words, where $u^{(k)}_{i}$ denotes the $i$-th word in the $k$-th utterance. For each utterance $\mathbf{u}^{(k)}$, likewise, there is a specified relevant document $\mathbf{s}^{(k)} = s^{(k)}_{1},...,s^{(k)}_{j},...,s^{(k)}_{J}$, which represents the document related to the $k$-th utterance containing $J$ words.
We define the document grounded conversations task as generating a response $\mathbf{u}^{(k+1)}$ given its related document $\mathbf{s}^{(k+1)}$ and previous $k$ utterances $\mathbf{U}_{\leq k}$ with related documents $\mathbf{S}_{\leq k}$, where $\mathbf{U}_{\leq k} = \mathbf{u}^{(1)},...,\mathbf{u}^{(k)}$ and $\mathbf{S}_{\leq k} = \mathbf{s}^{(1)},...,\mathbf{s}^{(k)}$. Note that $\mathbf{s}^{(k)}, \mathbf{s}^{(k+1)},...,\mathbf{s}^{(k+n)}$ may be the same.
Therefore, the probability to generate the response $\mathbf{u}^{(k+1)}$ is computed as:
\begin{equation}
\begin{array}{ll}
& P(\mathbf{u}^{(k+1)}|\mathbf{U}_{\leq k}, \mathbf{S}_{\leq k+1}; \theta) \\
& =\prod_{i=1}^{I} P(u^{k+1}_{i}|\mathbf{U}_{\leq k}, \mathbf{S}_{\leq k+1}, u^{(k+1)}_{<i};\theta)
\end{array}
\end{equation}
where $u_{< i}^{(k+1)} = u_{1}^{(k+1)},...,u_{i-1}^{(k+1)}$.
\subsection{Model Description}
\begin{figure}[t]
\centering
\small
\includegraphics[width=0.48\textwidth]{ACL2019-figure3.pdf}
\caption{The framework of Incremental Transformer with Deliberation Decoder for Document Grounded Conversations. } \vspace{-10pt}
\centering
\label{model architecture}
\end{figure}
\begin{figure*}[t]
\centering
\includegraphics[width=0.98\textwidth]{ACL2019-figure2.pdf}
\caption{(1) Detailed architecture of model components. (a) The Self-Attentive Encoder(SA). (b) Incremental Transformer (ITE). (c) Deliberation Decoder (DD). (2) Simplified version of our proposed model used to verify the validity of our proposed Incremental Transformer Encoder and Deliberation Decoder. (d) Knowledge-Attention Transformer(KAT). (e) Context-Knowledge-Attention Decoder (CKAD).} \vspace{-10pt}
\centering
\label{model modules}
\end{figure*}
Figure \ref{model architecture} shows the framework of the proposed Incremental Transformer with Deliberation Decoder. Please refer to Figure \ref{model modules} (1) for more details. It consists of three components:
1) Self-Attentive Encoder (SA) (in orange) is a transformer encoder as described in \cite{vaswani2017attention}, which encodes the document knowledge and the current utterance independently.
2) Incremental Transformer Encoder (ITE) (on the top) is a unified transformer encoder which encodes multi-turn utterances with knowledge representation using an incremental encoding scheme. This module takes previous utterances $\mathbf{u}^{(i)}$ and the document $\mathbf{s}^{(i)}$'s SA representation as input, and use attention mechanism to incrementally build up the representation of relevant context and document knowledge.
3) Deliberation Decoder (DD) (on the bottom) is a two-pass unified transformer decoder for better generating the next response. The first-pass decoder takes current utterance $\mathbf{u}^{(k)}$'s SA representation and ITE output as input, and mainly relies on conversation context for response generation. The second-pass decoder takes the SA representation of the first pass result and the relevant document $\mathbf{s}^{(k+1)}$'s SA representation as input, and uses document knowledge to further refine the response.
\subsubsection*{Self-Attentive Encoder}
As document knowledge often includes several sentences, it's important to capture long-range dependencies and identify relevant information.
We use multi-head self-attention \cite{vaswani2017attention} to compute the representation of document knowledge.
As shown in Figure \ref{model modules} (a), we use a self-attentive encoder to compute the representation of the related document knowledge $\mathbf{s}^{(k)}$. The input ($\mathbf{In}_{s}^{(k)}$) of the encoder is a sequence of document words embedding with positional encoding added.\cite{vaswani2017attention}:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{In}_{s}^{(k)} = [\mathbf{s}^{(k)}_{1},...,\mathbf{s}^{(k)}_{J}]
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{s}^{(k)}_{j} = \mathbf{e}_{s_{j}} + {\rm PE}(j)
\end{equation}
where $\mathbf{e}_{s_{j}}$ is the word embedding of $s_{j}^{(k)}$ and ${\rm PE}(\cdot)$ denotes positional encoding function.
The Self-Attentive encoder contains a stack of $N_{x}$ identical layers. Each layer has two sub-layers. The first sub-layer is a multi-head self-attention ($\rm MultiHead$) \cite{vaswani2017attention}. ${\rm MultiHead}(\mathbf{Q}, \mathbf{K}, \mathbf{V})$ is a multi-head attention function that takes a query matrix $\mathbf{Q}$, a key matrix $\mathbf{K}$, and a value matrix $\mathbf{V}$ as input. In current case, $\mathbf{Q}$ = $\mathbf{K}$ = $\mathbf{V}$. That's why it's called self-attention. And the second sub-layer is a simple, position-wise fully connected feed-forward network ($\rm FFN$). This $\rm FFN$ consists of two linear transformations with a ReLU activation in between. \cite{vaswani2017attention}.
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{A}^{(1)} = {\rm MultiHead}(\mathbf{In}_{s}^{(k)},\mathbf{In}_{s}^{(k)},\mathbf{In}_{s}^{(k)})
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{D}^{(1)} = {\rm FFN}(\mathbf{A}^{(1)})
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
{\rm FFN}(x) = \max (0, xW_{1}+b_{1})W_{2} + b_{2}
\end{equation}
where $\mathbf{A}^{(1)}$ is the hidden state computed by multi-head attention at the first layer, $\mathbf{D}^{(1)}$ denotes the representation of $\mathbf{s}^{(k)}$ after the first layer. Note that residual connection and layer normalization are used in each sub-layer, which are omitted in the presentation for simplicity. Please refer to \cite{vaswani2017attention} for more details.
For each layer, repeat this process:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{A}^{(n)} = {\rm MultiHead}(\mathbf{D}^{(n-1)},\mathbf{D}^{(n-1)},\mathbf{D}^{(n-1)})
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{D}^{(n)} = {\rm FFN}(\mathbf{A}^{(n)})
\end{equation}
where $n=1,...,N_{s}$ and $\mathbf{D}^{(0)} = \mathbf{In}_{s}^{(k)}$.
We use ${\rm SA}_{s}(\cdot)$ to denote this whole process:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{d}^{(k)} = \mathbf{D}^{(N_{x})} = {\rm SA}_{s}(\mathbf{s}^{(k)})
\end{equation}
where $\mathbf{d}^{(k)}$ is the final representation for the document knowledge $\mathbf{s}^{(k)}$.
Similarly, for each utterance $\mathbf{u}^{(k)}$, we use ${\mathbf{In}}_{u}^{(k)} = [\mathbf{u}^{(k)}_{1},...,\mathbf{u}^{(k)}_{I}]$ to represent the sequence of the position-aware word embedding. Then the same Self-Attentive Encoder is used to compute the representation of current utterance $\mathbf{u}^{(k)}$, and we use ${\rm SA}_{u}(\mathbf{u}^{(k)})$ to denote this encoding result. The Self-Attentive Encoder is also used to encode the document ${\mathbf{s}}^{(k+1)}$ and the first pass decoding results in the second pass of the decoder. Note that ${\rm SA}_{s}$ and ${\rm SA}_{u}$ have the same architecture but different parameters. More details about this will be mentioned in the following sections.
\subsubsection*{Incremental Transformer Encoder}
To encode multi-turn document grounded utterances effectively, we design an Incremental Transformer Encoder.
Incremental Transformer uses multi-head attention to incorporate document knowledge and context into the current utterance's encoding process.
This process can be stated recursively as follows:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{c}^{(k)} = {\rm ITE}(\mathbf{c}^{(k-1)}, \mathbf{d}^{(k)}, \mathbf{In}_{u}^{(k)})
\end{equation}
where ${\rm ITE}(\cdot)$ denotes the encoding function, $\mathbf{c}^{(k)}$ denotes the context state after encoding utterance $\mathbf{u}^{(k)}$, $\mathbf{c}^{(k-1)}$ is the context state after encoding last utterance $\mathbf{u}^{(k-1)}$, $\mathbf{d}^{(k)}$ is the representation of document $\mathbf{s}^{(k)}$ and $\mathbf{In}_{u}^{(k)}$ is the embedding of current utterance $\mathbf{u}^{(k)}$.
As shown in Figure \ref{model modules} (b), we use a stack of $N_{u}$ identical layers to encode $\mathbf{u}^{(k)}$. Each layer consists of four sub-layers.
The first sub-layer is a multi-head self-attention:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{B}^{(n)} = {\rm MultiHead}(\mathbf{C}^{(n-1)}, \mathbf{C}^{(n-1)}, \mathbf{C}^{(n-1)})
\end{equation}
where $n = 1,...,N_{u}$, $\mathbf{C}^{(n-1)}$ is the output of the last layer and $\mathbf{C}^{(0)} = \mathbf{In}_{u}^{(k)}$. The second sub-layer is a multi-head knowledge attention:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{E}^{(n)} = {\rm MultiHead}(\mathbf{B}^{(n)}, \mathbf{d}^{(k)}, \mathbf{d}^{(k)})
\end{equation}
The third sub-layer is a multi-head context attention:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{F}^{(n)} = {\rm MultiHead}(\mathbf{E}^{(n)}, \mathbf{c}^{(k-1)}, \mathbf{c}^{(k-1)})
\end{equation}
where $\mathbf{c}^{(k-1)}$ is the representation of the previous utterances. That's why we called the encoder "Incremental Transformer". The fourth sub-layer is a position-wise fully connected feed-forward network:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{C}^{(n)} = {\rm FFN}(\mathbf{F}^{(n)})
\end{equation}
We use $\mathbf{c}^{(k)}$ to denote the final representation at $N_{u}$-th layer:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{c}^{(k)} = \mathbf{C}^{(N_{u})}
\end{equation}
\subsubsection*{Deliberation Decoder}
Motivated by the real-world human cognitive process, we design a Deliberation Decoder containing two decoding passes to improve the knowledge relevance and context coherence. The first-pass decoder takes the representation of current utterance ${\rm SA}_{u}(\mathbf{\mathbf{u}^{(k)}})$ and context $\mathbf{c}^{(k)}$ as input and focuses on how to generate responses contextual coherently. The second-pass decoder takes the representation of the first-pass decoding results and related document $\mathbf{s}^{(k+1)}$ as input and focuses on increasing knowledge usage and guiding the following conversations within the scope of the given document.
When generating the $i$-th response word ${u}^{(k+1)}_{i}$, we have the generated words $\mathbf{u}^{(k+1)}_{<i}$ as input \cite{vaswani2017attention}. We use $\mathbf{In}_{r}^{(k+1)}$ to denote the matrix representation of $\mathbf{u}^{(k+1)}_{<i}$ as following:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{In}_{r}^{(k+1)} = [\mathbf{u}^{(k+1)}_{0}, \mathbf{u}^{(k+1)}_{1},...,\mathbf{u}^{(k+1)}_{i-1}]
\end{equation}
where $\mathbf{u}^{(k+1)}_{0}$ is the vector representation of sentence-start token.
As shown in Figure \ref{model modules} (c), the Deliberation Decoder consists of a first-pass decoder and a second-pass decoder. These two decoders have the same architecture but different input for sub-layers. Both decoders are composed of a stack of $N_{y}$ identical layers. Each layer has four sub-layers.
For the first-pass decoder, the first sub-layer is a multi-head self-attention:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{G}^{(n)}_{1} = {\rm MultiHead}(\mathbf{R}^{(n-1)}_{1}, \mathbf{R}^{(n-1)}_{1}, \mathbf{R}^{(n-1)}_{1})
\end{equation}
where $n = 1,...,N_{y}$, $\mathbf{R}^{(n-1)}_{1}$ is the output of the previous layer, and $\mathbf{R}^{(0)}_{1} = \mathbf{In}_{r}^{(k+1)}$. The second sub-layer is a multi-head context attention:
\begin{equation} \label{eq18}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{H}^{(n)}_{1} = {\rm MultiHead}(\mathbf{G}^{(n)}_{1}, \mathbf{c}^{(k)}, \mathbf{c}^{(k)})
\end{equation}
where $\mathbf{c}^{(k)}$ is the representation of context $\mathbf{u}_{\leq k}$. The third sub-layer is a multi-head utterance attention:
\begin{equation} \label{eq19}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\begin{array}{cc}
\mathbf{M}^{(n)}_{1} = {\rm MultiHead}(\mathbf{H}^{(n)}_{1}, & {\rm SA}_{u}(\mathbf{u}^{(k)}), \\
& {\rm SA}_{u}(\mathbf{u}^{(k)}))
\end{array}
\end{equation}
where $SA_{u}(\cdot)$ is a Self-Attentive Encoder which encodes latest utterance $\mathbf{u}^{(k)}$. Eq. (\ref{eq18}) mainly encodes the context and document knowledge relevant to the latest utterance, while Eq. (\ref{eq19}) encodes the latest utterance directly. We hope optimal performance can be achieved by combining both.
The fourth sub-layer is a position-wise fully connected feed-forward network:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{R}^{(n)}_{1} = {\rm FFN}(\mathbf{M}^{(n)}_{1})
\end{equation}
After $N_{y}$ layers, we use softmax to get the words probabilities decoded by first-pass decoder:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
P(\mathbf{\hat{u}}^{(k+1)}_{(1)})= {\rm softmax}(\mathbf{R}^{(N_{y})}_{1})
\end{equation}
where $\mathbf{\hat{u}}^{(k+1)}_{(1)}$ is the response decoded by the first-pass decoder.
For second-pass decoder:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{G}^{(n)}_{2} = {\rm MultiHead}(\mathbf{R}^{(n-1)}_{2}, \mathbf{R}^{(n-1)}_{2}, \mathbf{R}^{(n-1)}_{2})
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{H}^{(n)}_{2} = {\rm MultiHead}(\mathbf{G}^{(n)}_{2}, \mathbf{d}^{(k+1)}, \mathbf{d}^{(k+1)})
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\begin{array}{cc}
\mathbf{M}^{(n)}_{2} = {\rm MultiHead}(\mathbf{H}^{(n)}_{2}, & {\rm SA}_{u}(\mathbf{\hat{u}}^{(k+1)}_{(1)}), \\
& {\rm SA}_{u}(\mathbf{\hat{u}}^{(k+1)}_{(1)}))
\end{array}
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
\mathbf{R}^{(n)}_{2} = {\rm FFN}(\mathbf{M}^{(n)}_{2})
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
P(\mathbf{\hat{u}}^{(k+1)}_{(2)}) = {\rm softmax}(\mathbf{R}^{(N_{y})}_{2})
\end{equation}
where $\mathbf{R}^{(n-1)}_{2}$ is the counterpart to $\mathbf{R}^{(n-1)}_{1}$ in pass two decoder, referring to the output of the previous layer. $\mathbf{d}^{(k+1)}$ is the representation of document $\mathbf{s}^{(k+1)}$ using Self-Attentive Encoder, $\mathbf{\hat{u}}^{(k+1)}_{(2)}$ is the output words after the second-pass decoder.
\subsubsection*{Training}
In contrast to the original Deliberation Network \cite{xia2017deliberation}, where they propose a complex joint learning framework using Monte Carlo Method,
we minimize the following loss as ~\citeauthor{xiong2018modeling}~\shortcite{xiong2018modeling} do:
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
L_{mle} = L_{mle1} + L_{mle2}
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
L_{mle1} = - \sum_{k=1}^{K}\sum_{i=1}^{I}\log P(\mathbf{\hat{u}}^{(k+1)}_{(1)i})
\end{equation}
\begin{equation}
\setlength{\abovedisplayskip}{4pt}
\setlength{\belowdisplayskip}{4pt}
L_{mle2} = - \sum_{k=1}^{K}\sum_{i=1}^{I}\log P(\mathbf{\hat{u}}^{(k+1)}_{(2)i})
\end{equation}
\section{Experiments}
\subsection{Dataset}
We evaluate our model using the Document Grounded Conversations Dataset \cite{zhou2018dataset}. There are 72922 utterances for training, 3626 utterances for validation and 11577 utterances for testing. The utterances can be either casual chats or document grounded. Note that we consider consequent utterances of the same person as one utterance. For example, we consider \textit{A: Hello! B: Hi! B: How's it going?} as \textit{A: Hello! B: Hi! How's it going?}.
And there is a related document given for every several consequent utterances, which may contain movie name, casts, introduction, ratings, and some scenes. The average length of documents is about 200.
Please refer to \cite{zhou2018dataset} for more details.
\begin{table*}[!t]
\centering
\scalebox{0.95} {
\begin{tabular}{lccccc}
& & & & Knowledge & Context \\
Model & PPL & BLEU(\%) & Fluency & Relevance & Coherence\\
\hline
Seq2Seq without knowledge & 80.93 & 0.38 & 1.62 & 0.18 & 0.54\\
HRED without knowledge & 80.84 & 0.43 & 1.25 & 0.18 & 0.30\\
Transformer without knowledge & 87.32 & 0.36 & 1.60 & 0.29 & 0.67\\
Seq2Seq (+knowledge) & 78.47 & 0.39 & 1.50 & 0.22 & 0.61\\
HRED (+knowledge) & 79.12 & 0.77 & 1.56 & 0.35 & 0.47\\
Wizard Transformer & 70.30 & 0.66 & 1.62 & 0.47 & 0.56\\
\hline
\textbf{ITE+DD} (ours) & \textbf{15.11} & \textbf{0.95} & 1.67 & \textbf{0.56} & \textbf{0.90}\\
\textbf{ITE+CKAD} (ours) & 64.97 & 0.86 & \textbf{1.68} & 0.50 & 0.82\\
\textbf{KAT} (ours) & 65.36 & 0.58 & 1.58 & 0.33 & 0.78\\
\hline
\end{tabular}
}
\caption{Automatic evaluation and manual evaluation results for baselines and our proposed models.} \vspace{-10pt}
\label{Automatic Evaluation and Munual Evaluation}
\end{table*}
\subsection{Baselines}
We compare our proposed model with the following state-of-the-art baselines:\\
\textbf{Models not using document knowledge}:
\textbf{Seq2Seq}: A simple encoder-decoder model \cite{shang2015neural, vinyals2015neural} with global attention \cite{luong2015effective}. We concatenate utterances context to a long sentence as input.
\textbf{HRED}: A hierarchical encoder-decoder model \cite{serban2016building}, which is composed of a word-level LSTM for each sentence and a sentence-level LSTM connecting utterances.
\textbf{Transformer}: The state-of-the-art NMT model based on multi-head attention \cite{vaswani2017attention}. We concatenate utterances context to a long sentence as its input. \\
\textbf{Models using document knowledge}:
\textbf{Seq2Seq (+knowledge)} and \textbf{HRED (+knowledge)} are based on Seq2Seq and HRED respectively. They both concatenate document knowledge representation and last decoding output embedding as input when decoding. Please refer to \cite{zhou2018dataset} for more details.
\textbf{Wizard Transformer}: A Transformer-based model for multi-turn open-domain dialogue with unstructured text facts \cite{dinan2018wizard}. It concatenates context utterances and text facts to a long sequence as input. We replace the text facts with document knowledge.
Here, we also conduct an ablation study to illustrate the validity of our proposed Incremental Transformer Encoder and Deliberation Decoder.
\textbf{ITE+CKAD}: It uses Incremental Transformer Encoder (ITE) as encoder and Context-Knowledge-Attention Decoder (CKAD) as shown in Figure \ref{model modules} (e). This setup is to test the validity of the deliberation decoder.
\textbf{Knowledge-Attention Transformer (KAT)}: As shown in Figure \ref{model modules} (d), the encoder of this model is a simplified version of Incremental Transformer Encoder (ITE), which doesn't have context-attention sub-layer. We concatenate utterances context to a long sentence as its input. The decoder of the model is a simplified Context-Knowledge-Attention Decoder (CKAD). It doesn't have context-attention sub-layer either. This setup is to test how effective the context has been exploited in the full model.
\begin{table}[t]
\centering
\scalebox{0.95} {
\begin{tabular}{|c|c|c|}
\hline
& Knowledge & Context \\
Model & Relevance(\%) & Coherence(\%)\\ \hline
Wizard & 64/25/11 & 58/28/14\\
\hline
\textbf{ITE+CKAD} & 67/16/17 & 40/37/23 \\ \hline
\textbf{ITE+DD} & 64/16/20 & 38/34/28 \\ \hline
\end{tabular}
}
\caption{The percent(\%) of score (0/1/2) of Knowledge Relevance and Context Coherence for Wizard Transformer, ITE+CKAD and ITE+DD.} \vspace{-10pt}
\label{Score Distribution}
\end{table}
\subsection{Experiment Setup}
We use OpenNMT-py\footnote{\url{https://github.com/OpenNMT/OpenNMT-py}} \cite{opennmt} as the code framework\footnote{The code and models are available at \url{https://github.com/lizekang/ITDD}}. For all models, the hidden size is set to 512. For rnn-based models (Seq2Seq, HRED), 3-layer bidirectional LSTM \cite{hochreiter1997long} and 1-layer LSTM is applied for encoder and decoder respectively. For transformer-based models, the layers of both encoder and decoder are set to 3. The number of attention heads in multi-head attention is 8 and the filter size is 2048. The word embedding is shared by utterances, knowledge and generated responses. The dimension of word embedding is set to 512 empirically. We use Adam \cite{kingma2014adam} for optimization. When decoding, beam size is set to 5. We use the previous three utterances and its related documents as input.
\begin{table*}[!t]
\centering
\scalebox{0.95} {
\begin{tabular}{|rp{13cm}|}
\hline
\multicolumn{2}{|p{15cm}|}{\textbf{Document}} \\ \hline
\multicolumn{2}{|p{15cm}|}{moviename \underline{\textbf{despicable me}} ... \underline{\textbf{cast: steve carell as gru}} ... \underline{\textbf{rotten tomatoes: 81\%}} ... it is the debut film of \underline{\textbf{illumination entertainment}}. ... gru, a \underline{\textbf{supervillain}}, is disheartened when an unknown supervillain steals the great pyramid of giza. gru, with the assistance of his colleague dr. Nefario and his \underline{\textbf{minions}}, resolves to one-up this mystery rival by shrinking and stealing the moon. as it would be costly to steal the moon, \underline{\textbf{gru seeks a loan from the bank of evil}}. ... upon learning that an up-and-coming \underline{\textbf{villain}} named vector was responsible for the pyramid theft ...} \\
\hline
\textbf{Utterance 1} & what do you think about \underline{\textbf{despicable me}}? \\
\hline
\textbf{ITE+DD} & i think it is an awesome movie, \underline{\textbf{what about you?}} \\
\textbf{Wizard} & i think it's a great movie! \\
\hline
\textbf{Utterance 2} & i rather liked it. it wasn't what i was expecting but it was still good. \\
\hline
\textbf{ITE+DD} & yeah, \underline{\textbf{it makes me laugh}}, even when they make a movie about it. \\
\textbf{Wizard} & it's a great movie for kids and adults. \\
\hline
\textbf{Utterance 3} & i like it too. \underline{\textbf{funny and heart warming at the same time}}. \\
\hline
\textbf{ITE+DD} & i think it's interesting that \underline{\textbf{gru decided to take a loan from the bank of evil}}. \\
\textbf{Wizard} & i think they should have made a sequel. \\
\hline
\textbf{Utterance 4} & \underline{\textbf{gru was a really interesting character}}, too. \underline{\textbf{i liked steve carell and the voice he}} \underline{\textbf{used for gru}}. \\
\hline
\textbf{ITE+DD} & yeah, now that you mention it, what did you think of the \underline{\textbf{minions}}? \\
\textbf{Wizard} & i think the entire cast was great. \\
\hline
\textbf{Utterance 5} & yes, he did an excellent job portraying the character. \underline{\textbf{81\% in ratings}} i think is great. \\
\hline
\textbf{ITE+DD} & yes, \underline{\textbf{81\%}} is a great score! \\
\textbf{Wizard} & i also liked the \underline{\textbf{villain}} of the movie. \\
\hline
\end{tabular}
}
\caption{Responses generated by Incremental Transformer with Deliberation Decoder(\textbf{ITE+DD}) and the Wizard Transformer(\textbf{Wizard}). These utterances are from continuous dialogues. \textbf{ITE+DD} and \textbf{Wizard} generate responses using context utterances and a given document. Note that \textbf{Utterance $i+1$} is the gold response of \textbf{Utterance $i$}.} \vspace{-10pt}
\label{Case Study}
\end{table*}
\subsection{Evaluation Metrics}
\textbf{Automatic Evaluation}:
We adopt perplexity (PPL) and BLEU \cite{Papineni02bleu:a} to automatically evaluate the response generation performance.
Models are evaluated using perplexity of the gold response as described in \cite{dinan2018wizard}. Lower perplexity indicates better performance.
BLEU measures n-gram overlap between a generated response and a gold response. However, since there is only one reference for each response and there may exist multiple feasible responses, BLEU scores are extremely low. We compute BLEU score by the \emph{multi-bleu.perl}\footnote{\url{https://github.com/google/seq2seq/blob/master/bin/tools/multi-bleu.perl}} \\
\textbf{Manual Evaluation}:
Manual evaluations are essential for dialogue generation. We randomly sampled 30 conversations containing 606 utterances from the test set and obtained 5454 utterances from the nine models. We have annotators score these utterances given its previous utterances and related documents.
We defined three metrics - \textbf{fluency}, \textbf{knowledge relevance} \cite{liu2018knowledge} and \textbf{context coherence} for manual evaluation. All these metrics are scored 0/1/2.
\textbf{fluency}: Whether the response is natural and fluent. Score 0 represents not fluent and incomprehensible; 1 represents partially fluent but still comprehensible; 2 represents totally fluent.
\textbf{knowledge relevance}: Whether the response uses relevant and correct knowledge. Score 0 represents no relevant knowledge; 1 represents containing relevant knowledge but not correct; 2 represents containing relevant knowledge and correct.
\textbf{context coherence}: Whether the response is coherent with the context and guides the following utterances. Score 0 represents not coherent or leading the dialogue to an end; 1 represents coherent with the utterance history but not guiding the following utterances; 2 represents coherent with utterance history and guiding the next utterance.
\subsection{Experimental Results}
Table \ref{Automatic Evaluation and Munual Evaluation} shows the automatic and manual evaluation results for both the baseline and our models.
In manual evaluation, among baselines, Wizard Transformer and RNN without knowledge have the highest fluency of 1.62 and Wizard obtains the highest knowledge relevance of 0.47 while Transformer without knowledge gets the highest context coherence of 0.67. For all models, ITE+CKAD obtains the highest fluency of 1.68 and ITE+DD has the highest Knowledge Relevance of 0.56 and highest Context Coherence of 0.90.
In automatic evaluation, our proposed model has lower perplexity and higher BLEU scores than baselines. For BLEU, HRED with knowledge obtains the highest BLEU score of 0.77 among the baselines. And ITE+DD gets 0.95 BLEU score, which is the highest among all the models. For perplexity, Wizard Transformer obtains the lowest perplexity of 70.30 among baseline models and ITE+DD has remarkably lower perplexity of 15.11 than all the other models. A detailed analysis is in Section \ref{Analysis}.
\subsection{Analysis and Discussion} \label{Analysis}
To our surprise, ITE+DD reaches an extremely low ground truth perplexity. We find that the ground truth perplexity after the first-pass decoding is only similar to the ITE+CKAD. It shows that the second-pass decoder utilizes the document knowledge well, and dramatically reduced the ground truth perplexity.
As shown in Table \ref{Score Distribution}, ITE+DD has a higher percent of score 2 both on Knowledge Relevance and Context Coherence than ITE+CKAD. This result also demonstrates that Deliberation Decoder can improve the knowledge correctness and guide the following conversations better.
Although the perplexity of ITE+CKAD is only slightly better than KAT, the BLEU score, Fluency, Knowledge Relevance and Context Coherence of ITE+CKAD all significantly outperform those of KAT model, which indicates that Incremental Transformer can deal with multi-turn document grounded conversations better.
Wizard Transformer has a great performance on Knowledge Relevance only second to our proposed Incremental Transformer. However, its score on Context Coherence is lower than some other baselines. As shown in Table \ref{Score Distribution}, Wizard Transformer has Knowledge Relevance score 1 results twice more than score 2 results, which indicates that the model tends to generate responses with related knowledge but not correct. And the poor performance on Context Coherence also shows Wizard Transformer does not respond to the previous utterance well. This shows the limitation of representing context and document knowledge by simple concatenation.
\begin{table}[t]
\small
\centering
\scalebox{0.95} {
\begin{tabular}{|c|p{3cm}|p{3cm}|}
\hline
\textbf{ID} & \textbf{Utterance} & \textbf{Two-pass Responses} \\
\hline
1 & \multirow{2}{3cm}{I think rachel mcadams had an even better role as regina george however! would you agree?} & i'm not a fan of \underline{\textbf{kristen bell}}, but i think \underline{\textbf{she}} did a great job. \\ \cline{3-3}
& & i'm not a huge fan of \underline{\textbf{rachel mcadams}}, but \underline{\textbf{he}} did a great job. \\
\hline
2 & \multirow{2}{3cm}{yeah, I guess that's always worth it, and a truce was made as well.} & yeah, \underline{\textbf{not only}} does she reconcile with the \underline{\textbf{plastics}}. \\ \cline{3-3}
& & yeah, she reconciles with \underline{\textbf{janis}} , \underline{\textbf{damien}} and \underline{\textbf{aaron}}. \\
\hline
3 & \multirow{2}{3cm}{i liked the scene where buzz thinks he's a big shot hero but then the camera reveals him to be a tiny toy.} & i think that's one of the best scenes in the movie. \\ \cline{3-3}
& & oh, i think that is what makes the movie unique as well. \underline{\textbf{have}} \underline{\textbf{you seen any of the}} \underline{\textbf{other pixar movies}}? \\
\hline
\end{tabular}
}
\caption{Examples of the two pass decoding. Underlined texts are the differences between two results. For each case, the first-pass response is on the top.} \vspace{-10pt}
\label{examples}
\end{table}
\subsection{Case Study}
In this section, we list some examples to show the effectiveness of our proposed model.
Table \ref{Case Study} lists some responses generated by our proposed Incremental Transformer with Deliberation Decoder (ITE+DD) and Wizard Transformer (which achieves overall best performance among baseline models). Our proposed model can generate better responses than Wizard Transformer on knowledge relevance and context coherence.
To demonstrate the effectiveness of the two-pass decoder, we compare the results from the first-pass decoding and the second-pass decoding. Table \ref{examples} shows the improvement after the second-pass decoding. For Case 1, the second-pass decoding result revises the knowledge error in the first-pass decoding result. For Case 2, the second-pass decoder uses more detailed knowledge than the first-pass one. For Case 3, the second-pass decoder cannot only respond to the previous utterance but also guide the following conversations by asking some knowledge related questions.
\section{Related Work}
The closest work to ours lies in the area of open-domain dialogue system incorporating unstructured knowledge.
~\citeauthor{ghazvininejad2018knowledge}~\shortcite{ghazvininejad2018knowledge} uses an extended Encoder-Decoder where the decoder is provided with an encoding of both the context and the external knowledge.
~\citeauthor{parthasarathi2018extending}~\shortcite{parthasarathi2018extending} uses an architecture containing a Bag-of-Words Memory Network fact encoder and an RNN decoder.
~\citeauthor{dinan2018wizard}~\shortcite{dinan2018wizard} combines Memory Network architectures to retrieve, read and condition on knowledge, and Transformer architectures to provide text representation and generate outputs.
Different from these works, we greatly enhance the Transformer architectures to handle the document knowledge in multi-turn dialogue from two aspects: 1) using attention mechanism to combine document knowledge and context utterances; and 2) exploiting incremental encoding scheme to encode multi-turn knowledge aware conversations.
Our work is also inspired by several works in other areas.
~\citeauthor{zhang2018improving}~\shortcite{zhang2018improving} introduces document context into Transformer on document-level Neural Machine Translation (NMT) task.
~\citeauthor{guan2018story}~\shortcite{guan2018story} devises the incremental encoding scheme based on rnn for story ending generation task.
In our work, we design an Incremental Transformer to achieve a knowledge-aware context representation using an incremental encoding scheme.
~\citeauthor{xia2017deliberation}~\shortcite{xia2017deliberation} first proposes Deliberation Network based on rnn on NMT task.
Our Deliberation Decoder is different in two aspects:
1) We clearly devise the two decoders targeting context and knowledge respectively; 2) Our second pass decoder directly fine tunes the first pass result, while theirs uses both the hidden states and results from the first pass.
\section{Conclusion and Future Work}
In this paper, we propose an Incremental Transformer with Deliberation Decoder for the task of Document Grounded Conversations. Through an incremental encoding scheme, the model achieves a knowledge-aware and context-aware conversation representation. By imitating the real-world human cognitive process, we propose a Deliberation Decoder to optimize knowledge relevance and context coherence.
Empirical results show that the proposed model can generate responses with much more relevance, correctness, and coherence compared with the state-of-the-art baselines. In the future, we plan to apply reinforcement learning to further improve the performance.
\section{Acknowledgments}
This work is supported by 2018 Tencent Rhino-Bird Elite Training Program, National Natural Science Foundation of China (NO. 61662077, NO.61876174) and National Key R\&D Program of China (NO.YS2017YFGH001428). We sincerely thank the anonymous reviewers for their thorough reviewing and valuable suggestions.
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Airborne respiratory droplets spread the novel coronavirus. Such a spread, however, does not depend on the intensity of coughing.
A mathematical model, developed by researchers from the Indian Institute of Technology in Mumbai shows that a cough cloud slowly traps ambient air as it spreads out after ejection from the mouth of an infected person1.
With time, the droplet concentration inside the cloud reduces significantly. Since the virus requires liquid droplets to survive, the possibility of its spread declines, the researchers explain.
The findings of this research will help devise ways to reduce the chances of infection in a closed space, they say.
The IIT scientists used the mathematical model to study a cough cloud's spread through most air in an enclosed space without any airflow.
They found that the front of the cough cloud covers the first two metres of its total distance from the source within two seconds of being ejected. Hence, the cloud has the maximum probability of spreading the viral liquid immediately after release.
The analysis suggests that the first five to eight seconds after the commencement of the cough event are crucial for suspending the exhaled droplets in air, and the infected air volume without a mask is around 23 times more than that exhaled during normal coughing.
A mask drastically reduces this volume, considerably cutting down the risk of spreading the infection to other persons in a room. N95 masks, the researchers say, perform much better than surgical masks, decreasing it by as much as 23 times.
1. Agrawal, A. et al. Reducing chances of COVID-19 infection by a cough cloud in a closed space. Phys. Fluids. 32, 101704 (2020)
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El North American Building es un edificio histórico de gran altura. Cuenta con 21 pisos y se eleva 81 m sobre la calle, y está situado en el 121 de South Broad Street, en Filadelfia, Pensilvania. Fue diseñado por el arquitecto de Filadelfia James H. Windrim (1840-1919) como la sede del periódico The North American y encargado por Thomas B. Wanamaker, editor del periódico e hijo de John Wanamaker, el fundador de los grandes almacenes.
Véase también
Anexo:Edificios más altos de Filadelfia
Primeros rascacielos
Referencias
Enlaces externos
"A Brief History of the Illuminated Buildings Along the Avenue of the Arts", by Fatima Adamu, Project Coordinator, Center City District.
Listing and photographs en Philadelphia Architects and Buildings
Arquitectura de Estados Unidos de 1900
Rascacielos de oficinas de Filadelfia
Rascacielos inaugurados en los años 1900
Edificios de oficinas de Estados Unidos del siglo XX
Escuela de Chicago (arquitectura)
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Anskar-Kirche är ett evangelikalt och karismatiskt kristet trossamfund i Tyskland, grundat av den lutherske prästen Wolfram Kopfermann.
Kopfermann hade under sin tid som präst i St. Peterskyrkan, Hamburg berörts av den karismatiska väckelsen inom Tysklands evangeliska kyrka och grundade 1978 Geistlichen Gemeindeerneuerung (GGE), en förnyelserörelse som påminner om den svenska Oasrörelsen.
Så småningom upplevde han att det blev för trångt att verka inom den evangeliska kyrkan och grundade 1988 Ansgar-kyrkan i Hamburg, uppkallad efter Nordens apostel och Hamburgs förste ärkebiskop. Kopfermann hänvisade till att Ansgar i sin tjänst bejakade och använde sig av andliga gåvor som omnämns i Nya testamentet, bland annat helandegåvan, och att han vägleddes av andliga uppenbarelser och visioner, att han uppvisade andligt mod och ivrade för mission. Något som man även önskade skulle känneteckna den nya kyrkan.
Inledningsvis kallade sig den nya kyrkan fortsatt för luthersk men efterhand kom man att anamma en baptistisk dopsyn.
Idag består kyrkan av sex församlingar och fler församlingsplanteringar planeras. Den scoutliknande barn- och ungdomsverksamheten är en del av internationella Royal Rangers.
I samband med kyrkans 25-årsjubileum 2013 avgick den då 75-årige grundaren Wolfram Kopfermann och överlämnade ledarskapet för Anskar-Kirche till teologen Tillmann Krüger.
Ekumenik
Anskar-Kirche är ekumeniskt sinnad och tillhör Vereinigung Evangelischer Freikirchen och Arbeitsgemeinschaft Christlicher Kirchens (ACK) regionala råd i Hessen-Rheinhessen. Tillmann Krüger är engagerad i tyska Evangeliska alliansen och ingår i ledningen för dennas arbetsgrupp för evangelikal teologi.
Källor
Anskar-Kirche Officiell hemsida
Protestantiska samfund i Tyskland
de:Vereinigung Evangelischer Freikirchen
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| 4,808
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{"url":"https:\/\/math.stackexchange.com\/questions\/671738\/bound-on-number-of-iterations-for-fixed-point-method","text":"# Bound on Number of Iterations for Fixed Point Method\n\nGiven the fixed point iteration\n\n$$p_n = \\frac{p_{n - 1}^2 + 3}{5},$$\n\nwhich converges for any initial $p_0 \\in [0, 1]$, estimate how many iterations $n$ are required to obtain an absolute error $\\left| p_n - p \\right|$ less than $10^{-4}$ when $p_0 = 1$. No numerical value needed, just give an expression for $n$.\n\nI know that the bound is given by\n\n$$\\left| p_n - p \\right| \\leq k^n\\mbox{max}\\left\\{ p_0 - a, b - p_0 \\right\\}$$\n\nwhere $[a, b]$ is the interval in which the function lives and $k$ is the bound on the derivative of the function for the interval $[a, b]$. However, I'm not sure what to do since there is no explicit function given. Can anyone help me?\n\n\u2022 $f(x)=\\frac{x^2+3}{5}$. Your turn. \u2013\u00a0Andr\u00e9 Nicolas Feb 11 '14 at 2:08\n\u2022 How did you know to do that? \u2013\u00a0michael straws Feb 11 '14 at 2:09\n\u2022 Fixed point iteration is $x_n=f(x_{n-1})$. \u2013\u00a0Andr\u00e9 Nicolas Feb 11 '14 at 2:12\n\u2022 So this would be used to find a zero of the function $g(x) = \\frac{x^2 + 3}{5} - x$? \u2013\u00a0michael straws Feb 11 '14 at 2:13\n\u2022 Yes, for example. \u2013\u00a0Roland Feb 11 '14 at 2:15\n\nIf there's an interval $[a,b]$ such that $f$ maps $[a,b]$ to $[a,b]$ and $f'$ is bounded by some $k<1$ in that interval, then the fixed-point iteration $x_{n+1}=f(x_n), \\ n=0, \\dots$ converges for every $x_n \\in [a,b]$ towards an unique fixed point $x^*$. Furthermore, we have $$\\vert x - x^* \\vert \\leq \\frac{k}{1-k}\\vert x_{n+1} - x_{n}\\vert\\leq \\frac{k^n}{1-k}\\vert x_1 - x_0\\vert.$$\nIn your case, we have $f(x)=\\frac{x^2 +3}{5}$, which maps indeed $[0,1]$ into itself (as $f$ is strictly increasing and $f(1)=\\frac{4}{5}<1$). We have $f'(x)=\\frac{2}{5}x$, i.e. $k = \\max_{x\\in [0,1]} \\vert f'(x)\\vert = \\frac{2}{5}$. Since $x_0 \\in [0,1]$ and $x_1\\in [0,1]$, the last term of the equation above is bounded by $$\\frac{(2\/5)^n}{3\/5}*1=\\frac{5}{3}\\left( \\frac{2}{5}\\right)^n.$$ In order to make this sma ller than $10^{-4}$, let's look for the $n$ where $5\/3*(2\/5)^n=10^{-4}$ or $(0.4)^n=0.0006$, i.e. $$n=\\frac{\\ln(0.0006)}{\\ln(0.4)}\\approx 8.1,$$\ni.e. you're going to need 9 iterations to guarantee that your error is less than $10^{-4}$.","date":"2019-05-27 13:00:58","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9807906746864319, \"perplexity\": 145.5871778133888}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-22\/segments\/1558232262600.90\/warc\/CC-MAIN-20190527125825-20190527151825-00555.warc.gz\"}"}
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About Facilities and Maintenance
Elementary School Lobby
Elementary School Main Office
High School Boiler Construction
High School Construction
High School Pole Barn
Phone: 441
Mr. Robert Taylor
The Facilities and Maintenance Department is committed to providing a clean, safe and healthy environment for students, staff and the community at large.
The average size of a home today is between 1,800 to 2,200 sqft. At the school we have between both buildings 198,000 square feet. Let's say the average size of a house is 2,000 square feet. Take 198,000 divide 2,000 into it, which comes to 99. So cleaning 198,000 square feet is the same as cleaning 99 homes per day. We have 9 staff members that do custodial duties here, so means each custodian cleans an equivalent of 11 homes every day.
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G.I. Joe: Retaliation Trailer: The White House Has Been Compromised
Dec. 12. 2012 10:58 AM
With G.I. Joe action figures being a prevalent part of American childhoods for the past several generations, a live-action movie inspired by the all-American hero seems an obvious move. However, the 2009 attempt G.I. Joe: Rise of the Cobra was trashed by critics and required the boost of its international box office to get its $175 million budget in the black. Still, Paramount and MGM are giving the Joes a second shot with G.I. Joe: Retaliation.
Originally set to be a summer 2012 release, the feature was pulled from Paramount's schedule so that its spectacle could be beefed up with 3D--- and extra Channing Tatum. Gearing up once more for the action-packed pic's release, the studio has unveiled a new trailer over at Yahoo that shows off its brawny and badass cast along with plenty of boom!
Introduced by Dwayne "The Rock" Johnson, the trailer cuts to the chase revealing the Joes disowned by an imposter in the White House who brazenly riles America's enemies with threats of their utter anihilation. But there's also plenty of swagger to be seen here. From the introduction of Bruce Willis's "Call me Joe" Colton to Johnson's smack talking Channing Tatum's attempted catchphrase to I Saw The Devil's Byung-hun Lee swatting down bullets with his blade like it's nothing, this glimpse at G.I. Joe: Retaliation has got plenty to geek out about. To be perfectly frank, I found the last G.I. Joe movie to be laughably bad. But this trailer has me game to get give its sequel a shot.
G.I. Joe: Retaliation will open at last on March 29th, 2013. For lots more on the movie, including trailers, interviews and an extensive gallery of stills, click here.
news Another G. I. Joe Spinoff Is In The Works
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news The G.I. Joe Retaliation Scene The Writers Were Forced To Include
news Will G.I. Joe's Jon M. Chu Take Over Star Trek 3?
Tyler Perry Responds To Eddie Murphy's Filmmaker Comparison With Dolemite Is My Name news
Academy Awards 2020: What Movies Got The Most Oscar Nominations? news
With Three Little Words, Robert Downey Jr. Gave Iron Man Fans Hope For His Return news
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Exclusive to MedicAlert – Bring colour and style to your relaxed fashion attitude with a smart leather cuff. Designed to combine practicality, ruggedness and style, this Roots cuff with the durable stainless steel MedicAlert emblem is a cool and modern wristband. Made of genuine leather, the cuff is geared to add style to your everyday look.
Available in one size, adjustable from 5" to 7.5"
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{
"redpajama_set_name": "RedPajamaC4"
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| 8,216
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Q: Difference between VVVV.EmguCV and EmguCV.221.x64 Can someone please throw some light on the difference between VVVV.EmguCV and EmguCV.221.x64. I am new to image processing itself.
Do they serve different purposes. As I understand they both are EmguCv wrappers to OpenCv. Is there any thing else to note?
A: VVVV.EmguCV and EmguCV.221.x64 are just two different packages by separate publishers.
VVVV.EmguCV installs the newer 2.4.X verison of EmguCV where as EmguCV.221.x64 uses the 2.2.X series of Emgu.
Apart from the usual changes EmguCV 2.4.X added support for Android and iOS devices.You can check the difference between the versions here.
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John Milton, född 20 april 1807 i Jefferson County, Georgia, död genom självmord 1 april 1865 nära Marianna, Florida, var en amerikansk politiker. Han var guvernör i Florida från 1861 fram till sin död, medan Florida var en av Amerikas konfedererade stater.
Milton gifte sig 1830 med Susan Cobb. Paret fick fyra barn. Hustrun Susan avled 1842 och Milton gifte om sig två år senare med Caroline Howze. Paret fick tio barn.
Milton flyttade 1846 till Florida och inledde sin politiska karriär. Han var elektor för Lewis Cass i presidentvalet i USA 1848. Han var 1850 ledamot av Florida House of Representatives, underhuset i delstatens lagstiftande församling.
Milton vann guvernörsvalet i Florida 1860 som demokraternas kandidat. Han efterträdde följande år Madison S. Perry som guvernör. Amerikanska inbördeskriget hade brutit ut redan innan Milton tillträdde guvernörsämbetet. Milton stödde starkt den konfedererade saken. I hans sista budskap till Floridas lagstiftande församling ingick orden "Death would be preferable to reunion", att döden skulle vara att föredra framom återföreningen med nordstaterna. Guvernör Milton begick självmord genom att skjuta sig i huvudet.
Miltons grav finns på St. Luke's Episcopal Cemetery i Marianna.
Externa länkar
Biografi på National Governors Associations hemsidor
Florida Governors' Portraits
John Milton Letter Book and Correspondence 1861-1863 vid Florida Historical Society
Political Graveyard
Guvernörer i Florida
Amerikanska demokrater
Politiker som begått självmord
Amerikanska politiker under 1800-talet
Personer från Jefferson County, Georgia
Födda 1807
Avlidna 1865
Män
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Forever bows out of its first. Forever episode 22 review: The Last Death Of Henry Morgan. 1.22 The Last Death Of Henry Morgan.Happy New Year everyone! And Martin Luther King, Jr. Day. Man, we are just blowing right through 2014. This week's SNL episode, hosted by Drake, and which I'll.The Tuesdays at 10pm timeslot has been a big ratings problem for ABC for quite awhile. Show after show has been cancelled. Will their new Forever series change that.All 6 songs featured in Forever (2014) season. is investigated as a New York City medical. Abigail and Abraham at the end of the episode. Download.
Add new page. Series Info. Retrieved from "http://forever.wikia.com/wiki/Abraham_Morgan?oldid=8251". Forever Wiki is a FANDOM TV Community.
Forever Young 2 Episode 21 Information, Forever Young 2 Episode 21 Reviews, Synonyms: Oneuldo Cheongchun2; Tuổi Thanh Xuân2.Reviews and detailed complete recap for Forever (UK) - Season 2 Episode 21: D.I.V.O.R.C.E. Watch Forever Love episode 21 engsub, Forever Love ep 21 full hd, download Forever Love ep 21, watch online free Forever Love ep 21 in dramafire, dramacool, kissasian.
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All the Episodes of V Best Friends Forever. V Best Friends Forever Episodes. V Best Friends Forever 7th January 2013 Episode 21 Part 1.Watch Forever Season 1 - Episode 21 - The Night In Question (2014) online. The Forever Season 1 - Episode 21 - The Night In Question has got a 0.00 rating, of 0 total...Watch full episodes free online of the tv series True Love Next Door Season 2 Episode 21 with. her life and those around her forever. her nerdy new neighbor.
Episode 21 - The Forever Knot. Tyler decides to be more optimistic abut Butch's recovery while Farrah questions her mom's relationship with her fiance. Episode 27.
Metacritic TV Reviews, Forever (2014), New York City medical examiner Dr. Henry Morgan (Ioan Gruffudd) seeks the answers to his immortality as he helps Detective Jo.Watch Forever season 1 episode 21 (S01E21) online free (NO SIGN UP) only at TVZion, largest online tv episode database. Updated everyday.Episode 7 - New York. Episode 21 - The Night. You can watch Forever online for free on this page by streaming the movie in the video player above or by.CSI - Season 3 Episode 21: Forever watch online for free in HD quality with English subtitles.
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Pat had been big forever—so big that he could gain 100 pounds in a little over a. Podcast Episode 21:. From 600 Pounds to the Stage with "Possible" Pat.#5205-21 Old Meets New. "Rock And Roll Is Forever" Jem and the Holograms. The episode title was "Le Rock De La Nostalgie" (The Rock Of The Nostalgia.Yu-Gi-Oh! ZEXAL Forever ZEXAL. Feel the flow for the final time as Yuma and Astral high-five the sky in the cosmic conclusion to Yu-Gi-Oh! ZEXAL!.
Happy & Love Forever Episode 30 (Part 1) / Multi Language subtitles Details Title: 幸福一定强 / Xing Fu Yi Ding Qiang English Title: Happy & Love Forever.Watch Forever: Season 1 Episode 21 | The Night in Question Full Episode. Henry tackles the most important case of his career: the disappearance of the love of his. Forever 21 is the authority on fashion & the go-to retailer for the latest trends,. Forever 21, Fashion 21, XXI, XXI Forever, Love. If you get a new mobile.
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Bolton-based domestic appliances retailer AO.com has raised £50m through a share placing.
The group announced that brokers Jefferies International and Numis Securities placed just under 37.8m new shares, representing around 9.9% of the company at a price of 132.5p per placing share.
The cash will be used to support its growth ambitions, provide flexibility to react to market opportunities and changes, and strengthen its balance sheet for supplier partners.
Chief executive Steve Caunce and founder John Roberts participated in the placing by buying 1.5 million shares each.
The company also reported that turnover is expected to be around £700m for the year to the end of March 2017, up 17% year-on-year.
Caunce, who replaced Roberts as CEO last month, said: "This is our first capital raising since our IPO and the proceeds will support our continued growth and increasing scale as we pursue our proven strategy.
"We have seen another year of strong growth - in the UK and in Europe - as we continue to deliver on our 4C's strategy and opened our European distribution centre in Bergheim. This was achieved in spite of the challenging dynamics in our markets.
"We remain as committed as ever to doing business the AO way and continuing to deliver for our customers, our people, our supplier partners and our investors. The strength in our UK business and our investment in mainland Europe have positioned us well for the future, and this will be further strengthened by the capital raising."
AO, which was founded by Roberts in 2000, floated in February 2014 with a £1.2bn value.
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\section{Introduction}
A recent trend in machine learning and AI research is that old algorithms work remarkably well when combined with sufficient computing resources and data. That has been the story for (1) backpropagation applied to deep neural networks in supervised learning tasks such as computer vision \cite{krizhevsky2012imagenet} and voice recognition \cite{voicemsr2011}, (2) backpropagation for deep neural networks combined with traditional reinforcement learning algorithms, such as Q-learning \cite{watkins1992q,mnih2015human} or policy gradient (PG) methods \cite{sehnke2010parameter,mnih2016asynchronous}, and (3) evolution strategies (ES) applied to reinforcement learning benchmarks \cite{salimans:arxiv01}. One common theme is that all of these methods are gradient-based, including ES, which involves a gradient approximation similar to finite differences \cite{williams1992simple, wierstra2008natural, salimans:arxiv01}. This historical trend raises the question of whether a similar story will play out for gradient-free methods, such as population-based GAs.
This paper investigates that question by testing the performance of a simple GA on hard deep reinforcement learning (RL) benchmarks, including Atari 2600 \cite{bellemare2013arcade,brockman,mnih2015human} and Humanoid Locomotion in the MuJoCo simulator \cite{todorov2012mujoco,schulman2015trust,schulman2017proximal,brockman}. We compare the performance of the GA with that of contemporary algorithms applied to deep RL (i.e.\ DQN \cite{mnih2015human}, a Q-learning method, A3C \cite{mnih2016asynchronous}, a policy gradient method, and ES). One might expect GAs to perform far worse than other methods because they are so simple and do not follow gradients. Surprisingly, we found that GAs turn out to be a competitive algorithm for RL -- performing better on some domains and worse on others, and roughly as well overall as A3C, DQN, and ES -- adding a new family of algorithms to the toolbox for deep RL problems. We also validate the effectiveness of learning with GAs by comparing their performance to that of random search (RS). While the GA always outperforms random search, interestingly we discovered that in some Atari games random search outperforms powerful deep RL algorithms (DQN on 3/13 games, A3C on 6/13, and ES on 3/13), suggesting that local optima, saddle points, noisy gradient estimates, or some other force is impeding progress on these problems for gradient-based methods. Note that although deep neural networks often do not struggle with local optima in supervised learning \cite{pascanu2014saddle}, local optima remain an issue in RL because the reward signal may deceptively encourage the agent to perform actions that prevent it from discovering the globally optimal behavior.
Like ES and the deep RL algorithms, the GA has unique benefits. GAs prove slightly faster than ES (discussed below). The GA and ES are thus both substantially faster in wall-clock speed than Q-learning and policy gradient methods. We explore two distinct GA implementations: (1) a single-machine version with GPUs and CPUs, and (2) a distributed version on many CPUs across many machines. On a \emph{single} modern desktop with 4 GPUs and 48 CPU cores, the GA can train Atari in {\raise.17ex\hbox{$\scriptstyle\sim$}}4 hours. Training to comparable performance takes {\raise.17ex\hbox{$\scriptstyle\sim$}}7-10 days for DQN and {\raise.17ex\hbox{$\scriptstyle\sim$}}4 days for A3C. This speedup enables individual researchers with single (albeit expensive) desktops to
start using domains formerly reserved for well-funded labs only and
iterate perhaps more quickly than with any other RL algorithm. Given substantial distributed computation (here, 720 CPU cores across dozens of machines), the GA and ES can train Atari in {\raise.17ex\hbox{$\scriptstyle\sim$}}1 hour. Also beneficial, via a new technique we introduce, even multi-million-parameter networks trained by GAs can be encoded with very few (thousands of) bytes, yielding the state-of-the-art compact encoding method.
Overall, the unexpectedly competitive performance of the GA (and random search) suggests that the structure of the search space in some of these domains is not amenable to gradient-based search. That realization opens up new research directions on when and how to exploit the regions where a gradient-free search might be more appropriate and motivates research into new kinds of hybrid algorithms.
\section{Background}
At a high level, an RL problem challenges an agent to maximize some notion of cumulative reward (e.g.\ total, or discounted) without supervision as to how to accomplish that goal \cite{sutton1998reinforcement}. A host of traditional RL algorithms perform well on small, tabular state spaces \cite{sutton1998reinforcement}. However, scaling to high-dimensional problems (e.g.\ learning to act directly from pixels) was challenging until RL algorithms harnessed the representational power of deep neural networks (DNNs), thus catalyzing the field of deep reinforcement learning (deep RL) \cite{mnih2015human}. Three broad families of deep learning algorithms have shown promise on RL problems so far: Q-learning methods such as DQN \cite{mnih2015human}, policy gradient methods \cite{sehnke2010parameter} (e.g.\ A3C \cite{mnih2016asynchronous}, TRPO \cite{schulman2015trust}, PPO \cite{schulman2017proximal}), and more recently evolution strategies (ES) \cite{salimans:arxiv01}.
Deep Q-learning algorithms approximate the optimal Q function with DNNs,
yielding policies that, for a given state, choose the action that maximizes the Q-value \cite{watkins1992q, mnih2015human,hessel:arxiv01}. Policy gradient methods directly learn the parameters of a DNN policy that outputs the probability of taking each action in each state. A team from OpenAI recently experimented with a simplified version of Natural Evolution Strategies \cite{wierstra2008natural}, specifically one that learns the mean of a distribution of parameters, but not its variance. They found that this algorithm, which we will refer to simply as evolution strategies (ES), is competitive with DQN and A3C on difficult RL benchmark problems, with much faster training times (i.e. faster wall-clock time when many CPUs are available) due to better parallelization \cite{salimans:arxiv01}.
All of these methods can be considered gradient-based methods, as they all calculate or approximate gradients in a DNN and optimize those parameters via stochastic gradient descent/ascent (though they do not require differentiating through the reward function, e.g.\ a simulator). DQN calculates the gradient of the loss of the DNN Q-value function approximator via backpropagation. Policy gradients sample behaviors stochastically from the current policy and then reinforce those that perform well via stochastic gradient ascent. ES does not calculate gradients analytically, but approximates the gradient of the reward function in the parameter space \cite{salimans:arxiv01, wierstra2008natural}.
Here we test whether a truly gradient-free method, a GA, can perform well on challenging deep RL tasks. We find GAs perform surprisingly well and thus can be considered a new addition to the set of algorithms for deep RL problems.
\section{Methods}
\subsection{Genetic Algorithm}
We purposefully test with an extremely simple GA to set a baseline for how well gradient-free evolutionary algorithms work for RL problems. We expect future work to reveal that adding the legion of enhancements that exist for GAs \cite{fogel1994effectiveness, haupt2004practical, clune:ieeetec11,mouret:cec09,lehman:gecco11, stanley:alife09,mouret:arxiv15} will improve their performance on deep RL tasks.
A genetic algorithm \cite{holland1992genetic, eiben2003introduction} evolves a population $\mathcal{P}$ of $N$ individuals (here, neural network parameter vectors $\theta$, often called \emph{genotypes}). At every \emph{generation}, each $\theta_{i}$ is evaluated, producing a \emph{fitness} score (aka reward) $F(\theta_{i})$. Our GA variant performs \emph{truncation selection}, wherein the top $T$ individuals become the parents of the next generation. To produce the next generation, the following process is repeated $N-1$ times: A parent is selected uniformly at random with replacement and is \emph{mutated} by applying additive Gaussian noise to the parameter vector: $\theta^{\prime} = \theta + \sigma\epsilon$ where $\epsilon \sim \mathcal{N}(0,I)$. The appropriate value of $\sigma$ was determined empirically for each experiment, as described in Supplementary Information (SI) Table~\ref{tab:hyperparameters}. The $N$\textsuperscript{th} individual is an unmodified copy of the best individual from the previous generation, a technique called \emph{elitism}. To more reliably try to select the \emph{true} elite in the presence of noisy evaluation, we evaluate each of the top 10 individuals per generation on 30 additional episodes (counting these frames as ones consumed during training); the one with the highest mean score is the designated elite. Historically, GAs often involve \textit{crossover} (i.e.\ combining parameters from multiple parents to produce an offspring), but for simplicity we did not include it. The new population is then evaluated and the process repeats for $G$ generations or until some other stopping criterion is met. SI Algorithm~\ref{alg:ga} provides pseudocode for our version.
Open source code and hyperparameter configurations for all of our experiments are available: \url{http://bit.ly/2K17KxX}. Hyperparameters are also listed in SI Table~\ref{tab:hyperparameters}. Hyperparameters were fixed for all Atari games, chosen from a set of 36 hyperparameters tested on six games (Asterix, Enduro, Gravitar, Kangaroo, Seaquest, Venture).
GA implementations traditionally store each individual as a parameter vector $\theta$, but this approach scales poorly in memory and network transmission costs with large populations and large (deeper and wider) neural networks. We propose a novel method to store large parameter vectors compactly by representing each parameter vector as an initialization seed plus the list of random seeds that produce the series of mutations that produced each $\theta$, from which each $\theta$ can be reconstructed. This innovation was critical for an efficient implementation of a \emph{distributed} deep GA.
SI Fig.~\ref{fig:encoding} shows, and Eq.~\ref{equ:mutation3} describes, the method.
\begin{equation}
\label{equ:mutation3}
\theta^n = \psi(\theta^{n-1},\tau_n) = \theta^{n-1} + \sigma\varepsilon(\tau_n)
\end{equation}
where $\theta^n$ is an offspring of $\theta^{n-1}$,
$\psi(\theta^{n-1},\tau_n)$ is a deterministic mutation function, $\tau$ is the encoding of $\theta^n$ consisting of a list of mutation seeds,
$\theta^0 = \phi(\tau_0)$, where $\phi$ is a deterministic initialization function, and $\varepsilon(\tau_n) \sim \mathcal{N}(0, I)$ is a deterministic Gaussian pseudo-random number generator with an input seed $\tau_n$ that produces a vector of length $|\theta|$. In our case, $\varepsilon(\tau_n)$ is a large precomputed table that can be indexed using 28-bit seeds. SI Sec.~\ref{mutEncSI} provides more encoding details, including how the seeds could be smaller.
This technique is advantageous because the size of the compressed representation increases linearly with the number of generations (often order thousands), and is \emph{independent} of the size of the network (often order millions or more).
It does, of course, require computation to reconstruct the DNN weight vector.
Competitive Atari-playing agents evolve in as little as tens of generations, enabling a compressed representation of a 4M+ parameter neural network in just thousands of bytes (a 10,000-fold compression). The compression rate depends on the number of generations, but in practice is always substantial: all Atari final networks were compressible 8,000-50,000-fold. This represents the state of the art in encoding large networks compactly. However, it is not a general network compression technique because it cannot compress arbitrary networks, and instead only works for networks evolved with a GA.
One motivation for choosing ES versus Q-learning and policy gradient methods is its faster wall-clock time with distributed computation, owing to better parallelization \cite{salimans:arxiv01}. We found that the distributed CPU-only Deep GA not only preserves this benefit, but slightly improves upon it (SI Sec.~\ref{gaFasterThanES} describes why GAs--distributed or local--are faster than ES). Importantly, GAs can also use GPUs to speed up the forward pass of DNNs (especially large ones), making it possible to train on a single desktop. With our GPU-enabled implementation, on \emph{one} modern desktop we can train Atari in {\raise.17ex\hbox{$\scriptstyle\sim$}}4 hours what takes {\raise.17ex\hbox{$\scriptstyle\sim$}}1 hour with 720 distributed cores. Distributed GPU training would further speed up training for large population sizes.
\subsection{Novelty Search}
One benefit of training deep neural networks with GAs is it enables us to immediately take advantage of algorithms previously developed in the neuroevolution community. As a demonstration, we experiment with novelty search (NS) \cite{lehman:ecj11}, which was designed for deceptive domains in which reward-based optimization mechanisms converge to local optima. NS avoids these local optima by ignoring the reward function during evolution and instead rewarding agents for performing behaviors that have never been performed before (i.e.\ that are novel). Surprisingly, it can often outperform algorithms that utilize the reward signal, a result demonstrated on maze navigation and simulated biped locomotion tasks \cite{lehman:ecj11}.
Here we apply NS to see how it performs when combined with DNNs on a deceptive image-based RL problem (that we call the \emph{Image Hard Maze}). We refer to the GA that optimizes for novelty as GA-NS.
NS requires a behavior characteristic (BC) that describes the behavior of a policy $BC(\pi)$ and a behavioral distance function between the BCs of any two policies: $\text{dist}(BC(\pi_{i}), BC(\pi_{j}))$, both of which are domain-specific. After each generation, members of the population have a probability $p$ (here, 0.01) of having their BC stored in an \emph{archive}. The novelty of a policy is defined as the average distance to the $k$ (here, 25) nearest neighbors (sorted by behavioral distance) in the population or archive. Novel individuals are thus determined based on their behavioral distance to current or previously seen individuals. The GA otherwise proceeds as normal, substituting novelty for fitness (reward). For reporting and plotting purposes only, we identify the individual with the highest reward per generation. The algorithm is presented in SI~Algorithm~\ref{alg:gans}.
\section{Experiments}
Our experiments focus on the performance of the GA on the same challenging problems that have validated the effectiveness of state-of-the-art deep RL algorithms and ES \cite{salimans:arxiv01}. They include learning to play Atari directly from pixels \cite{mnih2015human,schulman2017proximal,mnih2016asynchronous,bellemare2013arcade} and a continuous control problem involving a simulated humanoid robot learning to walk \cite{brockman,schulman2017proximal,salimans:arxiv01,todorov2012mujoco}. We also tested on an Atari-scale maze domain that has a clear local optimum (Image Hard Maze) to study how well these algorithms avoid deception \cite{lehman:ecj11}.
For Atari and Image Hard Maze experiments, we record the best agent found in each of multiple, independent, randomly initialized GA runs: 5 for Atari, 10 for the Image Hard Maze. Because Atari is stochastic, the final score for each run is calculated by taking the highest-scoring elite across generations, and averaging the score it achieves on 200 independent evaluations. The final score for the domain is then the median of final run scores. Humanoid Locomotion details are in SI. Sec~\ref{humanoidLocomotion}.
\subsection{Atari}
Training deep neural networks to play Atari -- mapping directly from pixels to actions -- was a celebrated feat that arguably launched the deep RL era and expanded our understanding of the difficulty of RL domains that machine learning could tackle \cite{mnih2015human}. Here we test how the performance of DNNs evolved by a simple GA compare to DNNs trained by the major families of deep RL algorithms and ES. We model our experiments on those from the ES paper by \citet{salimans:arxiv01} since it inspired our study. Due to limited computational resources, we compare results on 13 Atari games. Some were chosen because they are games on which ES performs well (Frostbite, Gravitar, Kangaroo, Venture, Zaxxon) or poorly (Amidar, Enduro, Skiing, Seaquest) and the remaining games were chosen from the ALE \cite{bellemare2013arcade} set in alphabetical order (Assault, Asterix, Asteroids, Atlantis). To facilitate comparisons with results reported in \citet{salimans:arxiv01}, we keep the number of game frames agents experience over the course of a GA run constant (at one billion frames). The frame limit results in a differing number of generations per independent GA run (SI Sec. Table~\ref{tab:atari_gens}), as policies of different quality in different runs may see more frames in some games (e.g.\ if the agent lives longer).
During training, each agent is evaluated on a full episode (capped at 20k frames), which can include multiple lives, and fitness is the sum of episode rewards, i.e. the final Atari game score. The following are identical to DQN \cite{mnih2015human}: (1) data preprocessing, (2) network architecture, and (3) the stochastic environment that starts each episode with up to 30 random, initial no-op operations. We use the larger DQN architecture from \citet{mnih2015human} consisting of 3 convolutional layers with 32, 64, and 64 channels followed by a hidden layer with 512 units. The convolutional layers use $8 \times 8$, $4 \times 4$, and $3 \times 3$ filters with strides of 4, 2, and 1, respectively. All hidden layers were followed by a rectifier nonlinearity (ReLU). The network contains over 4M parameters;
interestingly, many in the past assumed that a simple GA would fail at such scales.
All results are from our single-machine CPU+GPU GA implementation.
Fair comparisons between algorithms is difficult, as evaluation procedures are non-uniform and algorithms realize different trade-offs between computation, wall-clock speed, and sample efficiency. Another consideration is whether agents are evaluated on random starts (a random number of no-op actions), which is the regime they are trained on, or on starts randomly sampled from human play, which tests for generalization \cite{nair2015massively}. Because we do not have a database of human starts to sample from, our agents are evaluated with random starts. Where possible, we compare our results to those for other algorithms on random starts. That is true for DQN and ES, but not for A3C, where we had to include results on human starts.
We also attempt to control for the number of frames seen during training, but because DQN is far slower to run, we present results from the literature that train on fewer frames (200M, which requires 7-10 days of computation vs. hours of computation needed for ES and the GA to train on 1B frames). There are many variants of DQN that we could compare to, including the Rainbow \cite{hessel:arxiv01} algorithm that combines many different recent improvements to DQN \cite{hasselt:arxiv01,wang2015dueling,schaul2015prioritized,sutton1998reinforcement,bellemare2017distributional,fortunato2017noisy}. However, we choose to compare the GA to the original, vanilla DQN algorithm, partly because we also introduce a vanilla GA, without the many modifications and improvements that have been previously developed \cite{haupt2004practical}.
In what will likely be a surprise to many, the simple GA is able to train deep neural networks to play many Atari games roughly as well as DQN, A3C, and ES (Table~\ref{tab:atari_results}). Among the 13 games we tried, DQN, ES and the GA produced the best score on 3 games, while A3C produced the best score on 4. On Skiing, the GA produced a score higher than any other algorithm to date that we are aware of, including all the DQN variants in the Rainbow DQN paper \cite{hessel:arxiv01}. On some games, the GA performance advantage over DQN, A3C, and ES is considerable (e.g. Frostbite, Venture, Skiing). Videos of policies evolved by the GA can be viewed here: \url{https://goo.gl/QBHDJ9}. In a head-to-head comparisons, the GA performs better than ES, A3C, and DQN on 6 games each out of 13 (Tables~\ref{tab:atari_results} \&~\ref{tab:atariHead2Head}).
The GA also performs worse on many games, continuing a theme in deep RL where different families of algorithms perform differently across different domains \cite{salimans:arxiv01}.
However, all such comparisons are preliminary because more computational resources are needed to gather sufficient sample sizes to see if the algorithms are significantly different per game; instead the key takeaway is that they all tend to perform roughly similarly in that each does well on different games.
\begin{table*}[htb]
\centering
\begin{tabular}{l r r r r r r}
\toprule
& DQN & ES & A3C & RS & GA & GA \\
Frames & 200M & 1B & 1B & 1B & 1B & 6B \\
Time & $\sim$7-10d & $\sim1$h & $\sim4$d & $\sim1$h or $4$h & $\sim1$h or $4$h & $\sim6$h or $24$h \\
Forward Passes & 450M & 250M & 250M & 250M & 250M & 1.5B \\
Backward Passes & 400M & 0 & 250M & 0 & 0 & 0\\
Operations & 1.25B U & 250M U & 1B U & 250M U & 250M U & 1.5B U \\
\midrule
amidar & \textbf{978} & 112 & 264 & 143 & 263 & 377 \\
assault & 4,280 & 1,674 & \textbf{5,475} & 649 & 714 & 814 \\
asterix & 4,359 & 1,440 & \textbf{22,140} & 1,197 & 1,850 & 2,255 \\
asteroids & 1,365 & 1,562 & \textbf{4,475} & 1,307 & 1,661 & 2,700 \\
atlantis & 279,987 & \textbf{1,267,410} & 911,091 & 26,371 & 76,273 & 129,167 \\
enduro & \textbf{729} & 95 & -82 & 36 & 60 & 80 \\
frostbite & 797 & 370 & 191 & 1,164 & \textbf{4,536} & \textbf{6,220} \\
gravitar & 473 & \textbf{805} & 304 & 431 & 476 & 764 \\
kangaroo & 7,259 & \textbf{11,200} & 94 & 1,099 & 3,790 & \textbf{11,254} \\
seaquest & \textbf{5,861} & 1,390 & 2,355 & 503 & 798 & 850 \\
skiing & -13,062 & -15,443 & -10,911 & -7,679 & ${}^\dagger$\textbf{-6,502} & ${}^\dagger$\textbf{-5,541} \\
venture & 163 & 760 & 23 & 488 & \textbf{969} & ${}^\dagger$\textbf{1,422} \\
zaxxon & 5,363 & 6,380 & \textbf{24,622} & 2,538 & 6,180 & 7,864 \\
\bottomrule
\end{tabular}
\caption{\textbf{On Atari a simple genetic algorithm is competitive with Q-learning (DQN), policy gradients (A3C), and evolution strategies (ES).} Shown are game scores (higher is better). Comparing performance between algorithms is inherently challenging (see main text), but we attempt to facilitate comparisons by showing estimates for the amount of computation (\emph{operations}, the sum of forward and backward neural network passes), data efficiency (the number of game frames from training episodes), and how long in wall-clock time the algorithm takes to run. The ES, DQN, A3C, and GA (1B) perform best on 3, 3, 4, and 3 games, respectively. Surprisingly, random search often finds policies superior to those of DQN, A3C, and ES (see text for discussion). Note the dramatic differences in the speeds of the algorithm, which are much faster for the GA and ES, and data efficiency, which favors DQN. The scores for DQN are from \citet{hessel:arxiv01} while those for A3C and ES are from \citet{salimans:arxiv01}. For A3C, DQN, and ES, we cannot provide error bars because they were not reported in the original literature; GA and random search error bars are visualized in (SI Fig. \ref{fig:learnigcurve_atari_ga_rs}). The wall-clock times are approximate because they depend on a variety of hard-to-control-for factors. We found the GA runs slightly faster than ES on average. The $\dagger$ symbol indicates state of the art performance. GA 6B scores are bolded if best, but do not prevent bolding in other columns.}
\label{tab:atari_results}
\end{table*}
Because performance did not plateau in the GA runs, we test whether the GA improves further given additional computation. We thus run the GA six times longer (6B frames) and in all games, its score improves (Table~\ref{tab:atari_results}). With these post-6B-frame scores, the GA outperforms A3C, ES, and DQN on 7, 8, 7 of the 13 games in head-to-head comparisons, respectively (SI Table~\ref{tab:atariHead2Head}).
In most games, the GA's performance still has not converged at 6B frames (SI Fig.~\ref{fig:learnigcurve_atari_ga_rs}), leaving open the question of to how well the GA will ultimately perform when run even longer. To our knowledge, this 4M+ parameter neural network is the largest neural network ever evolved with a simple GA.
One remarkable fact is how quickly the GA finds high-performing individuals. Because we employ a large population size (1k), each run lasts relatively few generations (min 348, max 1,834, SI Table~\ref{tab:atari_gens}). In many games, the GA finds a solution better than DQN in only one or tens of generations! Specifically, the median GA performance is higher than the \emph{final} DQN performance in 1, 1, 3, 5, 11, and 29 generations for Skiing, Venture, Frostbite, Asteroids, Gravitar, and Zaxxon, respectively. Similar results hold for ES, where 1, 2, 3, 7, 12, and 25 GA generations were needed to outperform ES on Skiing, Frostbite, Amidar, Asterix, Asteroids, and Venture, respectively. The number of generations required to beat A3C were 1, 1, 1, 1, 1, 2, and 52 for Enduro, Frostbite, Kangaroo, Skiing, Venture, Gravitar, and Amidar, respectively.
Each generation, the GA tends to make small-magnitude changes (controlled by $\sigma$) to the parameter vector (see Methods). That the GA outperforms DQN, A3C, and ES in so few generations -- especially when it does so in the first generation (which is before a round of selection) -- suggests that many high-quality policies exist near the origin (to be precise, in or near the region in which the random initialization function generates policies). That raises the question: is the GA doing anything more than random search?
To answer this question, we evaluate many policies randomly generated by the GA's initialization function $\phi$ and report the best score. We gave random search approximately the same amount of frames and computation as the GA and compared their performance (Table~\ref{tab:atari_results}). In every game, the GA outperformed random search, and did so significantly on 9/13 games (Fig.~\ref{fig:learnigcurve_atari_ga_rs}, $p< 0.05$, this and all future $p$ values are via a Wilcoxon rank-sum test). The improved performance suggests the GA is performing healthy optimization over generations.
Surprisingly, given how celebrated and impressive DQN, ES and A3C are, out of 13 games random search actually outperforms DQN on 3 (Frostbite, Skiing, \& Venture), ES on 3 (Amidar, Frostbite, \& Skiing), and A3C on 6 (Enduro, Frostbite, Gravitar, Kangaroo, Skiing, \& Venture). Interestingly, some of these policies produced by random search are not trivial, degenerate policies. Instead, they appear quite sophisticated. Consider the following example from the game Frostbite, which requires an agent to perform a long sequence of jumps up and down rows of icebergs moving in different directions (while avoiding enemies and optionally collecting food) to build an igloo brick by brick (SI Fig.~\ref{fig:frosbite_seq}). Only after the igloo is built can the agent enter the igloo to receive a large payoff. Over its first two lives, a policy found by random search completes a series of 17 actions, jumping down 4 rows of icebergs moving in different directions (while avoiding enemies) and back up again three times to construct an igloo. Then, only once the igloo is built, the agent immediately moves towards it and enters it, at which point it gets a large reward. It then repeats the entire process on a harder level, this time also gathering food and thus earning bonus points (video: \url{https://youtu.be/CGHgENV1hII}). That policy resulted in a very high score of 3,620 in less than 1 hour of random search, vs.\ an average score of 797 produced by DQN after 7-10 days of optimization. One may think that random search found a lucky open loop sequence of actions overfit to that particular stochastic environment. Remarkably, we found that this policy actually generalizes to other initial conditions too, achieving a median score of 3,170
(with 95\% bootstrapped median confidence intervals of 2,580 - 3,170) on 200 different test environments (each with up to 30 random initial no-ops, a standard testing procedure \cite{hessel:arxiv01, mnih2015human}).
These examples and the success of RS versus DQN, A3C, and ES suggest that many Atari games that seem hard based on the low performance of leading deep RL algorithms may not be as hard as we think, and instead that these algorithms for some reason are performing poorly on tasks that are actually quite easy. These results further suggest that sometimes the best search strategy is not to follow the gradient, but instead to conduct a dense search in a local neighborhood and select the best point found, a subject we return to in the discussion (Sec. \ref{discussion}).
\subsection{Image Hard Maze}
This experiment seeks to demonstrate a benefit of GAs working at DNN scales, which is that algorithms that were developed to improve GAs can be immediately taken off the shelf to improve DNN training. The example algorithm is Novelty search (NS), which is a popular evolutionary method for exploration in RL \cite{lehman:ecj11}.
NS was originally motivated by the Hard Maze domain \cite{lehman:ecj11}, which is a staple in the neuroevolution community. It demonstrates the problem of local optima (aka deception) in reinforcement learning. In it, a robot receives more reward the closer it gets to the goal as the crow flies.
The problem is deceptive because greedily getting closer to the goal leads an agent to permanently get stuck in one of the map's deceptive traps (Fig.~\ref{fig:hardmze_plot}, Left). Optimization algorithms that do not conduct sufficient exploration suffer this fate. NS solves this problem because it ignores the reward and encourages agents to visit new places \cite{lehman:ecj11}.
\begin{figure}[htb]
\centering
\begin{subfigure}{0.4\columnwidth}
\centering
\includegraphics[width=\textwidth]{imagehardmaze_start_annotated}
\end{subfigure}%
\begin{subfigure}{0.6\columnwidth}
\centering
\includegraphics[width=\textwidth]{learningcurve_imagehardmaze}
\end{subfigure}
\caption{\textbf{Image Hard Maze Domain and Results.} Left: A small wheeled robot must navigate to the goal with this bird's-eye view as pixel inputs. The robot starts in the bottom left corner facing right. Right: Novelty search can train deep neural networks to avoid local optima that stymie other algorithms. The GA, which solely optimizes for reward and has no incentive to explore, gets stuck on the local optimum of Trap 2. The GA optimizing for novelty (GA-NS) is encouraged to ignore reward and explore the whole map, enabling it to eventually find the goal. ES performs even worse than the GA, as discussed in the main text. DQN and A2C also fail to solve this task. For ES, the performance of the mean $\theta$ policy each iteration is plotted. For GA and GA-NS, the performance of the highest-scoring individual per generation is plotted. Because DQN and A2C do not have the same number of evaluations per iteration as the evolutionary algorithms, we plot their final median reward as dashed lines. SI Fig. \ref{fig:imagehardmaze_progress} shows the behavior of these algorithms during training.}\label{fig:hardmze_plot}
\end{figure}
The original version of this problem involves only a few inputs (radar sensors to sense walls) and two continuous outputs for speed (forward or backward) and rotation, making it solvable by small neural networks (tens of connections). Because here we want to demonstrate the benefits of NS at the scale of deep neural networks, we introduce a new version of the domain called Image Hard Maze. Like many Atari games, it shows a bird's-eye view of the world to the agent in the form of an $84\times84$ pixel image (Fig.~\ref{fig:hardmze_plot}, Left). This change makes the problem easier in some ways (e.g. now it is fully observable), but harder in others because it is much higher-dimensional: the neural network must learn to process this pixel input and take actions. SI Sec.~\ref{ImageHardMazeAdditionalDetails} has additional experimental details.
We confirm that the results that held for small neural networks on the original, radar-based version of this task also hold for the high-dimensional, visual version of this task with deep neural networks. With a 4M+ parameter network processing pixels, the GA-based novelty search (GA-NS) is able to solve the task by finding the goal (Fig.~\ref{fig:hardmze_plot}). The GA optimizes for reward only and, as expected, gets stuck in the local optima of Trap 2 (SI Fig.~\ref{fig:imagehardmaze_progress}) and thus fails to solve the problem (Fig.~\ref{fig:hardmze_plot}), significantly underperforming GA-NS ($p<0.001$).
Our results confirm that we are able to use exploration methods such as novelty search to solve this sort of deception, even in high-dimensional problems such as those involving learning directly from pixels. This is the largest neural network optimized by novelty search to date by three orders of magnitude. In an companion paper \cite{conti:arxiv17}, we also demonstrate a similar finding, by hybridizing novelty search with ES to create NS-ES, and show that it too can help deep neural networks avoid deception in challenging RL benchmark domains.
As expected, ES also fails to solve the task because it focuses solely on maximizing reward (Fig.~\ref{fig:hardmze_plot} \& SI Fig. \ref{fig:imagehardmaze_progress}). We also test Q-learning (DQN) and policy gradients on this problem. We did not have source code for A3C, but were able to obtain source code for A2C, which has similar performance \cite{wu2017scalable}: the only difference is that it is synchronous instead of asynchronous. For these experiments we modified the rewards of the domain to step-by-step rewards (the negative change in distance to goal since the last time-step), but for plotting purposes, we record the final distance to the goal. Having per-step rewards is standard for these algorithms and provides more information, but does not remove the deception. Because DQN requires discrete outputs, for it we discretize each of the two continuous outputs into to five equally sized bins. To enable all possible output combinations, it learns $5^2=25$ Q-values.
Also as expected, DQN and A2C fail to solve this problem (Fig.~\ref{fig:hardmze_plot}, SI Fig.\ \ref{fig:imagehardmaze_progress}). Their default exploration mechanisms are not enough to find the global optimum given the deceptive reward function in this domain. DQN is drawn into the expected Trap 2. For unclear reasons, even though A2C visits Trap 2 often early in training, it converges on getting stuck in a different part of the maze. Of course, exploration techniques could be added to these controls to potentially make them perform as well as GA-NS. Here we only sought to show that the Deep GA allows algorithms developed for small-scale neural networks can be harnessed on hard, high-dimensional problems that require DNNs.
In future work, it will be interesting to combine NS with a Deep GA on more domains, including Atari and robotics domains. More importantly, our demonstration suggests that other algorithms that enhance GAs can now be combined with DNNs. Perhaps most promising are those that combine a notion of diversity (e.g. novelty) and quality (i.e. being high performing), seeking to collect a set of high-performing, yet interestingly different policies \cite{mouret:arxiv15,lehman:gecco11,cully:nature15,pugh:frontiers16}. The results also motivate future research into combining deep RL algorithms (e.g. DQN, A3C) with novelty search and quality diversity algorithms.
\subsection{Humanoid Locomotion}
The GA was also able to solve the challenging continuous control benchmark of Humanoid Locomotion \cite{brockman}, which has validated modern, powerful algorithms such as A3C, TRPO, and ES. While the GA did produce robots that could walk well, it took {\raise.17ex\hbox{$\scriptstyle\sim$}}15 times longer to perform slightly worse than ES (SI Sec.~\ref{humanoidLocomotion}), which is surprising because GAs have previously performed well on robot locomotion tasks \cite{clune:ieeetec11, huizinga2016does}. Future research is required to understand why.
\vspace{-.5em}
\section{Discussion}
\label{discussion}
The surprising success of the GA and RS in domains thought to require at least some degree of gradient estimation suggests some heretofore under-appreciated aspects of high-dimensional search spaces. They imply that densely sampling in a region around the origin is sufficient in some cases to find far better solutions than those found by state-of-the-art, gradient-based methods even with far more computation or wall-clock time, suggesting that gradients do not point to these solutions, or that other optimization issues interfere with finding them, such as saddle points or noisy gradient estimates. The GA results further suggest that sampling in the region around good solutions is often sufficient to find even better solutions, and that a sequence of such discoveries is possible in many challenging domains. That result in turn implies that the distribution of solutions of increasing quality is unexpectedly dense, and that you do not need to follow a gradient to find them.
Another, non-mutually exclusive hypothesis, is that GAs (and ES) have improved performance due to \emph{temporally extended exploration} \cite{osband2016deep}, meaning they explore consistently since all actions in an episode are a function of the same set of mutated parameters, which improves exploration \cite{plappert2017parameter}. This helps exploration for two reasons, (1) an agent takes the same action (or has the same distribution over actions) each time it visits the same state, which makes it easier to learn whether the policy in that state is advantageous, and (2) the agent is also more likely to have correlated actions across states (e.g. always go up) because mutations to its internal representations can affect the actions taken in many states similarly.
Perhaps more interesting is the result that sometimes it is actually \emph{worse} to follow the gradient than sample locally in the parameter space for better solutions. This scenario probably does not hold in all domains, or even in all the regions of a domain where it sometimes holds, but that it holds at all expands our conceptual understanding of the viability of different kinds of search operators. A reason GA might outperform gradient-based methods is if local optima are present, as it can jump over them in the parameter space, whereas a gradient method cannot (without additional optimization tricks such as momentum, although we note that ES utilized the modern ADAM optimizer in these experiments \cite{kingma2014adam}, which includes momentum). One unknown question is whether GA-style local, gradient-free search is better early on in the search process, but switching to a gradient-based search later allows further progress that would be impossible, or prohibitively computationally expensive, for a GA to make. Another unknown question is the promise of simultaneously hybridizing GA methods with modern algorithms for deep RL, such as Q-learning, policy gradients, or evolution strategies.
We still know very little about the ultimate promise of GAs versus competing algorithms for training deep neural networks on reinforcement learning problems. Additionally, here we used an extremely simple GA, but many techniques have been invented to improve GA performance \cite{eiben2003introduction,haupt2004practical}, including crossover \cite{holland1992genetic,deb2016breaking}, indirect encoding \cite{stanley:gpem07,stanley:alife09,clune:ieeetec11}, and encouraging quality diversity \cite{mouret:arxiv15,pugh:frontiers16}, just to name a few. Moreover, many techniques have been invented that dramatically improve the training of DNNs with backpropagation, such as residual networks \cite{he:arxiv15}, SELU or RELU activation functions \cite{krizhevsky2012imagenet, klambauer2017self}, LSTMs or GRUs \cite{hochreiter:nc97,cho2014properties}, regularization \cite{hoerl1970ridge}, dropout \cite{srivastava:dropout14}, and annealing learning rate schedules \cite{robbins1951stochastic}. We hypothesize that many of these techniques will also improve neuroevolution for large DNNs.
Some of these enhancements may improve the GA performance on Humanoid Locomotion. For example, indirect encoding, which allows genomic parameters to affect multiple weights in the final neural network (in a way similar to convolution's tied weights, but with far more flexibility), has been shown to dramatically improve performance and data efficiency when evolving robot gaits \cite{clune:ieeetec11}. Those results were found with the HyperNEAT algorithm \cite{stanley:alife09}, which has an indirect encoding that abstracts the power of developmental biology \cite{stanley:gpem07}, and is a particularly promising direction for Humanoid Locomotion and Atari we are investigating. It will further be interesting to learn on which domains Deep GA tends to perform well or poorly and understand why. Also, GAs could help in other non-differentiable domains, such as architecture search \cite{liu:arxiv17,miikkulainen:arxiv17} and for training limited precision (e.g.\ binary) neural networks.
\vspace{-0.5em}
\section{Conclusion}
Our work introduces a Deep GA that competitively trains deep neural networks for challenging RL tasks, and an encoding technique that enables efficient distributed training and a state-of-the-art compact network encoding. We found that the GA is fast, enabling training Atari in {\raise.17ex\hbox{$\scriptstyle\sim$}}4h on a single desktop or {\raise.17ex\hbox{$\scriptstyle\sim$}}1h distributed on 720 CPUs. We documented that GAs are surprisingly competitive with popular algorithms for deep reinforcement learning problems, such as DQN, A3C, and ES, especially in the challenging Atari domain. We also showed that interesting algorithms developed in the neuroevolution community can now immediately be tested with deep neural networks, by showing that a Deep GA-powered novelty search can solve a deceptive Atari-scale game. It will be interesting to see future research investigate the potential and limits of GAs, especially when combined with other techniques known to improve GA performance. More generally, our results continue the story -- started by backprop and extended with ES -- that old, simple algorithms plus modern amounts of computation can perform amazingly well. That raises the question of what other old algorithms should be revisited.
\section*{Acknowledgements}
We thank all of the members of Uber AI Labs for helpful suggestions throughout the course of this work, in particular Zoubin Ghahramani, Peter Dayan, Noah Goodman, Thomas Miconi, and Theofanis Karaletsos. We also thank Justin Pinkul, Mike Deats, Cody Yancey, and the entire OpusStack Team at Uber for providing resources and technical support. Thanks also to David Ha for many helpful suggestions that improved the paper.
\setlength{\bibsep}{0.0pt}
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{
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For Trudie
And with heartfelt thanks and love to my family and friends, who have made the events in this book so special
First published under the title _The Whispering Years_ in 2001
This fully revised and updated edition first published in Great Britain in 2015 by
Michael O'Mara Books Limited
9 Lion Yard
Tremadoc Road
London SW4 7NQ
Copyright © Bob Harris 2015
All rights reserved. You may not copy, store, distribute, transmit, reproduce or otherwise make available this publication (or any part of it) in any form, or by any means (electronic, digital, optical, mechanical, photocopying, recording or otherwise), without the prior written permission of the publisher. Any person who does any unauthorized act in relation to this publication may be liable to criminal prosecution and civil claims for damages.
A CIP catalogue record for this book is available from the British Library.
ISBN: 978-1-78243-360-6 in hardback print format
ISBN: 978-1-78243-361-3 in e-book format
www.mombooks.com
Cover design by Patrick Knowles
Designed and typeset by Design 23
Contents
Foreword by Robert Plant
Introduction
ONE A Passion for Music and Radio
TWO 'DJ Wanted ...'
THREE _Old Grey Whistle Test_
FOUR The States, the President and Punk
FIVE 'Who's Out for '78?'
SIX Rex Bob Lowenstein
SEVEN Return to Radio 1
EIGHT 'The World Ends on a Whisper'
NINE Music City USA
TEN A Rocky Road
ELEVEN Still Whispering...
Acknowledgements
Picture Credits
Index
List of Illustrations
Foreword to the 2015 Edition
THE ROCK'N'ROLL DOCTOR OF SEVENTIES MUSIC TV MOVES THROUGH the years with style and grace. His own excitement and love of music and his infectious enthusiasm to bring his audience the rhyme, reason and sounds of a new world is a work of heart.
He champions the unknown, the obscure and the legendary with equal zest and detail. He has stayed the distance – the good times and the others – with character and resilience, always digging deep and deeper.
ROBERT PLANT
Introduction
FOR AS LONG AS I CAN REMEMBER I'VE ALWAYS LOVED MUSIC, A passion that has largely defined my life. I'm extremely fortunate to be able to express that passion through my work. I've visited many of the major music centres in Europe and America, seen some of the great concerts and spent time with some of the biggest stars in the world. I've interviewed John Lennon in New York, Led Zeppelin and Bruce Springsteen in Los Angeles, The Rolling Stones in Munich, the Bee Gees in Miami, the top country stars in Nashville and found myself in situations most could only dream of. I've toured with T. Rex, David Bowie and Queen, compered at most of the major festivals. I've met royalty and an American president, produced records and presented on television and radio in what has sometimes seemed to be a cavalcade of once-in-a-lifetime experiences. But it hasn't all been good. My personal life has been through crisis, I've been so ill I nearly died. I've been threatened and derided. I've had to completely rebuild my career no less than four times. I've been a bankrupt. The following pages are the story of it all, beginning at a time when optimism was still a national characteristic.
ONE
A Passion for Music and Radio
HAVING BEEN ENCOURAGED TO MOVE TO THE SMOKE BY JON BIRD, a boyhood friend, I have to say, 1966 was a fantastic time to arrive in London. Jon and I met when my parents and I moved into the house next door to the Bird family when I was about 11 years old. Like our previous home, No. 63 Greenfield Road in Northampton was a police house. My Dad was in the local force, retiring in 1967 as an acting detective chief inspector, having spent most of his career in the CID. I'm an only child, so it was a great feeling to discover this terrific kid at No. 61.
Jon was a year older than me and was already a talented artist and sculptor. I remember a painting he did in the third year at school of horses pulling a plough across a field and away into the sunset, a typical country scene and the subject matter of many pictures before and since. But this painting was really memorable, particularly the use of colour. Jon was not afraid to take risks, and the gold, brown, burnt orange hue he'd created was particularly striking. He had a tremendous talent and soon qualified for the Central School of Art in Holborn, taking up his place there in 1965.
My own scholastic career ended rather less impressively. In the summer holiday between sixth form and my final year at Trinity High School, I was spotted by one of my teachers drinking a half of lemonade shandy at the bar of a local pub. The pub was on the outskirts of Northampton at Weston Favell, where I used to cycle to hang out with some local friends and go swimming in the lock near the mill house. I returned to school in September to find myself on report and summoned to the headmaster's office, where I found him red-faced in anger and brandishing his cane.
'Bend over, Harris,' is all he said. With all efforts at explanation summarily dismissed and in the knowledge that were this to happen I would be the first sixth-former in the school's history to get the cane, a sense of personal dignity and righteous indignation dictated my response. I turned tail, walked out of his office, cycled home, packed my saddle-bags with all the school books I could find, went back, dumped them on his desk and left. I hadn't enjoyed school anyway, except when I was on the sports field. I walked away from my education with two O levels, Art and English.
'Brilliant,' said Dad, who was waiting for me when I arrived home. 'What are you going to do now?' My father had been brought up in the depression-hit south Wales mining community of Pontardawe in the 20s and 30s, when a good education meant escape to university and a decent job, away from the pit closures and poverty of the valley. The punishing hours of a detective's life seemed a reasonable trade-in to a man schooled in the philosophy of hard work.
We spent many summers visiting relatives there when I was a child, although I always felt slightly claustrophobic, hemmed in by those tall, purple mountains. But the people were fantastic, a closely knit and truly supportive community. I spent a lot of time with Mair Jones, the girl who lived next door to my Mumgu and Dadcu in Edward Street, and with my cousin, Mary Hopkin, who lived higher up the valley in Altwen. Dad already knew how much I wanted to be on the radio, but a career in broadcasting seems a million miles away when you're 17, living in an East Midlands boot and shoe town, haven't got a job and have just walked out of school. Dad and I did a deal. He was very keen for me to follow in his footsteps. 'Have a go at it, Rob,' he said. 'Join the Police Cadets, have a look and see if you like the life. When you're 19, make the decision. If you're still determined to get into the music business and honestly decide you don't want to take up a police career, I'll back you one hundred per cent, but on one condition. You must give it everything for the next 18 months.' We shook on it. I joined the Northampton County Police Cadets, stationed at Wellingborough. And it wasn't too bad, particularly on the sports side.
I'd played in my school first XV at centre three-quarter, wearing the No. 13 shirt and modelling my game on that of Mike Weston, an England International of the time who, along with the great Richard Sharp, was a massive hero. Rugby was a major part of my life in the Cadets and I was given a lot of time off for games, training and trials. In the winter it seemed as if I was spending more time on the rugby pitch than at the old-fashioned plugs and wires switchboard I was detailed to answer, which was fine by me. (My other major duty was making endless pots of tea for station officer PC Gray.) I even reached Midland Counties level, playing under floodlights in Stratford-on-Avon in front of six and a half thousand people, one of the few times in my life I've been genuinely nervous.
I completed my Duke of Edinburgh Award with an outward bound course in Eskdale, Cumberland (now Cumbria). Part of the course was an expedition that took us to the top of Scafell Pike, the highest mountain in England, which, to be honest, was a huge anti-climax. It's just a flat bit of shale with a plaque. We were shrouded in cloud, so I can't comment on the view. I just remember this ruddy New Zealander appearing out of the mist, wearing shorts and a short-sleeved shirt, sickeningly hearty while we stood shivering.
The other good thing about the Cadets was getting out in the cars on motor patrol, the big treat! The worst part was the monthly drill training and the fact that I had to keep my hair short to avoid the sergeant major screaming in my ear. But I can honestly say that I had a good time. I bought a Citroen Light 15, complete with running boards and three-speed dashboard gear change, from a bobby at the Wellingborough nick and have always been proud that it was my first car.
But I knew the life was not for me and although Dad was disappointed he was as good as his word and has backed me fully ever since. Bizarrely, his police work and the music industry had already overlapped. It was Dad who arrested P.J. Proby onstage at the Northampton ABC, during Proby's notorious trouser-splitting tour in 1965!
Proby was a Texan, brought to England by producer Jack Good in 1964 for a Beatles television special. A man of manic energy, Good's contribution to the development of British rock'n'roll was immense. He'd joined the BBC from Oxford University in 1956 as a trainee and, intrigued by rock'n'roll and the media's fear of it, devised _Six-Five Special,_ the first British television pop music show. Having got the show on air by hoodwinking the Corporation into thinking it was to be a magazine show for young people, he moved across to ITV and unleashed the hysteria of _Oh Boy!_ onto our screens in 1958. Recorded in front of a theatre audience of hundreds of screaming girls, the show helped launch the careers of Cliff Richard, Marty Wilde, Billy Fury, Adam Faith and a host of other UK Elvis-inspired lip curlers. The show was raw and fabulously exciting, showcasing some of the authentic American rock'n'rollers, among them Gene Vincent, who appeared clad in his customary black leather and wearing the leg iron that was a legacy from a teenage motorcycle accident. Good was the definitive opportunist and, as Vincent approached the microphone at the front of the stage and came into camera range, his Oxford accent could be heard clearly above the screaming girls, as he shouted his instructions to the afflicted singer. 'Limp, you bugger,' he implored. 'Limp!'
Following his appearance on _The Beatles Special,_ P.J. Proby's career took off. Within a year he'd had five Top-20 hits and in early 1965 set off on a package tour of ABC theatres, with Cilla Black topping the bill. I found it hard to see his appeal. He had the voice of a pub singer, face contorted with sincerity as he wheeled out excruciatingly overblown versions of already melodramatic ballads, 'Somewhere' ('Thar's a per-lace foor wusss/some-a-where a per-lace foor wusss') and 'Maria' from _West Side Story._ But he had an image – ponytail and breeches. The problem was that the breeches kept splitting in the middle of his pelvis-swaying set and he didn't believe in wearing underwear. The first night he got a warning to cool it down or face being thrown off the tour. The second night he got massive press as public outrage, Eminem-style, was ignited. There were young children in the audience! The third night was the ABC Northampton and as Dad made his way across the stage, the curtains closed on the Proby career. Off the tour, he was a bankrupt three years later. Dad also arrested my future wife.
Sue Tilson was really cool. Everyone I knew seemed to know her name. She was three years older than me, had beautiful long, auburn hair, pale white skin and always dressed in a black rollneck sweater and jeans. She was a Beatnik and hung out with a whole crowd of arty, seemingly interesting people, some of whom were gay, all of whom dressed more or less the same as she did. They were mostly into John Coltrane and the Modern Jazz Quartet and read the Beat Poets, Jack Kerouac or J.D. Salinger's _Catcher In The Rye._ We met at a party, me stepping in when she was being hassled by some bloke she didn't want to know. She invited me to meet her and her friends at the Sunnyland Jazz Club, held weekly at one of the pubs near where she lived. She was a fantastic dancer and a wonderful person and I was drawn to her. She cared about people and talked passionately about her work with mentally handicapped children. She was politically aware and liked to discuss the issues of the day, most of which were beyond me. To start with, I was probably something of an embarrassment for her, this rather lovelorn police cadet hanging around in full view of all her cool friends. It took a bit of time to win her confidence, but we gradually began to see more of one another until finally I invited her home.
Like many of her friends, Sue had joined the Campaign for Nuclear Disarmament and had taken part in a major demonstration that had closed Mercer's Row and brought chaos to the centre of Northampton. 1963 was the time of the Aldermaston marches, and protests on both sides of the Atlantic about the Cold War America/Russia stand-off over Cuba. For a while we really did feel that there was a finger poised above that red button. Although it was all happening on what seemed like the other side of the world, we felt the implications and were aware of the potential consequences of the nuclear muscle-flexing that was part of the early-60s East/West political relationship. We were scared of it all and Sue had been one of the people sitting in the middle of Abingdon Street with the protesters, refusing to move even when Dad and other members of the Force arrested her and several of her friends. Blissfully unaware of all of this, I took her home to meet my parents. It was a very cold and difficult atmosphere when she and Dad finally stood face to face in the front room of our house! Still, despite everyone's initial reservations, she and my parents began to forge a friendship and affection that survived throughout the years. Sue and I got married in the summer of 1967.
Jon Bird had been regularly in touch, telling me how fantastic life was in London, that I must get up to town and visit him at his flat in Hampstead. 'The house is great, you'll absolutely love it,' he told me. And he was right.
Built in 1846, the building sits at an angle to the main road, taking up the entire corner of Rosslyn Hill and Hampstead Hill Gardens, which curves around and down at the back of the house. It was constructed across different levels, three stories at the front, four stories at the back, with a basement extension curving round into the small side garden. Inside, it seemed like a labyrinth, with little staircases and corridors linking the various sections of the house. The interior design was random, with lots of rooms of different sizes, some at opposite angles to one another, with big sash windows and loads of nooks and crannies.
The house was run by Hetta Empson, wife of author William Empson, famous for _Seven Types Of Ambiguity_ , regarded as an important literary reference work at the time. I only met him once. He was a lecturer at Sheffield University and was away most of the time. Hetta lived on the ground floor and rented the rest of the house, a room here, a flat there, to students. The place always seemed to be packed with people, mostly from the London School of Economics (famously militant at the time). Jon shared a flat with a photography student called Roger Perry and the whole house had a vibrantly creative feeling. The atmosphere struck me as being totally amazing. I was desperate to move to London anyway and began regular visits to plug into the feeling.
Eventually one of the students vacated a small room on the first floor, just about big enough for a bed, a chair and my record player. I painted the walls purple, put up a couple of posters and moved in. It was £4 a week. I had no money at all, no real plans and certainly no prospects. But suddenly I was in London. I couldn't have felt more excited.
Recently I went to see the house again. I was looking up at the window of my old room when a woman strode purposefully across Hampstead Hill Gardens towards us, two teenage boys trailing behind. 'Why are you looking at that house?' she demanded.
'I lived there in the late 60s,' I explained. Her expression softened.
'Did you know Hetta?' she asked me.
'Yes, she was very kind,' I ventured, adding she would let me off the rent if I didn't have the money in return for doing a bit of cleaning in the hall and the stairwells.
'Hetta wouldn't like it here now,' she told me. 'The house has changed completely. It's all been renovated and split up into modern flats, something she never wanted to happen.' She went on to tell me more of the recent history, before introducing the two boys. 'These are Hetta's nephews,' she said. I asked her why they were there.
'Like you,' she said, 'we've just come to have a look.' It was a strange coincidence.
The memories came flooding back. Hampstead village was just a short walk up the hill and was so pretty to look at, with its narrow, cobbled streets and flower baskets. The residents looked colourful and interesting; the High Street buzzed with life. The wide open spaces of Hampstead Heath and Parliament Hill Fields were on the doorstep, the latter via South End Green, with its grocery shops, patisseries and pavement cafes, the former overlooked by Jack Straw's Castle, at the time one of the best pubs in London. There were galleries and bookshops selling the latest editions of new-generation publications like _International Times_ and _Oz_. And there was the Everyman cinema.
I didn't see it immediately as it was tucked back, just behind the main crossroads at the top of the High Street, but eventually I noticed the glass-fronted cabinet on the outside wall of the cinema, full of stills of the featured programme, a film by François Truffaut. I'd never heard of him before, but the pictures looked great and I wandered in – to be spellbound by _Jules et Jim_ starring Jeanne Moreau. I'd never seen anything like it before, the story of a _ménage-à-trois_ , and was fascinated by the style and gentle pace of the film. I wanted more of this, and with time on my hands, for a while I was able to see just about every new film that was featured in this beautiful, tiny cinema. I saw Fellini's _8½_ and _La Dolce Vita_ , discovered the Jean-Luc Godard movies _Alphaville_ and _Masculin Féminin_ and thought Jean-Paul Belmondo and Anna Karina were a sensational couple, radical, dangerous and cool. I couldn't believe what I was seeing on the screen. Sex, controversy, self-absorption, excess, revolution, existentialism. Previously I'd had no idea films like these existed. You certainly didn't see them at the Essoldo in Northampton, despite the row of double seats for the snoggers at the back of the balcony. The most exciting thing on screen had been the occasional naturist movie with an X certificate. But celluloid was the least of my culture shock.
I moved very few things to London with me, but I did take my record player and my record collection – all singles, dating back to 1957. Among them was 'Diana' by Paul Anka, my first record. I've kept that old 78, on the green Columbia label, 'the finest name on record', catalogue number DB3980. Still inside its original sleeve, it is now in a frame on my studio wall. My parents bought it for me when I was 11, along with a rather battered wind-up gramophone. My love affair with records had begun.
I first heard the sound of 'Diana' coming out of a jukebox as I was walking past a coffee bar in Cromer, on holiday with my parents. I stopped dead, went in, changed all my pocket money into threepenny bits and fed them into the jukebox, playing that record over and over until my money ran out. I couldn't wait to buy it and be part of the excitement that record represented to me. Buying records was the thing I wanted to do most. I started doing a paper round to fund my new obsession. While Mum did her shopping I'd be in the record department of our local Co-op, playing singles in the listening booths. I can still identify the ones I bought there because, for some reason, they used to cut off the top left-hand corner of the sleeves. Or I'd be down at John Leaver's record shop in Gold Street in the centre of Northampton. I'd cycle down there and just hang around, listening to the music they were playing in the shop, or waiting for the Decca delivery van to arrive with new releases on a Thursday evening at about 5.30. Decca had all the great labels at the time – London American, Coral, RCA, Brunswick. I could pick up the latest Elvis or Duane Eddy, Jerry Lee Lewis, Everly Brothers, Little Richard, Ricky Nelson or Buddy Holly single and have the thrill of feeling that I'd got this record a day before it was officially released!
John Leaver's even did imports, not that I could afford them. But I thought American records just looked so great, with the big jukebox holes in the middle. I finally got the money to invest in Del Shannon's 'From Me To You' in 1963, the first time a Lennon and McCartney song had made the American chart, on the pink Big Top label in a white and blue sleeve. It looked fabulous.
I was a big Del Shannon fan, and actually got to meet him on _Whistle Test_ in 1974. He told me that he gave Max Crook a 50 per cent songwriting credit for creating the middle solo that makes 'Runaway' such a distinctive record. Not that either of them gained much financially, as they hardly received a penny in royalties. Despite having had 14 hit singles in the five years from 1961 to 1966 he was penniless by the end of the decade. It was particularly sad that, like Roy Orbison, he passed away just as a Tom Petty/Jeff Lynne-inspired revival was gathering momentum. There was even talk of him replacing the 'Big O' in The Wilburys. He recorded the album _Rock On,_ which came out on Silvertone in 1991, with Lynne, Petty and Heartbreaker Mike Campbell, but died shortly before the album was released.
Music was the backdrop to my entire childhood. My Mum always loved the radio and I vividly remember my early years spent in the glow of the light from the radiogram, the biggest piece of furniture in our living room. I was born in 1946 and, like most other families, we didn't have a television in the house. The radio was our entertainment, our television of the mind. _Listen With Mother,_ then Archie Andrews, and _Journey Into Space_ were part of my daily routine. (I suffered scarlet fever when I was seven and radio was a big part of my recovery. Mum and I were in isolation in the house for more than two months. I can still remember the nightmare deliriums that came with a temperature of 105 degrees.) As I grew older I graduated to _The Goons,_ started listening to the music shows on the Light Programme, and then discovered Radio Luxembourg, whooshing in on 208 metres medium wave.
Jack Jackson was the first DJ I really noticed and was the first, to my knowledge, to use a sound effect, a gag or some other device played in from tape to link from one record to the next. He'd tell jokes based on the lyrics of the song, or use the opening lyric line as the answer to a question he asked as he talked over the intro. He'd mess around. Compared to the very austere approach of most 'announcers' of the 50s, he sounded completely different. I didn't know it at the time, but this was the prototype developed so brilliantly by Kenny Everett in the 60s.
I also liked David Jacobs, mainly because he did _Pick Of The Pops_ at 10.40 on Saturday nights on the Light Programme. I remember him playing 'There's A Moon Out Tonight' by The Capris when it made the charts, an absolutely fantastic record. He did a dedication for me on my 15th birthday, my first-ever mention on the radio, requested by my mother. She continued to write to him and it was nearly four decades later that he learned I was related to this person with whom he'd been exchanging listener/broadcaster correspondence. She didn't tell him she was Bob Harris's mother until I started doing programmes for Radio 2. I went along to his studio at Broadcasting House and 'came out'. He was taken aback, but was lovely about it and whenever I met him he would always smile and ask 'How's your mother?' Wogan always asks after Dad, but that's another story.
For my 12th birthday Mum and Dad bought me one of the original Dansette record players and I purchased my first two 45s – 'Problems' by the Everly Brothers and 'To Know Him Is To Love Him' by The Teddy Bears, my introduction to Phil Spector. I was never a great fan of the 78s – big, heavy 10-inch chunks of breakable black shellac, with that tiny little label stuck there on the middle. By comparison, the new vinyl single looked sleek, beautiful and cool, a light, flexible seven-inch disc with the thin, shiny playing surface dominated by a huge, imposing label. I thought my two new singles were amazing and I took them to bed with me that night so that I could lie there and look at them. I propped them up against my bedside light and fell asleep gazing at the blue and white striped sleeves and the black London American label, with its triangular centre. I woke up the following morning to discover them distorted, warped and unplayable under the heat of the light.
I soon replaced my damaged copies and as I built up my singles collection I started recording reel-to-reel tapes on my newly acquired Grundig tape machine in Mum and Dad's back room. By now I'd replaced my Dansette with a Decca stereogram, my first and only autochange machine. I'd hold the microphone close to the speaker while the music played, then talk while the arm lifted and the little shelf on the spindle retracted to let the next record drop onto the turntable. The old Decca group 45s were all pressed with one groove, so as the needle touched the clear black vinyl at the edge of the record the groove would instantly hook the needle right to the front of the music. From the top of the fade to the beginning of the next track the whole process took approximately 14 seconds, enough time for me to back announce the record, talk about the music and introduce the next song. I got all my information about tours, new releases and gossip from the _New Musical Express_ ( _NME_ ) and I used to cut out the Top-30 singles chart each week and underline the records that I owned, compiling my own weekly Top-20 chart, which became the basis of the shows.
I loved rock'n'roll and feel very lucky that I caught most of it first hand – Eddie Cochran records in particular. He cut a lot of stuff that was fairly ordinary, but the good stuff was absolutely outstanding.
I still think 'Somethin' Else' and 'C'mon Everybody' are two of the best and most explosive records ever made. He was so good lyrically and in 'Summertime Blues' wrote one of the first pop songs to contain any kind of overt political message: 'I called my congressman and he said quote/I'd like to help you son but you're too young to vote.' Really great stuff.
I loved black music, blues and doo-wop. The stunning combination of strings and soul on The Drifters' 'There Goes My Baby' had absolutely blown my mind, a sound unique in 1959. Soon afterwards the group's lead singer, Ben E. King, released 'Stand By Me', still my all-time favourite single. The string phrases in the middle solo match any piece of classical music I've ever heard. Years later, I saw The Drifters performing on a retro-package tour in Great Yarmouth, of all places, and met Ben E. King backstage. I'd taken my original copy of the single with me (London Atlantic 45-HLK 9358) and he signed it, on one side, 'To Bob from Ben E. King, thanks for being a friend'.
The show mostly comprised sing-a-long, all-one-tempo medleys of greatest hits, one song merging seamlessly into the next. But midway through the set, as that familiar bass-lead introduction began, Ben E. King stepped forward to the main microphone and began to speak. 'I'd like to dedicate this song to a friend of mine who's in the audience tonight. Bob, this is for you.' I can't even begin to tell you how I felt. I never dreamed when I bought that record that, over 20 years later, the song would be dedicated to me from stage by the man who recorded it. He even recorded a special message to use whenever I played it on the radio!
I was avidly buying Sam Cooke singles and still marvel at his voice and the influence he had. I was gradually building up my Phil Spector collection, ('Then He Kissed Me' is my favourite single of his, although I think 'Baby I Love You' has the biggest 'wall of sound'). I was 17 when 'She Loves You' and 'I Want To Hold Your Hand' came out and I got them on the day of release. I even saw The Beatles live – at the _NME_ poll-winners' concert at Wembley in 1966, their last UK appearance. It was pandemonium as everybody crushed forward trying to get to the stage. Two girls fainted onto me from the tier above. You couldn't hear a note above the screams. I thought it was totally intoxicating. I had no idea, of course, that seven years later I'd be up on that stage collecting my own award.
The music scene was absolutely buzzing at the time. Pirate radio was revolutionizing the airwaves, _Ready Steady Go_ started the weekend, the British beat boom arrived in a sweep of energy from bands like The Kinks and The Who. The Animals released 'House Of The Rising Sun', the Stones put out 'Satisfaction'. The Byrds recorded 'Mr Tambourine Man', and John Sebastian was beginning to produce the run of sunshine singles that characterized the sound of The Lovin' Spoonful. I arrived at Hampstead Hill Gardens with boxes full of them, along with other irreplaceable rock'n'roll stuff and priceless rarities. I thought it was a pretty good collection but I was quickly disillusioned.
My fellow inmates at Hampstead Hill Gardens were unimpressed by the teen side of Beatle-mania. _Revolver_ got them interested, particularly 'Tomorrow Never Knows', but they weren't really into The Beatles, they were more into the Stones (few people, in those days, were into both). I'd been collecting chart singles while they were buying albums. I'd heard Bob Dylan's 'Rainy Day Women' and 'I Want You' as they had been played on the radio, but they were buying _Blonde On Blonde_. I loved The Yardbirds, but they'd discovered Cream, along with Davey Graham, John Martyn, Roy Harper and a whole load of people I'd never heard of before. For the first time I experienced the extraordinary guitar playing and hauntingly melancholy voice of English folk singer Bert Jansch. Paul Simon had recently lived in London, playing the folk clubs, and _Parsley, Sage, Rosemary and Thyme_ was always on the turntable. They were passionate and knowledgeable about people I'd hardly even heard of. They liked acid rock while I was chewing bubble gum. 'Sue's Gonna Be Mine' by Del Shannon suddenly felt like a very uncool place to be.
I'd been in London less than a fortnight when I ditched two-thirds of my entire collection at one of the local second-hand record shops. I didn't care to start with as the money paid the rent. It took a while before it dawned on me what I'd actually done! I spent a lot of time during the next few years ferreting around in various junk shops, trying to find copies of some of the gems I'd so casually discarded.
Having no money was a problem and, outside of the house, I didn't know anybody in this big city. I spent a lot of time, as I always had done, with the radio. At last I could get good reception on Radio London, which was broadcasting, like the other pirate stations, from a boat anchored just outside Britain's three-mile coastal limit. I still think the Big L was one of the best radio stations I've ever heard. It opened my eyes to what music radio could do. The station generated a fantastic new energy, transmitted by a roster of new broadcasting talent – Dave Cash, Tony Blackburn, Dave Dennis (the Double D) – and through a package of fantastic jingles, a lot of them crafted by on board genius Kenny Everett. And, miraculously, starting at midnight, they had John Peel.
_The Perfumed Garden_ was a revelation. The first time I heard it everything somehow fell into place. More than anything else before or since, listening to John ('broadcasting in my stoned solitude') sending out these programmes from the middle of the North Sea crystallized everything I'd ever felt I wanted to do with my life, that building up my record collection, spending all those hours and hours making tapes in the back room of my parents' house really could lead to something. I now knew that I wanted to be doing exactly what John was doing – turning people on to the most amazing music I could find. This was my plug-in moment. If I could've just pressed a button that very second and made it happen, I would have.
At that moment the passion I've always felt for music and the radio fused.
The music John was playing was sensational, a mix of progressive American rock, folk and UK psychedelia by people I'd mostly never heard of before. He was introducing Jefferson Airplane, The Misunderstood, The Creation, Love and The Doors mixed with tracks from _Revolver_ , _Pet Sounds_ by The Beach Boys and some of the 'Epistle To Dippy' stuff that Donovan was recording at the time. It was clear that he'd somehow managed to establish the freedom to play what he liked. I really wanted to meet this person.
I used to go to a club called Middle Earth in Covent Garden. Right through 1967 I was there almost every weekend. It was situated in a huge, dark cellar basement, illuminated by liquid light shows and black-and-white films projected onto the walls. They'd sometimes show Kenneth Anger movies and have naked girls wrestling in mud. There were magazine and clothing stalls and a lot of pot smoking. Alcohol was banned, live bands played all night. I saw sets from The Byrds, Pink Floyd, Brian Auger and Julie Driscoll, Traffic and, memorably, Captain Beefheart and his Magic Band, introduced by a tearful Peel, overcome that he was meeting his favourite band.
I saw Arthur Brown performing 'Fire' wearing a silver motorcycle helmet-like crown, which he had set alight in the middle of the number while he cavorted around the stage, flames dancing around the top of his head. The headband got so hot his hair started burning. For a few moments he carried on, trying to ignore the searing heat burning into his temples. But he eventually had to concede to the inevitable and with all semblance of cool discarded, wrestled the whole contraption off his head and hurled it to the back of the stage, where it landed in a firework display of sparks and flame, instantly igniting the back curtain. In the absence of any fire extinguishers or procedures, several burly roadies were seen stamping on the flames with their size 13s while Arthur Brown poured cold water over what remained of his hair.
Sometimes the club would move to the Roundhouse in Chalk Farm, a building that had previously been a maintenance bay/roundabout for steam engines, then a Gilby's gin warehouse before Arnold Wesker attempted to realize his dream to turn the place into an arts centre. In 1965 he moved in with his theatre project 'Centre 42' and opened the doors of the old building for the _International Times_ Christmas party and for the 'happenings', drama, mixed-media events and concerts that followed. The Stones played there, so did Pink Floyd, Jefferson Airplane and The Doors. And I was there for a magical evening a few weeks before the release of The Beatles' _Sgt. Peppers Lonely Hearts Club Band_ in the spring of 1967. I'd heard a rumour that there was to be a playback of some of the tracks from the album and was one of a few dozen people to turn up at the Roundhouse on the off-chance, not really knowing what to expect. We wandered into that dark, cavernous building, a few bare bulbs lighting the way, to discover DJ Jeff Dexter with a turntable he'd borrowed from Tiles club and a couple of 4 by 12 Marshall speaker columns. He was playing 'Fixing A Hole', 'Lovely Rita' and 'It's Getting Better' from an acetate given to him by Paul McCartney, and it was fabulous to sit and listen to those amazing songs echoing around that dark old dusty place – and exciting to think that we were the first people outside of the band to hear them.
Jeff was a central conduit in the underground music scene and he looked amazing – a little elf-like in figure, with long blond hair and rainbow clothes. He was the resident music man at Middle Earth and I still believe him to be the best DJ never to have broadcast. Occasionally, John Peel would be there to do a guest spot but I made no attempt to introduce myself and bridge that gap between icon and fan. At that time it just seemed to be too big a gap to jump. But the meeting was not as far away as I imagined.
I'd been buying a lot of the new magazines and university newspapers that were proliferating at the time, writing off to the editors, asking if there was anything I could do. I'd done a bit of writing (well, I'd had a letter published when I was 15 in the Northampton _Chronicle & Echo_!) and thought that maybe I could be some kind of London correspondent. I finally got a reply from _Circuit_ magazine, published jointly by Queen's College, Cambridge and University College, London. They needed someone to distribute copies of the magazine around the newsagents and bookshops in central London. So I stacked a few hundred copies of _Circuit_ into the back of my car and trundled them around the West End. I didn't care that it was menial. I could now say I was working for a magazine.
Soon after, a friend of Roger Perry's came to visit him at Hampstead Hill Gardens. His name was Tony Elliott and he was editor of the Keele University magazine, _Unit._ He told me he was looking for someone to feed stories and articles up from London into the magazine, a kind of London correspondent. It was perfect! He immediately commissioned me to write an article about an experimental mixed media group called The Exploding Galaxy, led by a kinetic sculptor called David Medalla, who were living in a commune in North London. I moved in and joined them for a while. Here's part of what I wrote. (Remember this is 1967, OK?!)
It is 3 a.m. at the Roundhouse in Chalk Farm, scene of London's UFO Club. Over a white circular screen that surrounds the central area, projected slides dribble a hundred magnified strobes of colour. Behind the screen it is dark except for a small circle of soft white light, around which, in the unfamiliar silence, sit nearly one thousand people. David Medalla announces the first dance and The Exploding Galaxy begin.
Four men and three women dance for almost 30 minutes. They wear a sash of flowers around their necks and tiny bells are attached to bands around their ankles. They dance barebreasted to the sound of bongos and a flute. The Exploding Galaxy are happy and people applaud and throw money. Someone says: 'Their dancing is like early morning with the sun rising and the mist and the wet yellow leaves falling in a gentle yellow sunlight.'
The Exploding Galaxy was formed only six months ago by David Medalla and Paul Keeler, but already it has expanded to contain almost 50 people. This, says Paul Keeler, is the significance behind the name.
'We hope the Galaxy will continue to expand until it contains one thousand, two thousand, even three thousand people. Then the audience as such will cease to exist.' But all attempts to define clearly how this will happen or what The Exploding Galaxy actually does or is are dismissed by them as being 'irrelevant' or 'of no real importance'. Almost the fact that they just 'be' is sufficient justification for what they are doing. 'The Exploding Galaxy does not have any specific aims,' says Paul Keeler. He speaks of the Galaxy as being 'a spirit of mind'.
Things happen in the moment they occur. The Exploding Galaxy experiment in almost every field of visual and verbal communication – ballet, poetry, kinetic drama, sculpture, painting, spontaneous happenings and films. Recent events include 'The Evolving Documents Show' at the Arts Lab, an open-air poetry reading by Michael Crawford and dancing by David Medalla and J. Henry Moore, watched by nearly 300 people; a five-hour ballet at the Roundhouse; and a people's show held at the Middle Earth club, Covent Garden, in which many of the audience joined in.
In addition, as reported in a July issue of _International Times_ , 'The Exploding Galaxy gave a performance which must constitute London's most liberated theatrical performance in history. Arthur Brown, singing while wallowing on the floor with four Galaxy nudes, reached an all-time high in erectile music ... never have so many been so nude so early and for such good reason.'
The Exploding Galaxy have little or no money and this is one of its greatest problems. 'We are desperately trying to overcome the problems of poverty until it is not important,' says David Medalla.
While there is talk in the underground of a possible 'Underground Arts Council' which would help support The Exploding Galaxy and others like them, this idea is a long way from realization and for the present, at least, it seems the Galaxy must continue to live at poverty level.
They share a house where they have lived, without electricity, for the past five months. The house has been the subject of regular police raids and following an article which appeared in the _News Of The World_ earlier this year, heavily criticizing both the people of the Galaxy and their activities, giving their North London address, they have received harassment from the police and general public. The _International Times,_ however, was not slow to speak on their behalf. 'A secure and free place to live is what makes life possible for them. The police actions to deprive them of this constitutes state censorship of the lowest form – to deprive artists of their most basic needs in order to suppress what they have to say.'
Indeed, the police have been neither skilful nor tactful in their handling of The Exploding Galaxy in recent months, but this appears to have done little to suppress the extrovert and enigmatic personality of the group or the remarkable talent of some of its members.
It was odd to be writing all this, considering my background. The culture shock for me was total. Dad was none too pleased, reading about the raids in _News Of The World_ and reading my criticism of the way the police had handled it all. I think he was most concerned that I might be getting into drugs. But despite the worries he had about the new life I was living, we didn't argue. Ultimately, I knew he trusted me.
Tony thought the article was fine and published it in the edition of _Unit_ dated December 1967. He asked me if I'd like to do another piece and did I have any idea what I'd like to write about next. 'John Peel,' I said. 'I'd love to do an interview with him.' A couple of days later Tony phoned me to say John would do it and soon I met John at his place in Fulham. He was there with Marc Bolan, who was sitting cross-legged on the floor, strumming an acoustic guitar.
John went everywhere with Marc at the time. He was promoting the hell out of him and had it written into contracts that Tyrannosaurus Rex would appear with him at gigs and interviews. I began a close friendship with both of them that lasted through the next five years.
I liked Marc immediately. He was tiny and looked very pretty and mischievous, wearing his pastel-coloured silks, with his long, black corkscrew hair and elfin face. He had an incredibly cheeky grin I found immediately endearing. But he was very focused. I got the impression of someone who knew exactly what he was doing and where he wanted to go. John was more resolute, world-weary. As I was setting up the tape machine, he told me that he'd been living in America and that the stacks of albums he'd brought back with him provided the soundtrack to his early Radio London shows.
The introduction to this interview was already written.
Pop music seems to be splitting in two. In one direction Engelbert and his mimics rush away with their adoring fans, whilst towards the other extreme, various groups and individuals led by The Beatles progress to a freer, improvised and distinctly creative sphere. Though most people seem content with the 'wallpaper' and fab-40 Radio 1, a freer and creative presentation is creeping in under the figurehead of disc-jockey John Peel.
John Peel, with his _Perfumed Garden_ programme on Radio London, a mixture of records, poetry, letters and conversation, immediately satisfied a demand for intelligent listening and 'involvement' from the public. He will shortly have another _Perfumed Garden_ on Radio 1 and at present is joint host of Sunday's _Top Gear._ In a conversation with Bob Harris he talks about the way pop music is evolving and about his career and attitude to pop resulting in his becoming Britain's first really creative DJ. Perhaps one day, when the oldish DJs at present monopolizing the network are eventually pensioned off, John Peel will be seen as a prototype for the future.
I switched on the machine and John began to talk.
I think it is unfortunate to have a concept of what pop music is because it is expanding so much now. It is difficult to say whether the principal writers at the moment are songwriters, poets or what they are. Groups are veering towards the theatre and all kinds of elements are being introduced into popular music, which I think can only result in the improvement of all of them.
I think eventually it'll all just become one; everything will become fused. Pop music will become television will become pop music will become theatre will become poetry will become whatever ... things are progressing in this direction. The theatre is becoming involved, for example the lightshow type ideas and the film clips groups are doing, and The Beatles' _Magical Mystery Tour._ Already pop music, poetry, films and TV are getting mingled in with one another until you won't be able to say where one begins and the other ends.
I only wish that when I was younger there was a _Perfumed Garden_ scene, because I was so incredibly hung up and I'm sure it would've taken less time to get my ideas straightened out.
When I started to work for Radio London, I began by doing the 'fab 40' stuff and then I volunteered to do the late night show (12–2 a.m.), because no one else wanted to do it. After a time I began bending the format a little more each night until, by the time the attention of the station management had been drawn to it, it was already an established fact.
The other disc-jockeys reacted against it to begin with because this is something a disc-jockey has always wanted to do, to have this freedom thing, but the Radio London programme administrator, Alan Keen, was quite jazzed about the idea, so I started doing the whole _Perfumed Garden,_ just bringing in more stuff as I thought of it, whatever happened to come up or whatever was suggested.
Letters played an important part in it. People would say: 'Hey, will you try to do this?' and I would try to do it. I think it is the way a radio programme should be, although not all radio programmes because obviously you have to have some of the wallpaper music that Radio 1 is providing so well at the moment.
But you also need, somewhere in your day or in your week, a programme where the people listening are not treated as though they are totally moronic. I don't know why I called the programme _The Perfumed Garden_. I didn't know about the book at the time, it was just a nice idea, wandering at night through a perfumed garden. As far as I was concerned, it was a state of mind.
I would like to think that it was more than just a pop record show because it did, I suppose, try to influence people into at least sitting up and thinking about the ideas that I believe are important. It doesn't mean that I thought everyone else had to believe in them, it was more a question of 'here you are – do what you like with them'.
But so many people became involved with it. I got incredibly involved myself and I think if you are doing that regardless of what it is you are doing, it communicates to other people. But you have to know that as you get involved in something, people are going to appreciate your involvement and perhaps try to become involved also and in this way the whole thing can just spill over.
I really think that it can have consequences beyond anyone's wildest hopes, because if people become really strongly involved in something and they really believe in it and can get other people involved as well, you've got the start of something very important.
You see, the people who were deeply involved with _The Perfumed Garden_ weren't, in the main, people who were involved with the music scene. They were just very ordinary people living very ordinary lives in very ordinary places. The ideas behind it and the sense of involvement I felt may have communicated something new to them and they became involved. Something existed for them to become involved in, whereas previously nothing had.
Reading this again now, it strikes me how accurate John was with his 'pop will become television will become pop' theory. Yes, The Beatles had done _Magical Mystery Tour_ and the surreal and wonderful film for 'Strawberry Fields Forever', which pioneered the idea of making a video to promote a new single. But no one could have predicted MTV (although Ronan O'Reilly, founder of Radio Caroline, did have a wacky scheme for a flying television station, pre-dating satellite) and the massive power of mainstream pop television.
As I packed the equipment to go, John passed me an album and asked if I'd heard it. I said I hadn't. 'Take it with you,' he said. 'I think you'll like it.' It was _Forever Changes_ by Love on the Elektra label, one of the most brilliant and extraordinary records ever made. Even by today's standards it's a powerful album; surreal lyricism and biting, staccato guitar licks mixed with lush, romantic string arrangements in a kind of musical schizophrenia. I still love it, regularly play tracks on air.
My friendship with John and Marc grew over the next few months, during which I embarked on the only 'proper job' I've ever had. I'd worked in the dressing-gown department of Selfridges during Christmas 1966 to earn money and then, briefly, in a clothes-packing warehouse just off Petticoat Lane when I again fell behind with the rent at Hampstead Hill Gardens. But in spring 1967 I saw an advert for a job at Tiranti's, later known as the London Art Bookshop, in Charlotte Street and went for an interview. I didn't think I was really qualified but for some reason the Tiranti family seemed to take to me and offered me the job of assisting in the shop and looking after customers. It was one of the premier art bookshops in London and had the most serene and beautiful atmosphere, like a small private library. I couldn't believe how lucky I was, working in this beautiful place, with access to the best literature, meeting the artists, photographers, sculptors and designers who used to visit the shop from all over the world. I was like a sponge, soaking up all the new colours of my life.
Sue joined me in London later that year in my tiny bedsit, but we soon realized we needed more space and moved across Hampstead and into the top floor flat of 77 Platt's Lane. Sue had bought me a Philips portable record player and I would sit on the balcony overlooking the road, pretending I was playing music to a festival crowd. Little did I know that 25 years later I'd be back in Platt's Lane, fighting a legal battle with a fellow Radio 1 DJ that threatened the whole structure of my life.
Sue and I were at home one evening in the early summer of 1968 when we got a phone call from Tony Elliott saying he'd like to drop in and see us. He was on his way to France to take a year's sabbatical from university, but was planning to spend a couple of months in London. He had an idea for a one-off summer events magazine and asked if I wanted to help him get it published. It would be full time and I'd have to give up my job at Tiranti's. I was sad to leave, but I just couldn't deny this exciting new project.
The magazine consumed us from then on. I edited the music sections, Tony did movies and theatre, and all other editorial was shared. We made loads of phone calls to gather the information. Tony borrowed £70 from his aunt to fund a 5000 print run and Tony, his girlfriend Stephanie, Sue and I began laying out the first edition on the table in our kitchen, using Letraset and glue. The magazine was designed as a poster, to be pinned up on a wall or folded down and carried in the pocket. Cost was imperative and a magazine with staples was out of our price range. The name came last, but _Time Out_ seemed the best two-word description of what the magazine would offer and we had the underground market to ourselves; there was nothing else like it. We were creating a magazine we wanted to read. The first edition cost one shilling and was published on 12 August 1968.
John Peel invited me onto his new BBC _Night Ride_ programme to talk about it all. My first-ever broadcast, on a John Peel show! Marc Bolan was the first to react, sending me a most beautiful letter of congratulation.
We sold most of the copies of the first edition of _Time Out_ to the queues at the Sunbury Jazz Festival and at the Hyde Park free concerts, such a glorious feature of the summers of the late 60s. So many great bands played there. I saw sets from Family, Fleetwood Mac, Pink Floyd, Roy Harper, Blind Faith and, memorably, The Rolling Stones with their new guitarist Mick Taylor and Mick Jagger dressed all in white, reading Shelley and releasing butterflies in memory of Brian Jones, who'd died a few days earlier. The money we made from the sale of those first copies financed edition two, for which Cream lyric writer Pete Brown wrote the editorial.
Much as I'd done with _Circuit_ , I was filling the boot of my car with copies and driving all over London, trying to get the magazine into all the cool bookshops and other places I liked. I called in at Indica Books in Holborn, the Compendium Bookshop in Camden Town, the Arts Laboratory in Drury Lane, the Marquee in Wardour Street, Klooks Kleek Club in West Hampstead and the Country Club in Hampstead. I also stopped off at Musicland in Berwick Street, my favourite record shop, along with Simon's Stable in Portobello Road. Musicland always had loads of American imports and you could listen to them in the shop. I bought the new H.P. Lovecraft LP and asked the guy who was serving if he'd stick a dozen copies of _Time Out_ on the counter for me, sale or return. He looked through the magazine for a few moments before agreeing to take a dozen copies if we reviewed his new album in our next edition. He handed me a copy of _Empty Sky_. The shop assistant was Elton John, earning a few bob on the side prior to the full-time launch of his career with the release of 'Lady Samantha' a few months later.
But it was the third edition of _Time Out_ that really got us noticed. The cover was designed by one of my Tiranti customers, Alan Aldridge, a really hot name in graphic art at that time. It was a controversial cover, featuring a profile photograph of a woman's naked torso, onto which Alan had drawn an eye above the breast and a smiling mouth below it. By outlining the side of the breast to make it look like a nose, he created an image that looked at first glance like a face. It was a closer look that revealed it to be a nude woman.
With the combination of Alan Aldridge and naked female flesh, suddenly the media picked up on us. We got proper distribution, Eric Clapton was said to want to invest. We moved into the basement of 70 Princedale Road in Holland Park, underneath the offices of Blackhill Enterprises, the people who staged the Hyde Park festivals and managed Pink Floyd. Peter Jenner was one of the leading lights there, still one of the most intelligent and respected of music business figures. Keyboard player Rick Wright was around a lot, his wife Juliet was the receptionist. Vocalist Syd Barrett would often hang out, mostly motionless, staring into space. _Oz_ magazine had their office a few doors away and Caroline Coon was on the same block, running the drug-advisory service 'Release' from No. 52. It felt like we had our own little underground community there.
_Time Out_ 's arrival at Princedale Road roughly coincided with Sue and I having to move from Platt's Lane. The owners of the house decided to sell and we had to go. On the recommendation of photographer Ray Stevenson we stayed briefly at Sandy Denny's house in Parson's Green, before moving into a ground floor flat in a large Victorian house in Blackheath on the other side of London. Initially we liked it, living on the edge of that big heath at the top of the hill, but we quickly realized we'd made a mistake. We were too far from the West End, at least an hour in the car most times. I'd previously been able to drive to Northampton in the time it was now taking me to get into central London.
Within only a few days of moving in we were burgled. Thankfully, he'd only just got in when I disturbed him and in his dash for the open window didn't have time to grab very much, but these things shake you up. A few days later we heard someone shouting from our front porch. As I opened the door a young guy fell into the hallway covered in blood. He'd been beaten up. It didn't bode well.
The one good thing about the house was the owner, Tim, who'd inherited it from his family. He was a medical student, ran the local college disco and kept all the equipment at home. He had a double deck unit, cassette, microphone, amplifier, speakers, all set up in the sitting room. The bass sound off that thing was fantastic. He said I could mess around with it as much as I wanted to and it was so great to be able to work with proper equipment at last. As my technique improved he took me out to do a set on one of his gigs. I took David Bowie with me.
I'd met David at a Tyrannosaurus Rex session at Trident Studios in Soho. He and Marc occasionally played on each other's records and both worked with producer Tony Visconti. The press later played up a rift between Marc and David but it wasn't like that at the time; they got on great. I still believe Marc's best piece of recorded guitar playing is his solo for 'The Prettiest Star', David's follow-up to 'Space Oddity'. Marc was a much better guitarist than people give him credit for, although he never had a great ear for tuning. Producer Tony Visconti was forever trying to devise diplomatic ways of telling him that the guitar was out. It became a big thing.
I loved those sessions, experiencing record production for the first time and the layering of the sound. It was fascinating what could be done and I was even able to contribute. Sue and I called into Trident one evening with Tony Woollcott, who eventually became a vice-president at Sony Music. David and Tony Visconti were recording the vocals for 'Memory Of A Free Festival' for the _David Bowie_ album and needed to get some crowd atmosphere on the fade. Tony, Sue and I went into the studio, gathered round the microphone and began to sing. 'The sun machine is coming down, and we're gonna have a party, uh-huh-huh.'
We didn't have great voices, but it didn't matter. Having recorded the lines once, we recorded them again, then again and again, Tony Visconti gradually building up the voice tracks to resemble a festival crowd singing along with the song, adding some hearty whoops, yells, hollers, whistles and claps on the final fade. That first gig with David, however, had a completely different vibe.
It was a college end-of-term student celebration night in the East End of London and subtlety was not part of the mix. My job was to fill the dance floor, and keep it filled, with Motown, Stax and heavy rock. About halfway through the evening I introduced David to a predominantly male crowd, already agitated that the dance records had suddenly stopped. He ambled out with his new girlfriend, Angie, who sat to David's right, her legs dangling over into the audience now packed up against the front of the stage. David switched on a small amplifier and plugged in a microphone and his guitar. He slid a tape into the cassette machine on the front, and as he pressed the start button, we heard the opening acoustic guitar chords of the backtrack to 'Space Oddity'.
Compared to the decibels I'd been blasting out, David's system sounded like a transistor radio. He hadn't even got to 'Major Tom to ground control ...' before the booing started. Wrong person, wrong night. Pints of beer started landing on the stage, glasses being smashed. By halfway through the song it was impossible for him to continue.
I suddenly found myself striding out into the middle of the stage in a red-faced state of righteous indignation. 'You mark my words,' I shouted, 'You'll remember the night you booed David Bowie off stage, you morons. More fool you. This man is going to be a big star!' I really did say that. Hasty exit left, grabbing record box en route.
_Time Out_ was becoming a success. Sue and I managed to move back across the river, albeit into a small bedsitter in Hammersmith, and things were looking good. But I was getting uncomfortable with the way _Time Out_ was going. Tony had a very specific agenda. He wanted to do a glossy, to be the editor of a successful, Nova-like commercial magazine, whereas I'd always thought of it as a conduit for the underground. It sounds very hippy-ish, but then that's what I was. Now we had an office and an expanding editorial board, office politics began to evolve. Tony began to realize I'd stopped enjoying this. I'd disappear for a couple of days, come back, make a few phone calls – my heart really wasn't in it any more. I arrived one morning to discover the locks had been changed and I couldn't get in. I'd been voted off the editorial board in my absence. Tony produced a letter, in which I relinquished any right to claim any ownership of any aspect of _Time Out_ from then on, which I signed. I should have seen it coming, of course. I wasn't committed to the 'drive' ethos that was now propelling things along. Nor do I regret it. People have pointed out to me since what I might now be worth if I'd managed to maintain some kind of interest in _Time Out_ (Tony Elliott is worth millions), but there you go. I just didn't like that office life. Now it was time to get myself on the radio.
TWO
'DJ Wanted ...'
SUE AND I, TOGETHER WITH OUR CAT MUMBLES, SPENT CHRISTMAS 1969 in a small stone cottage we'd rented next to the river in Bibury, in the middle of the Cotswolds. It was a really beautiful place, spoiled only by the ice-cream van that parked opposite every afternoon, and the constant influx of tourists. The place is a genuine English beauty spot and attracted hundreds of visitors each week. We regularly had people wandering into the garden and taking photographs through our windows.
With me out of work and Sue now at college we had absolutely no money. We were like Scratchet, throwing the odd lump of coal onto the fire, but as we listened to the church bell ringing in the New Year, I suddenly felt a tremendous sense of excitement and optimism. I had the strongest possible feeling that 1970 was going to be a good year.
Three days into January I got a call from Jonathan Green, editor of _Friends,_ the UK equivalent of _Rolling Stone_ magazine. He was planning to feature an article about Radio 1 and asked if I'd like to write and research it. Would I?! I jumped at the chance to plug in to where I wanted to be. I put the framework of the piece together and began to set up the interviews I wanted to do – DJs Jimmy Young, David Symonds and some of the programme producers. I asked John Peel who else I should talk to. 'Jeff Griffin,' he said. 'I think you and he will get on really well.'
Jeff invited me to meet him at Aeolian Hall, the home of the Light Entertainment and Popular Music Department for BBC Radio (full title!) in New Bond Street. I was surprised that this old building, in the West End of London, was so quiet and austere. Radio 1 was supposed to be a happening pop station and here were my long hair and loon pants being chided by middle-aged men in suits! But the atmosphere in Jeff's office was great and, reassuringly, a track by Family was playing as I walked in.
Family were just about my favourite live band at that time. I must have seen them play dozens of times, at Klooks Kleek or the Marquee, or in Hyde Park at one of the free summer festivals. Roger Chapman is, without doubt, one of the all-time great lead vocalists and I'd never seen him give less than a hundred per cent. I was at the band's final concert, at the De Montford Hall in their home town of Leicester in 1974, to witness the ultimate Chappo high-energy assault. By mid-way through the set he'd worked himself into a frenzy, stomping and prowling around the stage, pounding the beat with every footstep. But as he bore down on the microphone he stumbled and fell. People rushed from the side of the stage to help him to his feet, as he crashed his foot right through the stage. He was stuck almost up to his waist and rescue wasn't easy. It took some time getting him out of there: the floorboards had splintered like a vice around his leg and it was clear he was in considerable pain. For a time he couldn't move at all, but it didn't stop him singing. He just carried on with the set while they got him free. What a trooper! The evening was completed by a wild end-of-term party at the Leicester Holiday Inn. Based around the pool and involving increasing nudity and general celebration, all was eventually brought to a halt by the hotel management at around 5.30 a.m., following many complaints.
Jeff's office was the definition of organized chaos – records piled up in stacks on the desks, seven-inch sleeves and LP covers scattered everywhere, shelves over-spilling with albums and interesting-looking 'A' label promotional singles. There were reference books, running orders, correspondence, cassettes and reel-to-reel tapes, rock posters on the walls. Half a dozen black BBC programme boxes were on the floor, labelled for different shows. Jeff introduced me to fellow producer Bernie Andrews, with whom he shared Room 421. There was a great banter going on between them and it was clear they also shared a massive enthusiasm for music and an absolute determination to get more of it into the system at Radio 1.
When the Labour government came up with the Marine Offences Bill and closed down the offshore pirate radio stations in 1967, the BBC was instructed to accommodate the new teenage audience the pirates had located and entertained so brilliantly. The resulting reorganization within the Corporation was radical, involving the updating (or rebranding, as we would now call it!) of the Light Programme, Third Programme and Home Service networks into Radios 2, 3 and 4 and the launch of a new pop music station.
Radio 1 was never going to be the same as the pirates. The BBC had draconian needle-time restrictions to adhere to and an old-school approach to shake off. At first, Radio 1 was only on air for 12 hours a day. (The 24-hour service was finally launched by my good self in 1991.) Some of the programmes were shared with Radio 2, most were packed with 'features' and live music sessions of one sort or another, often the equivalent of the Northern Dance Orchestra's version of 'Strawberry Fields Forever'. Jeff and Bernie saw this as a tremendous challenge – to make in-house recordings, with high-quality musicians, that sounded at least as good as their commercial counterparts, and feed that material onto the airwaves. They succeeded. A series of _At The Beeb_ CDs by Fleetwood Mac, Led Zeppelin, Jimi Hendrix, David Bowie and others was released decades later, demonstrating the enduring quality of those recordings. Featuring fantastic live material and rarities from various BBC sessions in the late 60s and early 70s, they represent the best of BBC music heritage.
Jeff had joined the BBC in 1959 as a technical operator. He became a specialist tape editor and was part of the award-winning team, headed by producer Christopher Holme, that carried off the coveted Italia Prize for their production of Muriel Spark's _The Ballad Of Peckham Rye_ in 1961. (All part of BBC 'training', as was a series with Mrs Mills and a stint as producer of the daily big-band programme _Workers' Playtime,_ broadcast at mid-morning to coincide with factory tea-breaks.) He moved to the music department in 1964, producing shows for the Light Programme and for the World Service, where he launched a long-running series of blues and R&B shows, presented by Alexis Korner, a pivotal figure in the development of the UK blues–rock scene, the man who, in 1962, put The Rolling Stones together!
Jeff had just launched the weekly _In Concert_ programme introduced by John Peel at the Paris Theatre, Lower Regent Street, another beautiful old BBC building. He was also producing the Radio 1 magazine show _Scene And Heard_ presented by Johnny Moran. Bernie was working with Peel on the cutting-edge music show _Top Gear._
We finished the interview and I started to talk about some of the ideas I had. I'd brought with me a running order I wanted Jeff to look at. The theme was to do with musicians expressing their feelings about the state of the world through their music and was based on a track list I'd been asked to put together the previous year for a show I hosted at the Royal College of Art:
1. FORD THEATRE:
'Theme For The Masses'/'From A Back Door Window'
LP: _Trilogy For The Masses_
2. THE BEATLES:
'While My Guitar Gently Weeps'
LP: _The Beatles/White Album_
3. AMERICAN AMBOY DUKES:
'Shades Of Green And Grey'
LP: _Migration_
4. SIMON & GARFUNKEL:
'America'
LP: _Bookends_
5. TOM RUSH
'Child Song'
LP: _Tom Rush_
6. CREAM
'We're Going Wrong'
LP: _Disraeli Gears_
7. THE ROLLING STONES:
'Street Fighting Man'
LP: _Beggars Banquet_
8. RICHIE HAVENS:
'Oxford Town'
LP: _Electric Havens_
9. THE DOORS:
'The Soft Parade'
LP: _The Soft Parade_
10. BLIND FAITH:
'Presence Of The Lord'
LP: _Blind Faith_
Jeff was impressed and liked the way I'd sequenced the tracks together and the work and the logic behind it. He suggested we do a pilot programme and said that if it sounded OK he'd submit it.
We recorded the pilot on 22nd April 1970 at Broadcasting House. I literally shivered with the thrill of walking into the place. I still do, despite all the changes that have taken place over the years. We went through the gold doors into the marbled reception hall and up to the first floor, where the continuity studios for all four national radio networks were clustered together next to the main technical area. The nerve centre.
Jeff dimmed the lights as I settled into Con C, one of the two main Radio 1 transmission studios. I got my albums and tapes out of the programme box and addressed the mixing desk in front of me. There was a row of rotational faders (volume controls) and switches, set back to allow room for paperwork – scripts, letters and running orders. Above the desk were three cartridge machines, used for playing in the station jingles and trails from eight-track tape. I had a microphone suspended in front of me, with two others on the opposite side of the desk for guests. There were three turntables, a record rack, a pair of funny, hard, shiny old black BBC headphones – and clocks. Clocks everywhere. One built into the desk, one on the wall ahead of me, one in each corner of the room, all of them illuminated. All I could hear in that silent, soundproofed room was the synchronized ticking of the passing seconds. There was a glass window on my left, through which I could see the control room, where an engineer was sitting, waiting to monitor the sound levels and record the show. I could hardly believe this was happening. I'd dreamed of this moment.
I made mistakes. We stopped and started a number of times during the recording as I mastered the pre-fade buttons (to listen to tracks off-air), the cueing of tracks, the layout of the faders and the general rhythm of it all. I've never found it particularly difficult to get my brain around the operation of broadcast desks. They look complicated, but you don't actually need a lot of that stuff. I just decide which faders and facilities I need and ignore the rest. It's like driving a car. You reach a point where you don't have to think about the mechanics of it.
The big problem I had to overcome was my reaction to my own voice. I'd never used headphones before and every time I spoke I kept putting myself off, distracted by how different I sounded from what I expected. You have to use headphones. Opening the microphone fader 'kills' the sound from the speakers, otherwise there would be feedback. For the first time in my life I was hearing myself as others heard me – and right in the middle of my head! That apart I didn't feel particularly intimidated by the occasion and things gradually began to go well. By the end of the evening we'd got a complete programme on tape.
Jeff called me a few days later to tell me that he'd passed the show to Radio 1 management as a DJ audition tape and that he'd let me know if and when he got some reaction. Needless to say, I couldn't wait. I called within a day or so, pestering him for news. He was irritated. 'Don't start phoning me the whole time. I said I'd call you.' I was going to have to be patient.
Marc Bolan's wife, June, had arrived unexpectedly at our flat a couple of hours before I was due to leave for the recording. 'I've been thinking about all this, Bob,' she said. 'You need advice from a good DJ.' We got into her car and headed across London to see Jeff Dexter.
'It's what you've always wanted. When you get to the BBC just smile, be nice and say yes to everything,' is what he told me. 'And get yourself some gigs. You need to get more experience.'
I started scanning the small ads under 'DJs Wanted' in the music papers and, along with about 50 others, I turned up for an audition on a wet Thursday evening at a dubious-looking, run-down pub near King's Cross station. The place was full of smoke, nicotine-brown paint was peeling everywhere and the facilities were basic, to say the least. Eight or nine regular pub tables had been pushed together to make a rudimentary stage, with three more tables placed on top, lined up to support the equipment. We were told to get up on the tables, play three records and do two links – about ten minutes in total. It was chaotic. The needle kept jumping across the records as the DJs teetered and tottered precariously on the tabletops, trying to keep their balance. Everyone got their feet stuck in the gaps between the tables. Somebody tripped, sending one of the decks crashing to the floor, so everything paused for a while for the necessary re-wiring and repair, hilarious entertainment as we all lined up to go on. I was near the back of the queue, just behind a guy called John Hall, who told me that he worked at the Birds Nest on the King's Road. We finally made it to the front after about an hour and a half and, despite the equipment, I thought he sounded great. He stuck around to hear my set, too. Thank God we didn't get the job. 'Come down and meet me this Saturday lunchtime,' he said before we left. 'I'll buy you a drink.'
King's Road was extremely fashionable at the time, with great shopping, particularly for records, clothes and expensive interior design. Trendy new restaurants, wine bars and boutiques were packed with bright young things. It was like a psychedelic promenade. In the middle of it all, the Birds Nest was probably the least hip place in the whole of Chelsea. A chicken-in-the-basket pub disco, very un-cool. But the equipment was superb. The DJ booth was right up against the edge of the small dance floor, and there were telephones on the surrounding tables so people could phone the DJ and ask for requests. The inside of the booth was like a mini radio studio. John taught me how to work the kit and said I could play a few records. It felt fantastic. I did about an hour, talking on the microphone, mixing in a few jingles, getting people onto the dance floor, taking a few requests in return for a couple of pints of beer and having a really good time. At the end of my set John introduced me to the manager. 'What are you doing this evening?' he asked me. 'We need someone to do a residency for us on Saturday and Tuesday nights.' This was just what I wanted.
I was on two shifts, 7.30 to 8.30, then 10 till 11. Kieran Travers did the show in between. I wonder what happened to Kieran. He had a great Kool & The Gang instrumental theme tune, which he'd jive-talk over to start his show, always in the same way. 'I've got some fingerpopping, hand-clapping, thigh-slapping, toe-tapping sweet soul music for you. Yeah!' Then straight into his first track. Great stuff.
The money wasn't good but I really didn't care. I'd been working there for only a week when a guy came up to the booth and said he'd like to talk to me at the end of my set. He told me that the Marquee was planning to launch a Saturday dance night and he was looking for a DJ. On the spot he offered me the gig and I started on 6th June 1970, beginning an association with that iconic rock venue that was to last for many years.
The facilities at the Marquee were pretty rudimentary. The equipment in the side-stage DJ booth was dangerous, more or less in bits, mostly covered by the gaffer-tape that was holding parts of it together. Every so often there'd be a crackle and you'd lose sound for a few seconds. The legendary, graffiti-scrawled dressing room behind that small black stage was about the size of a broom cupboard. It was always really hot and sweaty in the club, with a kind of gloop under your feet that seemed to glue your footwear to the floor.
I'd just got a copy of 'All Right Now' by Free and I played it at least half a dozen times that first night, along with 'American Woman' by The Guess Who, 'Whole Lotta Love' by Led Zeppelin and 'Vehicle' by the Ides of March. 'Spirit In The Sky' by Norman Greenbaum had just been at No. 1 and was a major floor-filler. I played 'The Green Manalishi' by Fleetwood Mac and 'In The Summertime' by Mungo Jerry, mixed in with some Stones and Creedence Clearwater Revival, a selection of Motown and Stax dance tracks, some James Brown, Aretha Franklin and the occasional burst of rock'n'roll. (Rule No. 1 on live gigs: you've got to know your audience!) The evening worked out great and the place got packed out every week. We started getting live bands in. Dream Police played on 18th July, Status Quo the following Saturday. I was beginning to earn a living!
Sue and I finally found a decent-sized flat that we could actually afford and moved to West Hampstead, about 15 minutes' drive from Broadcasting House through Regent's Park. We'd needed to find somewhere bigger because Sue was now expecting our first baby, due in November.
Jeff Griffin called at last. Radio 1 had recently launched _Sounds Of The 70s,_ a new 'progressive' music programme strand, broadcast each weekday evening from 6 to 7 p.m., with a different presenter each night. David Symonds was on Monday, Mike Harding did a heavy metal show on Tuesday, the lovely, late Stuart Henry played mainly soft-rock and psychedelia on the Thursday programme and Alan Black was the jazz–rock man on Friday nights. Wednesday featured a repeat of the previous weekend's _In Concert_ programme.
Jeff told me that John Peel was about to take a month's holiday (the last one I can remember him taking – he always said he didn't like being away from his show in case his stand-in did too well and replaced him). The plan was to re-broadcast a _Best Of In Concert_ series while he was away but Jeff didn't want to repeat the repeat on the Wednesday evening, so instead he suggested that Radio 1 try someone fresh in that slot. On the basis of my pilot tape they agreed to give me a trial run, so he was phoning to offer me the four Wednesday programmes, beginning on 19th August.
'Hang on a second,' I thought, 'let me get this right. I'm going to be on Radio 1, sitting in for John Peel!' My first programmes ever, on national radio, deputizing for my great hero and mentor. I didn't think they wrote scripts like this.
'You'll only have 20 minutes needle-time each show,' Jeff interrupted. 'There'll be two sessions, recorded at the BBC, probably three/four numbers each. We'll use some stuff from the archives (Tyrannosaurus Rex, David Bowie, Graham Bond Organisation and Free), but we also need to get out and have a look at a few bands you'd like to have on.' Where to start?!
Jeff's call coincided exactly with the release of the _Elton John_ album. Elton and I had kept in touch following our first meeting at Musicland and we immediately called him to book a session. He came in with a sharp new backing band called Hookfoot and within a couple of hours had recorded four songs for a combined session fee of £25!
I recommended a terrific little band I'd seen in Portsmouth called Aubrey Small, whose keyboard player, Rod Taylor, was the spitting image of Paul McCartney. I was a big fan of Argent, so we got them in as well. For a reason I can't remember, Family couldn't do it, so we needed one more new name for the first show. With that in mind, we went to see Wishbone Ash at the Marquee on 15th June. I thought they were absolutely stunning, with the two lead guitarists, Ted Turner and Andy Powell, à la The Yardbirds, in their Jeff Beck/Jimmy Page era, right out on the front of the stage, trading licks. Those guys really could play. At the end of the set we all crowded into that cramped dressing room and Jeff booked them on the spot. Their first-ever broadcast was on my first-ever show.
I also needed to top up my record collection. I did a systematic tour of London's import shops and we arranged appointments with the major record labels to raid those LP cupboards! I did an enormous amount of listening, and spent hours putting that first show together.
I arrived in the studio to discover a pile of telegrams wishing me luck, from Mike Hales at Elektra Records and Tessa Siddons at Transatlantic, from Tony Elliott at _Time Out,_ David Bowie's office and Marc and June Bolan. And from Mum and Dad: 'Good luck this evening, every success in future'. The line-up on Radio 1 that day was Stevi Merike on _Breakfast,_ Johnnie Walker at 9, Tony Blackburn at 10, then DLT with the _Radio 1 Roadshow_ (from the Paris Theatre) at 12. Tony Brandon was on at 2, Dave Cash at 3 and Tommy Vance did the latest releases on _What's New_ at 5.
As the programme began, I was amazed not to feel over-nervous. I just felt that this was where I'd always wanted to be – in a radio studio, doing a live show. To the point of over-confidence. Half an hour into the programme I was already congratulating myself on how well everything was going.
The first track was 'Cinnamon Girl' by Neil Young followed by 'Pavilions Of The Sun' by Tyrannosaurus Rex, Van Morrison's 'Into The Mystic', and the first Wishbone Ash song, 'Errors Of My Way'. Then came 'Silver And Gold' by Country Joe and The Fish, and some beautiful world music from _La Flute Indienne_ by Los Calchakis, an album which has stayed with me ever since. I still play tracks from that old vinyl copy on air from time to time.
Everything felt great and I was on a roll as I pressed the button to fire the news jingle into the 6.30 headlines. I felt loose enough to talk over the music as I trailed the newsreader: '... and over to the newsroom we go, with Kingy Jimsbury.'
Jimmy Kingsbury was head of Radio Presentation at that time and was not amused. I think he sent upper management some formal bit of paper of complaint. My first lesson: don't even begin to take this thing for granted. Other than that, the programme went well. We got some correspondence and I felt I was already beginning to locate the core of what it was I wanted to do – to establish a real contact with the people who were listening, play them beautiful music and keep it simple.
Suddenly the pace of life increased. I got a call from the manager of T2, a new group just signed to Decca, inviting me to see them play at the Isle of Wight Festival. He took me down there in a small private jet and we buzzed the crowd! It was incredible flying over such a vast arena containing so many people. More than 450,000 people were there, many to see what was to be the last major live performance by Jimi Hendrix, who was appearing with his new group, Band Of Gypsys. We stayed for about three hours, enough time for me to walk up the bank and look out over the site in an attempt to take it all in. It was beautiful weather, the sun beating down from a clear blue sky, the ground dry enough for the crowd to stir up a cloud of dust that seemed to envelop the site in an orange haze.
I went backstage briefly and was introduced to Joan Baez, a woman of daunting intellect and strength. She paid me the huge compliment, following a _Whistle Test_ interview a few years later, of thanking me for not asking her any 'dumb questions', which made a refreshing change from the '... so how long have you spent making this album?' kind of stuff I sometimes used to land the guests with!
As it turned out, T2 weren't actually playing at the main festival. They did a short set to about three dozen people, on a makeshift trailer stage which was tethered to the back of a lorry, just outside the perimeter fence. I thought they were pretty good. Then it was back to the plane, a final buzz of the site and home again by the middle of the evening. It felt surreal.
I was invited to compere for jazz group Centipede, formerly known as the Whole World (they'd changed their name to avoid a clash with Kevin Ayers's new group), who were doing a short tour of France and wanted me to introduce them on stage. I was thrilled. I'd never even been abroad before!
The group comprised 50 people, led by pianist Keith Tippett and his wife, Julie Driscoll, formerly the 'face of '68' and still idolized in France at that time. She was mobbed when we arrived at the airport. Zoot Money, Robert Wyatt and various members of the band that was to become Patto, lead vocalist Mike Patto and guitarist Ollie Halsall helped provide the rock 'spine', while the jazz collective improvised. I don't remember the venues, except that they were located deep in the French countryside. We stayed in a large manor house, where the bizarre after-gig, bar-room cabaret consisted of various male members of the ensemble, in the beam of a torch, contorting their genitalia into shapes silhouetted on the walls. The puppetry of the penis. 'Ducks In Flight' is a particular memory.
The frenetic pace lasted until the final programme of the series came to an end, then everything went quiet again. Jeff was away on holiday, my link with the BBC was severed and I felt a tremendous sense of anticlimax. The lull before the storm.
I'd got to know David Symonds quite well and really liked him. He'd been slotted into the BBC's Sunday morning schedule in 1966 as their main weapon against the runaway ratings success of the Radio London _Fab 40_ chart show. In fact, Kenny Everett had opted to join him at the Light Programme several months before the demise of Radio London, making jingles, doing sketches and creating various inserts for the show. The BBC promoted David heavily – he was their boy.
He was a good, if rather earnest broadcaster, very independent-minded, had a wry sense of humour, a resonant, very 'English' voice, and was completely dedicated to furthering the career of his protégé group, Fairfield Parlour, music made in the mould of his other great love, The Moody Blues. He'd helped fund Fairfield's recordings, part-mortgaging his house to cover the bills. Their main chance came with the release of a sweet single called 'Bordeaux Rose' in 1970, prior to the planned launch of their début album for the fashionable Vertigo label, recognizable by its distinctive, psychedelic 'bull's eye' label design. It just didn't happen for them, despite major television exposure including an appearance on _Top Of The Pops_ , usually the key to chart success. At the crucial moment, the stock of the singles had dried up and by the time the feed line had been repaired the record had slipped out of chart contention. The band never recovered the lost ground, and David never recovered his investment. It happens all the time, unfortunately, but worse was to follow.
David had been battling with the BBC over the content of his new _Sounds Of The 70s_ programme. They were at odds over the style. It came to a head when he arrived in the studio on 9th November in an apparent state of shambles for what proved to be his last show for Radio 1. I really felt for him, he had his heart in the right place. The following day I got a phone call from David's producer, John F. Muir, offering me the show until the end of the year to start with, then on from there, one six-week contract at a time. I broadcast my first _Monday Programme_ on 16th November.
My daughter Mirelle was born exactly one week later, at the tiny cottage hospital in Hampstead. Sue and I had been to see Argent at the Roundhouse the night before, partly in the hope that the volume level would motivate some action from this baby, who was now a few days late. It worked, because early the following morning Sue went into labour. I didn't attend the birth, and wasn't really given the option. Pacing up and down the corridor outside is what expectant fathers were supposed to do in those days and I was still pacing a couple of hours before my radio show. Miri was born at 4.10, I had just enough time to see her and give her and her mum a hug before rushing to Broadcasting House and straight on air. Tommy Vance brought a celebratory bottle of champagne into the studio. Definition of happiness.
John Peel was incredibly supportive, talking about my show on air and promoting me in whatever way he could. Sue, Miri and I regularly stayed with him and his wife, Sheila (the Pig), at his house, Peel Acres, in Suffolk – visits he'd write about in his column in _Disc And Music Echo._ He'd become just about my best mate.
The tiny pine tree is the halfway line. If the ball bounces before going into the ditch it's a point to the kicker. If the ball bounces on the paving before going into the flowerbed it's fair. Some of the rules of the complex football/tennis game Bob Harris and I played until we could hardly stand. We were out at the cottage and had spent two days dragging our ladies with us from junk shop to junk shop in search of bizarre old 78s [still looking for those singles I'd sold in Hampstead!]. The game evolved while Sue and the Pig (or Stig or Biggle) cooked the evening meal. In the end Bob won, but only just and I had a sore toe from the previous day. 'There's an incredible shop in Ipswich,' said Bob, so off we went. We finally parked about 30 minutes from a shop Bob assured us was 'really amazing ...'
Press coverage, generally, was starting to build up. It was complimentary and warm, in sharp contrast to the stick I was to get a few years later! _Record Mirror_ published the first major Bob Harris profile article in January 1971. I did the sought-after 'Blind Date', a record review column for _Melody Maker,_ and started figuring in DJ polls. Unexpectedly, I was becoming famous and life was getting excitingly hectic.
I left the good old Birds Nest in Chelsea and started doing rock club residencies, at the Tricorn in Portsmouth and the Country Club in Hampstead, often with a new band called America, managed by Jeff Dexter. Soon after we broadcast their first-ever sessions on my show, Jeff issued the following press release.
Please don't tell anyone, but we hear from usually reliable sources that America is about to conquer Britain and eventually win over the rest of the world.
Already, America's invasion has taken place here very quietly. Severe brainwashing has been carried out. We can reveal that this took place in the unlikely area of Hampstead, in the very British-sounding Country Club.
The initial converts may have been few, but they include those with connections in high places. Whisper it to no one, but even the mighty British Broadcasting Corporation may not be immune. A certain producer, who would be unable to deny that his name is Bob Harris, was spotted at the very first of these meetings by the invaders of our shores. It has not gone unnoticed that on no less than four occasions this same Bob Harris has allowed no less than 50% of his _Sounds Of The 70s_ programme to be taken over entirely by America.
It may have been by stealth in the UK, but America's impact in the States was meteoric. Less than a year later, in March 1972, they went to No. 1 in the _Billboard_ chart with their début single 'Horse With No Name'. They went on to score 17 further hit singles, spanning 12 years, generating millions of dollars of income. But by then Jeff had lost them.
As the group began to develop, Jeff sought advice from an aspiring and already influential record company executive who was visiting London. David Geffen said he didn't like them, that they were 'a poor man's Crosby, Stills and Nash'. Nevertheless, Warner Brothers said they wanted to 'explore America's potential' and took them to Los Angeles, where the group found their careers put on temporary hold while the record company concentrated on another important project, the launching of The Eagles. Not that America minded this hiatus. They were ensconced in a house in Beverly Hills, with a pool, attendant female company and entertainment and were ecstatic to discover that this kind of stuff really did happen to guys in a band!
Shortly after they settled in California, Jeff received notification from the States that his management contract had been dissolved. In the legal battle that ensued, Jimmy Page referred Jeff to Led Zeppelin's management team, who helped Jeff to get some compensation but it barely covered his costs. He didn't even get a credit on the first album! The music industry is a tough business. America was just one of a number of guest bands to play live on my Radio 1 programme. Curved Air, Syd Barrett, Lindisfarne, Cat Stevens, The Faces and, at last, Family, all recorded sessions early in 1971. I was literally bombarding myself with sounds.
I saw Led Zeppelin at the Marquee. Bernie Taupin collected Sue and me in his new white Rolls Royce to see Elton's first big UK gig, at the Fairfield Hall in Croydon. I was there at the first-ever London gig by Thin Lizzy on 20th April, a showcase at the Speakeasy Club in Margaret Street (scene of later misadventures). I was mesmerized by bass player and vocalist Phil Lynott, the sheer intensity and power of his performance, the confidence he had. There weren't many black–Irish bass players around. He had a lot of bottle and he was making the most of it. The following day was a Loudon Wainwright showcase, totally destroyed by the heckling of a rampant Keith Moon, who kept complaining from the audience that Loudon's hair was too short! I even saw Grand Funk Railroad at the Albert Hall which, along with Blue Cheer at the Roundhouse a couple of years earlier, is one of the loudest concerts I've ever experienced.
Alan Black and I started a 'Sounds Of The 70s' night at the Marquee, with Argent headlining the first gig. But we weren't destined to be promoters. Maybe it was because we launched on 1st April. We made £6 that first night, the only really profitable gig of the whole three-month run, the low point of which was the no-show of Stone The Crows on a night we made just 63p.
Sue and I were spending an increasing amount of time with Marc and June Bolan, who were now living not far from us, in Little Venice, close to the canal. It was all happening for all of us, our careers seemed to be taking off at exactly the same time. 'Ride A White Swan' had gone into the charts three weeks before I started on Radio 1. Four months later we were at _Top Of The Pops_ for the performance that marked 'Hot Love' hitting No. 1, the first T. Rex chart-topper, on 24th March 1971. We went out for a celebratory meal after the show.
Marc was absolutely ecstatic, talking about a forthcoming tour. He invited me to compere, saying that he'd like me to go out on stage for about 40 minutes, play music and chat while people arrived. There would then be a short break and I'd go back out to introduce the band. We did the first date at the Bournemouth Winter Gardens on 9th May. The crowd was excited but reasonably reserved. We really weren't prepared for what happened next. The following gig at the Portsmouth Guildhall on the 11th ended in total chaos.
The audience comprised mostly pubescent girls in a frenzy. You couldn't hear a note, the noise was so loud, and an all-pervasive smell began to envelop the auditorium as the band got into the set, the front row seat cushions filled with the urine of hormone hysteria. The girls were literally wetting themselves! I hadn't witnessed scenes like this since seeing The Beatles at Wembley in 1966.
We sat in the dressing room after the concert, reflecting on the madness we'd just experienced. We had a couple of beers, met a few people and chilled for a while. We could hear noises outside, but didn't know yet that almost the entire audience had emptied from the auditorium and reconvened outside the stage door, waiting for the group to show. It was pandemonium out there. By the time we were ready to leave, dozens of police were attempting to open up a corridor through the pressing crowd so that we could get to the cars – five big, gas-guzzling Vauxhall Crestas. The cars were already a mess. Everything that could be ripped off them had been. The number plates and windscreen wipers were missing, and one of the door handles was half hanging off.
The crowd surged forward as Marc appeared and we were immediately surrounded. It was frightening. Some of the girls were trying to get his jacket off as he struggled to get free. There were flashes of steel at exactly eye level, as a dozen pairs of scissors tried to cut locks from Marc's corkscrew hair. I really thought one of us might have an eye ripped out as people fell in the crush. Eventually we were bundled into the car and began to inch forward through the crowd. It was like being inside a tin can. People were on the bonnet, people were on the roof, faces pushed contorted against the glass of the windscreen. Someone was trying to smash a window to get in. Marc leaned back into his seat, snuggling down behind the feather boa he had round his neck, a big impish grin spreading across his face. He was absolutely loving it! Suddenly there was a grating crunch as the suspension collapsed under the weight of so many bodies. Three of those five cars were written off that night. We had to have a police escort back to the hotel.
It was exhilarating but genuinely scary. We clearly couldn't do things the same way again. From then on, even as the final note of the guitar was still resonating on stage, we were out of the venue, into the cars and gone. A headline in the _Glasgow Herald_ on the 21st really summed things up. 'T Rextasy'. Simple. It was the first time I'd seen it referred to that way.
The other guys in the band were amused and bemused by the hysteria. Bass player Steve Curry and drummer Bill Legend were on a wage, while Mickey Finn had been around since Tyrannosaurus Rex had undergone its metamorphosis into T. Rex and gone electric. I didn't get to know him particularly well because Marc was the focus of it all. The other guys had to adapt to being in his shadow.
John Peel was getting increasingly agitated about the direction Marc had taken. He'd given lukewarm reviews to the previous singles, but could contain his disapproval no longer with the release of 'Get It On'. He slated it in his column, saying the only bit he liked was the '... meanwhile I'm still thinking' reference to Chuck Berry on the fade. Other than that, he felt Marc had abandoned his roots. Marc felt completely betrayed. To my knowledge, they never spoke again.
T. Rex records were also the cause of some consternation at Radio 1. Some of the daytime guys were complaining that Marc was giving me acetates and white labels, sometimes weeks in advance. They had a point, I suppose. Outside of Marc, I didn't play much chart stuff and they were being denied their 'exclusives', but Marc wanted to do it this way and I thought it was up to him.
I was having a fantastic time on the programme. Mark Wight, the network controller, seemed keen to promote me as a Radio 1 discovery. I hadn't joined from the pirates, or from Radio Luxembourg. I was all BBC.
Dad came up to London to sit in on one of the shows. I liked to get into the studio early, and usually arrived about 4.45, 15 minutes before the end of the _Terry Wogan Show_ , which was broadcasting from Con C until 5. He and Dad hit it off immediately and sat chatting while I set up my show. 'What are the prospects like in the job?' Dad asked.
'Well, Mr Harris,' Wogan replied, 'it's very insecure. I'm on the fifth week of a 13-week contract and have no idea whether the BBC will give me another one.' That's been my position more or less ever since!
I've come to the conclusion that broadcasting is about as secure as coaching a football team, only in our case, results don't matter. You can have the best figures in the world, but if they want to take you off air – for realigning, repositioning, restructuring, refocusing – they will. Audience support, petitions, demonstrations – they really don't matter. If management don't want you, you're gone. Four times in my career I've been sitting on successful shows and lost them overnight. I'm not complaining about this, it's reality and you learn to be resilient.
Some years after that first meeting, Dad was waiting for me in Broadcasting House reception when Wogan came down the stairs. He walked over immediately, hand outstretched. 'Mr Harris! How good to see you again.' So warm. They were still chatting when I arrived and Dad was absolutely amazed he'd been remembered in this way. Good man, Wogan. It was only recently that we began to get to know each other, working together in Nashville covering the Country Music Association Awards for Radio 2. I'm a big fan.
Out of the blue I got a call from Roy Harper. I first saw him play in 1967 at one of the free concerts in Hyde Park and he hadn't changed, always completely uncompromising on stage, veering from angry rant to sweet melody. Stubborn, occasionally wild, but deeply kind-hearted, I warmed to Roy from day one.
He'd phoned to say that he'd got a leading part in a new movie and did I want to be in it. I thought he was joking. He told me that he was co-starring with Carol White, who'd played the lead in the groundbreaking and controversial television play _Cathy Come Home_ five years earlier, that the film was called _Made_ and he was playing the part of a rock star. Two of the scenes involved being interviewed by a television reporter, and he'd recommended me. They needed me in Brighton on 28th September to begin filming.
From the moment I arrived someone was assigned to stay with me, to make sure I didn't get injured or incapacitated in any way. Once you're committed to film you become expensive to replace. I was driven to the first location on the seafront, where we were to be filmed doing part of the interview in the back of a car – and what a car! – a white Rolls Royce convertible. Roy was sitting in the back seat, smoking a joint. 'This is the life,' he said and started to laugh his exaggerated, infectious laugh.
The front passenger seat had been removed and a camera bolted in. The lens was about three feet away from our faces, the cameraman squeezed in with his back pushed against the dashboard. For the next three hours, we drove up and down the promenade, Roy and I sitting in the back in the sunshine, talking about whatever came into our heads. None of it was scripted, most of it inane. They just asked us to 'improvise'. We couldn't stop giggling. It was pathetic!
The next day followed a similar pattern. We moved location to the pier, where Roy was holding a press conference and I was asking questions. We'd just embarked on the umpteenth take when a swooping seagull started cawing loudly above us. Roy leaned back, looked up at the bird and started laughing. 'There you go, man, far out.' He turned and addressed the camera. 'That's what it's all about, man.'
Cut. That was it.
'Thank you, Mr Harris. We won't need you again.' Amazingly, they left my scenes in. I saw it on television a few years ago; really dreadful film but fantastic fun to do. As it happened, those few hours in front of the camera would prove invaluable experience.
_Sounds Of The 70s_ had become a poll-winning success. Towards the end of 1971 Radio 1 opened up a new slot, 10 p.m. to midnight, and for the first time broadcast the programmes in stereo, borrowing the Radio 2 transmitter. _The Monday Programme_ was extended to two hours and I additionally began to do an album review show with Alan Black on Friday nights, produced by Aidan Day, who later moved on to the new London commercial station, Capital Radio. He was to become a central figure in my Sex Pistols experience a few years later.
After a very enjoyable year working in the relaxed atmosphere that surrounded John E. Muir, I was re-united with Jeff Griffin, who immediately imposed a stricter discipline on my routine, insisting that I attend his office at Egton House, the new home of Radio 1. He wanted me there every Monday morning at 11 o'clock sharp to go through the programme with me, to make sure my building was up to scratch. He also wanted me to improve my notoriously bad time-keeping. For every five minutes I was late he would take a track out of my running order and put in one of his own. It worked to start with, but then I began to slip. I lost one track, then three or four tracks the following week. A couple of weeks later I overslept. Oh my God! I arrived in the office in a fluster at about 1.15, to discover that Jeff had completely rebuilt the show. 'What's wrong with you, leaving me sitting here like this?' was one of the kinder things he said. He wouldn't budge, saying I'd forfeited the right of contribution. In all aspects, Jeff was teaching me the disciplines of programme building!
I was doing a lot of _Roundtable_ programmes on Radio 1 with DJ Rosko 'the Yank who could crank', who was like a one-man force field, shouting into the microphone, careering around the studio. He had an amplification box for his headphones that generated awesome volume, like a pair of mini bass speakers strapped to his head. He'd get hot and sweaty and take off his shirt, then off would come his T-shirt in a swell of bare-chested ego. Nicky Horne was his assistant, soon to establish his own broadcasting career with _Your Mother Wouldn't Like It_ on Radio Luxembourg.
The dynamics of this new DJ culture meeting the old-style BBC presentation was perfectly encapsulated on a handover midway through a _Roundtable_ on which I was appearing with Alan Freeman. Rosko hit the jingle button as he introduced the bulletin, animated and insistent, sounding like a cross between a wrestling announcer and Wolfman Jack on double-speed. 'It's 5.30 on Radio 1, the station of the nation. Rosko's got the vibe, baby, and we got some newwwws you can uuuuse.' His voice lifted to a crescendo. 'It's yer main man, John Dunn!' There was a long pause, before we heard John deliberately clear his throat and begin the bulletin. 'With the news ... in English!' Absolutely priceless.
As 1972 began, I felt I was surfing the crest of a wave. I didn't feel particularly in control of events, but I was loving it all. _Melody Maker_ published a most wonderful article I still treasure. Under the headline 'Bob Harris, just being himself', Michael Watts had written the following:
DJs are, essentially, extensions of their own private selves, or at least how they would like themselves to appear. And that's what makes Bob Harris so intriguing. Not only is he successful to the point of attaining the sort of following that Peel used to have, but his reason for being successful exactly reflects his own nature. To be a little banal, he's a thoroughly nice person, and he must be the foremost living proof within the pop world that you can make it on those terms.
Bob Harris is strictly a product of the English media. There's no fast American spiel; his voice is soft and intimate, his conversational approach low-key and aimed at the second-person pronoun. He's not an entertainer, as are, say, Tony Blackburn or Kenny Everett. His popularity, which is becoming considerable for his type of format, is based on the respect of his listeners for his musical taste: they know he's going to play what they will like. Some people would say he's John Peel's natural successor, in that he has cemented a firm relationship between himself and the audience with music as the primary justification. Of how many Radio 1 DJs can you say that?
Very complimentary and it meant a lot. But this was the Michael Watts who, in the same paper six years later, wrote the famous 'pen quills in the back' piece that demonstrated the extent to which press affection had turned to hostility. In fact, many things were to change during the next few years. My home life, my career, my sense of self. I had no idea, at this moment, how much television was about to shape my future.
THREE
_Old Grey Whistle Test_
LIKE MANY PEOPLE IN BRITAIN AT THE TIME, MY MUM AND DAD GOT our first television set to watch the Coronation in 1952, when I was six. Just as the Queen was being crowned our cat gave birth to kittens on the front room sofa – much the more momentous event for me at the time.
It seems to me that each decade since then has produced one outstanding television music show, a programme that featured the best music and successfully captured the spirit of the time. _Six-Five Special_ was the first to bring rock'n'roll to British screens, in 1957. _Ready, Steady, Go!_ was arguably the best of the lot and truly reflected the excitement of the Mersey Beat era and the club culture of the mid-60s. _The Tube_ gloried in the anarchic mood of the post-punk 80s and _Later, With Jools Holland_ reflects the wonderful diversity that characterizes modern-day, non-mainstream music.
In the 70s the No. 1 show was _Old Grey Whistle Test_ , launched on 21st September 1971. By the end of that year I'd become a devoted fan. I thought there was something unique about the programme, an intimacy that made it special. The mix was great, with live performances, interviews, films and discussion, put across in an understated style that was new, honest and refreshing.
The show immediately featured people I liked. Family, Wishbone Ash and America were among the first bands to appear, along with The Who, Cat Stevens and Lindisfarne. Alice Cooper, catsuit open to the navel, swaggered onto my television screen, looking the epitome of sleaze, his pet snake wrapping itself around the microphone as he sang 'Under My Wheels'. Frank Zappa came on, talking about being banned from the Royal Albert Hall, and showing clips from his new film _200 Motels_. Muddy Waters was featured in a profile interview. Stevie Wonder previewed his new album. There was vintage film of Hendrix, The Doors and the Stones. Poco played 'Just For Me And You'. It was clear that this was a programme that really knew what it was doing. Where else on British television could you get to see all of this stuff?
The man who made it happen was producer Michael Appleton. Like Jeff Griffin, Mike joined the BBC in 1958, as a studio manager in Bristol. It could be really good fun, working in the regions. In London, TV and radio were located in different areas of the city, with consequent impact on flow between them. In contrast, in Bristol, both radio and TV were housed in the same buildings in Whiteladies Road, so there was plenty of overlap between the two.
Mike's first job was to provide sound effects for radio drama productions using various devices found in the corners of the studios – slamming the miniature door, or stepping through the little gravel pit, for crunchy footsteps. Gradually, he began to get opportunities to put down the coconuts and other contraptions in the sound booth and take up the faders in the vision-mixing gallery, feeding material into the primetime current affairs programme _Tonight._ It was Mike's ambition to eventually join the _Tonight_ production team but, by the time he made it to London, the show had been taken off. Nevertheless, it was a good time to land at Television Centre and Mike found himself in the presentation department, working on pilot programmes, in the lead-up to the launch of the Corporation's second national television channel – BBC2.
Mike was the producer of a new arts programme called _Late Night Line Up_ , fronted by Joan Bakewell. Broadcast seven nights a week, _Line Up_ featured news and reviews from the whole arts spectrum, from television output and the new film releases to the latest exhibitions and gallery showings.
There was a freedom at the BBC that allowed programme makers to express themselves. Outside of the Light Entertainment department there was little in the way of a budget, but the upside was that Mike was left to get on with producing his shows with very little interference from management. He took full advantage, increasingly filtering popular music features into _Line Up,_ before launching a new, dedicated album music show in 1968, timed to reflect the recent introduction of colour television to the UK.
_Colour Me Pop_ began as a short series of 25-minute programmes, each devoted to one LP. The first featured The Small Faces, playing live versions of tracks from their new album, _Ogdens' Nut Gone Flake_. Audience reaction was reasonably good and Mike began to refine the prototype, founding a series called _Disco 2_ in 1969 (it wasn't a disco show, the word had a different meaning in those days) a new release showcase that incorporated some vintage film and studio material and was introduced, briefly, by Tommy Vance. The format wasn't quite right, so Mike began to experiment with different presentation devices, including the amazing telestrator, with which he handwrote details of the music onto the screen while the act was actually performing. A particular memory as a viewer is of Nico, sitting flame-haired and solemn as she droned at her harmonium, gradually disappearing behind the handwriting filling the screen, as Mike put lines through several attempts to telestrate her Velvet Underground connections, like a teacher crossing out with chalk on a blackboard.
But the defining moment came away from the studio, with the arrival of James Taylor's _Sweet Baby James_. It was the atmosphere of this album, the tone and feel of the music, that set the agenda for a final programme re-launch. Mike was getting closer and closer to the format he envisaged: what he needed now was a name for this creative new show, something that reflected the strength of the centrepiece of the whole concept – the song.
The Beatles had revolutionized the pop scene in ways more profound than just record-breaking singles sales. Specifically, they wrote their own material, almost unheard of when the band first emerged in 1962. Reinforced by the later popularity of Bob Dylan, they proved you could do it yourself. Until then, many of the successful hit makers performed material fed to them from music publishers.
The 50s and early 60s had been the halcyon days for the great songwriting factories, the Brill Building in New York being the most famous. Situated on Broadway, it contained an amazing array of solid gold talent. From their tiny cubicles, young writers such as Carole King, Gerry Goffin, Doc Pomus, Mort Shuman, Neil Sedaka, Barry Mann, Cynthia Weill, Jeff Barry, Ellie Greenwich and Leiber and Stoller were pumping out songs on a 9 to 5 conveyor belt of Top-10 hits. Some of the greatest records of all time come from that magical era of Tin Pan Alley. Mainstream Nashville still works in the same way.
The Brill Building had its own designated doormen, cleaners and ancillary workers, known as the Old Greys. At the end of the working week, all were invited into a playback room to listen to a selection of the new songs (a process now known as auditorium testing). The mantra was the 'hook'. If the Old Greys could hum or whistle along to the chorus of a song having heard it only once, it proved the song was catchy, had a good hook and was likely to be a hit. In other words, it passed the 'Old Grey Whistle Test'. That's how the programme got its name. It was the title Mike had been looking for.
_Whistle Test_ began in Presentation B, a tiny studio usually used for the weather forecast, tucked behind a lift shaft on the fourth floor of Television Centre. In terms of size, facilities and access it was hardly Abbey Road. The black walls were hung with wires and all kinds of electrical paraphernalia, the mixing desk had only six faders, with a total of eight microphone points, just about enough for the average drum kit. The studio wasn't even properly soundproof. Turn up the volume and the beat could clearly be heard in main reception, on the other side of that huge, circular building, and bands began to bring in their own sub-mixers to fuel the level. Edgar Winter's performance of 'Frankenstein' was so loud it was impossible for the cameramen to hear directions. One of them was so affected by the impact of the bass beats that he was physically sick.
The choice of studio was a needs-must. Incredibly, the budget for the first series was only £500 a show. Everything had to come out of that, including appearance money, payments for rights clearances for music and film, design (in-house designer Roger Ferrin came up with the opening sequence and the star-kicker logo), hospitality, facilities and even the presenter's fee of £40 per programme!
Presentation was the lynch pin. Mike wanted a journalist who was able to broadcast, someone to whom he could delegate full responsibility for scripts and research. He auditioned a few people and finally settled on a double header of _Melody Maker_ writer Richard Williams and author/singer Ian Whitcomb. Ian was a hit-maker in the States, making the Top 10 in 1965 with 'You Turn Me On (The Turn On Song)'. The follow-up single was called 'N-E-R-V-O-U-S!', a song he'd written to describe his frustration at his own tendency to stutter when under pressure, a condition about which Mike was unaware.
Mike had already resigned himself to losing Richard for the first two shows (his wedding coincided with the beginning of the series and he was away on honeymoon!) and had decided to use Ian in the main anchor role. Unfortunately, the closer it came to transmission, the more Ian began to struggle. Despite his assurances that once the show was underway he'd be all right, Mike felt he couldn't take the risk and rebuilt the entire programme minutes before transmission, voicing the links himself from a nearby sound booth.
Things didn't quite gel with Richard. His preference was for jazz and he just didn't feel right about some of the music featured on the show. 'There were some great moments on that first series,' he told me. 'Curtis Mayfield played live, Dr John sat at the piano giving me a 10-minute potted history of New Orleans music, John Martyn came in with his Echoplex. And I interviewed Captain Beefheart, a great moment for me. But I didn't like progressive rock or heavy metal and didn't feel comfortable introducing them on air.' Nor did he enjoy the television experience.
'I couldn't stand being recognized,' he explained. 'I hated being accosted in the supermarket by people berating me because Jeff Beck or someone hadn't been on the show.'
It was also difficult for Richard, juggling between the programme and his full-time work on _Melody Maker_. 'I'd arrive at Television Centre at 8 o'clock on Tuesday morning, write the script, then go on to work at the newspaper,' he recalled. 'I'd work through my day, get back to the studio by about 7.30 that evening in time for a couple of run-throughs, then the programme would go on air. I never really plugged in, didn't particularly want to be on television and eventually couldn't wait to get back to the rest of my life. I think I got out just in time, to be honest, before I became too identified with it.'
Apart from a three-year diversion to head the A&R department at Island Records, Richard has been working for newspapers since: as editor of _Time Out_ magazine, features editor at _The Times,_ editor of the _Independent Sunday Review_ and later as a writer with the _Guardian_ on Sport and Editorial Features. 'The best part about the experience was Mike Appleton, a real gentleman,' he concluded. 'The fact that the music was his taste didn't make it bad taste.'
By the middle of the first series Mike was beginning to look for Richard's successor. He had plenty of time. _Whistle Test_ ran for 42 weeks a year.
Mike phoned and invited me onto the show to chair a live discussion about the Night Assemblies Bill, draconian measures being proposed in Parliament at the time. The rock fraternity was up in arms because they were convinced that implementation would mean the end of music festivals and other events where people gathered overnight.
Although I didn't know it, this was my audition. Soon after, Mike asked me if I'd like to present the programme full-time, beginning at the start of the second series, in September 1972. I didn't really think about it too much. I'd never particularly wanted to be on television, it wasn't an ambition. I've always felt completely satisfied by radio. But I certainly wanted to be a part of a programme that was putting out so much good music.
I arrived for my first day at the office with my shoulder bag stuffed with albums, tapes and ideas. Mike convened a production meeting and handed me a piece of paper. 'It's the running order,' he announced, before turning to talk technicalities with the rest of the team – production assistant Jenny Carson, researcher Alma Player and director Colin Strong.
'The running order?!' I'd expected things to be like they were at Radio 1, with me doing all the building. 'What if I have to introduce people I don't like?'
'Ah ... then that's the challenge,' replied Mike, smiling in his urbane way. This was all something of a shock.
'Er ... maybe we should've talked more about this before I said yes ...'
But Mike was unshakeable and it took me a while to get my brain around the way this was going to work. Eventually I realized that the best tactic was to bombard Mike with loads of stuff, then wait for some of it to filter into the programme. I'd play him tracks, recommend live bands, cajole, persuade and then be patient. Nagging was counterproductive. Some weeks the programme would be full of things I liked, other weeks not. It took time and a few arguments, but gradually we built up a deeply felt trust in one another, and a belief that it was the programme that was important, above spats over personal taste.
I was still adjusting to the implications of all this the following evening, as the opening title sequence began to roll at the beginning of my first-ever show. As the drumbeat kicked in on 'Stone Fox Chase' by Area Code 615, the programme's theme tune, I suddenly felt incredibly nervous. I'd transferred my script onto the autocue machine, a device that reflected my words up into the lens of the camera that faced me a few feet away and I'd read through the links a million times that day. We'd done two run-throughs and one complete dress rehearsal. What could possibly go wrong? But this was the real thing and it hit me that in a few seconds' time I would be appearing live on television sets across Britain. Mum and Dad would be watching, Sue, my little daughter Miri, all my friends ... just like I'd watched the first series. I had this massive panic that I'd just go completely speechless and let everyone down. As the floor manager began to count down the last 10 seconds, my eyes flashed to the gallery next door. I could see the bank of screens through the darkened glass, Colin Strong poised, finger raised, ready to shout 'Cue studio'. I started to shake.
This was very different from radio, where I built my shows, drove my own equipment and felt completely in control. Sitting in the harsh glare of the key light, in the middle of that bare, black studio, I felt vulnerable and alone. As my face appeared on the monitor set, I turned to the camera and automatically began to read as the autocue rolled through my script. It was my voice coming out, but not as I knew it. I was speaking at roughly half my normal volume and twice my normal speed, trembling round the edges. I introduced a film of 'Just Like A Woman' performed by Bob Dylan onstage with George Harrison and Leon Russell. The Everly Brothers played live in the studio and I interviewed American Spring, talking with Marilyn Wilson about her husband, Brian, and playing 'Good Time' from the new American Spring album, illustrated by a clip of film, edited to the music.
There were no videos then. The new technology wouldn't be making an impact for another four or five years, so the film clips compensated for an almost total lack of available promotional material. The films came from the collection of Philip Jenkinson, one of the _Line Up_ presenters, who'd listen to the tracks Mike gave him and trawl through his library to find an appropriate visual, often to stunning effect. The cartoon express train that accompanied 'Keep Yourself Alive' by Queen, and the vintage black-and-white footage of Alpine skiers that provided such an appropriate setting for Mike Oldfield's _Tubular Bells_ are particularly memorable. Phil Carson, UK label manager of Atlantic Records (and future husband of Mike's assistant, Jenny) was in the control room when the _Tubular Bells_ sequence was transmitted. Massively impressed, he recommended the album to his opposite number in New York. Atlantic rush-released it in America, where it hit the Top 3, went gold and spent nearly six months on the 'Billboard' chart, success that underpinned the expansion of Richard Branson's Virgin empire.
By the end of that first show I'd begun to conquer my nerves and had actually begun to enjoy myself. There were no major hitches and I was further amazed by the extent of the adrenaline rush I felt afterwards. Live television was a buzz.
Four months later, the 1972 _Melody Maker_ readers' poll was published. _Whistle Test_ was voted the No. 1 television show, _Sounds Of The 70s_ was the No. 1 radio show and I was voted No. 2 in the DJ poll, second to John Peel (Noel Edmunds was third, Kid Jensen fourth and Pete Drummond fifth). The _NME_ results were the same, and as Mike and I walked out to collect the award at the Poll Winners' Concert at Wembley I couldn't have felt more proud and happy. Only a few years earlier I'd been in that audience, watching as The Beatles received the accolades. Now I was on that very same stage, holding the trophy aloft like I'd won the World Cup.
'Nobody at Wembley could dispute the unsurpassed supremacy of BBC2's _Old Grey Whistle Test_ , voted Britain's top TV show,' read the photo caption in _NME_. 'A deafening ovation greeted host Bob Harris and producer Michael Appleton when they came on stage to receive the award.' To this day, I can still recall the way I felt at that very moment.
It was clear that _Whistle Test_ was beginning to make an impact. Following the appearance of Focus on the programme early in 1973, the reaction was so great that for the next 10 days their record company had to concentrate the entire resource of their pressing plant on fulfilling demand for their two available albums.
As well as _Whistle Test_ and my two shows on Radio 1, I was piloting an American radio programme ( _Hands Across The Water_ ), writing for several music magazines, rushing around seeing bands, and introducing gigs. I compered the five-day London Music Festival with Argent, Nazareth and Ten Years After. I introduced Genesis at the Reading Festival and Elton John at the Sundown in Edmonton, following which Elton launched his Rocket Record label at a party aboard the 'Sloop John D' on the River Thames, described by the _Melody Maker_ as 'the biggest name-dropping rave-up of recent times'.
The report read as follows:
Through your Raver telescope, we spied Rod Stewart, clad in leopard skin jacket and sipping expensive brandy, the rest of The Faces circumnavigating the deck. Ahoy, who's that in the sunglasses? Cat Stevens, hiding behind naval beard, and gracious, who's that chappie in the sporty white hat – it's Paul Simon, looking diminutive and rather lost. Avast, the heavies – Ringo in Battle of Jutland beard, and Harry Nilsson demonstrating a pocket tape recorder, the size of a Swan Vesta. Elton cut his cake with the aid of June Bolan and Bob Harris sat cross-legged in the corner, pretending not to notice the stripper removing what little remained of her clothing.
I introduced Terry Reid, Family and all-girl band Fanny at Lincoln Rock, a nasty experience, as it turned out, when we discovered the promoter had left town before paying anyone. Everyone was up all night, sitting in the lobby of the hotel – a bunch of angry, ragged rock'n'rollers furious at having lost their money and resentful at being interviewed by the local police. I travelled to Germany to see The Rolling Stones play the Olympic Stadium in the middle of their 1973 European tour, and filmed an interview with Mick Jagger in the City of Munich Restaurant. I went to David Bowie's party at Haddon Hall and out to dinner with Bernie Taupin. I was at Morgan studios in Willesden, north London with Marc Bolan, for a crazy night of filming for Ringo Starr's T. Rex documentary _Born To Boogie._ Rod Stewart and Harry Nilsson were among those who contributed to the creation of a new record at the studio – the highest ever bar-bill in a single session. I was on the guest list, having a really good time. I was a married man living a single man's life. It was beginning to mix badly with commitments at home. I was rolling in late too many nights.
Sue had little respect for the music business and thought it was shallow. Nor was she impressed by fame, or the material benefits that came with it. She loved the radio and believed in my programmes, but television had now added a whole new dimension to our life together. She had deep reservations that I was becoming intoxicated by it all.
Our second daughter, Emily, was born on 2nd February 1973, two months premature. I was in Northampton, visiting Mum and Dad, when I got the call telling me Sue had been taken to hospital. I rushed back to London and arrived as Emily was born soon after 8 o'clock that evening. She was such a little thing, all scrawny in her incubator. We weren't allowed to touch or hold her while she fought for her life for the next 10 days – agonizing, when that's all you want to do. But she's a strong one, our Ems, and soon she recovered and was home with us.
I began to realize how much I was losing touch with the rhythm of my family, but what could I do? I'd signed contracts, made commitments. My work was taking me away, but this is what I'd always dreamed of. I couldn't understand why Sue felt so unhappy, when things were going so well and it's clear to me now that my thoughts were selfish. I loved the girls with all my heart, but I wasn't spending enough time with them, and Sue and I were finding it harder and harder to talk.
John Peel began to express his disapproval of my apparent disregard. He was very fond of Sue and thought she was getting a raw deal. Soon after I started on _Whistle Test_ he stopped talking to me altogether. We were walking towards each other along the third-floor corridor at Egton House, home of Radio 1. He walked straight past me. I caught him up and pulled him by the arm into the nearest empty office. He wouldn't look at me, staring at the floor, impassive as I tried to get him to tell me what I'd done wrong. Eventually I just had to let him walk out of there, our friendship in ruins. I never discovered the full reason and the silence lasted nearly 20 years.
Family life was about to be stretched even further by the arrival of a new group in my life. I first saw Wally at a _Melody Maker_ band competition final at the Roundhouse, in June 1973. They were from Harrogate in Yorkshire, and had an unusual sound for a British band, comprising drums, bass, guitar, keyboards, violin, pedal steel and vocals, melded together in swirling, extended jams. They didn't win the competition but I thought they were fantastic, and immediately got them in to do a session on _The Monday Programme_ and recommended them to Phil Carson at Atlantic Records. Unbeknown to me, Rick Wakeman had seen them too, at their London 'warm-up' gig a few days earlier, at the Greyhound in Fulham, and had also given Atlantic a glowing report. Along with Led Zeppelin, Rick's group Yes was the label's biggest seller and Phil signed them straight away, asking Yes's manager Brian Laine to look after them and commissioning Rick and me to co-produce their first LP, starting immediately. The band couldn't believe it and neither could I. Everything was happening so fast for all of us.
Atlantic brought the band down to London to begin rehearsing for the sessions. I spent a lot of time with them in pre-production mode, familiarizing myself with their songs and going through the arrangements. Vocalist Roy Webber was the main inspiration, with influences similar to mine – David Crosby, Neil Young, Jackson Browne, West Coast and country rock. We immediately forged a friendship that thrives to this day. He is a wonderful person – bright, creative, charismatic, generous, humorous and kind. And he's a red, my contact for tickets to Old Trafford. Red Webber.
The band began to hang out at our flat, often sleeping over. Roy, guitarist Pete Cosker and steel player Paul Middleton were the most frequent visitors, and their runner, Dennis. Occasionally, all seven of them would be crashed out in sleeping bags on the floor in my music room, or on the front room sofa. Miri thought the chaos was fantastic, particularly all the instruments everywhere and the jam sessions.
I'd never done any production work in my life, so I was relying heavily on Rick to give me a beginner's guide, but it didn't happen. I arrived at Morgan studios to discover that he was in America with Yes. I'd had no idea he was going to be away and stood staring blankly at the state-of-the-art, 72-channel mixing desk that shimmered in the middle of the control room in front of me, wondering what the hell I was going to do. It looked like the control panel of a _Star Trek_ space ship. Rick's engineer, Paul Tregurtha, waited for me to give him some instructions. 'Where do we start?' was about as much as I could manage.
'Sorry, mate, can't hear a thing,' he said and laughed. My heart sank. 'No, seriously. The first thing we do is get a drum sound.'
We began work on a song called 'Your Own Way', and I immediately enjoyed the process – creating the right sound for each of the instruments and placing them into the overall sound picture, of balancing each instrument with the others and the decision-making involved. What to put in and what to leave out. I've always thought of production as creating the right setting to highlight the songs, as opposed to being a featured device in its own right. It's all too easy to use all the available technology and 'swamp' the recording.
I really liked the idea of what I call 'corner chords' – putting in a rich guitar chord every four or eight bars to bind everything together and create dramatic impact. (The Bee Gees have often used corner chords on their productions, to great effect. Think of 'Heartbreaker' by Dionne Warwick, for example.) It's a kind of 'signature' that crops up on most of the things I've recorded. Roy called it the 'Harris Strum', from which came my nickname with the group – Harry Strum.
Apart from a string section on the fade that Rick arranged for us later (I hummed a riff to him, which he notated), we'd all but finished 'Your Own Way' by the end of that first day. It was a wonderful and emotional experience – hearing our work take shape in those huge speakers.
The album had an open-ended production budget, and Atlantic additionally set up a tab for us on the bar with unlimited access to free food and alcohol. The temptation was just too much. Within hours of the band's violinist, Pete Sage, making a couple of phone calls, friends began to arrive from Harrogate. It seemed like coach loads turned up, putting stuff on the tab, shrouding the place in a cloud of dope smoke. By the start of our fourth session they'd been joined by the guys from Black Sabbath, who were recording across the road, and the bar-bill record that had stood since that crazy night with Marc Bolan and Ringo Starr was consigned to history. Pete told me he'd taken a few Polaroids of the ensuing madness and sent them to Phil Carson, so he could see how the work was coming along. The following day Brian Laine arrived at the studio to impose some discipline and, within minutes, everybody but the band and Dennis were heading back up to Yorkshire.
Brian was getting the band a lot of work. They would frequently break off from the sessions to go out on the road, first with Leo Sayer, then with Lindisfarne. They supported Yes at Alexandra Palace and turned up at festival gigs throughout the summer. The album was released to a four-star 'spotlight' review in _Billboard._ They came into _Whistle Test_ and then embarked with me on a college-tour 'Whistle Stop Roadshow', taking us all over the country in a three-and-a-half-hour package that also featured an acoustic performer, an audience question-and-answer session and a selection of films from the programme. I took Marc Bolan's top road manager, Pete Walmsley, out with me to help with the organization.
The support act was singer/songwriter John Golding, who'd sent me a copy of a most beautiful LP called _Discarded Verse_ , which he'd recorded in a little studio in Daventry, in my home county of Northamptonshire. I was so impressed by what I heard that I immediately called up the number on the letter he'd stapled to the album sleeve. It rang for ages. I was just about to put the phone down when a voice grudgingly responded.
'Do you know what time it is?' he said. I must admit I didn't. I'd been listening to music for hours, picking tracks for my radio programmes. 'It's 2 o'clock in the bloody morning!' he told me. I apologized and explained that this was Bob Harris from Radio 1 and that I'd like him to come into _The Monday Programme_ to do a session – news that did nothing to lighten his mood. 'Whoever you are, will you please stop phoning and leave me alone!' With that, he hung up.
I didn't know that he'd also sent the album to John Peel. John's reaction had been exactly the same as mine, and he too had called to talk about an appearance on his show. Having already taken some persuading that this really was John Peel, my call an hour later convinced John Golding that someone was playing a practical joke. All became clear when we spoke again the following day.
I passed _Discarded Verse_ across to Atlantic Records and they signed him on the spot. When we finished the first Wally album I went back into Morgan studios to make a record with John called _Photographs_ , using the same production team as before – Paul Tregurtha, tape engineer George Nicholson and Rick Wakeman. Unfortunately, Rick was in poor health at the time and suffered a mild heart attack soon after we started. But he was brilliant, composing the arrangements from tapes I sent him in hospital and in the middle of it all discharging himself for a day, to come into the studio to supervise the 57-piece orchestra he'd booked to play on 'All My Words Were Taken Away', which closed the first side of the LP. It was a spectacular moment but the title of the song somehow summed up John's attitude to it all. He resented the production process, sitting around while all this stuff was being added to his songs. He felt that they were being 'stolen' from him, which I can understand. Nevertheless, there are some wonderful tracks on that album. 'Loner' on side two is my favourite, with Wally featured as backing musicians.
The band was really great to be around; funny, gentle, creative people I really cared for a lot. They were also totally chaotic, seemingly unaware of the concept of taking responsibility. Important meetings to shape their future came and went without them, publicists would set up top-line magazine and newspaper interviews they couldn't see the value of turning up to. Trying to keep them organized on tour was exhausting. I'd introduce them onstage to discover that half of them were still in the bar. Even when I did a head count before going on, they'd still somehow manage to disappear between then and the end of my introduction, off somewhere, maybe in the dressing room area, in a haze, blissfully ignoring the concern around them that they were beginning to blow it.
Atlantic continued to pump in money. Wally briefly visited America's West Coast and toured Japan with Yes. Roy was increasingly, if reluctantly, taking on the role of spokesman, particularly during the Japanese trip. 'Who does your lighting?' asked a local journalist at the gig in Tokyo.
'We don't have our own lights,' replied Roy. 'We use the Yes rig.'
'No, you don't understand. Your lighting. Who does your lighting?'
'Well, as I say, Yes let us use theirs.'
The journalist was getting frustrated. 'I'm not asking you about that. I want to know about the songs!'
Roy laughed as the penny dropped. 'Oh ... our _writing_. It's me. I do our writing!'
There was something different about them when they got back, somehow. Some of the spirit seemed to have gone out of them, replaced by an unsettling world-weariness. Pete Cosker was becoming particularly affected by the tantalizing possibility of graduating to the successful rock star lifestyle he was already attempting to live, and was finding normal routines more and more difficult to adjust to. At the same time, Atlantic were doing some totting up, to discover that they'd so far underwritten the band to the tune of £87,000. The guys were told this was make-or-break time and that the pressure was now on. Having started the second album at Morgan, we were relocated to Chris Squire's home studio in Virginia Waters, where it seemed to do nothing but rain. We recorded the sound of a particularly heavy downpour, which we used as a backing track for a song called 'The Mood I'm In', during which Pete wound out a guitar solo that literally cried with pain. He was standing under a spotlight, his skin a kind of porcelain-yellow colour, bathed in the unhealthy sweat of the alcohol and amphetamines that had kept him awake for the previous three days.
The album got great and much appreciated support from Johnnie Walker, who made the single 'Nez Percé' his record of the week on Radio 1. I'm still really proud of that track, recorded during our last weekend at Morgan. Roy had arrived at the studio with the song as a work in progress, having been inspired by a book he'd been reading about Elizabeth Wilson, wife of the chief of the Nez Percé Native American tribe. For the next two days we worked on the arrangement, beginning with a lone piano introduction up to Roy's vocals, adding more voices on the first chorus. As other instruments come in one by one, the track gradually builds through Pete Sage's beautiful violin section to a glorious, swirling steel guitar solo by Paul Middleton, arriving at the final chorus before the instruments pull back Phil Spector-style, re-building again on the fade. By the end of the second afternoon the track was mixed and finished. I thought it sounded absolutely wonderful, but Roy had reservations.
'It needs something on the fade,' he ruminated as we walked across to the bar. 'You know the vocal on 'Dark Side of the Moon'? We need something like that.' We walked into the bar and couldn't believe our luck when we found Madeline Bell, taking a break from her session, relaxing with a cup of coffee and a newspaper. As well as having been a big hit maker with Blue Mink, she was among the most sought-after session singers in London. 'Perfect!' said Roy. 'Go and ask her if she'll do it.' She said she only had a few minutes but agreed to come and listen to the track.
'I'll only do it if I like it,' she announced. We waited apprehensively as she put on the headphones and stood under the light facing the microphone, waiting for the music. 'Just play the bit you want me to sing,' she instructed. We played her the tape and took a quick voice level while she was humming along for pitch. After a few seconds she stopped and told us to do a take. George put the machine in record, and for the next 30 seconds we sat spellbound as she instinctively melded with the music, her voice soaring effortlessly around the top notes, mixing perfectly with the texture of the track. Roy was right, it was the consummate finishing touch. 'Was that all right?' she asked us, looking at her watch. 'I've got to get to my session.' She didn't even have time to hear a playback, but it was wonderful, Madeline. You made the track.
Despite our best efforts, Atlantic declined to give the _Valley Gardens_ album much support. They were reluctant to add much to their already heavy investment and soon pulled the plug altogether. Roy started getting calls from Dave Dee, the new Atlantic label boss, demanding the return of all their equipment. Simultaneously, Brian Laine told them he was no longer representing them. No record company, no gigs, no gear. After struggling on for a while with some equipment they'd borrowed from Manfred Mann's Earthband, the guys were faced with the reality that the band was finished. It's a tough business.
For Pete Cosker, the loss of the band was catastrophic. Saddled with a chronic drug problem and with no money, he returned to Yorkshire, drifting through a few gigs, a few jobs, then gradually into homelessness. The other guys tried to help, but Pete became increasingly resentful, occasionally threatening and abusive. Over the next few years his life collapsed completely and he eventually died a truly horrible death in a Harrogate squat. Following a massive overdose, he was found slumped on top of the faulty electric fire that provided his only heating, the front of his body so badly charred that he was hardly recognizable. It nearly breaks my heart, just thinking about it. It's so tragic that the life of the sensitive, smiling, baby-faced lad who spent so many happy hours with us in those long-ago days in West Hampstead, mesmerizing us all with his beautiful guitar playing, should have changed so much as to end like that.
I was getting increasingly desperate to talk to someone about everything, to get advice on how to handle what was happening in my life. Pete Walmsley said I needed proper management and introduced me to Philip Roberge, a New Yorker working in London, looking after the UK affairs of Dee Anthony, who managed Peter Frampton and Gary Wright. Rod Stewart's ex-girlfriend Dee Harrington was his secretary, Judy Garland his idol. Philip also represented jazz–rock group Back Door, British blues maestro Duster Bennett and the incomparable Alexis Korner.
I'd met Alexis through Jeff Griffin a few years earlier and, as our friendship grew, I increasingly turned to him for advice. He'd done it all, having first worked for the BBC soon after the Second World War, before founding the Blues and Barrelhouse Club with Cyril Davies in the early 50s, a venue that soon became a famous stopping-off place for visiting American blues exponents. When Chris Barber began to include blues into his otherwise traditional jazz set, he called in Cyril on harmonica and Alexis on guitar, to augment his live band and accompany singer Ottilie Patterson. It was a learning curve for both of them, and they soon broke away to form Blues Incorporated in 1961 and set up the Ealing Rhythm and Blues Club in a basement underneath the local ABC bakery.
Blues Incorporated variously included musicians drawn to the Ealing Club from all over Britain. Young hopefuls such as Long John Baldry, Jack Bruce, Ginger Baker, Eric Burdon, Graham Bond, Charlie Watts, Brian Jones and, briefly, Mick Jagger were part of the ever-changing line-up of the group. The encouragement and on-going support and enthusiasm Alexis so willingly offered were proving crucial to the development of a whole new generation of young British talent, his protégés going on to find later success with bands such as Cream, The Animals and The Rolling Stones. Later, he was the guiding influence in the formation of Free and in the early career of Robert Plant, as well as having hit singles of his own as a part of the band CCS, whose version of 'Whole Lotta Love' opened _Top Of The Pops_ for many years.
After hosting programmes with Jeff for BBC World Service, he took his unique musical approach to Radio 1, where his idiosyncratic mix of 'any music with soul', effortless knowledge and rich, chocolate voice proved an irresistible magnet to this young broadcaster.
I loved hanging out with Alexis, particularly going to gigs. I learned so much. He took Sue and me to see Bob Marley, at the famous 'Live At The Lyceum' concert, in the summer of 1975. The music was fantastic but it turned out to be a nightmare experience. Midway through the evening I began to feel really weird. I couldn't understand what on earth was happening, everything seemed to be turning to liquid in front of my eyes. I felt an uncontrollable urge to dive into the pool of people around me. I couldn't understand why I couldn't find Sue, who reappeared to tell me she'd been sick and urgently suggested that we leave. Someone offered to run us home, and we piled into a Mini, the sunroof open on that hot June night. As we drove through the West End of London, the buildings seemed to be bending over and coming in through the gap in the roof, ejecting a thick liquid into the car that I really thought was going to drown us. Sue tried to restrain me as, consumed by terror, I desperately tried to haul us out of the car.
Somehow we made it home, but the problem of getting me up the 67 stairs of our mansion block was immense. I was violently sick as I fell in through our front door, feeling gruesomely unwell. Sue dialled 999.
It was LSD. Someone must have spiked our drinks. We'd put our glasses down onto the floor for a few moments to light a cigarette. It must have happened then. It was the only explanation we could come up with. What I knew for sure was that I didn't want to experience anything like it again and that Sue's resilience was getting stretched to the absolute limit. Rock'n'roll was completely taking over my life and, on top of everything else, I'd begun to see another woman.
I first saw Jackie at the Speakeasy Club. She was sitting with a group of friends in the restaurant. Having just been on holiday she had a deep brown tan, shown to good effect by a loose white top, which had fallen off her shoulder. She got up to dance and I followed her through the club. I thought she looked amazing, with her long black hair and the way she moved when she danced. I went over to her table and we sat and talked for a while. She gave me her telephone number. On the way home I resolved not to call her. About ten days later a postcard arrived at Jeff's office from the States, addressed to me. 'Noo Yoik, just like I pictured it. Love Jack.' That was it. I suddenly really wanted to see her again.
She'd modelled in the late 60s, then started her own clothes business, working with record companies and promoters to design merchandizing for tours and album launches. She really loved rock'n'roll, knew loads of people, seemed to understand the industry, and had clear ambitions for my role in it, which was more than could be said for me at the time. I was more aware of being in the whirl of becoming famous, an experience I was struggling to come to grips with.
Loads of work was coming in, people I'd never met before were telling me how great I was. Everybody seemed to want me to do something for them, with big smiles on their faces. Press coverage was extensive and complimentary (among my awards in 1973 was one from _NME_ for 'talking soft and saying little'). Doors opened everywhere.
I began to believe all this stuff. I could feel my radar going haywire and I didn't like it. I just couldn't work out who was sincere any more, a confusion I even tried explaining to the press. 'It seems to be automatic that immediately you get a television programme, people expect you to get all big-time,' I wrote in 1973 in _Sounds_ magazine. 'And they don't just expect, they accept the fact that you already have done. It's been really disappointing to see people who previously I was close to get like this. You know, suddenly I'm not just Bob, someone they could maybe come round and listen to a few albums with. Suddenly I've become "Bob Harris". But I don't think I've changed.' I needed somebody to help and support me and Jackie offered wise council and protection, with not a hint of disapproval.
The resulting devastation on my home life was total and I began to do damage. One day I was staying with Sue, the next I'd be with Jackie. Miri was hysterical with fear, throwing herself to the floor and gripping my ankle with all her might, in an attempt to stop me from walking out the door. She and Em heard constantly raised voices and witnessed their mother's deep unhappiness. Sue told me years later that she'd felt completely trapped. Her priority was the girls, yet not even the maternal instinct was completely clear-cut in those new-found days of strident feminism.
'Do you remember how many couples around us at the time were breaking up?' she asked me. 'The pressure was on young women to break out and express their own identity. I felt it too, but you don't necessarily want to if you have kids. You want to be with them.' Sue didn't particularly want to be out at the concerts and parties with me, the music industry just didn't impress her. But neither did she want to spend so many evenings on her own, stuck in the flat, looking after the girls and, for the first time, everything wasn't 'really great' any more. America was my escape.
FOUR
The States, the President and Punk
I LEFT THE SLEET AND RAIN OF A STRIKE-TORN, POWER-CUT BRITAIN on 8th February 1974 and headed for the sunshine of California, to record material for the six-part _The Beach Boys Story_ for Radio 1. Sitting there on that 11-hour journey, I couldn't believe my luck. Here was a chance to give my brain a break, enjoy a new experience and spend time with one of my all-time favourite bands.
Jeff Griffin was already there. He'd spent a couple of weeks in Los Angeles with Bill Fowler, head of the Warner Brothers UK Promotion Department, talking to people, getting background information and setting up interviews. They met me at the airport and took me to our hotel, The Beverly Rodeo, on Rodeo Drive in Beverly Hills, right in the heart of one of the best shopping streets in the world, enveloped by palm trees, and a short drive from Sunset Strip. The weather was glorious, with a cloudless blue sky. Overnight I'd flown from winter weather into summer sunshine, a first-time experience for me.
The freeway system was incredible, with anything from three to seven lanes, all packed with traffic. The fumes were so bad they made our eyes smart. Exits and entrances fed cars in and out on both sides, tailgating was the norm, despite all the 'Keep Your Distance' decals. With a speed limit of 55mph, everyone just cruised their 5.5-litre engines in the nine-miles-per-gallon sunshine, filling the LA basin with a smog so thick you could photograph it. I was in the front of the car, dialling across the radio stations, looking for 93KHJ. The Love Unlimited Orchestra was No. 1 with Barry White's 'Love's Theme', soon to give way to 'Seasons In The Sun' by Terry Jacks. Al Wilson was in the Top 3 with 'Show And Tell', such a great record.
Los Angeles sprawls across an area more than 60 miles from top to toe, in straight lines and rectangles. You can see across the whole city from the Hollywood Hills, an incredible sight, particularly at night. A poolside view is best of all and we soon realized that getting anything done in Los Angeles was a _mañana_ affair. 'The weather's great and the vibe's laid-back. Let's do it tomorrow, man.'
Before we met the Boys, we decided we had to see the beach – specifically Venice Beach, with its writers and actors, and all those browned-skinned Californian girls in their bikinis, roller-skating past the murals and the street entertainers on the promenade, while the guys worked out at the beach gymnasiums. The music seemed to pump at us from everywhere, from the brightly coloured psychedelic clothes shops and cafes that edged the sand, or from a hundred ghetto blasters that provided the accompaniment to the hand-ball games. Serious research, of course, exploring the culture of The Beach Boys' music.
Many of the most exciting late-night activity centres were situated close together, on or near Sunset Strip. Three great music clubs, the Roxy, the Whisky-A-Go-Go and the Troubadour, where Elton John made his American début, were within a few blocks of each other, all within walking distance of the famous Continental Hyatt House Hotel, where most of the main bands stayed when they were in town, complete with its ABC cinema-style awning, announcing their arrival. In the centre of it all was the main social centre, a disco called the Rainbow Bar and Grill, and there was even a Tower Records store at the end of the block. Add the X-rated clubs and cinemas and it seemed to me that these few hundred yards offered a greater concentration of rock'n'roll lifestyle than anywhere else in the world. Alice Cooper, having just joined us from the local golf course and the unlikely pleasure of a couple of rounds with Johnny Mathis, offered to take us out for a night on the town.
The Rainbow Bar and Grill struck me as being the Los Angeles version of the Speakeasy and was full of Brits. Hamish Stuart and Robbie McIntosh were there, celebrating the completion of the new Average White Band album, featuring their American No. 1 single 'Pick Up The Pieces'. Frankie Miller had a table, Phil Lynott was holding court. We bumped into Iain Matthews, then Gerry Beckley from America, who told us that there was a party at Danny Hutton's house in the hills, if we wanted to go. (Mama told me not to, but we did call in.) Alice introduced me to Al Kooper. Wow, this was amazing.
With some other people from Warner Brothers, we finished up at a little studio off the Strip, meeting Frank Zappa for an early-hours playback of some new stuff he'd just recorded. Having had virtually no sleep since I'd arrived in town, I sank down gratefully into a beanbag in the middle of the control room and, as someone pressed the playback button and manic Zappa improvisation filled the speakers at a million decibels, I fell asleep. I woke to an embarrassed silence, everybody looking at me. The man was not best pleased.
By the following morning I'd completely lost my voice. The combination of the smog, Marlboro cigarettes, late nights and loud conversation meant that I arrived at Carl Wilson's house to record our first interview with a throat so sore I could hardly speak.
Arrangements with The Beach Boys were best described as 'loose'. They were supposed to be gathering for rehearsals for a big tour, due to start in ten days' time, but so far none of them had turned up. Al Jardine was expected 'sometime soon', Mike Love was at a transcendental meditation centre in Switzerland, Dennis Wilson was – God only knows where. Carl was planning to rehearse the backing musicians with the help of drummer Ricky Fataar from The Flame, who'd joined the group with Blondie Chaplin and Daryl Dragon to replace the missing Bruce Johnston and Brian Wilson, but Ricky didn't seem to be in town either. Meanwhile, the rehearsal studios stayed empty, apart from a few roadies and a couple of prospective back-up guys, just hanging out and jamming.
The Beach Boys were enjoying a remarkable renaissance at that time. Having been America's answer to The Beatles in the mid-60s, producing records described as having 'changed the face of American music for the next 30 years', they'd drifted dramatically into decline. Brian Wilson, the main creative inspiration, took to his bed, brother Dennis took up with Charles Manson. Their record sales collapsed as new psychedelic bands dominated the charts. They just weren't cool any longer and when they left Capitol Records in 1969 in a blaze of litigation, it seemed their time had gone.
But the release of the glorious _Surf's Up_ album in 1971 not only revived their musical and commercial viability, but in songs like 'Don't Go Near The Water' and 'Student Demonstration Time' they demonstrated an ecological and political awareness hitherto unsuspected. Carl Wilson had taken the production reins in the absence of his brother Brian, and had brought a more cerebral, mellow approach to the music.
I liked Carl a lot. He was friendly and helpful, a very warm, peaceful person, but with a melancholy air about him, I thought. His house was situated in Coldwater Canyon, at the end of a long tarmac drive, enclosed by the hills. We started recording our interview in his 'meditation room', before the combined interruptions of young son and telephone calls caused us to postpone further conversation until a couple of days later, at the group's studio in Santa Monica. It was a truly magnificent complex, converted from an old cinema, with state-of-the-art equipment, stained glass windows, kids' rooms, chill-out areas and creature comforts, situated a few miles from the beach. The band had recently transported most of the main equipment to Baambrugge, in the Netherlands, where it had been reassembled for the recording of their 1973 _Holland_ album, broken back down and returned to Santa Monica, an eight-month project that had cost the group almost a million dollars.
I called Mike Appleton to alert him to the possibility of a television interview, excuse enough for him to get on a plane and join us (hobbling on a stick as he'd hurt his back) in time to record a separate piece at the studio with Carl for _Whistle Test_. After several attempts, Jeff had also managed to pin down Al Jardine for a couple of hours, so we now had material in the can. Predictably, Dennis failed to turn up the following day, so while we waited outside we recorded an impromptu interview with Ricky Fataar, in the back of his station wagon.
Jeff had tried all kinds of ways to get in touch with Brian Wilson, but with no success. He hadn't given any interviews for several years and we knew that just talking to him would be a major coup. Carl told us that Brian didn't even come out of his room these days, that he didn't want to see us, and that we should plan to finish off without him. But we persevered, phoning the record company, contacting his manager, trying to break down the wall of people protecting him. It was probably people like us, and the weight of expectation, that sent him to his room in the first place.
We explained the problems to Brian's co-writer, Van Dyke Parks, while he sat crunching celery on the corner of my bed, following an interview in my room at the Beverly Rodeo Hotel the following day. He picked up the phone and dialled a local number. 'Hi, Brian. Yeah, fine. I'm with some guys from the BBC. They want to come over and talk to you. I'll tell them to be there at 8.' After all our frustrating attempts to get through, we couldn't believe it was that easy!
One of the nicest moments of the whole trip was an interview that afternoon with Dory Previn, an intelligent and controversial woman, formerly married to orchestra leader André Previn. We sat in the rustic kitchen of her home in Hollywood Hills as she performed 'Coldwater Canyon' and 'Brando', two songs from her new LP. She told us that she liked to drive out into the desert and primal scream to relieve her inner stress. I kept thinking of Brian Wilson.
Two hours later we checked in at the security post on the perimeter of the exclusive Bel-Air estate as the guard phoned ahead to get clearance from the Wilson family to open up the electronic gates and let us through. Brian's wife, Marilyn, was waiting for us at the house and took us through a thick, oak doorway, down a short staircase and into a long, high-ceilinged, wood-panelled room, empty except for two leather sofas, a mahogany coffee table and a white piano. As Jeff set up the recording equipment we could hear what sounded like electronic music, thumps and odd wailing noises coming from somewhere in the building but Marilyn seemed unconcerned. She and I had met before, on my first-ever _Whistle Test_ and she was friendly, relaxed and happy to talk. We'd been recording for 10 or 15 minutes when suddenly the door burst open and there at the top of the staircase, hands in pockets, stood Brian Wilson. He looked dishevelled and uncertain, transferring his considerable weight uncomfortably from one foot to another, staring at the polished wood floor.
Marilyn explained why we were there and, after standing for a while making up his mind what to do, he slowly came down into the room towards us, staring intently at the stereo microphones Jeff had placed in stands on the table. 'What is that?' was the tentative, straight-faced enquiry, as he circled the table to look at the microphones more closely. 'Is that a submarine?' Jeff and I looked at one another, not really knowing what to say. This was a serious question. Brian stood for a minute or so in the silence, examining the microphones. Finally, he looked up and around the room, then walked over to the piano. 'I tell you what, you guys, I'll play you a song.'
This was an incredible moment, more than we'd ever hoped for. Here we were, in Brian Wilson's piano room, about to hear an exclusive preview of a brand new song. The feeling was electric. Jeff clicked the tape machine into record mode as Brian lifted the piano lid and prepared to play. He paused for a moment, then wrung his hands and looked across at Marilyn. 'Er ... honey, what's wrong with the piano?'
'Oh, Brian, don't you remember?' She smiled sympathetically. 'It's being fixed. You know ... they've taken some of the keys with them.'
My heart sank as I saw the gap under that piano lid, looking like a huge open mouth without any teeth. Brian sat for a moment, thinking. Then, without another word, he slowly got to his feet, stuffed his hands back into his pockets, and ambled reflectively out of the room. A few moments later, the electronic music started again. We thanked and cursed our luck in equal measure.
The Beach Boys' schedule meant that we couldn't do any more recording until the first gig of their tour, when Mike Love and Dennis Wilson were due to arrive. So we took up an offer to spend a couple of days filming and recording with Jesse Colin Young, one of my favourite artists at that time. Originally from New York, he gained great success on the West Coast, writing the hippie anthem 'Get Together', a Top-5 single, recorded with his group, The Youngbloods. The resulting residuals and royalties had funded the building of a dream – a remote house, situated 15 minutes off the nearest highway, close to the ridge top in a hillside forest near Point Reyes, northern California, about 30 miles from San Francisco. The view was absolutely breathtaking, stretching 15 or 20 miles through the trees across to the Pacific Ocean, sparkling in the distance. He'd added a log-cabin studio below the house and put a glass roof on it, so that he and his family could see each other while he was working. The studio was also the focal point of the Racoon record label, with Michael Hurley the most prominent and eccentric of the roster of local roots-based artists the label featured. It was such a beautiful, organic place I didn't want to leave. The close family feeling that existed there touched a chord with me, and the visit triggered a friendship that lasted several years. Jesse and his wife, Suzi, came over to London a few months later, when Jesse supported Crosby, Stills and Nash at Wembley on 14th September, on a bill that also included The Band, Joni Mitchell and Tom Scott. My wife, Sue, had a particularly strong affinity with Suzi and felt that, as a couple, they'd found a way to successfully integrate the pull of the music industry with the demands of family life.
Jeff and I briefly returned to Los Angeles before flying on to Colorado Springs to complete our final recordings with The Beach Boys. We met Mike Love and his girlfriend at the airport and drove them to the Airforce Academy, the rather austere opening venue of the tour. No one seemed to be approaching the gig with any enthusiasm. In contrast to the temperature on the West Coast it was freezing cold under a threatening grey sky. The building had an icy chill, as we echoed our way through the corridors to the dressing room, where we found Dennis Wilson having a shower. 'I'll only do the interview if we record it now,' he told us through the steam. 'You're gonna have to come in and join me.' Jeff suspended a microphone above the water and I tried shouting questions at him from outside the cubicle. Eventually, Carl persuaded him to relent and come out so we could finally get about 15 minutes of his undivided attention.
The gig wasn't good. The band played in a huge gymnasium inside the Academy building and the sound was awful, echoing back off the walls. The guys seemed to be doing little more than going through the motions, mechanically playing their 'greatest hits' medleys. The atmosphere remained flat throughout. But I got to meet Jim Stafford, who was supporting them on the tour, a really nice guy. I still play 'Spiders & Snakes' on the radio from time to time.
We left the venue immediately after the show and got to the hotel just as it started to snow. It was already past midnight, yet we still had to record the interview with Mike Love, a matter of some urgency since we were leaving at 6.30 that morning to catch a plane. Mike, Jeff and I sat up all that night, talking. Carl joined us, then Al Jardine. It was like a gathering of old friends and provided all the remaining material we needed. We lost time completely and by the time I finally opened the curtains and looked out, four or five inches of snow had fallen.
It was just getting light as we slithered towards the airport in our hired car. I still have no idea how Jeff managed to find the way in that blizzard. Every road sign was a white-out – and this was way before satnav. After a 90-minute delay while ice was removed from the wings of the plane, we finally took off, heading for New York, where we arrived exhausted, late that afternoon. After California it looked disgusting. The city was almost bankrupt at the time and it showed. There were piles of rubbish everywhere, the roads were badly potholed. The springs were poking up through the back seat of the yellow cab as we careered into Manhattan, the bullet-shielded driver hurling us past what seemed like endless blocks of boarded-up, graffiti-covered building fronts, burnt-out cars and people sleeping rough. There was a tangible atmosphere of menace on the streets. After the sunshine and glamour of Hollywood, with all those manicured lawns and movie star houses, the contrast was dramatic. I wasn't to know then, but each time I've been back to New York I've liked it more and more. Over 20 visits, spanning more than 25 years, I've watched as the place has gradually been transformed from the ugly neglect of the mid-70s into one of the safest and cleanest big cities in America.
Yes were playing at Madison Square Garden that evening and, despite feeling flat and sleepy, Jeff and I joined up with Mike Appleton again and made it to the gig. It was a spectacular triumph, one of the high spots of the band's entire career. They were in commanding form, sharp and structured, the audience lapping up the spectacular stage presentation to the extent of three encores. I recorded a conversation with Steve Howe and Rick Wakeman the following day, before going over to Atlantic Records to film interviews with Aretha Franklin and her legendary producer, Jerry Wexler, a great hero of mine.
We then embarked on a celebratory evening on the town with Dave Cousins and a couple of the guys from the Strawbs, Bill Fowler and Rick, who set us up at the table of a local bar with a pack of cards, for a game of Jacks. 'The rules are simple,' he explained. 'When the cards are dealt, the first person who gets a Jack nominates a drink. The second person nominates a mixer. The third person pays for it. The fourth person drinks it. If it's some vile combination like sherry and tomato juice you can drink something of your own choice, except you've got to have a double.'
We all agreed it sounded fair enough except, for some reason, I kept getting the fourth Jack. Surrounded by glasses, I remember very little of the rest of the evening, except that we finished up at CBGB's Club at about 2 o'clock in the morning where I probably fell over.
We sat on the plane home the following day feeling absolutely exhausted, in my case hung over, but thrilled and excited by our American experience. We had loads of good material in the can and we now knew we could make this work, picking up local crews and planning as we went along. It was the trip that paved the way for many future visits.
When we got back we went straight from Heathrow Airport to Television Centre to broadcast that week's _Whistle Test_. As well as a live Babe Ruth session and concert footage of Loggins and Messina, the programme featured the Yes interview, already rush-edited from the conversation we'd recorded in New York 36 hours earlier. When I finally got home, I slept for two days solid.
_The Beach Boys Story_ was broadcast on Radio 1 at the end of 1974, after my _Monday Programme_ had teamed up with _Whistle Test_ for a concert by Van Morrison and the Caledonia Orchestra, live from the Rainbow Theatre, on 21st May that year. It was the first time BBC radio and television merged for a stereo rock simulcast. I left a long track running in the studio at Broadcasting House, jumped into a fast car, pelted down the Westway and arrived at Television Centre in time to back announce the track and introduce the concert. You couldn't do that today. You'd be gridlocked for about an album and a half.
I didn't know it then but the first part of my Radio 1 career was coming to a close. Derek Chinnery, who'd taken over from Mark Wight as Network Controller, didn't much like the kind of music we were featuring on _Sounds Of The 70s_ , and took all the programmes off the air early in 1975. It was the first time I'd ever lost a programme and the last time I appeared on Radio 1 for more than 14 years.
I immediately joined Radio Luxembourg, recording two shows a week at their studios in Mayfair, central London. I didn't really enjoy the experience, to be honest. Despite the fact that Alexis Korner came in with me a few times, my heart wasn't in it and I've always preferred to do programmes live. But with the rest of my life so busy, it didn't seem overly important. It would be a couple of years before I really locked back into radio again.
The Van Morrison concert was part of a new expansion of _Whistle Test_ output. More facilities had been made available to the programme with a move to TC5, a huge, hanger-like studio on the ground floor of Television Centre, also used for _Top Of The Pops_. The extra space meant that we could now accommodate two full band line-ups, all live. War came in to play 'Baby Brother', Bob Marley and the Wailers performed a brilliant version of 'Stir It Up'. The late Jim Croce and Bill Withers, two of the nice guys of the music industry, came in to perform, Tim Buckley did 'Dolphins' and 'Honey Man', Captain Beefheart larged his way through 'This Is The Day'. We broadcast The Rolling Stones and Stevie Wonder specials, concert footage of Steely Dan and a Joni Mitchell concert at the New Victoria Theatre. Supertramp and Manfred Mann's Earthband did excellent studio sets and we regularly featured Queen, with whom we had, by now, become good friends.
We began to stage the occasional concert at the Shepherd's Bush Theatre, with Jackson Browne, Eric Clapton, Bonnie Raitt and, famously, Dr Hook, changing out of their mock Bay City Rollers outfits behind a thin screen, which did little to cover their modesty. Mike Appleton and Jeff Griffin additionally extended their collaboration with the introduction of _Sight and Sound In Concert_ and _Rock Goes To College_.
_Whistle Test_ also forged a particularly strong association with Led Zeppelin. Their manager, Peter Grant, was otherwise keen to keep them off the small screen. They didn't put out singles, so they didn't do _Top Of The Pops_ and they refused invitations onto the big American TV shows that had traditionally been an important part of the circuit. They wouldn't normally do television interviews but they really liked our show, so whenever they had anything to say, they said it to us. I interviewed them in all sorts of places, from American hotel rooms to a boat on the River Thames, mostly talking to Robert Plant.
Led Zeppelin had recently launched their Swan Song record label and threw a huge Halloween Party 'on the night of the full moon of 31st October 1974', to mark the UK release of the label's first album, _Silk Torpedo_ by The Pretty Things. Coaches ferried us to Chislehurst Caves in Kent for one of the most bizarre events I've ever attended. It was like being at a medieval orgy. Flames from huge torches flickered light across the dark, dank recesses of the caves, while a crowd of maybe 200 people watched George Melly perform jazz tunes and bawdy songs in a nun's habit, naked girls wrestling in jelly in open coffins at his feet. Some people were covered in fake blood, others were wearing Dracula outfits or bondage gear. Horror films were projected onto the walls while theatre groups enacted torture plays and executions. In all, it was a strange and disturbing night, one of many Led Zeppelin experiences through the years.
_Whistle Test_ ended 1974 with the now traditional 'best of the year' selection on New Year's Eve, preceded by an 'Elton John Special', live from the Hammersmith Odeon, and simulcast on Radio 1. It was a wonderful night, with Elton at his happiest and best. Looking out from the side of the stage, it felt so good to see so many smiling faces expressing their deep affection for Elton, arms waving, joining in with every lyric of every song.
I bumped into Elton again a few weeks later at a Labelle reception in Kensington to mark the release of 'Lady Marmalade'. He was leaving as I arrived, rushing off to Heathrow Airport to catch a plane to the States. He told me he was playing at Madison Square Garden in a few days' time and planned to invite John Lennon to the concert. It was an appearance that proved to be a high point in Elton's American career, with John Lennon joining him onstage for a triumphant performance of 'Whatever Gets You Through The Night', after which John was quoted as saying, 'Yeah, I enjoyed it. But I wouldn't want to do it for a living.'
I'd asked Elton to tell John how much we wanted to talk to him and a few days later Mike and I were in the office when John Lennon called from New York. He told us that he would love to do something around the release of the _Rock 'N' Roll_ album, that he was missing England, and that this would be a perfect opportunity to send his son, Julian, a postcard from America. He talked about possible times and dates, and Mike asked him if he'd like the fee sent out immediately. 'I don't want a fee,' he retorted at the suggestion.
'This is the BBC, John,' explained Mike. 'There are systems. We have to draw up a contract and pay you a fee, otherwise you're not a credited contributor and we won't be able to use the piece on the programme.'
'How much is it?' asked John.
'Fifteen pounds,' replied Mike.
'You're not serious?' I could hear John's laughter from the other side of the room. 'Well, I'll tell you what to do,' he suggested. 'Bring me £15-worth of chocolate olivers. I can't get them over here.'
With the handwritten rider clause added to the contract, we delivered the chocolate olivers (a version of Bath Oliver biscuits, covered in dark chocolate) when we met, at the beginning of April 1975, at the BBC offices in the Rockefeller Center on 5th Avenue.
John had recently returned to Yoko in New York, following his 18-month 'lost weekend' in Los Angeles with his new love, Yoko's assistant, May Pang, working with Phil Spector on the _Rock 'N' Roll_ album, a period of 'avoiding reality', as he put it. 'I was sick of that thing where "John Lennon writes new song ... is it about Paul or is it about himself?",' he explained. 'I told Phil I just wanted to be [his wife] Ronnie on this one. It was the first time since the early days of The Beatles that I'd let an album get out of my control. I'll never do it again. The sessions got really crazy. There'd be 27 people there and 15 of them would be out of their minds. Phil Spector works in strange ways, his woodwork to perform.'
While he was in Los Angeles, John had also been working on the production of the new Harry Nilsson album. 'We had some fun. There was Harry, Keith Moon, me and Ringo, all living in the same house, and we had some moments, folks.' John laughed. 'But it got a little near the knuckle. Harry was encouraging me. Usually there's someone there saying "shut up, Lennon", but there was nobody there and it all got totally ridiculous. That's when I straightened out, then suddenly I was the straight one in the middle of all these mad, mad people.'
We talked a lot about his fight for a green card, without which he wouldn't leave America, fearing immigration would never let him back in. During protracted legal wrangling and court appearances he'd met opposition from the Nixon administration and the right wing, the same kind of people who burnt Beatles records after his famous 'we're bigger than Jesus' quote in 1966.
'It keeps the Conservatives happy that they're doing something about me and what I represent,' he told me. 'But it also keeps the Liberals happy that I haven't been thrown out yet.' He went on to tell me about being followed and having his phone tapped. 'At that time it was pre-Watergate, so you can imagine ... John Lennon says his phone's being tapped, men following in car. I think they wanted to scare me, and I was. I was scared paranoid. People thought I was crazy ... well, they do anyway. You know, "Lennon, you big-headed maniac, what do they want to follow you around for?" And that's what I'm saying. What do they want? I'm not going to cause them any problems.'
He'd been told that Elvis Presley regarded him as subversive and had colluded with President Nixon to compile evidence of extreme political activity and possible drug use. Lennon and Presley met once, in a Los Angeles hotel room in 1965, and had taken an immediate dislike to one another. 'The whole thing was affecting my work,' he reflected. 'I tried to pretend that it wasn't happening to me, that it was water off the back, or whatever that thing is. But when I got right down to it, and I got down to it, folks, I realized that it was a constant thing, non-stop, like a toothache that wouldn't go away. I think I've come to terms with it a bit, but it was interfering with everything. It was affecting my whole life, actually.'
'I go through these troughs every few years,' he went on. 'It was less noticeable in The Beatles because the image of The Beatles would carry you through it. I was in the middle of a trough when we were doing _Help!_ but you can't really see it. I'm singing _Help!_ for a kick-off. But it was less noticeable, because you were protected by the image and the power of The Beatles. Now, when it happens, I'm on my own, so it's easier to get sniped. So, I've been in a trough and now I'm coming out of it. Whoopee! I'll be around for the rest of my life in this business and I just don't take it too seriously any more.'
I asked him if he regretted writing 'How Do You Sleep?', a stinging condemnation of Paul McCartney. 'No,' was the reply. 'Somebody said the other day it was about me.'
He thought for a moment. 'Two things I regretted,' he said. 'There was so much talk about Paul that people missed the track. It was a good track. And I should've kept my mouth shut. It could've been about anybody and I regret the association. But ... why do you wanna regret? He lived through it, and the thing that matters is how he and I feel about it. Him and me are OK, so I don't care what writers or commentators say about it, I go through my thing. You know, "Lennon Blasts Hollies", that kind of thing.' We laughed.
'I've always been that. Our first national press was about me beating up a disc jockey at Paul's 21st birthday party. That was the first Beatles national press and we got the back page of the _Mirror_. I've always been a little loose. I hope it'll change, because I'm fed up with waking up in the papers. But if it doesn't, my friends are my friends, whatever way.'
Personally, I've always really liked McCartney. We first met outside Broadcasting House, soon after I started doing _Whistle Test_. Jeff Griffin and I had got out of my car and I was just locking the door when I felt a tap on my shoulder. 'Are you Bob Harris?' enquired a familiar, smiling figure. I nodded, completely taken aback. 'Good one. Keep up the good work.' He gave me a thumbs-up sign. 'Sorry, can't stop. Just wanted to say hello.' And with that, he ran back to a waiting taxi. We stood transfixed, watching as the cab headed into the traffic and on towards Oxford Circus. A double thumbs-up from the back window and the car was gone. I turned to Jeff.
'Err ... that wasn't who I thought it was ... was it?'
'Nah,' said Jeff. 'Couldn't have been.'
After contemplating the event for a few moments, I was inclined to agree. By the time we reached Jeff's office in Egton House, we'd convinced ourselves that it must have been someone else.
Eighteen months later I met Paul formally for the first time, to record an interview with him about Buddy Holly. He'd recently acquired the publishing rights for the Holly song catalogue and was promoting 'Buddy Holly Week'. 'Yeah, 'course it was me. I'm a fan,' he told me.
We met again for an interview when the _Wings Over America_ album was released in 1976. Linda invited me to the MPL offices in Soho Square and took me down to where Paul was working on some new music. I was amazed to discover that he'd entirely recreated the EMI Studio 2 control room in the basement of the building, complete with the analogue equipment, tape machines and mixing desk The Beatles had used on the _Sgt. Pepper_ album. The real Abbey Road control room has a window through which you can look down, as from a television gallery, into the cavernous studio below. In an attempt to re-produce this sense of space in such a small basement, Linda had taken a photograph of the studio through the control room window, blown it up to full size and put it on the appropriate wall. They'd built in a false door where the real door should have been and even put a battery behind the tiny clock on the wall, so it said the right time. It was a perfect recreation of the famous control room that had housed so many Beatles memories, built with meticulous and affectionate attention to detail.
Watching the John Lennon interview again, I was struck by how informal it was. No publicists rushing around saying 'You can't say that.' Thirty minutes, one camera – you don't see television like that any more. Yet the relaxed atmosphere promoted the intimacy that led to John being extraordinarily open about his thinking. I was able to learn a lot about him as a person by giving him the space to talk. So it was with Mick Jagger, Robert Plant and others. A mutual level of trust existed, which led to people feeling comfortable and willing to open up about themselves.
John called us when we got back to the UK to say that he'd really enjoyed the experience and that he planned to record a couple of songs for us with his band Elephant's Memory, especially for the show. We were still waiting for the film a few hours before the programme went out, but it arrived just in time, with 'Stand By Me' and 'Slippin' And Slidin'' the two featured songs.
Live television can be a hazardous experience. I was intrigued that Lou Reed needed to have a minder on each shoulder when he joined me in the studio. Then I noticed that those two huge guys were literally supporting him, one under each arm, the toes of his black boots dragging across the floor as they dumped him into the chair beside me. I looked at him as he sat there motionless, his eyes closed, with 20 seconds to go before we went live. I did the introduction and asked him the first question. The few seconds of subsequent silence felt like a lifetime but gradually, from deep in his throat came a kind of growl, developing into an approximation of speech. It was as if someone had slowly begun to turn a key in his back, as he gradually wound himself up enough to give me some kind of answer, and go on through the rest of the interview.
Soon after, Keith Richards arrived in the gallery, swigging from a bottle of Jack Daniels, half-empty by the time he ambled through to join me. By the end of the interview the bottle was finished, yet he was completely unaffected. The myth was reality. Keith really could take it, an impression confirmed by an after-programme visit to one of the top Knightsbridge restaurants, where a centre table had been reserved for our party of 14. Keith moved crockery and cutlery aside, casually pulled a foolscap envelope out of his pocket, and emptied several thousand pounds-worth of cocaine onto the middle of the table, oblivious to the reaction of people sitting nearby.
Yet, this kind of moment was and is not exceptional. Drugs and rock'n'roll have always had a close relationship, often more overt in the bomb-proof world of superstardom. Personally, I've acquired a strong aversion to hard drugs in general, cocaine in particular. It's a very insidious, persuasive addiction, fooling users by making them feel indestructible, while stripping away their health, their self-respect and their bank account. Unless you've got the constitution of a Keef and the spending power of a global multinational, stay clear.
If you ever thought that getting into drugs was a good idea, the appearance of Paul Kossoff on _Whistle Test_ in 1975, a few months before his death, must surely have changed your mind. Totally disorientated and incapable of cohesive speech, he should never have been wheeled out into the studio in front of live television cameras. After struggling for a minute or so to disguise the obvious, I called on the help of Leo Sayer, who was standing behind me ready to begin his live set, who immediately joined me, sitting on the edge of my little rostrum as he talked about Paul's career and expressed his sincere admiration for the musician he once was.
_Rolling Stone_ critic Jon Landau had, by now, famously identified the future of rock'n'roll. Summed up in two words it was ... Bruce Springsteen. The _Born To Run_ album had just been released to fantastic critical acclaim, an album that still has impact today as recording of high energy, magnificent intensity, great musicianship and potent lyrical imagery. With its songs about jobs, cars, girlfriends and escape, it touched a chord with a whole generation of young American working-class kids, accurately voicing their aspirations, frustrations and fears. The album and subsequent record-breaking tour became the biggest music event for years, and we decided that the next major _Whistle Test_ project would be to explore the possibility of screening Bruce's one-off UK show at the Hammersmith Odeon in the autumn of 1975. To discuss the various plans involved, his manager Mike Appel invited Mike Appleton and me over to Los Angeles for an end-of-tour showcase gig at the Roxy Club, on Sunset, on 17th October 1975. It was the week Bruce made the front cover of both _Time_ and _Newsweek_ magazines, a unique feat at the time. All the billboards on the Strip were saying the same thing, a big Columbia-funded advertising campaign reading 'Is The World Ready For ...?' Expectation had been set at stratospheric level and everyone was wondering if he could live up to the hype.
As I looked around the club, people were sitting back in their chairs waiting, arms folded, with 'OK, kid, let's see how good you really are' expressions on their faces. George Harrison was there, and The Carpenters. Jimmy Connors was at a table with some friends, all the big music business people were doing hospitality. Bruce Springsteen could easily have died that night, but instead he was sensational. After the first number we were all on our feet, people at the back were up on the tables for a better view. The atmosphere was incredible, the onstage camaraderie within the E Street Band spilling into the audience and adding to the vibe of warmth and excitement. They did six encores, including a memorable acoustic version of 'Pretty Flamingo', Bruce sweating in his denim shirt, bathed in a thin shaft of smoky blue light as he lived those lyrics. It was a fabulous 'right place, right time' experience. Now we knew what all the fuss was about, and why people have always said that to really 'get' Bruce Springsteen, you HAVE to see him live. While he, Mike Appleton and Mike Appel had their meeting the next day I got to play handball with the guys in the band on Santa Monica Beach.
I saw many wonderful concerts over the next couple of years. I introduced Queen in Hyde Park to a crowd of more than 150,000 people in September 1976, and the Knebworth Festival that same summer. Elton John took me to see The Eagles at Wembley and I saw Paul McCartney's triumphant Wings concert there in 1976. I compèred at the Whisky-A-Go-Go for Tom Petty and The Heartbreakers, then again in Los Angeles the following year at the Roxy, when we filmed The Cars. Rory Gallagher, Hall and Oates, and Lynyrd Skynyrd were among those who performed outstanding concerts for _Whistle Test_ at the Shepherd's Bush Theatre. Above all those fabulous nights, however, that magic performance by Bruce Springsteen was the best I'd ever seen.
As it happened, we weren't able to reach an agreement to televise the Shepherd's Bush gig, which is probably just as well, as he was strangely muted that night. Not so when we saw him next, in New Haven late in 1978. Without doubt, this is my all-time favourite concert, even better than that night at the Roxy, and this time we had the television cameras with us.
The venue was about the size of the Hammersmith Odeon, so it was big enough to generate a real atmosphere, but not too big that the performer was a distant dot on the stage. Bruce was absolutely electric, strutting around the stage like he owned it, coming down into the audience time after time, to be completely engulfed by mesmerized, dancing fans. We filmed a section of the set and put out 'Rosalita' on the programme a few weeks later.
It was a four-hour show, beginning at 8 o'clock, with just a short break midway through. He looked exhausted when I met him as he came off stage at the end of the final encore. 'When do you want to do the interview?' I asked, expecting him to tell us to wait while he chilled out for a while and recovered.
'Let's do it right now,' he said. We'd already set up the lights and the camera in his dressing room, so we just sat down and started to talk. He was eloquent, interesting and convincing, as he sat wiping away the sweat with the towel he'd draped round his neck, regularly thumbing his nose like a boxer. He talked passionately about his music, about the friendships within the band and about the frustrations of the two-and-a-half-year hiatus forced on his career by the litigation between himself and his now ex-manager, Mike Appel. We finished filming about 2.15 in the morning. 'Do you wanna come and see some music with me?' he asked us.
There was a local band playing at a club called Toad's Place, about five blocks away. A couple of the guys from the E Street Band came with us, along with Mike Appleton and our crew. It was an odd feeling, walking down the sidewalk on that frosty night, Bruce Springsteen in the middle of a whole crowd of us, like mates out on the town. My final memory is of Bruce, working his way to the front of the audience in that little club, getting the lead singer's attention and asking if it was OK for him to join the band on stage. The guys just couldn't believe it. (I never did find out who they were. Bruce didn't know, he'd just heard they were good.) After a short consultation, he took the microphone. Mike and I were leaving the club to collect our car and head back to New York just as they started into 'Pretty Flamingo'.
We were gradually spending more and more time in America compiling material for the show, particularly during the summer breaks when we would generally spend three or four weeks following leads wherever they took us. We might be in Los Angeles for a few days, then fly to Miami or San Francisco, picking up local crews as we went along. We tended to leave New York to the end of the trip, for a shorter hop home and the summer of 1976 began in Macon, Georgia, and the Capricorn Record Label picnic, held at a magnificent 180-acre lakeside park on the edge of the town, owned by company boss Phil Walden.
Phil had previously managed Otis Redding, and told me about the problems of a white guy managing a black guy in a segregated town. He showed us the 'white only' 'black only' signs that still disfigured the main street. 'There were clubs I couldn't go into,' he explained. 'A white guy wouldn't be safe in there. I could only hear Otis if they were carrying the show on one of the local radio stations. So I'd be a few blocks away, sitting in the car, listening to make sure the show went OK. There were a lot of places Otis couldn't play. It was hard in those days.'
The Capricorn picnic was a three-day event, showcasing members of the Allman Brothers Band, Wet Willie, the Marshall Tucker Band and other label favourites and involving venues all over town. Music-business people were invited from all over America to party. It was expected that presidential nominee Jimmy Carter would be attending, as he did every year, to thank those involved in the record company for the profits that pumped money into his political fund. We were told that he would be happy to meet the BBC, and we arranged to record an interview with him at the lakeside, in an open pavilion overlooking the water.
My day began at 6.30 in the morning with a visit by two secret service men who burst into, then took apart, my hotel room, luggage and belongings. Having vigorously established that I meant the future president no harm, they stayed, one on each shoulder, throughout the day to prevent the possibility of a last-minute change of mind, even accompanying me to the toilet, until the interview had been recorded. A few hours earlier, incumbent President Ford had declared his intention to run in the forthcoming presidential race, and the media attention surrounding Democratic candidate Carter that day was intense to say the least. But he'd agreed to do only one interview, and that was with us.
As Mike and I stood in the pavilion, waiting for him to arrive, I tried to take in the extraordinary scene being played out around me in the hot summer sunshine. We were in a cordoned-off area, surrounded by security men, looking out over the lake and the grounds. The band Stillwater were playing on a makeshift stage, close to the water's edge, partly obscured from where we were by the smoke of a huge barbeque cooking sizzling southern food. Girls in bikini tops and short skirts were playing handball on the grass, guys with long hair were hanging out, looking stoned. A whole harvest of people in 10-foot peanut costumes had formed a comical guard of honour at the bottom of the long staircase that brought people down into the area from the car park above. Their smiling faces were peeking through the square holes in the front of their costumes, while they hopped about in anticipation of Carter's arrival. We didn't have to wait long.
We saw the entourage first, a mass of hundreds of media people, cameras, popping bulbs and frenzy, spilling down the staircase and across towards the pavilion. It was several minutes before Carter appeared through the melee, a circle of minders pushing and pulling him through the throng of television crews and well-wishers and into the corner of the building we'd cordoned off for the filming. The man coordinating the operation was Mike Hyland, a Capricorn executive at the time. Years later, quite by chance, I met Mike in Nashville and was able to confirm the details of the day and look through his collection of photographs of this amazing experience.
Jimmy Carter told me how much he appreciated the support he got from Capricorn and talked about his love of music, particularly the lyrics of Bob Dylan and Paul Simon. I thought he was charming and sincere. He even wore a _Whistle Test_ badge. Some of the news channel crews tried to barge in on the filming, while the security guys did their best to keep stray microphones and equipment away, pushing people back as they encroached into our space. Personally, I didn't care about exclusives, but Carter was strict, and we were the only ones he talked to.
Mike and I spent most of the rest of the afternoon being interviewed about the interview. We even rushed back to the hotel for a few minutes to see ourselves on the CBS 6 o'clock news. Yet the most vivid moment happened immediately after the interview, just as Carter was leaving. One of the security guards suddenly broke ranks and stepped forward towards me, arms outstretched. We're talking American Football player-size here. This man was towering over me, muscles bulging, face red and quivering, his voice trembling as he began to speak. 'I wanna shake the hand of the man who talked to the future president of the United States.' As I took his hand, he began to cry. With tears streaming down his face, he pulled me into a long, suffocating hug, crushing my face into his plaid shirt. 'This man has met the future president,' he hollered. It was hot in there!
Having spent a beautiful day with Dickie Betts at his ranch a few miles from town, recording songs on his porch, we travelled to Miami to talk to Elvin Bishop, another Capricorn stalwart. Formerly with the Paul Butterfield Blues Band, he'd just enjoyed a huge Top-3 American hit with 'Fooled Around And Fell In Love'.
We stayed in Miami overnight, at the Sheraton Four Ambassadors on Miami Beach. Mike, our cameraman John and I were travelling back from the filming late that evening in the back of a cab when we realized that the radio station the driver was listening to was broadcasting live from the hotel. 'There's a club in the basement,' he told us. John and I decided we'd go down, have a drink and listen to the music for a while. 'I wouldn't do that if I were you,' he opined flatly as he dropped us off. As we walked across the marble lobby Mike decided on an early night. A wise move as things turned out.
We could hear the bass beats coming up to greet us as we walked down the stairs and into the club. It was really dark. The only light seemed to be coming from the strobes around the dance floor, each flash of light guiding us as we inched our way across the crowded bar, towards the one available free table. It took us a while, but we got there, sat down, sat back and ordered a drink.
As my eyes became accustomed to the light I began to look around and get my bearings. I could see the outside broadcast desk, close to the dance floor, gyrating with people. I looked around at the people on nearby tables and at the bar. I began to feel uncomfortable. It was dawning on me that we were getting a lot of attention. For the first time I realized that everyone I was looking at was black, that we were the only white people in the entire place. I started thinking about what Phil Walden had been saying, and looked across at John. At exactly that moment I felt a hand on my shoulder. John covered his eyes with his hands.
'You're in my seat,' I heard a voice say. The whole place seemed to freeze.
'There are a couple of other chairs empty ...' I ventured, gesturing around the rest of the table.
'No, you don't seem to understand, man. That's my seat.'
As John sank further down into his gin and tonic I got up and waited as the man seated his girlfriend, then parked myself opposite, on the only vacant chair. John stifled a nervous laugh as I sat for a moment, wondering what was going to happen next. I needed a cigarette.
I realized that my packet of Marlboro and my lighter were across the table, where I'd been sitting. The man and his girlfriend were staring at me intently. As I reached across, the girl curled her lip and disdainfully flicked the packet at me with the back of her hand. The lighter hit me in the chest, the cigarettes went spinning over my shoulder, spilling onto the floor a few feet away. Someone ground them into the carpet with their shoes. This was definitely the time to leave. Fifteen minutes after walking in there we'd made our escape and were knocking on Mike's hotel room door. 'Robert!' he exclaimed after we had recounted our story. 'When are you going to start to grow up?'
The following summer we covered the Bearsville Picnic, a similar event organized by label boss Albert Grossman, held in a forest setting near Woodstock and featuring The Band, Dr John, Mick Ronson and John Sebastian, very much the smiling hippie I expected him to be. All took part in an all-night jam session in the rustic Bearsville studio, their music mixing with the sound of the crickets that filled the scented summer air as I sat listening on the porch outside. The event ended with a spectacular late-night outdoor concert by Todd Rundgren, culminating in a 10-minute guitar solo, during which he climbed up to a narrow platform at the top of a 30-foot apex that dwarfed the stage. The higher he got the more the solo intensified, reaching a peak as he stood astride the apex in his rock-god loveliness. Suddenly, the solo fell away as he launched himself forward off his platform and into the blackness, falling towards the crowd below. Everyone screamed, convinced he was going to kill himself. Instead, at the end of the first bungee jump I'd ever seen, he bounced harmlessly down to the stage and into the encore.
Next, it was on to Los Angeles to meet up with Terry Reid at his house by the sea, to record the now famous interview that began with us stepping through a hole in the side of his house, straight onto the beach. 'I couldn't see the sea,' he explained. 'So I hammered a hole in the wall.'
Despite, or possibly because of its reputation, we often stayed at the Continental Hyatt House on the Strip, the world's most famous rock'n'roll hotel. We were there for five days with Led Zeppelin (the band Terry Reid turned down) on _The Song Remains The Same_ tour, their monster Winnebago in the parking lot. The hotel didn't need to advertise the fact that they were staying, it seemed the whole of California knew. The lobby was like Oxford Circus, 24 hours a day. Getting into an elevator was a major problem as the lifts were constantly crammed with people just cruising up and down, hoping that the doors would slide open and in would walk John Bonham, Jimmy Page, John Paul Jones or Robert Plant.
Mike and I arrived back at the hotel at about 2.30 in the morning, having rushed out to the airport to do a 20-minute interview with Kenny Loggins, who was changing flights and briefly available. The noise in the lobby was unbelievable when we got back. Bonham was holding a party on the sixth floor and hundreds of kids, groupies and Hollywood freaks were trying to gatecrash. I felt like going myself but neither Mike nor I had an invite and security was very tight. It was a happy surprise, therefore, to be joined by one of the band's management team, who walked over with us to the lift.
The three of us just managed to squeeze in, joining the expectant throng as we whooshed up to the sixth floor. As the doors slid open a David Johansen look-alike, made up like The New York Dolls, teetering in silver, thigh-length, stack-heeled boots, began to push his way to the front. A line of black-suited security men met him as he stepped forward, one of them barring his way by extending his arm across the lift doors. 'Where do you think you're going, man?' he asked the New York Doll. 'I'm going to the paaarteee,' was the affronted reply.
'Do you have an invite?' By now, the security man could have just let the lift doors close again, but he was beginning to have fun.
'No, you don't understand, man. I'm going to the paaarteee!!' He pushed hard against that outstretched security arm. It was a big mistake. First an elbow smashed his nose, then a knee jerked up into his groin. As he sank to his knees, the security men stepped forward and pulled him out of the lift, the doors catching the ankle of his trailing silver boot, trapping it for a moment, before the lift doors banged to. As we continued our journey, the occupants of the lift just picked up their conversations again, as if nothing had happened.
Violence and other casual exploitation is an unattractive reality of life around a lot of bands, as overzealous protectors take advantage of the wannabe invaders. Sometimes the band gets to hear about it, sometimes not, but it's always done in their name. It isn't just a band's music that's got the power.
In the mid-70s Led Zeppelin were absolutely awesome, a band at the peak of its powers, with Robert strutting, sliding and pouting around the stage, the audience eating out of his hand. The rhythm section was fantastic, with John Bonham beating out one of the biggest drum sounds ever, while Jimmy's playing was almost miraculous at times, an instinctive combination of feel, aggression and melody.
Through the years I've bumped into Robert many times, including a deeply emotional interview on the British Forces Broadcasting Service in 1993, during which he talked about the death of his son, Karac, 15 years earlier. He'd heard the news while the band was in the middle of the American tour. 'I was really out of it when the phone call came,' he recalled. 'At some party or other, girls everywhere ... I can't really remember. I had to pull myself out of all that madness and come back and face my son's death, in that condition, with journalists and television cameras ... That's when I straightened up. That's when I realized that some things are more important than rock'n'roll.'
My final memory of that week at the Continental Hyatt House was of Jimmy, having had a Harley Davidson motorcycle delivered literally to his hotel room, riding the machine up and down the 13th floor corridor as we were checking out.
A lot of the girls hanging out around the hotel were there more or less full time. As one band moved out, they'd just move in with the next. They cruised the Hollywood music scene, getting backstage and going to the parties, it was an amazing scene.
But there was still more to come, as we left Los Angeles, flew across to New York and onto a Dakota plane for the final short hop to one of the most magical experiences of my life.
James Taylor and Carly Simon had invited us to spend three days with them, filming at their home on the North Atlantic island of Martha's Vineyard. They'd built a fantasy house, like a Disneyland castle, with brightly coloured turrets and set in the middle of a wood. James's sister, Kate, lived in a tepee close by, his brother Alex ran a local store. James took Mike and the film crew on a tour of the island to meet the family. Carly invited me to stay behind and talk. She was elegant, interesting and incredibly sexy. I liked her very much, particularly that touch of vulnerability that led her to stutter a little when she felt nervous. When James returned they performed an impromptu living-room concert for us, rounding off with a version of 'How Sweet It Is', with Carly on piano and James on acoustic guitar. It was idyllic.
By way of stark contrast, the UK music scene was suddenly changing. Punk had arrived and the Americans simply couldn't understand it. To them it seemed like a lot of unattractive, parochial whining. However, to me personally (if not musically) it literally meant the force of change, as I increasingly felt the hostility directed towards me from this new wave of negative thinking. Let's face it, I was the identikit picture of everything the punk generation despised. Long haired, white, middle class, hippie, soft-spoken, son-of-a-policeman, BBC presenter, introducing the dinosaur stadium rock they hated with a vengeance. I was the coconut on their shy, a primary target for excessive bile. No one else was so obviously accessible, no one as symbolically perfect.
Back in Britain, the aggression soon became a menacing reality of my everyday life. People would stop me on the street and hurl insults and expletives. The prevailing atmosphere made it increasingly difficult for me to go to a club to watch a band. Standing in a crowd made me an easy target for abuse, and I was getting totally sick of the gratuitous air of violence, of being yelled at, kicked and spat on. It was degrading, depressing, confusing and unnerving and came as a major shock. I hadn't ever set out to antagonize people in this way, and couldn't understand how I'd managed to do so with such apparent blanket success.
This general feeling of discomfort came to a head in March 1977, first in a confrontation with The Clash at Dingwall's Club in London, then a few days later, in a meeting with the Sex Pistols that had repercussions far wider than I would ever have expected.
It was a Friday evening and I'd been doing some recording at Morgan studios with my good friend and session engineer George Nicholson, with whom I'd worked on the later Wally stuff for Atlantic.
I suggested to George that we stop off at the Speakeasy before going home, and we arrived at the club at about 11.30. As we walked in past the bar we bumped into Jim Diamond, who told us that the Sex Pistols were in the restaurant.
'They seem a bit rowdy,' he confided, with characteristic Scottish understatement. It was the day they'd signed with A&M records and they'd been celebrating. Having gone on a wrecking spree at the record company offices, they'd arrived at the Speakeasy with fuelled-up entourage and were having their own private party in the restaurant. George and I decided to leave and finished up our drinks. A tall, blonde guy in a green boiler suit had been pushing his way through the crowd around the bar and bumped into me as we turned to go. He confronted me immediately.
'When are the Pistols gonna be on the _Whistle Test_ then?' he demanded.
'This isn't the right time or place,' was my reply. 'Give me a call in the office on Monday morning.' It didn't matter what I said, he took a haymaker swing at me, cuffing me round the shoulder and knocking drinks off the bar. It seemed to be some kind of signal and suddenly all hell broke loose.
People were punching and kicking their way through the crowd, trying to get to me. People began to scatter as I was pulled round to the other side of the bar for protection. I couldn't see George. Glass was flying everywhere. People were either caught up in the mayhem or screaming in panic, trying to get out of the place.
As I tried to gather my senses I was confronted by about half a dozen Mohican-cut drunks, faces spitting hatred, their fists clutching broken glass. I was in serious trouble here, feeling as scared as at any time in my life.
Three options flashed through my mind as I struggled to maintain my composure. The first was to try to run, but I was in a cul-de-sac on the wrong side of the bar with a wall at my back, and they were barring my way. The second was to fight, but at six-to-one against, the odds weren't favourable. I decided on option three. 'Let's talk...' I began. 'What do you think you're going to achieve by this...' One of them kicked out at me while another tried to slash me with a beer glass as I slumped against the bar. I really thought this was the end of the line. I couldn't even begin to think what injuries I might soon be experiencing. I just tried to protect myself as best I could.
Miraculously, and seemingly out of nowhere, about a dozen guys appeared, forming a kind of human wall between the punts and me, surrounding me in a protective circle as they pushed and fought us through the madness and round the edge of the bar towards safety. I found out later that it was mainly the Procol Harum road crew who, like us, had just popped in for a quiet drink! You saved my life, guys. I was incredibly lucky to walk out of there with little more than a bruise on my leg and cuts on my back. George was not so fortunate.
As I was being pulled away, Sid Vicious had stabbed a broken bottle into George's face, who'd been quick enough to deflect the glass up and away from his eyes, but the jagged edge had torn into his wrist and opened up a wide, ugly gash right through the top of his head, from forehead to crown. I found him lying semi-conscious in a pool of blood in the reception area of the club. We had to get out of there, but it wasn't easy. The word was out and punk reinforcements were arriving from nearby clubs to join in the rumble and kick a hippie. It took about 20 people to get us through the door, across the road and into George's car. Someone told me that the police later cordoned off that whole block of Margaret Street in an effort to contain the trouble. I drove us straight to the Hammersmith Hospital, where George had 14 stitches in his head wound.
By now, Sue and I had given up the struggle of trying to keep our marriage together in the face of all the madness and Jackie and I had moved into a flat together in Putney, where I arrived at about 8.30 in the morning to find the press already gathering outside. I had absolutely nothing to say. 'Sex Pistol In Storm Over Brawl' ran the page 2 headline in the _Sunday Mirror_ on 20th March 1977.
All I wanted to do now was to have a bath and lick my wounds. If those people had wanted to shake me up, they'd succeeded. I felt wretched and deeply depressed. I wondered what the hell was going on and whether it was all worth it. I really hadn't got into music for this.
We were deluged with calls for days, from my family, the press, friends and inquisitive acquaintances. One of the first on the line was Derek Green, the UK boss of A&M Records. 'I'm so sorry to hear about all this,' he told me. 'You'll be glad to know that I'm dropping them from the label. We're making an official announcement on Tuesday.' Next to call was Aidan Day, my old producer on the Radio 1 _Review Show_. 'I've banned all Sex Pistols records from the playlist,' he told me angrily. 'The station will never play them again while I'm here. They shouldn't be allowed to get away with this.'
Some of the calls were more sinister, if not darkly amusing.
''Allo ... Mr 'Arris? You don't know me, but I thought I'd give you a bell to offer you our services. A lotta people were very upset by what happened at the Speakeasy and would like to take a bit of retribution, so to speak. We can do a very good job on their fingers of course, but what I recommend is the eardrums. A bit of perforation would be good. They're musicians, see? They need their ears ...'
'Stop! It's good of you to call ... but no thanks.'
FIVE
_'Who's Out for '78?'_
THE SEX PISTOLS INCIDENT LEFT ME FEELING SULLIED, INVADED AND very disillusioned. Dark clouds had gathered. The memory of the ugly violence of that night at the Speakeasy was proving hard to shrug off, but I was equally shaken by the wider hostility it provoked. The music press was now wading in with some witheringly personal attacks. Punk was the new thing, said the papers. The _Old Grey Whistle Test_ was – old and grey. A piece by Michael Watts in _Melody Maker_ accurately sums up the attitude towards me at the time.
He has undeniably been the most reviled personality both on television and within rock music. 'A wimp' has been the most general criticism. His questioning of interviewees has been deemed less than penetrating, and his eagerness to spread around gentle bonhomie has caused severe irritation. Always the music press has been the most personal and vitriolic. In this paper one writer, now gone, urged that a brown bag be placed over his head on screen; the following week he repeated his demand. Harris has simply had the ill luck to be the cause of outrageous spitefulness in others.
These words straddled a huge, dark pen drawing of myself, looking over my shoulder at three pen quills embedded in my back.
Even _Time Out_ endorsed the invective, using a typically cruel Gerald Scarfe cartoon to illustrate a poem in a 'Who's out for '78?' section of the magazine:
Groovy Bob is glad to serve
The PR apparat
He snuffles, 'Welcome To The Show'
Then settles back and off they go,
Dull-witted, vain or vicious.
Musicianship with every vice
Bob will opine 'really nice',
Not slack and repetitious.
Long bunny teeth; receding hair;
A tennis shoe; a swivel chair;
Just one more bureaucrat.
No matter how resilient you are, that kind of stuff gets through to you in the end.
Some of the criticism of the programme was justified and I think we handled punk badly. It was a long-established criterion that to appear on the show you had to have an album out. _Top Of The Pops_ was the singles show, we were the album show. Our problem was that the New Wave explosion happened on singles and for the first time on newly formed independent labels, not on the albums being released by the majors. The first wave of punk musicians didn't sign to the big multinationals, rejecting the corporate excesses, the big-budget recordings and stadium gigs they said had dulled the music's edge. Consequently, New Wave had been and almost gone by the time the programme began to embrace the second division album bands the bigger record companies were foisting on us. Introducing groups like The Depressions and The Fabulous Poodles felt rather demeaning. We were seen to first ignore this new phenomenon, hesitate, then try to catch up. It didn't work, and in retrospect, we probably should have just stuck to our guns, but the constant criticism was having an impact.
By now, in addition to the introduction of the weekly Newsdesk, presented by the wonderful and eccentric Andrew Bailey, two significant changes had been made to the _Whistle Test_ production team. Tom Corcoran had replaced Colin Strong as director of the show and Jill Sinclair had taken the place of Jenny Carson, now expecting her first child. Jill was a dynamic force for change, arguing strongly that the best of the new music should be given more airtime. But I had an increasing feeling that my life was spinning out of control.
Fame seemed shallow, fickle and confusing. Three years before, _Whistle Test_ had been the hippest show on TV, Britain's No. 1 music show. Our success had been toasted, now I was being roasted. Burnt alive, it felt like. Meanwhile, I hadn't changed and couldn't understand why what had recently been so great had now turned so sour. 'Things have hardened up,' I'd told Michael Watts. 'We are in a very aggressive, very cynical time right now and it's not my time. People don't really want my soft approach.'
He'd described me as being 'very much a child of the 60s. Now 32, Harris has never lost his belief in good vibes and mellow sounds and doing your own thing, and he deeply regrets that there is no longer an open atmosphere, that one's stance is always on trial.'
For 11 years I'd been surfing the crest of a wave. Everything had seemed to fall magically into my lap. I'd never had ambitions to be famous, or even had a major career plan in place. I'd been incredibly lucky, in a 'right time, right person' kind of way. But now things were going against me, I didn't feel like I was coping particularly well. Maybe the critics were right, maybe none of the work really amounted to very much. Maybe I should stop. I didn't know where to go from here, I just knew I wasn't enjoying it any more, and that compromising one's beliefs is never the answer.
Sue remained loyal and supportive throughout, as she and I struggled to retain our friendship following the break-up of our marriage. I was regularly travelling across London to see the girls and we have always been able to talk. But my dark mood pervaded my relationship with Jackie, who was trying to cope with living with a person going through a major identity crisis. She wanted us to settle down now, whereas I didn't know what the hell I wanted to do. I was very difficult company, when I was there. A lot of the time I was concentrating on escape, not from Jackie, but from myself, and the contradictions going on in my head. We were at the point of breaking up when she told me she was pregnant.
Even that didn't hold us together and for a while I moved out and shared a flat with George in West Hampstead, a mile or so down the road from Sue. I was spending a lot of time with Elton John's new lyricist, Gary Osborne, and his then-wife, Jenny, at their house in Regent's Park, a great stop-off place on the way home from the West End. Before writing 'Blue Eyes' and 'Little Jeannie' for Elton, Gary had made his name as co-writer of the massively successful _War Of The Worlds_ with Jeff Wayne, a rock concept that featured 'Forever Autumn' by Justin Hayward and narration by the great Richard Burton. He'd also written the English lyrics to a French song called 'Amoureuse', providing a hit for Kiki Dee, a regular visitor to the Osborne household. Another was Tarquin Gotch, who was part of the movie production company that made _Home Alone_ , its sequels and a string of films by the late John Candy.
Tarquin lived in West Hampstead, a couple of blocks away from George, in a flat he'd bought from Hazel O'Connor and shared with Kelly Le Brock, who used to come and go around modelling assignments and we all hung out together for a while. He was, at the time, one of London's hottest young record company A&R men, signing the Stray Cats to Arista, getting involved in the career of The Beat and taking Billy MacKenzie to Warner Brothers.
For the next few months Jackie and I rarely saw each other, but we never lost touch and I was there for the birth of our baby, Charlotte, on 30th September 1977. Although my first daughter, Mirelle, had been born only seven years previously, it had still been the convention then for dads to pace anxiously up and down in the hospital corridor outside. Emily had been born two months premature, and was rushed straight off to an incubator but this time I was there and being part of Charlie's birth was very emotional – the joy of seeing her come into the world was overwhelming. The closeness of the whole experience brought Jackie and I back together again and for a while I felt more settled and happy.
The big compensation for the flack we were taking on _Whistle Test_ continued to be the regular filming trips to America that fed so much new material into the show. I went to Miami to meet up with The Police at the NASA Headquarters, for the filming of the 'Walking On The Moon' video and to record a conversation with Sting. Frances Tomelty was there too, pushing their toddler around in a buggy.
I'd hitched part of the way to Miami with The Knack, joining them in Tampa Bay and filming an interview with their lead singer, Doug Fieger, on their tour bus, motoring down through the Florida late-summer sunshine. We had to turn the air-conditioning off to do the filming, and with the lights and camera equipment generating so much heat it was like a sauna in the back of that bus. It was the week the band hit the top of the American charts with 'My Sharona' and as we prepared for the interview Doug leaned forward, bathed in sweat, his face a few inches from mine. 'Bob, is it hot in here, or ... is it my career?!'
I really enjoyed the road. I'd recently spent a couple of weeks on an American tour with Queen, working with the band to compile material for a television documentary that, for some reason, was never shown. It was fascinating watching the activity that went on behind the scenes, and seeing the luxuries money can buy. I travelled with them in their private jet, their four individually appointed limousines waiting on the tarmac for them wherever or whenever the plane touched down.
I joined them for the leg of the tour that took in Chicago, Houston and then Las Vegas, the oasis in the desert, where they played at the world-famous Aladdin. I'd driven there once, a 12-hour journey from Los Angeles through the desert, travelling a straight road that looked exactly like the photograph on the _Best Of The Eagles_ album cover, in a temperature of around 110 degrees. Halfway across I ran into an unexpected ultra-violent thunderstorm, with attendant flash flooding from wind and rain so heavy I was forced to pull over to the side of the road. It was over an hour before I could get moving again, and I watched in wonder as the moisture miraculously brought the desert to life. The ground seemed to be covered by a green sheen of vegetation splashed with the colours of a thousand flowers, instantly transforming what previously had been nothing but miles and miles of lunar desolation into a beautiful summer landscape.
On the night of the Queen gig, the band had their drivers collect them from the front door of the hotel, four 40-foot white limousines waiting to take them to the venue, arriving one by one at the backstage enclosure. It wasn't a long drive. They were playing in the theatre at the back of the building. Although the Aladdin is a big complex, the car journey from front to back probably lasted no more than a minute and a half. It would have been a lot easier to have just walked through from their hotel suites, but where's the sense of occasion in that?
I always enjoyed watching Queen play live. They were four intelligent guys who applied their minds to their music, be it the theatrical expression of their stage show or the instrumental setting for their strong, operatic songs. They all wrote, the chemistry in the band was exactly right, and they could really rock, driven by Roger Taylor's classic drum style and embellished by the world-class guitar playing of Brian May, so nimble on the frets with those long, thin fingers. And, of course, in lead singer Freddie Mercury they had the showman supreme, someone who simply refused to give less than one hundred per cent. I'll always remember the effort he put into a 9.30 a.m. session at the BBC Langham Studios for my _Sounds Of The 70s_ show, veins standing out on his neck as he held the microphone, reaching for the very best vocal performance he could give. I also liked the way the band treated people, particularly the fan club, inviting members to special private concerts and video shoots and generally making them feel a part of what the band was about.
The Aladdin concert, however, turned out to be a very subdued affair. Las Vegas didn't really know what to make of them at all. But I had a fabulous time for the four days we were in town, sightseeing and club-hopping with Roger Taylor and his minder. We gambled (lightly), drank (heavily), saw a couple of Wet T-shirt competitions and spent an evening with the Dick Clark Nostalgia Show, watching The Shirelles and Bo Diddley performing on stage. Dick Clark was famous as the host of the great _American Bandstand_ television show, and the evening featured fascinating footage and on-air clips from the programme's rock'n'roll heyday, projected onto a huge screen at the back of the stage.
At the checkout desk the following morning I bumped into one of the guys from the Queen road crew. As we talked, he idly slipped a quarter into one of the hundreds of one-armed bandits scattered around the hotel lobby. To our great astonishment he won the jackpot. Coins spilled out everywhere, suddenly people were rushing around, handing us those little cardboard buckets and helping us to scoop up the money and the tokens. Having settled up his winnings, the cashier gave him a silver dollar, a token given to all jackpot winners by the management. As we waited for my car to arrive we stared at the monster slot machine that sat astride the hotel entrance. It was said to be the biggest one-armed bandit in the world at that time – a glittering, gaudy monument to gambling. It stood about 10 feet tall, used a power station-full of electricity, and only took silver dollars. He didn't know whether to keep his as a souvenir or take a chance of winning the world's biggest jackpot. After some deliberation, he slid that big, shiny coin into the slot. It took the weight of both of us to heave down the heavy, chrome handle and we stood transfixed as all the coloured lights started to flash. One by one, three identical symbols came down into the illuminated windows ... chunk, chunk, chunk. His luck was unbelievable. Sirens went off, the man was a hero. I stayed just long enough to learn that the jackpot he'd won was worth more than 17,000 dollars. And it all started with just a quarter.
I'd been to the Aladdin once before, with Emerson, Lake and Palmer, as part of a _Whistle Test_ special, reporting on their American tour. We'd followed them from Montreal, where they'd played the Olympic stadium, the setting for their striking _Fanfare For The Common Man_ video, with them knee-deep in snow. They'd filled the place with 80,000 people and 129 onstage musicians, including a full concert orchestra. It was massively expensive lumbering the equipment and personnel around America, a project for which they'd commissioned three chrome-plated juggernauts, issuing instructions that they always had to travel in the order of the letters painted on the roof. First was 'P', then 'L', then E', a very important point, because with 'P' leading, the convoy correctly read E L P when viewed from the sky. The tour couldn't sustain the extravagance and soon the orchestra was disbanded, the band playing the latter part of the tour as a three-piece. Even Carl Palmer had to downsize from the huge suites he used to book at every hotel stop, the rooms stripped, cushioned and especially appointed for his daily workouts with his personal fitness trainer.
We'd featured the band many times through the years although, to start with, I'd never really liked them. I'd been critical of them on air when they came in for their first live studio session some years earlier, calling them 'pretentious', or something like. One of their roadies came over and had a 'quiet word' in my ear about the possibility of me being more complimentary and changing the script before the programme went out.
Despite the early difficulties, I'd become good friends with Emerson, Lake and Palmer, particularly Greg Lake, with whom I enjoyed spending time. Filming with the band additionally took us to New York, Los Angeles and briefly to Memphis. I flew out of London on a Friday morning and with the time change landed in Memphis, via Atlanta, just before the band went onstage that evening. I watched the show, then we took a film crew out to a local restaurant to record the interview, finishing at about 3.30 in the morning. I just had time to get the taxi driver to take me to the Graceland gates before heading straight back to the airport for a 7.30 a.m. flight out, arriving back in London via two changes, at breakfast time on Sunday morning. I'll never do it again. I was jet-lagged for about two weeks.
We also did some filming together at the Compass Point Studio, right by the beach on the island of Nassau in the Bahamas. The band had been asked to organize a playback of their _Love Beach_ album for the famous and demanding Ertegun brothers, owners of the Atlantic Records label, who swooped in by helicopter to hear rough mixes of the new recordings. They'd lost a lot of money on the tour and this was a crucial album. I've rarely seen three people as nervous as Emerson, Lake and Palmer were that day, hands shaking on their appointed faders as they mixed together the tracks, the Ertegun entourage an intimidating presence at the back of the control room, puffing on their big cigars.
'When they forced us to make _Love Beach_ we were exhausted, frustrated and we had completed most things within our life as a band,' Carl Palmer said. 'We'd taken technology by the ears, as it were, with the Moog synthesizer. We recorded with an orchestra and toured with it. We didn't have a lot more to say musically, and I think we wanted some free time.'
Compass Point was owned by Chris Blackwell, founder of the Island record label. He also owned a house a few miles along the coast, situated on a low cliff top, overlooking the sea, and he invited me to stay for a few days, a wonderful opportunity to completely relax in a magnificent setting. From the pool I could see the housekeeper, Pearl, cleaning fishes on the beach below, throwing the remains into the sea. At the same time every evening a huge manta ray would swoop slowly and elegantly through the clear, turquoise water, circling in to steal the fish heads and remains Pearl was discarding. With the backdrop of the sun setting into the mouth of the cove it was a most beautiful sight, one I was determined to burn into my mind like a photograph. I didn't have a camera with me, but to this day I can still close my eyes and summon up that spectacular scene. Carl Palmer took me deep-sea fishing with Peter Frampton and his manager, Dee Anthony, which was very exciting. We even had a shark bump the boat.
Having completed the filming with Emerson, Lake and Palmer, and with the Average White Band, who were also recording at Compass Point, I flew to Miami to link up with the Bee Gees. We met at Criteria Sound, very much their 'home' studio at the time. The facilities were superb, as we knew from using their mobile unit to record the Macon Picnic, with top-of-the-range engineers, state-of-the-art equipment, and a fully operational film unit.
The band were absolutely huge at that time, having been enjoying a dramatic renaissance of fortune with the success of the _Saturday Night Fever_ soundtrack, at that moment the biggest-selling album of all time. On 18th March 1978 they occupied the top three places on the American _Billboard_ chart, with 'Night Fever' at No. 1, 'Stayin' Alive' at No. 2 and 'Emotion' by Samantha Song at No. 3 – a track they'd written and produced. With their brother, Andy, at No. 5 with '(Love Is) Thicker Than Water', this was chart dominance of Beatle proportions.
Despite their superstar status they were, as always, friendly, professional and polite, meeting me in reception and ordering us all a pot of tea. We chatted for a while, Maurice unexpectedly telling me about Lulu and what drove them apart. 'She was married to her career,' he told me. I felt married to mine.
They invited me through to a small, dimly lit, black-walled audio booth for a playback of their new LP, the hugely anticipated _Spirits Having Flown_. The backing tracks were almost finished but they were falling behind schedule. Only guide vocals had been added so far and none of the lead voices or harmonies had been recorded. The sheer scale of the project had thrown up a number of problems. They were using 96 separate channels in the recording process, which, with the technology available at that time, had meant hooking together two 48-channel mixing desks. It had worked to start with, but then the desks started slipping out of phase with each other, rendering the backing music useless as it hit the speakers like a cacophony of random sound. An army of technical support engineers had failed to come up with a solution, so they'd been temporally forced to strip back to 48 tracks, at the cost of much valuable time. The Bee Gees were philosophical about it all.
While I got myself comfortable facing the monitor speakers, they took up places just behind me, Maurice leaning over my left shoulder, Barry in the middle and Robin leaning over me on the right. 'Because we haven't recorded any vocals we thought we'd sing it through for you,' he said. 'You can tell us what you think of it and you'll know what you're talking about when we do the interview.' I sat absolutely spellbound for the next 40 minutes or so while they stood behind me and sang right into my ears, giving me a stunning, private, live performance of the album the whole industry wanted to hear.
I heard 'Too Much Heaven', 'Tragedy' and the album's glorious title song, their effortless harmonies filling that tiny room, voices so close that you could hardly prise them apart, instinctively perfect, like the Everly Brothers. I thought about what David Crosby had told me on Radio 1, about when he, Stephen Stills and Graham Nash had sung together for the first time, in Joni Mitchell's kitchen. They had to stop almost immediately, they were so amazed by the way their voices exactly fitted together. 'We started laughing, we couldn't believe it,' he'd recalled. 'I mean, how would you ever know. You can't legislate for a thing like that.'
I get shivers down my spine just thinking about it and skimming back through the memories of those trips to the States, it seems extraordinary that I was the person doing all that. It had been my escape, my enjoyment and, occasionally, my salvation. We'd worked our socks off and had a really fantastic time. I didn't know it then but that final _Whistle Test_ trip was to be my last to America for 20 years. Boy, did I miss it!
I found it hard adjusting to reality back home. The UK seemed immediately hostile. I felt jaded and completely worn down by all the ongoing press attacks and found myself increasingly locked within a kind of siege mentality, feeling defensive and suspicious.
Despite the first appearance of Dire Straits in the summer of 1978, a great Tom Petty concert soon after and the foundation-shaking studio performance of 'Paradise By The Dashboard Light' by Meatloaf, the fun was going out of doing the show. The contrast with the American experiences emphasized the increasing panic that was setting in around my inability to see a way forward from here. I felt I'd lost my identity to my television persona, that I'd become 'the Ken Barlow of Rock', as I was quoted as saying. I decided I'd outstayed my welcome and my main thought now was to step back for a while and take stock. I did my last live _Whistle Test_ studio presentation, co-hosting with my successor, Annie Nightingale, on 19th September that year.
_Whistle Test_ had completely dominated my life for the previous six years and it felt strange that it had come to an end, but I knew I'd done the right thing. There were no big announcements, no trumpet fanfares. It was just time to get back into radio.
Seeking anonymity and freedom I joined Radio 210 Thames Valley, a small commercial station housed in a converted ambulance depot near Tilehurst on the outskirts of Reading. My first broadcast was on a Saturday afternoon, sitting in on the _Sports Show_ , taking reports on all the local matches, reading out the scores and playing a few records. I'd never done a programme like that before but being a keen soccer fan I had a really good time. At 6 o'clock, one of the young station DJs arrived in the studio to do the _210 Club Show_ that followed, looking at me apprehensively over the pair of National Health glasses that sat precariously on his crooked nose.
He was armed with boxes, carts, tapes, discs, newspapers and letters, all spilling over the desk as we went through the hot seat changeover. I couldn't believe he needed all that stuff, until I heard his show come alive in the car on the way home. It was a revelation, a cavalcade of news items, sketches, phone calls, correspondence, characters and the occasional burst of music. It was exciting. I hadn't heard anyone as effortlessly madcap since the Everett days of Radio London. As I flashed back up the M4 to London I decided I wanted to be a part of this station, and all the time he was banging home his name. I wasn't about to forget it. This was Steve Wright, six months into a burgeoning radio career.
Radio 210 was owned by Neil ffrench-Blake, an eccentric Berkshire aristocrat. He'd wanted to have his own jukebox of the airwaves so, in the less-regulated days of the mid-70s, he'd bought one and staffed it with an extraordinarily high level of local talent. Steve was part of an original on-air line-up that featured Mike Read and Steve Crozier. Croze became a great mate, supportive and constructive. Many were the nights he put me up – and put up with me.
Radio 210 had a really good atmosphere at that time and we often used to sit around in the evening, talking, playing records, or joining Steve in the studio while he worked after-hours on the characters for his show. Neil used to preside over his apprentices like a benign sergeant major, ever-present cigarette pressed between his lips. 'You're going right to the very top,' he used to tell them all, billowing out smoke over his paper cup full of whisky and water.
He'd married into aristocracy, his wife being a distant relative of the Queen. Somehow, they managed to arrange a royal visit to the station soon after I arrived. The Queen wore a red coat and a black hat with a red feather in it and was accompanied by the Duke of Edinburgh, whom she kept chastizing for being grumpy.
'Oh do buck up, Philip,' she said as I demonstrated the studio equipment to them. 'Try and be nice.' You could tell it was the last place on earth he wanted to be.
I committed myself to a full schedule at 210, and Neil took full advantage. I soon found myself doing 20 hours on-air every weekend. I was on 9 p.m. to l a.m. Friday night, 10 till 2 Saturday lunchtime, 9 till 1 Saturday night, 10 till 2 Sunday lunchtime, rounding off with the _Oldies Show_ 9 till 1 Sunday night. Steve Crozier would put me up for the weekend at his cottage near the studios. It was a crazy schedule and, after various bits of music logging and administration, I'd arrive back in London around 6 o'clock on Monday morning absolutely worn out. I started the _Oldies Show_ one Sunday with The Hollies' 'I'm Alive', just to remind myself I was. But I enjoyed the move across into more mainstream radio and was very much inspired by the work of the guy doing the afternoon show on Capital Radio in London, who remains the best DJ I've ever heard. The late Roger Scott really was something special.
Like his idol, Bruce Springsteen, he was born to do what he was doing. Modest and bright, he had a great voice, a dry sense of humour and a wicked laugh. He made you feel part of his programme, as if he was talking directly to you and, crucially, he never lost sight of the fact that a DJ's primary function is to highlight the music. Roger was a huge influence on me, specifically in two ways.
One was the music mix, which he pitched just left of centre, playing quality rock and pop, some rock'n'roll and 60s singles, album tracks and rarities. He never played rubbish. You could tell how much he was into the music by his casual knowledge of it and by his sense of pulse, which gave his show a rhythm. He played Springsteen, The Beach Boys (his other great love), Queen, Steve Miller, Bob Seger, some soul, the hottest new records and a cavalcade of jukebox gems. It was a rarefied mix that proved to me that it was possible to do a mainstream radio programme packed full of high-quality music and still make it really accessible. Pointers are found in the lyrics of one of Roger's favourite songs, Mark Germino's 'Rex Bob Lowenstein', about a mythical American DJ:
He lives for his job and accepts his pay,
You can call and request 'Lay Lady Lay'.
He'll play Stanley Jordan, The Dead and Little Feat,
And he'll even play the band from the college down the street.
It's the kind of eclecticism and open-minded musical attitude that I've always thought important. Although written in 1987, the song also predicted radio's increasing reliance on computer-selected playlists and audience research figures, the antithesis of what Roger and 'Rex Bob' were all about:
Now one day a man in a pinstripe suit
Took the owner of the station to a restaurant booth.
His pitch was simple. 'You'll increase your sales
If you only play the song list we send in the mail.'
He guaranteed a larger audience
Less confusion and higher points
'But your Drive Time jock won't get to do his thing
Hey, he's not half bad, tell me what's his name?'
It's a wonderful song, full of irony and still much requested on my shows. Unfortunately, it's proved to be prophetic. Much of commercial radio today has much less to do with programmes than it does with shareholders' bank accounts, a harsh reality of the commercial world. Young broadcasters these days just don't get the same opportunities for self-expression as they did in the past.
The second big influence was on the technical side, particularly the way he used the microphone. Unlike most DJs, Roger didn't use 'ducking' devices, or surge the music up and down while he was speaking. Once a record was going he never touched the faders or chased the fades. He had the great gift of word economy, and set his voice level just above the volume of the non-stop music, blending in with it, letting hooks and riffs breathe as he paced his links around them, lifting his voice or moving closer to the microphone for emphasis. Roger's show was a masterclass in microphone technique. He was sharp, informative and loved his music, the complete professional package. Ask any of my contemporaries and they'll tell you the same. Roger Scott was the DJ's DJ.
I was thriving on the volume of broadcasting I was doing, but getting very tired. The weekend schedule was punishing and I wasn't looking after myself, still seeking escape routes of various kinds and staying up late, particularly when entertaining friends. A typically indulgent Thursday night at our Putney flat finished at about 4 o'clock, when I collapsed into bed. I woke up with a start at about 7.45. It was Miri's Christmas school play that morning and, although I felt absolutely dreadful, I'd promised to be there.
I drove across to West Hampstead through the heavy rush hour traffic hunched over the steering wheel, shifting around uncomfortably in an attempt to ease a dull, aching pain that was beginning to tighten down the sides of my chest. I almost collapsed into the chair beside Sue when I arrived for the performance.
'You look terrible,' she said. 'You should go straight back to bed.' After catching the opening few minutes I took her advice and struggled back to Putney, where I slept for the rest of the day. By the following afternoon I was feeling much better, and was watching the England Rugby Union International on television when the doctor arrived. I even asked him if I'd be OK to get down to Radio 210 the following afternoon. He said probably not, that I'd got a mild case of flu and should take it easy for a couple of days. There seemed no particular cause for alarm. A few hours later, however, things took a dramatic turn for the worse.
The discomfort in my sides returned, only worse this time. It felt like I was in the grip of a tightening vice. I started getting flashes of jagged pain right through the centre of my skull, like a meat cleaver cutting through the bone. It was so horrendous that I started screaming and bashing my head against the wall, trying to cause a diversionary pain. Then I started convulsing.
Jackie rushed me to the Queen Mary's Hospital in Roehampton, where the medical staff spent the next 15 hours working to save my life. As they were wheeling me through to the emergency department, I caught a glimpse of my reflection. My skin had turned yellow and my face had broken out in a hundred red-rimmed spots. How could I have got so ill so quickly?
They could neither sedate me nor give me anything to kill the pain for fear of masking the elusive virus that was doing so much damage. An initial diagnosis suggested a brain infection of some kind and I endured three lumbar punctures that dreadful night, needles inserted deep into my spine to withdraw the spinal fluid needed for testing. It wasn't until later that I discovered I'd contracted a form of legionnaire's disease, linked to pneumonia.
It was almost unbearable, yet equal damage was being done to my pride. I was absolutely frantic about the idea of being seen in this condition, of being recognized. I just couldn't bear the thought of being pushed into a general ward and having to face people. As they transferred me into a small private side ward of the intensive care unit, I felt peaceful relief. For the first time in many hours, the pain lifted and I was suspended in a tranquil silence. I became an observer, having an extraordinary out-of-body experience.
From some indeterminate height I was looking down at myself hooked up to all that life-saving machinery, while white-coated figures bent over me in urgent activity. I felt emotionally detached from myself, yet connected by what seemed to be a silver thread, as thin as a strand of a spider's web. I was hypnotized by an overwhelming feeling of serenity, a certainty that this feeling was not the end of my life, more a stepping stone into whatever came next. It was a tranquil and beautiful feeling. I sensed a tunnel of light, as if into another dimension. Then, click. Everything went black.
I looked up to see my mother come into my music room at my parents' house in Ardington Road in Northampton. I was probably about 13 years old. It was summer and the sash window had been pushed up a little, letting in a breeze that disturbed the net curtains my mum always used to hang. I looked at the pictures on the wall, feeling excited and happy, knowing this was no dream – I was really there. I could feel the breeze on my face. Everything was exactly as it was. Then, click. Everything went black again.
I remember briefly coming to and being hugged tightly by a woman, presumably a nurse, whose voice I didn't recognize. 'Thank God, oh thank God,' she said over and over again, before I fell back into my coma.
I finally opened my eyes and blearily began to take in my surroundings. As I came to, I became aware of someone sitting in one of those big old hospital chairs at the side of my bed. It was George. 'Hiya, man,' he said casually.
'Hiya, George,' I replied. 'What time is it?'
'Ten to five ... Thursday afternoon,' he told me. 'You've lost four and a half days.'
Sue and Jackie arrived, and sat talking together at the bottom of the bed and we all agreed my lifestyle had to change.
My hospital stay lasted 10 days and although initially I felt very weak, the first part of my recovery went well and within a few weeks I started working again. I didn't feel strong enough to go back to radio full time, but I did a couple of interviews and articles and even introduced The Police on stage at a fantastic gig in Slough in early spring. But I continued to feel very low, as if my resistance had been broken. Instead of improving, I started to regress. I didn't seem to have any energy for life and there were so many things about the whole hospital experience that I couldn't explain. The out-of-body sensation and the extraordinary time-travel moment with my mother remained vivid in my mind. Yet I was trying to pretend that the illness had not been serious. Despite my debilitated state and the scars that had now shown up on my lungs, I tried to tell myself that the threat to my mortality had been nothing more serious than a blip. I did not address the possibility that the illness was more likely a reflection of my state of mind and the late-night lifestyle I'd been living. I was in denial.
June Bolan had, by this time, introduced me to Danae Brook and her American husband, John, a student of psychologist R.D. Laing. Everyone knew John by his nickname, Pleasure, a handle he'd acquired at a San Francisco fancy dress party in his youth, where he'd arrived naked, apart from copious leaves, branches and bits of twig and shrub, which he'd entwined around his body. He'd rolled dozens of joints, and had carefully pushed them one by one into all the woody nooks and crevices of this extraordinary creation. He called himself The Pleasure Tree.
Danae was a quality writer. She and Pleasure had two young children and she'd recently published a book about natural childbirth, as well as writing regular features for the national press _._ They were planning to spend a family summer in Ibiza, at their holiday home near the village of San Miguel in the northern part of the island. The house sounded idyllic, a good 20 minutes' walk from the nearest main road, tucked away in trees, a short distance from Benirras Beach and unknown to tourists. They told me they were leaving the following week and invited me to join them. Pleasure was particularly insistent that it would be good for me and aid my recovery. Jackie couldn't come because of her business commitments, but she also thought a break was needed and promised to join me when she could. I could get fit and have a proper holiday for the first time in years. Filming had usually taken up the middle weeks of summer, but this year, without _Whistle Test_ , I was free and we set off in their Citroen Diane for a holiday that was to prove to be a major turning point in my life.
I loved Ibiza. There's something about the atmosphere of the place that seems to loosen people's inhibitions.
The tiny stone house had neither running water nor electricity, and it was my job to prime up all the lights with new wicks and paraffin and every morning pump the water up from the well. I loved bringing up that water and how pure it tasted. It would splash ice cold into the tank on the flat roof above, gradually heating under the hot summer sun to a temperature perfect for a shower and the washing up. At night, I sometimes took a mattress up onto the roof, lying on my back looking up at the sky, drifting off to sleep under a million stars, often to the sound of Mike Oldfield's _Tubular Bells_ playing in the house below.
I struck up a close, platonic friendship with a Danish woman called Asta, who was staying with friends nearby, and she was my companion for expeditions to the beach. It was quite a hike to get there, 25 or 30 minutes down a bumpy, rock-strewn dirt track, longer climbing back. Much to our relief, one morning a friend of Danae's offered us a lift in his Land Rover and Danae, Pleasure and the kids also decided to join us for a day on the beach.
By the time we'd all piled in there was very little room left, so I sat on the back frame of the vehicle, supporting myself by hanging onto the roll bar, children either side of me. It was a hot, uncomfortable journey as we sped down that hill, and the impact of the rocks and potholes seemed to jar through my body more and more. I began to hurt. That horrible vice-like pain began to grip my chest again. Arms above my head, I was holding onto the roll bar for dear life and as we bowled onto the beach the pain down my sides was excruciating. Despite my tan I'd turned deathly white and my head was beginning to pound. I began to panic, certain I was getting ill again and wondering what would happen to me in this remote, inaccessible place.
Pleasure took control and laid me on a beach towel under a parasol for protection against the fierce midday sun. He told me not to worry, to breathe deeply and to stay calm. His reassuring voice echoed in my brain as I began to relive the experiences of that first, desperate night in hospital when I nearly died. For the next few hours I was delirious, screaming out in pain as the needle sucked the life fluid out of my spine again while the thunder coursed through my head. Then I was calm once more as I relived the shimmering memory of the out-of-body sensation. I was certain now that I'd experienced a fleeting sensation of an afterlife, that death doesn't end everything.
I began to explore questions about myself that I'd been trying to ignore:
If I'd died, what was my personal legacy?
Had I lived my life in a way that made me proud?
Did I like myself?
For the first time, I realized that mortality is the great leveller. It doesn't matter how much advantage we seek to gain during our lives, our deathbeds will render us identically vulnerable.
I regained consciousness many hours later, just as it was getting dark. I felt absolutely drained. Pleasure put his arm around me as I struggled to sit up.
'You had to go through it,' he whispered. 'You had to exorcize it all.'
I felt completely different, as if I'd been reborn. I'd finally admitted to myself what I'd been through and the pattern of my life that had taken me there. I wasn't frightened any more. I'd been given a second chance to get myself right and I intended to take it. I'd learned a massive lesson about the simplicity of things, that it all comes down to being comfortable with one's self, nothing more or less. When you look at yourself in the mirror, there's a fantastic strength in knowing that you're doing the very best that you can. Treat each day as if it's your last and the revelation dawns that the more you put in, the more you get back. Karma, we used to call it. That's it, the key to a better life. To quote James Taylor: 'Any fool can do it, there ain't nothing to it.'
SIX
Rex Bob Lowenstein
I ARRIVED HOME FROM IBIZA AT THE END OF THE SUMMER OF 1979, feeling fitter and more positive than I had for years. I'd shaken off the shackles and now it was time to start rebuilding my life.
For the past few years I'd been hooked up in the web of 'celebrity', from which I was now keen to unravel. What had been said about me in the newspapers during my last two years on _Whistle Test_ had really hit home. I'd defy anyone who's had a real hammering from the press to say it doesn't hurt. It does. In the same way that you're inflated by all the good things you read, so you're hit by the blows. The greater the fame, the harder it can be to deal with. My experience was minor by comparison with that of a Paul McCartney or a Robert Plant. It's very hard to stay level at that kind of stratospheric height. I think it's to their massive credit that they've remained 'grounded' to the extent they have. It isn't easy. I really felt I was starting from scratch.
The idea was to find myself again and go back to my roots. I wanted to establish tighter links with the family. I had neglected my parents and my girls. I wanted to return to what I knew I did best. Radio was where I wanted to be. I also felt there was one piece of unfinished business. I'd left _Whistle Test_ with very negative feelings. I really felt I'd run my course. But despite the upheaval it had brought into my life, I still felt very proud to have been associated with the show through what are now seen by many as the halcyon days. When Mike Appleton invited me to call in, it was a wonderful feeling to go back simply for the enjoyment of being part of the programme again.
I visited the new studio set-up at Shepperton, with The Damned playing a live set. After the Sex Pistols incident I'd found it very hard to be objective about punk, but I always liked The Damned, particularly 'New Rose' with its massive energy and its 'Is she really going out with him?' intro, like the Shangri-La's 'Leader Of The Pack'. Mike invited me to introduce Blondie onstage at the Apollo in Glasgow, for the annual New Year's Eve ' _Whistle Test_ Special'. Blondie had topped the British singles charts twice that year with 'Heart Of Glass' and 'Sunday Girl' and were at the peak of their power and popularity. At the end of a sensational concert we all headed back to the hotel and, as the decade ended and the 80s began, I found myself in the snug bar, enjoying a post-concert jam session – Deborah Harry on vocals, Chris Stein on acoustic guitar and the rest of us banging out percussion and singing along for all we were worth. The evening seemed to round off the decade perfectly. I'd said goodbye to the past. Now it was time to address the future and get behind a microphone again.
I'd already begun a commission from London Radio Productions to work on a multi-part series called _The Moody Blues Story_ and I enjoyed meeting up with them all again, particularly Justin Hayward, with whom I always got on well. I rejoined Radio 210, where Chris Yates was as good as his word and had kept my old job open for me, with a more sensible schedule this time. I started broadcasting a Friday evening _Rock Show_ and two four-hour programmes through Saturday and Sunday lunchtimes. I absolutely loved it all and soon decided to move to Berkshire, where I rented a small semi-detached house in Southcote on the outskirts of Reading, five minutes from the radio station. Jackie and I had found it impossible to settle together after I got back from Ibiza and, although we've remained good friends, we both agreed that a clean break would finally be a good idea. For the first time for 15 years I was living on my own and happy to see the pace of my life slow down at last. I began to nest build.
An art student friend of Tarquin's moved in for a couple of weeks to help with the decoration, in return for being able to use the interior of the house as a blank canvas. He worked in the colour spectrum from white to black, mixing a light grey wash to cover the walls, then creating rows of squares under the picture rails like paintings – textured blocks of black, grey or white paint. He coated over them several times, maybe black on grey then white or black again, wet paint in all shades of grey dribbling down the walls from the layers on layers. It was unusual to say the least and a real talking point with visitors. 'How on earth do you live with it?' was one of the most regular comments. 'How the mighty have fallen since the heady days of _Whistle Test_ ,' was another. But I didn't care, maybe apart from the fact that I wished he'd worked in colours. I was really happy there in my odd little semi-detached.
My daughters came down to see me most weekends and we were able to spend quality time together at last. I even got a dog, a slightly neurotic, impossible-to-train labrador-cross called Cassie, bought for me on a whim for £8 by Mike Read from a bloke at a local pub in Theale. She was part of a small litter of puppies playing round our feet in the bar and I'd helped her scramble up onto my knee while Mike, Steve Crozier and myself sat supping our Sunday lunchtime pints. She had a glossy coat, completely black except for a tiny patch of white fur under her chin. I thought she was absolutely gorgeous, curled up asleep on my lap, and when we left the pub I had her blinking in the sunshine under my arm. I'd never owned a dog before and didn't realize the commitment. From then on she went almost everywhere with me.
As well as my own weekend programmes I began to sit in on weekday shows. I even spent a fortnight early in 1980 doing the 210 _Breakfast Show,_ not a good idea on the cold, dark mornings of early January. It certainly focused the mind. The station closed down for five hours overnight, so I had to get myself into the studio by 5.45 a.m. and literally switch everything into transmission in time to play the opening theme music and link with the Independent Radio News bulletin at 6. I made it in for the first show with only seconds to spare, making the mistake of explaining my breathlessness on air. A local bookie immediately started taking bets on how many times during the next two weeks I'd oversleep and arrive late. He offered odds for one morning or two mornings, with variations for five minutes late, 10 minutes late and every five minutes up to 30, by which time someone else would have rushed in to man the fort. I'm a late-night person. I hate getting up in the morning. I nearly put a bet on myself but to my own and everyone else's amazement, I wasn't late once.
I started to get to know David Byron, formerly the lead singer of Uriah Heep. He lived nearby in Sonning and Radio 210 was his local station. He was a regular listener and phoned a few times when I was doing the Friday _Rock Show_ , often just for a chat or sometimes to ask me for details of tracks I was playing. He invited me over to his place after one of the shows and, having shut the radio station down, I arrived at about 1.45 a.m. The house was magnificent, one of an avenue of millionaires' homes, set in trees in an acre of land, the garden skirting the River Thames. I parked my car beside his white Rolls Royce at the end of the long gravel drive. However, all was not as it seemed. Despite the apparent opulence he was a desperate and embittered man. The Uriah Heep years had taken their toll.
David had founded the band, initially named The Stalkers, in the mid-60s and stayed with them for ten turbulent years, their grandiose progressive rock style yielding seven Top-40 albums before his departure in 1976. Despite their success, they worked and partied themselves to the point of exhaustion, 'a bunch of machines plummeting to a death', according to keyboard player Ken Hensley. Dismissed by the critics as an anachronism, the band became locked in a series of internal arguments following the death of former bass player Gary Thain. In the resulting power struggle Ken Hensley walked out and David Byron was forced to quit. He briefly joined Rough Diamond but they broke up soon after and, following a failed attempt at launching the Byron Band, he was trying to build a solo career out of what remained of his reputation.
The scars of the previous few years were obvious, as was the reality of impending financial disaster. The money had dried up and the rock'n'roll lifestyle could no longer be funded. As he showed me around, I realized that the house was falling into disrepair and the car beginning to rust. I felt desperately sorry for him as he told me how difficult life had become, and could identify with him about the hammering he'd taken from the press. But he was unsettlingly unstable and the atmosphere wasn't good. When he brandished a gun and held it to his temple I felt it was probably time to leave. We spoke a few more times on the phone, but then fell out of touch. He died of a heart attack in February 1985. It can be a brutal business, rock'n'roll. I was pleased to be disentangling myself from the madness for a while.
Radio 210 had a private garden and on sunny days it was possible to feed a few leads across the lawn and broadcast outdoors, so long as there was someone in the studio to play the records in for you. Steve Wright would often trail a mobile broadcast unit down to the A4 at the end of the drive, weighed down by stickers, posters, pens and other station giveaways. He'd flag down passing motorists at random and interview them live on air, stuffing the microphone into their vehicle to see whether or not they were listening to the station, and dishing out loads of 210 paraphernalia. It became a regular _Drive Time_ event, a cacophony of music, car horns and traffic jams.
By the middle of 1980 the DJ roster was beginning to change. Mike Read, with whom Steve did the brilliant _Read and Wright Show_ , had already moved to Radio Luxembourg, and Steve was about to follow. The innovative Dave Glass was now part of the on-air team, as was Keith Butler, and Neil ffrench-Blake asked me to take another new DJ under my wing. I knew the name Mike Quinn from a hundred black-and-white posters I'd seen when I first moved up to London in 1966. At that time his name was almost as well known to clubgoers as that of Jeff Dexter, except he was much more into dance than psychedelia. Mike was the resident DJ at Tiles Club but I'd heard nothing of him since. Now he was coming to Radio 210 on trial and I was intrigued to meet him. Surprisingly, he'd done very little broadcasting in the intervening years, but arrived at the station with a fantastic record collection and a huge amount of enthusiasm. Not surprisingly, he used Manfred Mann's single 'Mighty Quinn' as his theme song. Later, when he was doing _The Late Show_ he'd close down the station every night with 'Goodnight My Love' by Jessie Belvin from 1960, the first time I'd heard that magical record.
He was what's known in the industry as a ducker and a diver. But his heart seemed to be in the right place and I got on well with this likeable rogue, regularly putting him up at my house if he needed to stay over. Over a period of a couple of months he more or less moved in, constantly raiding my record collection for stuff for his shows and getting all my covers muddled up!
Mike was the biggest Rolling Stones fan I've ever met. He travelled to London with me when I interviewed Mick Jagger at his home in Chelsea a few weeks before the release of the _Emotional Rescue_ album. Mick was in a great mood, very hospitable and warm, despite the fact that we arrived over half an hour late, having been stuck in the M4 traffic. Mike got him to sign loads of stuff, had his photograph taken with him and I got some wonderful material for a 'Rolling Stones Special' for Radio 210.
As well as all his Stones records, Mike had crates full of northern soul and 60s singles. We constantly played music at the house, listening to new releases for the 210 playlist, choosing tracks for our shows or just listening to our favourite sounds. He loved making tapes of his favourite tracks and one day asked me if I would deliver a cassette for him when I next went to London. My daughter Emily was staying with me for the weekend, and when I drove her back on Sunday afternoon we diverted to the Fulham address Mike had written on the tape box. As we waited in the early summer sunshine for the front door to open, Emily desperate to go to the loo, I had absolutely no idea that my life was about to completely change again.
After the hurt of the past few years I'd vowed to be on my own for a while. I had no desire to start a new relationship and had been taking the opportunity to let my life settle, catching up on lost time with my daughters. Miri was now nearly 10, Emily was seven and Charlie was nearly three. When we weren't together I was comfortable in my own company and I certainly didn't plan to let my life spin into a whirlwind love affair. But that's exactly what happened.
Valentina Scott opened the front door of her house and I handed her the tape. She invited us in and was immediately attentive to Ems, showing her the bathroom then offering her biscuits and a glass of Coca-Cola, a rare treat in my new health-conscious regime.
We stood talking in the kitchen while music, conversation and laughter spilled out of a half-open door along the hallway. Val eventually took us through and introduced us to her friends sitting round a table heaving with plates of pasta, cheeses, bread, fruit, panatone, bottles of wine and pots of coffee and scattered with Sunday review sections and magazines. The atmosphere was convivial and we immediately felt comfortable, sitting down to enjoy the banter.
Val introduced us to her brother Nick, who was sitting slightly aside from the main crowd. Conversation between him and his sister slipped easily into and out of English and Italian, the two languages woven together as they talked, three or four words spoken in English in the middle of an otherwise Italian sentence and vice versa. It was fascinating to listen to and very musical to the ear. Val told us that they'd been brought up bilingual, that the family had spent more or less equal time in England and in Italy and that Nick was one of three older brothers. 'I'm the baby of the family,' she told me, laughing. She was 22, eleven years younger than me.
Mike Quinn was positively beside himself when I got back home. 'What did you think of her?' he asked, bobbing up and down as he followed me into the music room.
'My daughter thinks she's a wild woman,' I announced.
'I thought I might invite her to the show next weekend,' he ventured. 'What do you think?' I thought about it for a second. Greg Kihn and his band were coming in to play live, which I knew would be good fun.
'Perfect,' I replied.
Mike handed me the phone when he called her the following day. 'Shall I bring my pyjamas?' she asked me.
'No, don't bring your pyjamas!' I replied. I put the phone down, realizing that Mike had played Cupid and that I was embarking on an exciting new romance.
Val and I began to spend more time together. She swept through my little house in Southcote, bringing a much-needed feminine touch to the sparsely furnished rooms of grey and black squares, filling them with flowers, rugs and knick-knacks bought from local antique shops. It even looked presentable when my parents came to visit and they took to her immediately, Dad in particular appreciating the trouble she'd taken creating the fabulous meal that was waiting for them when they arrived.
Val was passionate about food and wine. She enjoyed the whole process of cookery, from searching out the particular herb or type of parmesan cheese she needed to complete the ingredients of one of her favourite Italian dishes, to conjuring a glorious meal out of the most forlorn leftovers in the fridge. She loved throwing dinner parties and much of our time was spent surrounded by people, for extended lunches or long evenings of eating, drinking, conversation and music.
Val increasingly involved herself with my daughters, particularly Miri and Emily, often coming to West Hampstead with me, spending time talking with everyone in Sue's kitchen, the most inner of inner sanctums. It was clear to all of us that Val and I were falling in love. Sue and I had never thought to get a divorce but, having achieved the close friendship we'd worked so hard to restore, now seemed a good time, with no recriminations. Her opinion mattered very much to me, particularly regarding the influence of my new relationship on our daughters, so it meant a lot that Sue trusted Val and gave us her blessing.
Val and I began to look for somewhere to live and Steve Crozier told us about a converted chapel of rest he'd heard about in Oxfordshire. Everything was happening very fast, but I had no reservations whatsoever. My track record with relationships up to this point had not been good and maybe because of that I wanted to commit myself unreservedly to this one. I was determined nothing would go wrong, that I would be true to Val for the rest of my life. Within a few months of meeting, she and I decided to get married and began to make plans for our wedding in Italy the following summer.
I had already joined Val on a few trips to Tuscany and could understand why she loved it so much. It was becoming clear that her family was not only wealthy but also had a fascinating history. 'My mum is called Contessa Fiammetta Bianca Maria Sforza,' Val explained. 'Her father, Count Carlo Sforza, was an important Italian politician and anti-Fascist. The Sforza family is one of oldest and most established aristocratic families in Italy and we can trace our lineage right back to the crusades. My parents met at the end of the war when my mother returned from exile in America.'
Val told me how her mother had been smuggled out of Italy during the dark days of Mussolini. 'When my grandfather returned to Italy he resumed his political career but it was made very clear to him by the Establishment that they did not approve of the forthcoming wedding of his daughter to Howard Scott, a divorced, non-Catholic, father-of-two, destitute Englishman!'
Her grandfather, however, was unmoved by any such political pressure. 'What matters now is my daughter's happiness,' he stated and so Howard and Fiammetta married discreetly and lived in Milan, where Howard opened an English-language school. Their wedding present from Carlo Sforza was La Tambura, a villa in the seaside resort of Ronchi.
My first visit to La Tambura confirmed that this was somewhere special. Set back from the inner coast road, it stands square, proud and magnificent behind high hedges and wrought-iron gates, in the middle of its own private world. The grounds are beautiful, scented and serene, shaded by trees and I was absolutely spellbound by the feeling of the place
One of the most memorable nights of my life was spent in the centre of the nearby town of Forte Di Marmi with Nick, the night Italy won the World Cup in 1982. The place went absolutely crazy, people piling into the two main streets on whatever transport they could muster – cars, coaches, and hundreds of buzzy little sewing-machine motorbikes, converging with tractors pulling trailers full of people down into town from the mountain farms. It was a dazzling, deafening cacophony of horns, klaxons and colour, people dancing, kissing and yelling with the sheer ecstasy of it all. In the middle of the main crossroads stood a lone policeman, blowing his whistle and trying to direct traffic through the gridlock – an impossible task. Eventually, festooned with scarves and rosettes and with cap askew, he gave in to the inevitable. He threw up his arms, shrugged his shoulders in mock apology and joined the throng.
At La Tambura, I felt as if I'd moved into a completely different world and it was great not to be totally consumed by my work, as I had been for so long. Italy was bringing a whole new range of experiences and culture into my life, and when I was at home I had time to spend with my family instead of rushing off to gigs all the time. The pace of life was suiting me and I particularly enjoyed talking with the younger DJs at 210, exchanging radio gossip and discussing the skills of programme building and broadcasting. My shows felt wonderfully pressure-free, the atmosphere was good and I increasingly encouraged touring musicians to come into the studio and play live.
Harry Chapin joined us for lunch on 2nd February 1981 before I compered for him at the Reading Hexagon that evening. He was a man of boundless energy, performing nearly 300 concerts every year, half of them for charities, for which he raised millions of dollars a year. 'I play one night for me and one night for the other guy,' he explained simply. Harry had a wonderful narrative writing style and I was particularly impressed by the captivating 'Cats In The Cradle', which offered a warning about the consequences of putting careerism above family life, a lyrical theme that had touched my conscience when I'd first heard the song in 1974. We'd met a few months after the song had topped the American charts, to film a _Whistle Test_ interview in New York to mark the Broadway opening of his just-completed musical _The Night That Made America Famous_. I liked him very much and truly admired the wholehearted way he threw himself into everything he did.
He loved to talk and was a compelling orator – knowledgeable, challenging and politically driven, a Democratic Party activist. As we sat talking and laughing in the restaurant of our 210 local, he seemed larger than life. At close to six-foot-six and eighteen stone, he commanded the room, ordering a third, then a fourth bottle of red wine while eating at least two dishes from each of the three courses on the menu. After a pot of good strong coffee it was all washed down with a couple of glasses of the best port in the house. I was desperately sad to hear of his death a few months later, killed in a crash on his way to a benefit concert in New York. He loved life so much and had so much to give. Sometimes life just isn't fair.
Alexis Korner was another man of stubborn integrity whose company I greatly enjoyed. I invited him down to Radio 210 to spend an evening with me to record an interview for a special I was planning to mark his forthcoming birthday. As we settled in the studio he gave me a letter. I recognized the writing immediately and asked him how he'd got it.
'Somebody just handed it to me as I was leaving Egton House to come down here,' he stated.
'Did you see who it was?' I asked.
'No, I didn't really take much notice.' Alexis went to get us a coffee as I sat looking at the envelope.
It was from a girl who'd been writing to me for several years. She'd seen me on _Whistle Test_ and become fixated, God only knows why. She bombarded me with letters, photographs and all kinds of personal stuff. When I left the programme she became desperate, phoning local radio stations all round the country until she located me at 210. After failing in an attempt to persuade management to send her tapes of all my shows, she went first to the Independent Broadcasting Authority then to the Reading Police, before systematically phoning all the local numbers she thought might provide her with the recordings, including every hi-fi and electrical shop listed in the phone book. The letter, however, was a slightly discomforting new development. No one knew Alexis was visiting me. He hadn't told anyone, nor had I trailed it on air. Neither of us had any idea how she knew he was seeing me that night. It felt extremely weird being in the sights of this person I'd never met who, as well as being obsessive, was also eerily telepathic! I put the unopened envelope in the bin and a few weeks later the letters abruptly stopped. I didn't hear from her again for nearly 10 years.
More disturbing was the fact that Alexis was feeling unwell. He'd been ages getting the coffee and came back into the studio looking awful. It was an hour or so before he felt up to doing the interview but once we got underway he was riveting, talking in that deep gravel voice with all his usual passion and eloquence. We talked about the history of The Rolling Stones and the pivotal role he'd played in the formation of Free.
There is enormous peer affection for Alexis. Many of the great British blues musicians who emerged in the 60s acknowledge their debt to him to this day and many had joined the celebrations at Pinewood Studios a couple of years earlier to mark his 50th birthday, an event he talked about with great pride. His house band that night comprised Charlie Watts, Jack Bruce, Ian Stewart and Dick Heckstall-Smith, joined onstage by such as Eric Clapton, Zoot Money and Chris Farlowe in a two-hour jam session that had lifted the roof off. The whole event had been filmed for possible inclusion in an ambitious 13-part television series called _The History Of Rock._ Alexis told me he was working with director Luke Jeans, whom I'd met with Tarquin Gotch at Gary Osborne's house. They'd recently been to America with Del Taylor, Alexis's manager, recording interviews for the series. He was particularly thrilled to have spent time with Tina Turner, whom he described as being 'the real thing'. He asked me if I'd like to be involved with the project in some way and although it never made the screen I said I would be honoured. It was, as always, wonderful spending time with him but as he drove away at the end of the session I had a nagging feeling about his health. Never the most robust of people, he looked fragile and weary. I really didn't want anything to happen to Alexis.
A few days before the programme went out, Val and I moved to our eighteenth-century chapel of rest in Oxfordshire. The interior conversion was impressive, with an open-plan kitchen at the top end of the ground floor where the altar used to be, font still untouched by the builders. The original stained glass window threw mottled, multicoloured bands of light onto the landing and there was even a small study that became my music room, walls lined with album shelves. The house had a small garden, just big enough for a game of cricket and, as summer arrived, we started inviting friends over for regular Sunday knockabouts on the lawn. We called it the Garden Cricket Club, and much like those long-ago games of football-tennis at Peel Acres, the rules were, of necessity, complex. All overs were bowled from one end at one batter at a time, everyone had a bat and a bowl. Hit the wall of the house and it was a four, over the house was a six, over the fence was out. We split up into teams – our Oxfordshire friends against our friends from London. The games could get quite competitive but were fantastic fun, fielders spread around the garden, sandwiches, cakes and tea on a big trestle table on the patio, beer on tap. The star was usually David Duncan-Smith, an ex-Millfield boy who had to be got out early. Once he got his eye in, a century usually ensued. We even kept averages!
Life felt blissful and the future looked assured, a feeling enhanced by a call from Ted Gorton, station manager of the local BBC station, Radio Oxford. He'd heard that I'd moved in locally and had called to offer me the _Drive Time Show_ , Monday to Friday 3 p.m. to 5 p.m. It would be a wrench to leave 210. They'd treated me extremely well and I'd had a really good time there. But I was keen to return to BBC radio and agreed to join the station when I got back from our honeymoon.
Val and I were married in Ronchi a year and a day after we met, on 20th June 1981. Like her mother before her, Val had been refused permission by the Roman Catholic Church to marry an Anglican divorcee, so the ceremony was held at Val's aunt's house, a few minutes' walk from La Tambura, the only other Sforza property in Italy to survive Mussolini's wartime fire raisers. Friends and relatives travelled from all over Italy and the UK to be there, gathering in the shade of the courtyard. I'd ferried a carload of people down myself in the dear old Volvo 245DL Estate I'd bought for the now-regular journeys, including my best man, Steve Crozier, whose minister father performed the ceremony. The organization was unbelievable. My mum even flew for the first and only time in her life! Miri and Emily were bridesmaids.
It was a spectacular day in Tuscany, hot and still, Val arriving in the sunshine with her father in a horse-drawn carriage. The reception was held in a huge marquee on the lawn at La Tambura and Dad was one of the speakers. He and Val's father, Howard, had already begun to forge a friendship.
Val and I then whisked off to spend a night in Forte Di Marmi before flying to Bangkok for a three-day stopover en route to the paradise island of Bali, where we spent the next 10 days. To round off our honeymoon we flew back to Italy to visit relatives in Rome, before returning to Ronchi for the last few days, finally arriving home in Oxfordshire the day before my first show on Radio Oxford at the beginning of August.
I took over on _Drive Time_ from Timmy Mallett, who was moving to commercial radio before embarking on a successful career as a wacky children's presenter on TVAM. He was extremely popular locally and the contrast between our two shows must have come as a huge shock for the listeners. One week they were hearing novelty songs and being hit over the head with Mallett's mallet, the next it's all Steely Dan, Jackson Browne and Steve Miller. But the show went really well, the figures were good and soon the programme was extended by an hour to 6 p.m.
Radio Oxford linked with the main networks at certain times of the day. I followed _Woman's Hour_ on air at 3 p.m. and usually began my programme in an appropriately mellow mood, developing a feature called 'Sentimental journey' and playing a couple of oldies at the beginning of the show. I did a birthday and anniversary spot at 3.30, researching material that would eventually be published as _The Rockdate Diary_ in the early 90s. And once a month I did 'The Singles Cavalcade'. Starting at 3 o'clock on Monday afternoon, I'd spend the entire week playing through every record to have topped the British and American charts that month in years gone by, starting in 1955 and working up to the present day, phenomenally successful with listeners and really good fun to do. Miraculously, it always exactly fitted. Without having to chase fades or drop records I would hand over at 6 o'clock on Friday evening to John Dunn on Radio 2, having just played the current No. 1.
A young trainee used to come in straight from school and occasionally help out on my show, taking phone calls, making the tea and maybe doing a bit of tape editing. His name is Jon Briggs and, to me, he is a model of what can be achieved with the requisite amount of hard work and enthusiasm. He'd been bitten by the radio bug and just loved being around the station, learning all the skills. He qualified for Bristol University but just couldn't bear the thought of breaking away from radio to begin his course. 'At least give it go,' I told him, sounding like my father. 'You can always come back to radio when you've got your degree.' He followed my advice but was back within three months, hanging around in the hope of a job. Sure enough, someone phoned in sick one day and he found himself on air. He was a natural, blessed with a golden larynx and hasn't looked back since. These days he runs his own agency, 'The Excellent Voice Company', is the voice of _The Weakest Link_ and does voice-overs galore.
He became a regular member of our garden cricket club and was also in the Radio Oxford team that played the _Oxford Mail_ in the annual grudge match on the village green at Marsh Baldon in the summer of 1982. Our opponents had acquired the services of a couple of strapping fast bowlers from the local league who decimated our early batting. After seven overs of mayhem and injury Jon arrived at the crease, me at the non-strikers end, the scoreboard reading 5 runs for 3 wickets. The first ball he faced whistled over the top of his head. The second one hit him a fearful thump under the heart. He collapsed like a pack of cards. No one would have blamed him had he retired then and there but after several minutes of 'magic sponge' treatment he took guard again. Despite our protestations that this was supposed to be a 'friendly' game, the bowler thundered in and delivered a face-high bouncer. To his enormous credit, Jon stood up straight and hooked it to the boundary. That he was out a few balls later didn't matter. The boy had shown that he had guts. Early next over I was hit on the hand. Val said she heard the crack from the boundary. Exit to hospital, leaving my favourite pair of trousers in the pavilion.
I felt truly happy, secure and settled. Mornings were spent building my shows, piling singles into a wooden Schweppes crate. Armed with the crate, I'd arrive at the Radio Oxford studios soon after 2, do the programme, and be back home by 7. Weekends were free. I'd never been so organized before! Mum and Dad were frequent visitors to our chapel of rest and Miri, Emily and Charlotte came to stay with us most weekends. It was idyllic, and soon Val and I were telling everyone that we were expecting a baby. Our first son, Ben, a bright and beautiful boy, was born on 17th September 1982.
A few days later I received a letter from Radio 1, inviting me to take part in their 15th-anniversary celebrations on the _Dave Lee Travis Show_ at the Paris Theatre on 30th September and later that day to appear at a concert at the Hammersmith Odeon. It was the first time I'd done anything with the network since I'd lost my _Sounds Of The 70s_ programme seven years previously and I was keen to impress. Nothing doing, I'm afraid. Management was frosty, particularly one of the executive producers who, seeing me with a group of DJs gathering for a photograph, shouted to get my attention. 'You! Get out of the shot,' was his devastating command. So, I could knock out any thoughts of returning to Radio 1 then!
That wasn't the only setback. Things were beginning to feel uncomfortable at Radio Oxford. Unexpectedly, Ted Gorton was leaving to join the team producing Selina Scott and Frank Bough on the forthcoming BBC _Breakfast Show_ and John Bright, his successor, was not a fan of my programme. 'Why is he playing the American charts on a Thursday afternoon?' he said on his arrival. 'This is supposed to be local radio.' It wasn't encouraging when, six weeks after taking over, he called every member of staff into his office to discuss their futures – with two exceptions. When fellow DJ David Freeman and I discovered we weren't invited, we knew the writing was on the wall. I was a big fan of David's, an intelligent and creative broadcaster and a great bloke. He was popular with the listeners but it was clear that John Bright didn't like us.
My parents arrived at Radio Oxford a few days later with a copy of the _Oxford Mail_. 'What's going on?' my father asked as he handed me the paper. 'Top DJ Faces Axe' read the front-page headline above an article predicting my demise. The tone of the article and the information printed strongly suggested the story had come from management.
'I have no idea,' I assured him. 'This is the first I've heard of it.' I phoned John Bright from the studio and arranged to see him at the end of the show. He was unpleasant and unequivocal.
'Your programme isn't local enough, so as soon as I've found a replacement I'm taking you off air.' There was no logic to this decision and I felt a strong sense of injustice, much as I'd done in my headmaster's office many years before. Only this time I didn't walk out, despite being goaded to by the station manager. I told the local press people waiting in reception the truth, that I was devastated and really didn't want to leave. The reaction was amazing.
The papers began a 'Save Bob Harris' campaign and within days correspondence and petitions started to arrive. Under the headline 'Hands Off Our Bob!' the _Oxford Mail_ intensified its campaign: 'Programme organizer Stuart Woodcock said the station had not received any protests from listeners to his knowledge – but we have.' To prove their point, the 'Mailspin' music section published a page full of them.
'His show has the most varied musical content of any show on national or local radio,' said one.
'It seems to be the only programme where you stand a chance of listening to something which is not bland and middle of the road or pure chart fodder,' said another.
Every day the paper carried more protests. I thought it might all just go away, but it didn't. The papers became more insistent as the campaign intensified.
'It really does mean a lot,' I told the _Oxford Mail_ in an interview headlined 'Whispering Bob's Show Gets The Chop'. 'It makes it all worthwhile when you get that sort of reaction. It would be very nice to think they will have an effect but we'll just have to wait and see.'
Eventually, John Bright called me into his office and proposed a compromise. My programme would continue, in shorter form, if I increased the local content. We made specific agreements and issued a conciliatory statement. The local press trumpeted their victory and I was able to leave for our summer holiday in Italy with some peace of mind.
I loved the Italian way of life, their passion for food and culture, their expansive temperament, the way they enjoyed a good time and a good row. I admired their respect for their cultural heritage, marvelled at the chaos of their politics. There seemed to be less of a generation divide than exists in Britain; the family unit was still an important part of the social structure. Elderly people got more respect, children were more readily acknowledged and included in whatever was going on.
Miri and Emily were often there with us in the summer or at Christmas and we took them on excursions to see some of the most beautiful cities in the world – Florence, Venice, Milan and Rome. We explored the local fishing ports and mountain villages, tasting the wine and the delicious local cuisine. Val also spent time on her own expeditions, talking to shopkeepers, restaurateurs, local fishermen and farers, as she began the work of compiling information and recipes for the cookery book she was preparing to write.
When we returned, I started my new programme on Radio Oxford, convinced that I was keeping to the arrangements made with John Bright about content. We'd agreed that I'd occasionally feature star guests, and I began turning up at the Apollo Theatre in Oxford or the Wyvern Theatre in Swindon to record backstage interviews with Cliff Richard, Chas and Dave, Jimmy Tarbuck and Tom Paxton. I worked with a local amateur dramatic society, the 4 x 4 Theatre Company in Wallingford, charting the behind-the-scenes progress of their production of 'Godspell', first recording the auditions then following the rehearsals right through to their first-night performance. I cut down the music content of the programme and upped the speech. But ten days into the new regime I received a letter from John Bright, signed by his assistant, telling me I hadn't kept to the format laid down and that he was giving me a month's notice of the show being taken off.
I didn't even bother going to see him; I had no respect for him at all. I thought he was devious, spineless and rude; he didn't even have the balls or the courtesy to sign my letter of dismissal. To me it was entirely predictable that under his divisive stewardship the Radio Oxford audience figures sank like a stone. I felt strongly enough about the way I'd been treated to contact the local radio administration unit at Broadcasting House. They didn't want to know.
If I was ever going to give up on radio it was now. I was really struggling to get any sort of broadcasting work, or even get people to return my calls. In the era of Margaret Thatcher's yuppie-led, synthesizer-laced, chrome-plated 80s, it was clear that I was yesterday. I'd become uncool, past my sell-by-date, a relic of a different era. But radio is what I do. It's my job and my passion. I knew that if I was going to rebuild my broadcasting career I was going to have to grit my teeth and tough it out. I'd begun to answer Mike Appleton's question. I may be a late starter, but perhaps I was beginning to grow up at last.
More bad news arrived on 1st January 1984. Mark Ringwood, a friend from my days at Radio 210, phoned to tell me that Alexis Korner had died. I was desperately sad to hear of the death of such a wonderful man and good friend. I just put down the phone and cried.
By now Val was also working hard on her first book, _Perfect Pasta_ , published in October that year, so I was able to provide backup and spend time with our son Ben. We'd acquired a springer spaniel from Val's brother Nick, and Ben and I would take him and Cassie out for walks by the river near our house, or just mess around together. I loved being with Ben and we became very close. He was such a lovely, enthusiastic little boy, so bright. But I was fearful for the future and scared that my career had grounded. At 37, I didn't want to feel that I was all washed up but the reality was hammered home by an encounter at a local pub. 'Didn't you used to be Bob Harris?' enquired the barman as I asked for a pint. It was a cliché but it hurt.
I got in touch with Jonathan Holmes and asked if he could help. Jonathan ran a financial services and management company in Beeston in Nottingham and had a number of top-name clients in a mainly sporting portfolio. I'd contacted him during my last days on Radio Oxford to organize an interview with David Gower, for broadcast in my final week. I'd really wanted to meet David and, with the BBC connection coming to an end, I decided this might be my last chance. He gave me David's number and we arranged to meet at one of the service stations on the M1.
'It's too complicated to give you directions on the phone,' he told me. 'It will be easier if I come and collect you.' As I followed his white Audi through the outskirts of Leicester, I was half-amazed that his mere presence wasn't bringing the traffic to a standstill. David was a huge hero of mine and meeting him was a real thrill. I felt genuinely nervous when we arrived at his house and I began to set up the recording machinery. Interviewing John Lennon, Eric Clapton, Mick Jagger and most of the other major rock stars had never fazed me. But this was England cricket's golden boy, the future captain of England and one of the most elegantly gifted batsmen I'd ever seen. I was in awe of this person.
The house was relaxed but immaculate – pastel colours, lots of cushions and a white shag-pile carpet that submerged my shoes. David handed me a can of beer and I began to settle. I put the can down on the carpet for a moment while we chatted, before it occurred to me that I still hadn't plugged in the equipment. As I stepped forward towards the nearest power point, I managed to kick the open beer can. Becks would have been proud of me. The moment I made contact, I knew it was curling into the top right-hand corner ... of the painting hanging on the opposite wall, beer spurting all over the place, spraying a brown frothy foam down the side of the sofa and all over the white shag-pile carpet. I just wanted to disappear into it.
It's a moment David doesn't remember, thank God, and we've enjoyed a good, if spasmodic, friendship since. It gave me the greatest pride that he invited me to play in a pro-celebrity event on my birthday, of all days, the 11th April 1985. The team included England wicket keeper Paul Downton, fast bowler Fred Rumsey and Gary Lineker in a match to mark the opening of England's first quick-cricket facility, near Heathrow. I even got a 'Well done' from the captain for a sharp piece of fielding at cover. I got to bat and scored 5.
Jonathan Holmes offered to help in my quest for work and arranged an appointment with Jo Sandilands, top person at Capital Radio. We arrived at 2 o'clock and waited 15 minutes. 'You're late!' he said as she walked into the office. It was no surprise that the meeting didn't go particularly well.
As he had done in the past, Steve Crozier stepped in with assistance. He was now working at LBC, the London news station, and invited me in to meet Brian Hayes, the senior presenter. Brian was looking for an expert to join him once a month on his morning phone-in to talk about music and take calls on the subject. He had great authority, was commanding, often brusque on air but had a warm side and a dry, rather cynical sense of humour. We complemented each other well and soon I was invited to present the LBC music review programme for half an hour on a Friday night. To my great surprise and pride, the show won a Sony nomination in 1986, ironic in that it was the only music show on what was otherwise an all-speech station.
I also started working for GWR, a new commercial radio station based in Wootton Bassett near Swindon. I'd arranged a meeting with the managing director, Ralph Bernard, and arrived to find him kicking a football around his office, using his desk as a goal and practising his skills, walls covered in muddy football marks. I thought his attitude was great and immediately liked him. We began an association that lasted for the next four years, starting with a Sunday afternoon show, then adding a Saturday lunchtime show when Ralph took over the ailing Radio West, broadcast from their newly acquired studios in Bristol.
My first GWR show in Bristol followed an outside broadcast from Johnnie Walker, recently back from America. He'd left Radio 1 in the mid-70s to build a broadcasting career in the States. It was a very brave move but just hadn't worked out, and on his return he contacted Ralph, who immediately offered him a job. 'What a turn up for the books this is!' he remarked as he handed over to me. The following week I found myself doing a live outside broadcast with Samantha Fox from a local car showroom. Commercial radio works in strange ways, its woodwork to perform!
None of this work earned much money and, as finances continued to tighten, Val and I began to look for a smaller property, somewhere less expensive to run. George, who was now married and living in Norfolk, recommended we take a look at properties in East Anglia, and we realized we could get much more for our money there than was possible in Oxfordshire. We found a lovely, low-ceilinged cottage with about half an acre of land in the village of Northwold, south Norfolk, and moved in during August 1984.
For a while I commuted, leaving Norfolk on Friday for the LBC shows, staying over with Simeon David at his new flat in Oxford on Friday night, ready to travel to Bristol the following morning, and I loved listening to 'Loose Ends' on the car radio as I drove down the motorway. I'd stay in Oxford again on Saturday night, do my show in Swindon on Sunday afternoon, then drive all the way back to Norfolk. I didn't even have my Volvo – it had been a victim of the economy cuts – so I was doing almost a thousand miles a week in a Fiat Uno! The petrol cost me almost as much as I was earning.
Clearly, I couldn't keep this way of life going and began to search for work on my new local stations. I got a Saturday evening show on Radio Broadland in Norwich and a Sunday lunchtime show on Hereward Radio in Peterborough, staying on in the studio to record my programmes for GWR, which I'd post to the station to be broadcast the following week. It was hard work for low pay, averaging less than £40 a show, but I was doing it to keep myself on the roundabout, just to keep broadcasting.
My career reached a particularly low point on the day 'Live Aid' was broadcast in 1985. I was on air at Radio Broadland, doing my _Bob Harris Music Show_ , watching the concert on the monitor in the studio. Mike Appleton collaborated with Bob Geldof to coordinate worldwide television coverage of the event and it was very much a _Whistle Test_ day, using all the programme's facilities and expertise. I desperately wished Mike had asked me to be involved. I felt sad and unwanted, like I was a million miles removed from it all. I actually asked for people to phone in to my show, just to reassure me someone was listening. I got one call.
Thankfully, writing was coming to the rescue. Orbis Books commissioned me to write and compile a quiz and information book for them called _Rock and Pop Mastermind_. Despite originally coming into the business through journalism, I'd never tackled a project of this size before and really enjoyed the process of it, spending over a month in Ronchi at the beginning of 1985 to get it finished, working every day from l a.m. to 10 p.m. I loved that enclosed world-within-a-world writers retreat into. The book was published later that year.
To promote the book I did a radio tour, which included a visit to the British Forces Broadcasting Service (BFBS). I was interviewed by Tommy Vance and at the end of the programme asked his advice on how to get a job on the station. Funded by the Ministry of Defence, BFBS was able to cherry-pick the very best broadcasting talent and there was a lot of kudos attached to working there. Tommy introduced me to the station manager, Charles Foster, one of the really good guys of the industry, a man of his word. We talked through a number of ideas before he suggested _Black And Blues_ , a programme devoted to soul, blues and R&B. This was fantastic, just the sort of thing I wanted to get my teeth into and I started the first series at the beginning of the following calendar quarter. 'You Can't Sit Down' by Phil Upchurch was my theme tune.
It was all very hard work but I didn't mind that. After a period of uncertainty, everything seemed to be stabilizing again. By the time Val and I had our second son, Jamie, on 30th September 1985, I really thought we'd weathered the storm. But the financial structure of British Schools was coming under increasing strain and Val's father was becoming unwell. At the same time, the pace of Val's professional life was speeding up. She was writing another book and working up a few ideas for television, often heading off to London for meetings. She began to close off. Understandably, I thought, she was distracted and preoccupied, considering everything she had on her plate.
A short time later, LBC offered me the weekend _Nightline_ show, on air Friday, Saturday and Sunday nights, 10 p.m. to 1 a.m., with an open phone line and guests. It was a challenge I couldn't refuse. I could now let most of the other programmes go and concentrate on this main source of decent income. I'd never done all-speech radio before and relished the chance to talk to the wide range of people who arrived in the studio. I met some of my great sporting heroes – Trevor Bailey, Steve Coppell and Henry Cooper. I discussed fashion with Zandra Rhodes, cookery with Jill Cox and hosted political discussions with Edwina Currie and Frank Field. I even talked pets with a pet expert!
It was fantastic experience and a steep learning curve, with no music to fall back on if a caller swore or the pace got too hot. But I was spending time away from home again, trying to earn a living, unaware that Val now had her own agenda and that the fabric of my marriage was beginning to slowly unravel.
SEVEN
Return to Radio 1
'WHAT ON EARTH AM I DOING ON LBC?' WAS A THOUGHT THAT regularly crossed my mind. I didn't feel qualified to be hosting a late-night phone-in show. I have no real interest in politics or in politicians (except for an overall feeling that they're all more or less as bad as one another), I'm not particularly well educated or knowledgeable, I don't watch a lot of television and I'm not a great one for gossip. I never had any ambition to be a talk show host and probably used to irritate the hell out of listeners who tuned to the station as a refuge from pop radio by insisting on finding reasons to include the odd album track from time to time. But doing those shows gave my broadcasting a huge boost of confidence.
LBC was situated in Gough Square, and I would spend the early part of Friday evenings on my own in a little pub in Fleet Street, having a pie and a pint while reading the newspapers and researching my guests. The guys from the newly launched _Sunday Sport_ were often at a nearby table, coming up with their 'Routemaster Found On The Moon' type headlines over a few beers. To them life was just one big laugh.
I do a lot of reading and research for interviews but rarely make many notes other than jotting down a few basic topic headings. I avoid writing out a list of questions because I find I get glued to them. For me the most important thing is to establish eye contact with the interviewee and to listen to what they're saying, and you can't do that if you're constantly looking down at your notes. I work on the theory that the research will be there in my head as my guest and I talk, allowing me to follow the interviewee off subject, if that's an interesting place to go. I have a rough idea in my mind of the ground I want to cover but other than that I prefer things to be loose, to go for a conversation rather than an interview.
I'd get to the office about 8.30, meet up with producer Cathie Louie to discuss topics for the 'open line' section of the programme and plan the choreography of the show. My programmes went out across London every Friday, Saturday and Sunday night from 10 p.m. to l a.m. and I'd often feel slightly nervous as I went down into our scruffy, chocolate-brown basement studio, knowing that the microphone would be open for the whole of the next three hours and that somehow I had to fill that time with reasonably articulate comment and conversation, with only a few notes for support. I had a small screen in front of me with details of the next caller, half a dozen microphones around the table for guests and that was it. I didn't even have a fader to allow me to close my microphone for a moment if I wanted to take a breather. The whole show was driven from the control room through the glass ahead of me and I'd make signals to the engineer when I wanted to end a call or go to an advertising break, often taking instructions back through my headphones.
In this situation it's very important to establish a good rapport with the engineers. How you sound is in their hands and they can be extremely cruel. Tony Fox, a colleague from my Radio 210 days, had also recently joined LBC and made the mistake one evening of criticizing his engineer on air, a cardinal sin. Never blame an engineer, your producer, or anyone else for that matter; always take responsibility yourself. The guy had put the wrong caller through and Tony made a comment that he was incompetent or something like. In a huff, the engineer got up and walked out of the control room, leaving Tony live on air for nearly 15 minutes with no material feeding into the show apart from the listener currently on air. Tony desperately tried to persuade him to stay on the line for a while but the caller eventually got so bored he put the phone down, leaving Tony to keep things going on his own, a dialling tone buzzing faintly in the background. 'Filling' for any length of time is bad enough. Very few people would be able to keep talking for as long as Tony did then with absolutely nothing to work on – a perfect qualification for his current profession of artist management.
Having always been used to a record under my thumb and music to fall back on, speech radio felt very different. Holding a talk show together requires a very high level of concentration and my broadcasting abilities were tested to the limit, but I was learning a lot and it felt good to know that I was holding my own and improving. I also enjoyed meeting the guests who came onto the show.
Willie Rushton told me about his love of Surrey Cricket Club and his background at Shrewsbury School with John Peel and Richard Ingrams. Journalist Ed Harriman described the difficulties of reporting news from hot spots like El Salvador. John Conteh relived the feeling of beating Jorge Ahumada to become Britain's first light heavyweight boxing champion for two decades and explained why he subsequently took the sport to court. My regular experts included Dr Mike Smith, _Oxford Dictionary_ editor Tony Augarde, who set fiendishly difficult word quizzes, and legal man James McGovern, who later became my solicitor. We also ran a hi-fi clinic with writer Barry Fox, who would come in with all sorts of magic new electronic gismos, and predictions of a computer-led generation getting their entertainment from game stations and their music from new, indestructible CDs. It was easier doing an advice hour because I could hand the calls over to the expert for a while and just sit back and listen.
A single call could last 10 minutes, especially on subjects of law. Pete Murray, who hosted the Monday to Thursday phone-in, would do the _Evening Standard_ crossword while these conversations were going on, sipping coffee from a plastic cup and lining up his lit cigarettes on the edge of the broadcast desk, in the process burning long brown lines into the wood. I was in the control room one evening while he presided over a particularly mundane call to his gardening guru. As the conversation droned on we realized that Pete was falling asleep. Mulling over his crossword clues as usual, his head had begun to nod. The engineer sent a whistle and other low-level noises into his headphones in the hope of stirring him, but to no avail. Finally, he nodded off completely and, as his chin dropped to his chest, his forehead hit the microphone suspended in front of him. The 'clunk' cracked like a gunshot through our speakers and his headphones, straightening him up as if he'd seen a ghost, eyes wide open. The all-year suntan drained from his face for a moment as the shock reverberated through the middle of his head. But he was the ultimate professional as always and just got on with the programme as if nothing had happened, making faces and gestures at the producer, chiding him through the control room glass.
I was particularly pleased to meet Cathy McGowan, who came on my show one evening as a mystery guest to talk about her time on _Ready, Steady, Go!_. I liked her straight away and, although we'd never met before, we had an immediate affinity, based in part on our respective experiences in music television. She was interested in doing some presentation work for LBC so I introduced her to the management, who agreed she could do a few trial programmes. One of these evening shows was with agony uncle Phillip Hodson, whose job it was to advise callers on their personal problems. A teenage girl came on air in some distress. Her boyfriend had left her crying at King's Cross station, after coming down from Manchester to see her and rowing with her all weekend. Phillip began to counsel the girl, suggesting she give the boy another chance. Perhaps he was going through some problems of his own and, despite his behaviour, she should try to understand where he was coming from and make some allowances.
Cathy was unable to contain herself. 'That's rubbish!' she exclaimed before Phillip could go any further. 'I'll tell you what you should do,' she told the caller. 'Dump him. You sound much too good for him.' She'd hit the nail on the head, of course, but the interruption was an affront to Phillip who, turning red with rage, stormed from the studio, complaining bitterly that his professional authority had been undermined, that he'd never been so humiliated and that he would never work with that woman again. Mutually, she and the LBC management decided that the relationship probably wasn't going to work.
Val and I had become involved in the Great Ormond Street Hospital 'Wishing Well' appeal and I asked Cathy if she would help us organize some of the music events we were planning. She was absolutely brilliant, appearing on stage with me to co-host a special fund-raising concert at the Piccadilly Theatre in December 1987 and helping pull people in for a £75-a-head pop quiz at a country club in Buckinghamshire. Guests included Jess Conrad, Dave Lee Travis and an Elvis look-alike, who arrived in a pink Cadillac. We followed that up with a 60s evening at Stringfellows, thanks to the generosity of Peter Stringfellow and the then club manager Peter Stockton. Topping Elvis and the pink Cadillac was a tough one, but we did so in spectacular fashion with the arrival of a Harley Davidson in an explosion of dry ice, smoke, flashing lights and high revs. The bike blasted into the club from the street outside, onto a ramp and down into the basement where it accelerated onto the dance floor, strobe lights flashing, skidding sideways to stop in front of the stage, a stunt that required three days of meticulous planning and rehearsal.
Val's writing career was taking off. She seemed to be able to rattle off her cookery books at will and when she wasn't writing she'd often disappear to London for meetings. I would set off for LBC early every Friday afternoon, spend Friday and Saturday nights in London and drive back to Norfolk in the early hours of Sunday morning, so we spent less and less time together. Leading separate lives is never good for a relationship. I tried commuting but, by the time I'd put the programme to bed and made the two-hour journey home, it was usually well after 5 a.m. and I'd have to leave again at 4 in the afternoon to allow for the M25 traffic. The 180-mile round trip and lack of sleep were just proving untenable. For a while I stayed in London hotels, which was depressing, but I eventually rented a small top room in a house owned by Gill Pyrah, one of my colleagues at LBC.
This large, imposing house was situated in Islington, at the far end of the Essex Road, about a mile from Highbury football ground, but after a while, compared to the tranquillity of our Norfolk village, the area began to seem like an urban hellhole. It was a regular Saturday spectacle to see a group of any number of Arsenal supporters, standing in a long red line, urinating into the front gardens of the houses in the street. The railway track on the other side of the road carried the mile-long nuclear waste trains that boomed their way slowly through London in the middle of the night, rattling the pictures I'd put up on the wall. Within weeks my car had been broken into three times and I found myself constantly getting out of bed in the darkness to peer through the window to check it was still in one piece. I was finding it really hard to sleep and eventually my fears were realized.
The crash that disturbed me sounded horrendous and I rushed to the window to see what had happened. From my third-floor room, high above the street, I looked down in horror as a young joyrider hauled himself out of the battered Renault 16 with which he'd smashed into the back of my parked car. By the time I made it down the stairs he'd legged it with his mates, driver's door hanging by its hinges, steam hissing from the crumpled engine. By then some neighbours had joined me in the street but no one had seen a thing. My car was a total write-off; the Renault, it turned out, was uninsured. I lost my no-claims bonus and what was left of any sense of security. But worse was to follow.
I was due in London on New Year's Eve 1987 for the very final _Whistle Test_ broadcast, a 'Best Of' celebration that was to last all night. On the morning of the show I got a phone call from Gill telling me to get to London early as there'd been a break-in at the house. She was away on holiday and hadn't seen the extent of the damage but had been told that the burglars had smashed their way in through the front door, which had had to be boarded up. I arrived to find my room stripped of all belongings – my recording machine, tapes and records, even the clothes I'd planned to wear for the _Whistle Test_ special. The air was thick with a stench disgusting enough to make me want to vomit and it took only a few moments to discover the source. Whoever had been in my room had shat in my bed, piles of it soiled the sheets and the duvet. Who on earth would do a thing like that? Animals behave better. I put a handkerchief over my face, donned a pair of Marigolds and deposited all the bedclothes into the dustbin before having a bath and heading for Television Centre. It was the last time I ever set foot in that room. Jim Dowdall put me up for a while at his house in Olympia but alternative sleeping arrangements were not necessary for very long, as it turned out. I'm a great believer in fate – that things happen for a reason. 'Chance' is the only way to describe the way events conspired to influence my departure from LBC.
My producer at LBC, Cathie Louie, had devised a new 'rolling' format for my Friday night show, which I wasn't sure I fully understood. When an on-air test run started to go wrong, Cathie joined me in the studio for a quick briefing. The caller currently on air was launching into a monologue about the state of the country, and for the first and only time in the whole of the three years I spent at LBC, I took my headphones off and left the call running unattended on air while I concentrated on the instructions I was receiving from my producer. When I put the cans back on the line was silent. 'Well, thank you very much for your call. Some good points there. If you want to phone us, don't forget the number ...'
The hotline was already ringing when Cathie reached the control room. The bloke I'd left on air had gone into a foul-mouthed rant about Margaret Thatcher and the evil things he'd like to do to her. Distracted by the production problems none of us had been listening, and his poisonous tirade had even slipped through the ten-second delay system. I thought it was incredible that of all the thousands of calls I'd taken while doing those programmes, the only one I missed was the most explosive of all. Management were apoplectic and, with some relish, told me that my programmes the following weekend would be my last with LBC. Two days later they phoned me again, telling me not to bother going in at all. Out of a job again then.
For a short time I worked on The Super Station, Richard Branson's first venture into radio, helping with its launch as part of an on-air team that included Johnnie Walker, Nicky Horne, Jonathan Ross, Ruby Wax and Janice Long. The idea was a good one, to provide an overnight sustaining service, available via satellite, to commercial stations such as Radio 210 that would otherwise close down between l a.m. and 6 a.m. For me personally, however, it just wasn't right. It was the first time I'd worked for a station where Selector chose the music, and I didn't like it.
Selector was a computerized system that was programmed with information regarding the tone and tempo of individual tracks and notes about the style and the time of day of on-air programming. Click an icon and the machine blended the information together, churning out reams and reams of running orders as required. It sounds good in theory but was very rigid in application. Current chart songs and popular oldies would be given 'high' rotation, often coming around as quickly as once every two or three hours and the on-air repetition of such 'core tracks' can be brain-numbing. Although I fought successfully to keep my programmes out of the system, the environment was not sympathetic to my old-fashioned hand-building methods and I soon realized that this was the wrong place for me to be. One of my main strengths as a broadcaster is the enthusiasm I'm able to communicate about the music I play, given the freedom to express it. On The Super Station I felt flat and out of place. Doing it just for the money gave me no satisfaction at all.
My one remaining source of income was BFBS. Charles Foster had extended my hours and I was now doing a weekly three-hour show, broadcast around the world on Sunday afternoons. But it was not enough to support a family and Val was increasingly becoming the breadwinner. We began to change roles, with me looking after the boys while she was working. Val's father, Howard, had become ill and, to accommodate his wish to move to England, Val's family had funded the conversion of our dilapidated coach house. Soon Val's parents moved in, our new neighbours across the garden.
Howard was suffering from Alzheimer's disease and I was shocked by the cruel and degenerative nature of this illness. I knew a part of him was struggling to break out of the nightmare that had grid-locked his brain. Sometimes he would wander out into the garden as if searching for something, a look of panic on his face. Increasingly it seemed as though his body had become merely a shell, and that the soul of the person we knew had died. As the disease took deeper hold, I found it depressing and confusing that the fleeting windows of lucidity had become only painful reminders of the dynamic, deeply intelligent person I'd first met. I felt angry and resentful that he should be suffering in this way, and very sad for Val's mother, who was coping with her usual calm dignity. Val supported her mother in every way she could and my parents often visited from their new home on the north Norfolk coast. Dad would sit with Howard, talking to him and singing him old war tunes and Welsh songs, which he loved. Howard Scott died in 1991.
Without Howard's leadership British Schools had spiralled into debt. Nick did everything he could to hold things together but eventually even La Tambura was sacrificed in an attempt to keep the business afloat.
I spent a final summer in Italy in 1989 while Val was filming material for her first BBC TV series, _Italian Regional Cookery_. Things had got very bad between me and Val, who was no longer showing any interest in our relationship. With Sue and Jackie I'd been the principal force of change, but this time I was the one desperately trying to hold the relationship together. Val was away for much of the holiday, filming in different parts of the country, but I was able to spend a glorious, sunny summer with Ben and Jamie and with Dad, who joined us for a few weeks, probably the closest time we've ever spent together. At the end of the holiday Dad and I drove back to England together, on the way spending a night in Chamonix at the foot of Mont Blanc. Soon after we arrived home I realized my relationship with Val had finally broken down. It was a very difficult time for everyone.
Not for the first time I was becoming increasingly desperate for work. I'd been fired from LBC, left The Super Station and now my marriage was on the rocks. I really needed to start rebuilding again. I sent Jeff Griffin tapes of a couple of my, new three-hour, BFBS shows in the hope that he would pass them on to the Radio 1 management.
I recorded the programmes each week at the main BFBS London studios at Bridge House in Paddington. As always, I'd build the running orders at home and take the CDs and records into the studio with me. I'd be in charge of the recordings myself, loading video cassettes into the two main recording machines and setting the studio clock to 12 o'clock so I could record in 'real time'. The preparation work included timing the music to fit into the three 57-minute segments (punctuated by pauses for the three-minute news bulletins), allowing room for all the music to be played in full, links to be delivered and no early fading. (If you've ever wondered how this works ... take 60 minutes as the hour, minus 30 seconds for a link into the news. From the resulting 59 minutes 30 seconds, take away the time of the final track in that hour [e.g. 4.15] to establish the exact time the track needs to be started to be heard in full [in this case 55.15]. Working backwards, if the previous track is 3 minutes long it needs to be started at 52.15, or 51.45 if you allow time for a link between the two. You can back-time the whole hour this way to fit the maximum amount of music into the mix and always know how long you've got to talk. I usually manage to play 12–14 tracks an hour, blended into a flow.) Equal attention to detail was applied by BFBS to the distribution of the programmes.
Having completed my recordings, I'd deliver the tapes to a control room containing banks and banks of tape-duplicating machinery. There, the programmes would be copied onto labelled tapes and distributed individually to stations all over the world. At that time, BFBS had an estimated total worldwide audience of approximately 24 million. I was really proud of those programmes and the music mix I'd created. I played mainstream rock, vintage blues and R&B, fringe country and roots music, laced with anniversary classics from _The Rockdate Diary_. I'd put B.B. King next to Elvis Presley or Eric Clapton, segue a Simon & Garfunkel track or an Emmylou Harris song into Mary Chapin Carpenter, Bruce Springsteen or Bert Jansch. I've never cared what category of music a record comes from – if I like it, I'll play it. I really wanted Jeff to hear the eclectic nature of those shows. Suddenly it felt like 1970 all over again.
I started calling him to see if there'd been any reaction from Radio 1. 'For God's sake, Bob, stop bothering me,' he scolded. 'Didn't you learn from last time?' As before, I was going to have to be patient. I waited months for them to make up their minds. 'They're worried you're going to come back and say, "Wow, man, listen to the colours",' Jeff eventually explained. The _Whistle Test_ image died hard.
Finally, executive producer Stuart Grundy phoned to offer me two weeks sitting in for Richard Skinner on the Radio 1 _Late Show_. As the celebratory firework display exploded in my head I knew this was my big chance, and I intended to grab it for all it was worth. My first programme back on the network was the day after Ben's birthday on 17th September 1989, and serendipity again took a hand in shaping my future.
Johnny Beerling, the controller of Radio 1, was away during my first week and consequently missed the programmes. He was in southern Spain, on a sad mission to record material with Roger Scott, who'd been diagnosed with cancer, for a tribute programme to him called 'Radio Radio'. By chance, Johnny tuned in to BFBS broadcasting from Gibraltar, heard my Sunday show, really enjoyed it and decided there and then that he wanted me on the network. However, I knew none of this when he walked into Jeff's office the following week, hand outstretched, broad smile on his face. 'Welcome back,' he said simply. It was one of the best feelings of my life.
Trudie Myerscough-Walker had, by now, become a part of my life. She was the 24-year-old niece of Val's great friend Robin and we'd first met a couple of years previously. I'd seen her at the occasional party or cricket match and she'd visited our house from time to time with her uncle. We always seemed to gravitate towards one another and talk. I found her bright, positive, enthusiastic and straight as a die. She has a great sense of humour and is stunningly beautiful, with blonde hair and hazel eyes, one of them flawed with a tiny prism. We became so obviously close that people began to think we were having an affair, but we weren't. I loved her company. She was fun to be with and made me feel happy and good about myself, but neither of us thought to take the relationship any further. I was married, it was as simple as that. But when my marriage broke up, Trudie and I began to see one another more seriously.
She worked in Knightsbridge as personal assistant to the then chairman of Harrods, Mohamed Al Fayed, and at the end of her working day I would often meet her in the hushed, air-conditioned luxury of the management offices on the fifth floor of the store. Her desk was situated just outside the door to Mohamed's private suite and he usually came out to greet me and chide me about my beard. Egyptians have an aversion to facial hair and he was always trying to devise ways of tricking me into shaving it off, creeping up behind me with a razor or a shaving brush frothing with foam, a wicked smile on his face.
Mohamed and I got on really well and he became fond of my two boys, giving Ben sweets as a bribe to rub honey into my beard while I was asleep. He's a loveable rogue, Mohamed. He can be crude, mischievous and suspicious but he's an incredibly generous person with a quick wit and a most sensitive eye for beautiful things. Unlike many around him, Trudie wasn't afraid to stand up to him and tell him the truth and he respected her for that. He demanded loyalty but gave it in return and was completely supportive of Trudie when news of our relationship first hit the newspapers.
We'd been to see Eric Clapton play at the Albert Hall, our first public appearance together. Simon Bates was among a crowd of people in a box hired by Warner Brothers Records for the evening. All were very curious as to Trudie's background and fascinated to hear that she worked for Mohamed. Three days later, on the Monday afternoon, I got a call from Val. 'What's going on?' she demanded. 'I've had the press on the phone, asking about our break-up and what I think about you and Trudie. They quoted really nasty stuff you'd said about me, it was horrible.' I told Val that I hadn't spoken to any newspaper and that I knew nothing about it. It was only when Jackie phoned later to tell me there were photographers outside her front door trying to get a photo of our daughter, Charlotte, that I realized the press really were after a story.
The ingredients were really quite juicy ... 43-year-old father of five, rock DJ just about to return to Radio 1, leaves successful writer wife about to begin a major six-part television series on BBC2, for Mohamed Al Fayed's personal assistant, who is 19 years his junior. Mmm, good one. We soon discovered that one of the tabloids was planning to publish a 'Bob Harris exposé' the following weekend. Based on my experiences in the past, my gut instinct was to walk out and face them. The more you try to put the press off the more tenacious they become, so I suggested we just call the paper and arrange an interview, but it wasn't as simple as that. It was very important to get the approval of Radio 1 and mobilize the press office facilities and to do the same at Harrods. Trudie talked to Mohamed while I went to see Johnny Beerling. Both were supportive and promised to give us their full backing.
During the next two days most of the newspapers tried to make contact and on the Thursday morning, from the Harrods media office, Trudie returned the call of Chris Hutchins at the _Today_ newspaper. He was amazed to find her so open and co-operative and in return was surprisingly friendly. He even sent a photographer over to take pictures of us together in Hyde Park. He told us that the piece would be in the paper the following day and I phoned Cathie Louie later that evening to ask if we could call in to LBC to see the station's voucher copy, which I knew would arrive at the studio at about 10.30 p.m. Wouldn't you know it, _Today_ was the only paper that arrived late that night and we spent an anxious 90 minutes while we waited, but when we finally saw the article we knew we'd done the right thing. Under the headline 'Val Blows The Whistle On Rocker Bob's Bride' there was a wonderful, happy picture of Trudie and me smiling in the sunshine. The story accompanying the photograph was factual rather than sensational. They even described Trudie as 'stunning', and of course they were right. With no further material featured in the weekend tabloids we felt we'd effectively contained any potential journalistic excesses.
I was getting more and more involved with Trudie's world and I was with her at Harrods when Jason Donovan opened the annual winter sale there on 4th January 1990. Both my boys were desperate to meet him. Ben was seven and Jamie was four. Trudie made arrangements for us to wait in Mohamed's office in the hope of spending a few moments with him there. He was at the peak of his popularity at the time and as we waited we could hear the chaos in the store below us. Scores of screaming girls were being pushed to the ground in the stampede as they struggled to get a glimpse of their hero. The situation became so dangerous that anxious security bosses ordered the tour to be cut short and he was whisked up to the fifth floor, security men barring the stairs and the escalators as fans tried to follow him, their shrieks and squeals echoing round the stairwell.
He came through the outer office, exhaling loudly as he entered the calm, quiet atmosphere of the management suite and, as he got his bearings, Trudie introduced him to us. He was friendly and kind – Ben and Jamie were dumbstruck. One photographer penetrated the security cordon and managed to capture them together in a picture that dominated a page of the _Daily Mail_ the following day. It's a terrific photograph, Jason Donovan in the middle and the boys with wide grins on their faces, Jamie wearing a Harrods doorman's hat. 'It's not just the girls who think Jason Donovan's great' the caption read. 'Yesterday, as the star opened the Harrods sale under siege from screaming female fans, two little boys managed to snatch a quiet moment together with their idol.' In addition to all her other attributes, Trudie could also work miracles.
A few weeks earlier I'd been in Gibraltar at the invitation of the local BFBS station, sitting in for a fortnight on the _Drive Time_ show. Charles Foster thought it would be a good experience and he was right. I loved it. Trudie joined me for the second week and we stayed at the Holiday Inn, right in the centre of town. In the local pubs and restaurants I met many people who regularly tuned in to the show and received direct feedback in the form of comments and requests.
Just before we returned to Britain I got a call from the BBC, put through to me in the office of Dave Raven, the station manager of BFBS Gibraltar. It was from Stuart Grundy, phoning from London to offer me a permanent show on Radio 1, albeit in tragic circumstances. Roger Scott had lost his battle with cancer and died on 31st October 1989. Stuart asked me to take over his Sunday evening programme, 11 p.m. to 2 a.m., starting at the beginning of January 1990. It was the call I'd been dreaming of. Having done my last regular _Whistle Test_ broadcast on New Year's Eve 1979, I was returning to the national airwaves exactly a decade after I'd left. It was as if the 80s and I had somehow passed each other by.
A few days before the first show I met up with my new producer, Phil Swern, and we immediately forged a close friendship and working partnership. Phil is one of the most genuine people I've ever met. He's quirky, considerate, creative, generous and constant, he became a cornerstone of my life. He's also one of the world's premier music archivists, with a collection of records and CDs that runs to hundreds of thousands. Together we've raided record shops as far apart as Nashville and Hamburg and his knowledge of music, records, catalogue numbers, dates, statistics, facts and trivia is unrivalled.
Phil and I first met more than 30 years ago when I did some recording at his home studio in Wembley. He was working as a plugger for A&M Records at the time, promoting a wonderful Phil Spector single called 'Black Pearl' by Sonny Charles and The Checkmates, Ltd. and, although the record didn't chart, Phil was convinced that 'Black Pearl' was a hit song. Frustrated by its initial lack of success, he poured his savings into making a cover, an up-tempo version by Horace Faith, which became a Top-20 smash in October 1970. The record launched a production career that included hits by Blue Haze ('Smoke Gets In Your Eyes', 1972), The Pearls (four hits, including the Top-10 'Guilty' in 1974) and R & J Stone (who made the UK Top 5 with 'We Do It' in 1976). He also scored as a writer, penning 'Up In A Puff Of Smoke' for Pickettywitch lead singer, Polly Brown, who took it into the Top 20 of the _Billboard_ charts in America.
Phil even has a song on the album _Coming Out_ by Manhattan Transfer, submitted to the group by his publisher. He only realized it had been included when he bought a copy of the album from his local record shop. 'I saw the title "SOS" and thought, "I've written a song called that",' he told me. 'When I got home and played the album I discovered it was my song. The publishers had forgotten to tell me the group had recorded it!' It was the British New Wave movement that brought his production career to a close. 'When punk kicked in, I kicked out,' he declared.
Phil got into radio through a quiz show called _You Ain't Heard Nothing Yet_ on Capital. Producer Tim Blackmore was desperate for material for the show, and Phil volunteered his knowledge and music collection, beginning an association with the station that was to last several years. Soon he was producing the weekend output of the newly launched Capital Gold, hand-building the programmes in his studio at home.
When Roger Scott moved across from Capital to Radio 1, he took Phil with him, persuading Johnny Beerling to let him produce his Sunday show, which evolved a unique music mix. As well as Bruce Springsteen, John Mellencamp, The Beach Boys, Bob Seger and other Roger favourites, Phil mixed brand-new releases with a pile of jukebox singles, rock'n'roll, doo-wop and traditional country. It was a fabulous programme and essential listening. It was not lost on me that my return to Radio 1 was following a similar pattern to that of my arrival there 20 years before ... choreographed by Jeff Griffin and taking over from a hero and mentor figure, previously John Peel, now Roger Scott.
I immediately felt at home on the Sunday show and was comfortable with the music and the environment. It was fantastic to be back on Radio 1 and it was clear that controller Johnny Beerling had become a big supporter. Within three months I was broadcasting five nights a week, having additionally taken over from Richard Skinner on the Monday to Thursday midnight to 2 a.m. slot, initially with Jeff Griffin producing, then with Phil.
As my Radio 1 career resumed I moved into Trudie's west London flat, or our 'Shepherd's Bush love nest' as one tabloid put it. This was not at all amusing for Trudie's flat mate, Uncle Robin. As one of Val's closest allies he was caught right in the middle of a triangle he didn't want to be a part of. His best friend's ex-husband moving in to share his flat with his niece was something he had neither expected nor encouraged, and it was understandably difficult for him to get his brain around it all. The CDs that gradually cluttered the sitting room became symbolic of the space invasion, and over the next few weeks Trudie and I looked at literally dozens of places, all either unliveable in or way above our price range. We got more desperate to move as Robin's obvious stress increased.
Shortly before my return to Radio 1 I'd joined Tony Fox's roster of artists and he recommended that we take a look at a flat fellow DJ Bruno Brookes was selling. It seemed exactly right for us, with a large sitting room, two bedrooms (one for Ben and Jamie when they stayed), a small study, a kitchen and three tiny bathrooms. The flat took up the whole of the ground floor of a large Hampstead house situated, by coincidence, at the bottom of Platt's Lane, only a few doors away from where I'd lived with Sue in the late 60s. It was a few minutes' walk from Hampstead Heath, less than a mile from Sue's flat in West Hampstead and just 15 minutes from the BBC. Perfect. It even had a small, leafy garden, shaded by the surrounding trees. But this was early 1990, at the height of the property boom, and the value of the flat had inflated to £260,000, way above what we could afford. Bruno came up with a solution.
'I'll lend you half the money, interest-free, for two years,' he suggested. 'After two years you can either pay it back or sell the flat. Your career is expanding at Radio 1, Bob. You should be able to afford to do it by then.' We were apprehensive, but eventually Bruno seemed to make some sense. If we really did have to sell it after two years we felt we'd be able to get our money back and repay the loan. And, who knows, he could be right about Radio 1. After a great deal of thought and some reservations we decided to go for it and moved in at the beginning of May 1990. Bruno had been good to his word and completed a few agreed repairs, using a craftsman called John Monaghan, with whom we quickly became good friends.
My shows on Radio 1 were going really well and the next few months were extremely busy. I was one of the presenters of the network coverage of the Nelson Mandela Tribute Concert at Wembley Stadium, during which I interviewed Lou Reed, Bonnie Raitt and Peter Gabriel in a particularly cold and windy walkway at the top of the main stand. For several weeks in the summer I also presented the British Forces Broadcasting Services' fast moving flagship show, BFBS UK, a two-hour, Monday to Friday early afternoon programme with music and guests which was broadcast live all over the world, a really exciting show to do. I'd get home mid-afternoon, have a nap for a couple of hours, then leave for Broadcasting House at just after 10. I loved the pace of it all but, for me, the biggest event of the year was the Knebworth Festival, on the weekend of 30th June.
Radio 1 broadcast live from Knebworth for the entire day and Simon Bates and I were there to feed live location material into the output. Simon concentrated on the 'news' coverage while I got to hang out backstage. It was brilliant, like a huge _Whistle Test,_ and I spent most my time cruising the hospitality area, microphone in hand, bumping into loads of people I hadn't seen for years. It just felt so great to be back!
I interviewed Mick Ralphs from Mott the Hoople and Bad Company, who was smiling as always, and Dave Gilmour, who was his usual studied, circumspect self. I spent some time with Robert Plant and the larger-than-life Traffic drummer Jim Capaldi and bumped into Elton John, who promised me an interview later before disappearing into the artists' enclosure, frustratingly the only area of the site for which we didn't have laminates!
I was working as part of a three-man mobile broadcast unit coordinated by producer Phil Ross, and he was very keen on the idea of doorstepping the security compound and grabbing people as they headed towards the stage. Phil was determined to corner Paul McCartney in particular. We'd been told that he was giving no interviews that day so this represented a major challenge. After a vigil of over an hour, sweating in the hot sunshine, Phil rushed over to find me, literally pulling me back towards the security gate. 'Paul's coming out,' he announced. 'I want you to walk out in front of him and get him to say something.' I wasn't keen to do it. It would be great to get an interview with Paul, but not like that, forcing a microphone in front of his face. As he approached the wire mesh gate, surrounded by people, I stepped away.
Paul walked through and saw me standing a few yards back. I was thrilled to see his face light up and he immediately came over and gave me a hug, onlookers and minders watching bemused.
'What are you doing here?' he asked me.
'Hoping to interview you,' I replied.
'Really? When do you want to do it?'
'Now would be a good time,' I suggested, frantically gesticulating to Phil to bring the recording equipment over. All my experiences with Paul have been warm and friendly and this was no exception.
A few minutes after Paul had left to go onstage I felt a tap on my shoulder. I turned around to discover the smiling figure of Elton John. 'I've come to do the interview,' he said. 'See? I never break a promise.'
It was a wonderful day. Although I didn't get to see many people play, I did catch some of Cliff Richard's set, holding his own in the stratospheric company, Robert Plant and Jimmy Page dynamic together again, and the opening of Pink Floyd's bill-topping performance before Simon Bates told me it was time to go. He'd given me a lift to the site early that morning from the hotel in Luton where we'd stayed the previous night and where I'd left my car. He'd promised to run me back there after the show.
'If you want a lift you have to leave now,' he announced and, with no further explanation, strode purposefully away across the fields and into the darkness. This was all very sudden and I wasn't prepared. I rushed back to the production van, grabbed what stuff of mine I could find in 15 seconds and galloped after him, finally catching up with him a few yards from the car park. 'Do you know which way we're going?' he asked as I arrived puffing by his side.
'Er no,' I replied. 'Have you got a map?'
'Typical!' he snorted, as he slammed the driver's door. I made an attempt to ask the people on the gate for directions to Luton as we left the site, but Simon accelerated on through the checkpoint, grumbling about how late he'd be getting home.
'I think the guy said to go right at the end of this road,' was my only constructive suggestion.
An hour and a half later, as we turned into yet another cul-de-sac on yet another featureless estate, we realized we were completely lost somewhere on the outskirts of Luton. It was all too much for Simon, who suddenly screeched the car to a halt and turned accusingly to address me, face contorted with rage. 'You're ruining my life!' he announced in that deep, beefy voice. I burst out laughing, which seemed to inflame him even more.
'Right. Well, I'll just step out here then,' I suggested. 'I can call myself a taxi from the pub across the road.'
He reached across to stop me getting out of the door. 'I told you I'd run you back and I'm going to do it if it kills me.' We drove the rest of the way in silence. When we finally reached the hotel he continued the farce by driving off as I tried to gather my things from the back of his Volvo, boot lid bouncing up and down as I chased him across the car park. I only managed to rescue the rest of my stuff because he had to wait for traffic. It was as if I'd spent the last two hours in the middle of a sitcom.
The Knebworth broadcast was a fantastic success and a few days later I received a note from Stuart Grundy. 'Dear Bob,' it read. 'At last a moment to say a personal thank you for your work on the Knebworth show. It sounded as if you were enjoying it, despite the hassles. The received wisdom is that it was our most successful epic ever and we won't argue with that. You were bloody marvellous. Thanks again.'
It made me feel great that Stuart sent that note and it was a wonderful characteristic of the Radio 1 management team at the time that they took the time and trouble to do things like that. I have what I call a 'special drawer' in my desk at home where I keep objects of high personal value. In amongst pictures of Trudie, my parents and my children, school drawings (and a sealed champagne cork given to me by American blues guitarist Michael Katon from a bottle he shared with Muddy Waters), is a small bundle of letters from Johnny Beerling. It gave me enormous confidence to know that he appreciated my programmes and was thoughtful enough to praise me for extra effort.
It's amazing to think that at that time Radio 1 was still shutting down for a three-hour overnight break at the end of my show at 2 a.m. The Gulf War changed that. I'd just begun my programme on 7th August 1990 when hostilities were declared. Within a few minutes, senior producer Chris Lycett had joined me in the studio and when Johnny arrived later he took the decision to keep the network on air through the night. It was an exciting, if unsettling night as we constantly crossed to the newsroom for the latest news on the bombing raids, analyzing the lyrics of every song we played in case they jarred or caused offence. ('Eve Of Destruction' by Barry McGuire was probably one to avoid!) The long-term impact of this programme was immense. The circumstance of our all-night broadcast was the lever Johnny had been looking for to force through his desire to make Radio 1 a 24-hour station at last. A few days later I launched the BFBS service to the Gulf, broadcasting live from London at 3 a.m. on 12th August, beginning the first programme with The Bellamy Brothers' 'Let Your Love Flow', a rather forlorn hope in the circumstances. 'Whispering Bob Shouts For Our Boys' ran a headline in the _Daily Star_.
Ordering new CDs from the States for my programmes had become one of life's great pleasures, and to help feed our insatiable appetite for new music Phil and I subscribed to a weekly service called 'Hit Disc'. Originated by Century 21 in Dallas, Texas, it cost a fortune but was worth every penny. Each week we'd receive two CDs, comprising all the new entries from that week's various American _Billboard_ charts, maybe 35 tracks in all. I used to love those things plopping through the letterbox every week, always a few days before publication of the corresponding _Billboard_ chart. It reminded me of the excitement of getting the Decca label singles a day before their release at John Levers Record Shop when I was a teenager in Northampton.
The Hit Discs began to have a massive impact on the sound of the programme as we discovered and played more and more new names and unveiled UK radio exclusives. We championed Jude Cole's 'Baby It's Tonight', 'Just The Way It Is, Baby' by the Rembrandts and 'For You' by Outfield, an excellent but virtually undiscovered British band, bigger in America than in the UK. We were the first to play 'Losing My Religion' by R.E.M., and tracks from Neil Young's perfectly titled _Ragged Glory_ and the Black Crowes' _Shake Your Money Maker_ album. But of all the new records we were playing at the time, the one that created the biggest impact with our listeners was 'Walking In Memphis' by Marc Cohn, still one of my all-time favourite records. Soon after its release in the States Marc flew into London for a short visit to plan the release date and promotional schedule with Atlantic Records. After a long day of meetings, stuck in his hotel room and unable to sleep, he turned on the bedside radio and heard 'Walking In Memphis' literally as he tuned in. He stayed listening until the end of the show and the following afternoon I got a call from Joe Reddington, from the promotion department at Atlantic Records, telling me that Marc would like to come into the studio that night and meet me.
'I couldn't believe hearing my record being played on the radio three thousand miles from home,' he told me when he arrived in the studio. 'I had no idea anyone in Britain had heard it.' He went on to talk about his affection for radio and how much it had influenced him. 'Particularly when it came to the running order for _my_ album,' he explained. 'I spent a long time getting the songs into the right sequence and getting the flow exactly right, like a mini radio show. Around 1972, when I was about 12 or 13 years old, I used to listen to a late-night DJ on my local radio station playing James Taylor, Joni Mitchell, Van Morrison and Neil Young, all the music I liked. When my mom and dad had gone to bed I used to sneak down to the phone in the hall and call him up. He'd talk to me for ages off-air, about the way he put his shows together and the albums he recommended. The guy had a big influence on me. Listening to you last night reminded me of that show.' I liked Marc's music; he liked my radio programmes – the perfect recipe for a friendship.
Trudie was almost always in the studio with me, answering the phones, organizing the guests and attempting the almost impossible schedule of arriving home at 3 a.m. and then getting up again at 7.30 to get to Harrods. Lack of sleep eventually caught up with her following my appearance with Alan Freeman on the 'nose desk' of the 1991 'Comic Relief' programme. As Trudie and I stepped out of the main lift at Television Centre about 2 o'clock in the morning she collapsed, falling into main reception and dragging me down on top of her. People were stepping over us as they made for the exit. It was spectacular. Everyone thought we were drunk, but we hadn't touched a drop, it was sheer exhaustion. That's when she decided to leave Harrods, have a few lie-ins at last and get more involved in the running of my professional life, applying the energy and natural organizational skills that Mohamed Al Fayed prized so highly.
Trudie and I were now partners emotionally and professionally – a team. I knew how lucky I was to have found her. After the break-up of two marriages and a long-term affair, all involving children, I'd begun to wonder if I was capable of holding a relationship together. But when Trudie and I fell in love I knew, at last, that I'd found the person I'd always been looking for, my floozy, as Jeff Griffin calls her. 'You're not seriously thinking of marrying him, are you?' he asked her. 'With his track record? You must be mad!'
Despite Jeff's best efforts Trudie went ahead with the wedding, becoming Mrs Myerscough-Harris on 24th April 1991. We spent the next few days enjoying our wedding present from Mohamed – a honeymoon at the Ritz Hotel in Paris! It was another world, opulent beyond belief. Our bedroom had a marble fireplace, gilded mirrors, a walk-in cedar cupboard and a massive brass bedstead, the most luxurious environment imaginable.
While we were in Paris Mohamed invited us to visit the Duke and Duchess of Windsor's house on the edge of the Bois de Boulogne. Following the death of the Duchess in 1986, Mohamed had been granted the lease of the villa and had spent millions restoring it to its former glory and painstakingly cataloguing its contents, a process completed by the time of our visit. It was an awesome experience, to see the splendour of the house exactly as the Windsors had left it. We walked through the salon across the Aubusson carpet decorated with ostrich feathers and inhaled the opulent luxury of the library, used by the Windsors as their downstairs sitting room. We saw the Duchess's bedroom, decorated in her favourite 'Wallis' blue, pug dog cushions in all shapes and sizes scattered on the bed and the chaise longue, and we sat on the terrace looking out across the grounds. But, to me, the most memorable items were the rows and rows of tiny women's shoes, cabinets full of them, some in the Duchess's dressing room upstairs, some in the basement museum. She must have had feet as small as a child's. The property was in the charge of the Duke's former chauffeur, Gregorio Martin, who's lived behind the high hedges in that world-within-a-world since 1964, a life similar to that of the character played by Peter Sellers in the film _Being There._
Johnny Beerling had been very keen for Trudie and I to postpone the wedding for a few days and seriously proposed that we have the ceremony live on air, to launch the new 24-hour service on Radio 1. Thankfully, we managed to persuade him against. The service began regardless and I suddenly found myself with more output on the network than anyone else – 16 hours a week, Monday to Thursday 12 midnight to 4 a.m. I rarely got to sleep much before 6 a.m. and, as anyone who works the night shift will tell you, the hours mess with your body clock and you feel as if you're permanently jet-lagged.
Phil and I put the shows together between us, meeting up for an all-day building session every Monday at Platt's Lane, Phil arriving weighed down with three or four BBC programme boxes stuffed to the brim with new CDs. I hand-wrote the week's running orders, leaving gaps for new releases or last-minute ideas, sticking strips of paper over alterations we'd made in the absence of cut and paste in those pre-computer days. I'd then deliver the material to our programme assistant, Sue Baines, who would process it all, calling up anything extra we needed from the BBC library.
I kept my BFBS show going and even began to pull in the occasional voice-over job, always lucrative and consequently intensely competitive. It was a fantastic feeling to be earning decent money for the first time for more than a decade, a happy and successful time.
The listening figures for the overnights were genuinely spectacular and the shows were great to do. I broadcast from a small, purpose-built self-op studio on the second floor of Egton House and was amazed at the contact I was able to establish with listeners at that time of night. It was like an intimate, exclusive club, with a membership of approximately one and a half million.
Marillion recorded a great jingle for me, based on The Animals' 'House Of The Rising Sun' and most nights we featured sessions, either pre-recorded in the afternoon, or live on the show. Jimmy Barnes, Janis Ian, Taj Mahal, Alannah Myles, Leonard Cohen, Jackson Browne, David Crosby, Carlos Santana, Garland Jeffreys, Buddy Guy, Restless Heart, Mary Chapin Carpenter, Jimmie Dale Gilmore and Shawn Colvin all came in to talk and play. But one of the most touching moments of all was a meeting with Billy Falcon towards the end of 1991.
At the time, Billy was in the American charts with 'Power Windows', produced by Jon Bon Jovi, and came in to play the song on the show. He told me it was based on his own experience as a single parent when, trying to bring up his kids while juggling the demands of a career as a musician, he'd become desperate, trying to be all things to all people, and feeling guilty that he was neglecting his children. 'I was sitting at a traffic light thinking about what constitutes happiness when this big car pulled up alongside me,' he recalled. 'The driver was a middle-aged guy, sitting there in his air-conditioned luxury and I thought "he must have it all". Then I realized he was on his phone having an argument with somebody, veins standing out on his neck. At that moment a beaten-up old Dodge came up on the inside, two kids sitting back, listening to the radio and laughing, they didn't seem to have a care in the world. The two kids had no material wealth but they were in love and happy, the guy in the Mercedes was rich but stressed out. The contrast was amazing; money doesn't buy you happiness. I just drove straight home and wrote the song. In less than ten minutes it was finished.'
I still get requests for 'Power Windows' and it's a gem of a track, included on the album _Pretty Blue World_ on the Jambco Record label. A few days before the interview with Billy Falcon, Trudie and I received some fantastic news. We were overjoyed to discover she was pregnant and our first son, Miles, was born on 2nd June 1992. He was a breach baby, born by caesarean section at the exclusive Portland Hospital in London, funded by Trudie's medical insurance, and I was truly impressed by the VIP treatment we received when we arrived. They took charge of our car, swept us up to our room and generally made us feel special. It was like arriving at the Ritz! It was only when I went back down to rescue the car that I discovered the reason. 'Oh, I'm terribly sorry, Mr Harris,' said the receptionist. 'We thought you were Richard Branson!'
Rachel Hunter was having her baby at the Portland at the same time and it was extraordinary to see the lengths the paparazzi were prepared to go to in their attempts to get some pictures of her, Rod Stewart or the baby. As well as the vigil in the street outside, the first floor of the building opposite was commandeered and overrun with photographers, training their telephoto lenses on the hospital, some even climbing out and balancing precariously on ledges and window sills in desperate attempts to get a better angle.
Trudie is the perfect mother. She read Miles brilliantly and always seemed to know instinctively what was exactly right for him and Miles was a happy, contented child. Within weeks he was sleeping through the night and he used to love to jig up and down in his baby seat while I was playing my music and working on my shows. Our lives seemed idyllic, but nagging worries were beginning to surface.
Shortly before Miles was born I arrived at Egton House one evening to discover Dave Lee Travis waiting for me. He looked uncharacteristically serious as he followed me into Phil Swern's office, closing the door behind him and looking around the room as if to check that we weren't going to be overheard. He had a very powerful presence and I was genuinely apprehensive. 'They're taking us all off Radio 1,' he said in a hushed voice.
I couldn't believe what I was hearing. 'What on earth are you talking about? Things are going really well.'
'You don't understand, Bob. I've been talking to top management and they're going to reposition the network and get rid of us all. You and I will be the first to go.'
I was absolutely stunned. 'But what about Johnny Beerling?' I asked. 'He won't let it happen.'
'You mark my words, it's going to happen. I'm telling you as a friend. I wanted to warn you and tell you to start looking out for other work. Put some eggs in other baskets, your days here are numbered.'
I'd been aware for some time of the increasing pressure on Johnny to make the station more 'hip' but had never dreamed it would go as far as a complete re-vamp, something he was dead set against. In September 1992 I was onstage at the Radio 1 25th Birthday Party Road Show at Astor Park in Birmingham, introducing Del Amitri to the crowd of nearly 130,000 who had turned out despite the dreadful weather – hardly a demonstration of falling popularity! But the political ball was rolling and DLT was ultimately proved to be correct.
Meanwhile, the bottom had fallen out of the property market and we were becoming increasingly worried about our flat. We'd been trying to sell it for months, before our two-year loan period with Bruno Brookes expired, but already the value had fallen by more than £60,000. Despite the cut in price no one came round to view the property and we were beginning to realize we were caught in the negative equity trap everyone was talking about. Paying Bruno interest on his fixed loan of £130,000 at a rate of more than £1,300 a month, as well as a similar sum to keep up the mortgage payments, was crippling us and all the time the value of the property was falling like a stone. By the end of the year things were becoming really scary and our bank manager instructed us that we could no longer sustain these outgoings.
At that moment I knew we were in trouble. Bruno was adamant he was going to get his money and that was that. He wanted his cash and I couldn't pay. Stalemate. The next few months became a battle as Bruno applied increasing pressure to get us to pay the money he thought was his by right. Meanwhile, the press started baying for the blood of the dinosaur Radio 1 DJs, and I was at the top of the list.
EIGHT
_'The World Ends on a Whisper'_
A CHILL WIND OF CHANGE WAS BLASTING THROUGH RADIO 1. IT WAS becoming clear that Dave Lee Travis was right in his prediction of a major cull. The atmosphere at Egton House was very uncertain as rumours of who would stay and who would go gathered force. The national press was choreographing an increasingly vigorous campaign to see off the dinosaur DJs, with my name prominent in the published lists of potential casualties. Nevertheless, it came as a major shock when, in August 1993, DLT made his stand and resigned on air midway through his programme. Whatever else I thought about it, I had to admire the man's principles. His 'up with this I will not put' speech was a classic.
'As Dave Lee Travis packs his record box and prepares to leave Radio 1, he will leave behind a slight feeling of vulnerability among some of his 20 fellow disc jockeys' wrote the _Guardian_ a few days later, with droll understatement. 'While Radio 1 claims its target audience is between the ages of 15 and 35, the average age of the disc jockeys is just over 35. Some have been criticized for being staid and out of touch as the station attempts to inject a fresher, lighter approach and move towards a younger audience.'
Despite assurances to the contrary, I realized that it was all adding up to the end of my Radio 1 career. Let's face it, I'd been deemed unfashionable for the best part of the previous 17 years, ever since being castigated by the punks! In a funny sort of way it didn't really bother me. If I lost the programmes ... well, I'd just have to rebuild again. The fact that I'd successfully recovered from setbacks a number of times in the past had given me some resilience and trained me in the methods of 'moving on'. Of course, losing Radio 1 would be a massive blow, but it didn't represent as big a threat to the very heart of my home life as did the increasingly bitter financial battle with Bruno Brookes.
What made it so difficult from our point of view was the fact that Bruno was pressing for full payment of his loan to us, no matter what. We were desperately trying to sell the flat, which had now lost £85,000 of its value in 12 months. Even at the knockdown price of £172,000 we hadn't received one offer. With the equity on the flat mortgaged to the hilt we had no means of raising the lump sum of £130,000 we owed Bruno and we could no longer support the interest on the loan. I could understand him wanting his money, and never pretended anything other than liability, but the hostility was palpable as he increased the pressure on us. Several times he reduced Trudie to tears on the phone. At the end of March 1993 Bruno served us with a repossession order, giving us notice to quit the property by 5th July.
The hot seat changeovers between our shows at 4 a.m. were a nightmare of tension. I tried not to acknowledge him in any way when he came into the studio, other than to applaud the self-discipline that stopped me from punching him in anger. I'd never before experienced as high a degree of stress as was packed into those two or three minutes at the end of my programmes. What kept me going was my belief in the old-fashioned 60s concept of karma. I knew that whatever he was going to sling at us, I wouldn't lift a finger against him. I knew I didn't have to. My near-death experience had taught me that we make our own hell, and I cursed the obsession with money that made him so difficult to deal with.
As the summer ended I got a call from Matthew Bannister, the new controller designate of Radio 1, asking me to meet him at Broadcasting House. I can remember almost every word of our less-than-two-minute conversation in that bare, strip-lit office. 'Thank you for coming in,' he began, 'but I'm afraid I've got some bad news for you. I'm taking your programme off air.'
'What, from 16 hours to nothing?' Although I was expecting drastic news, this still came as a jolt.
'Yes, we're repositioning the network,' he answered. 'I want you to know that this in no way reflects the standard of your programmes, but we're moving Radio 1 forward. I'm changing the overnights and expanding the music base.'
I looked at him for a moment. My show was arguably the most eclectic on the network. 'You haven't heard my programmes,' I stated simply.
'I'm sorry,' he said. 'I hope you'll continue with some sort of presence on the network ... maybe documentaries ...'
There didn't seem much else to say. I didn't take it personally, and I had no axe to grind with Matthew, whom I'd never even met before. I'd had a fantastic time at Radio 1, had enjoyed a wonderful working relationship with Phil Swern and Jeff Griffin and been staunchly supported by the controller, Johnny Beerling. I couldn't have asked for more and I'd done my very best. I'd loved doing my programmes and knew I was going to miss them like mad. But hey ... life goes on. As I reached the door, I stopped and turned around. 'Just to let you know ... I won't be going to the press to slag you off, or anyone else for that matter. I've loved it here, it's as simple as that.' A lump rose in my throat at that bit, but the difficult part was going on air that night. With all information embargoed until the following Monday, I couldn't even explain why I was sounding so flat.
I'd been supporting a band called Cry Of Love, a four-piece American rock group in the style of Free and Bad Company and sporting an awesome guitarist in Audley Freed. On the strength of the plays I'd given their début album _Brother_ , Columbia Records brought them over to the UK for a special showcase gig at the Borderline in London on 21st September, a few days after my meeting with Matthew. Cry Of Love had asked me to compere the show and I turned up to find the place packed to the rafters. During the evening many people made a point of coming up to me, shaking me by the hand and thanking me for playing the band on the radio. The warmth was unbelievable. As I stood onstage looking out at the crowd, the evening seemed to define what I've always thought my job was about – making the introduction between the musicians and the audience, then stepping back while they explored the experience. After a brilliant, high-energy set in that sweaty basement club, the band piled down to Egton House with me for a live session on my overnight show. The evening was a triumphant but confusing experience. If the programme was the success it seemed to be, how come I was losing it?
'The World Ends on a Whisper' ran a headline in the _Independent_ on the morning of the final show. Earlier that week journalist Jim White had spent a night sitting in the studio with me, listening to the music, answering phone calls, helping me with the mail and generally picking up the vibe. Jim put together the following article:
Harris's 'repositioning' came as something of a shock for the million or so listeners who regularly tune in to his show. Sitting at the mixing desk in his studio, Harris has a heavy wodge of angry letters, several thousand thick. They come from across the country: from vicars in York, students in Lancashire and the night shift at the Mr Kipling Bakeries in Petersfield, Hampshire. They talk of 'betrayal', 'horror' and 'devastation' at the end of Harris's show. While most disc jockeys simply seem to inhabit another world, Harris found that his job took him into another universe altogether: that inhabited by computer buffs and long-distance lorry drivers, croupiers and hookers, cramming students and bored security guards. He played them an eclectic range of old and new rock, blues, soul, the kind of grown-up stuff that rarely, if ever, makes its way onto daytime Radio 1, delivered in a soft purr that doesn't jar at 3 o'clock in the morning. 'I had no idea there were so many people out there,' said Harris. 'I just assumed I was talking into the ether. I think that because nobody particularly advertised the show, people had to discover it for themselves, and therefore see it much more as their property.'
The article ended with a dedication to Trudie's brother, Brandon, whom I used to phone just after 2 o'clock every morning. The Myerscough family ran a dairy farm in Somerset and Brandon had to be up to load the van for the 4 o'clock milk round.
Musicians and friends called into the show to wish me their best. Nicky Campbell stayed on for a while (I used to really enjoy his show and our conversations at midnight. I saw him years later and he told me that someone had sent him a compilation tape of our 30 best handovers!) and Steve Wright turned up for a while. Marc Cohn phoned from New York, Walter Trout, the world's greatest rock guitarist, rang me from California and blues player Michael Katon called from Hell, in Michigan. Tom Robinson and others dropped by the studio, and Paul McCartney wrote me a most wonderful letter. Phil and Johnny were there, of course, their futures as uncertain as mine. Even Bruno, to his great credit, was gracious when he started his show. Thanking him for what he said was the last time I ever spoke to him face to face. Having played 'Rex Bob Lowenstein' by Mark Germino, 'I Won't Back Down' by Tom Petty and other appropriate stuff, I chose a Max Bygraves song to play out that final programme. 'When You Come To The End Of A Lollipop' seemed to sum it all up.
After it was over, Trudie and I just stood in the middle of the studio for a few moments, holding each other as tight as we could. As we packed to go, it was a really odd feeling to know that I didn't belong there any more. Finally, we trudged for the last time through the tunnel that ran under Langham Place, connecting Egton House with the main building. It was a very low moment but as we climbed the stairs up to the ground floor of Broadcasting House, I was amazed to discover that the place was bursting with people. I stopped at the top of the stairs and looked at the crowd, them looking back at me in a state of suspended animation. We all stood like that for a moment in a surreal kind of stand off, then someone started to applaud. Gradually the whole crowd joined in as I stood there in disbelief, the ovation echoing around that hallowed reception hall. Unbeknown to me, people had travelled from all over Britain, gathering together in a spontaneous vigil through the night in the streets around Broadcasting House. It had got so cold out there that the security guys had let as many as wanted to into the building to get warm.
As we all went outside, someone was playing Ben E. King's 'Stand By Me' on a sound system they'd set up in the boot of their car. People completely surrounded us, shaking me by the hand, telling me how much they were going to miss me. A gang of bikers revved their Harleys and gave Trudie a white-knuckle ride round the block while two women introduced me to the driver of the taxi they'd hired to bring them down from Coventry. 'We were going away on holiday this week but thought we'd rather spend the money coming down to support you.'
It was very emotional and I really felt I didn't deserve any of this. All I could think of to say was 'Thank you, thank you' to everyone, over and over again.
As chance would have it, Trudie, our son, Miles, and I were on a plane the following day, heading for the Seychelles. We'd booked the holiday months before and it was a wonderful coincidence that it fell exactly at the end of those final few hectic days on Radio 1. It was an opportunity to reflect and relax for a couple of weeks, a break we badly needed. I'd been doing programmes for In Flight, a company providing taped entertainment to airlines, and had opted to be paid in tickets. I'd almost forgotten I'd accumulated them and the company had called to tell me that the option was about to run out. It transpired that I'd saved up enough to get eight people somewhere really sunny and Roy and Karen Webber came with us, with their children Holly and Luke, taking care of the hotel as their part of the deal. Although I'd done the work to earn it, it felt like a free holiday for us, and it was great spending time with Roy and his family, an opportunity we rarely got.
The inhabitants of the Seychelles reminded me of the lyrics of the Blue Mink song 'Melting Pot' – 'multi-racial, coffee-coloured people by the score'. The islands are situated just south of the equator, in the middle of the Indian Ocean, about 1000 miles east of the African coastline. The islanders are gentle people who've absorbed any number of cultural and genetic influences and there was no community tension of any sort on those crime-free paradise islands.
We stayed on the island of Mahe, roughly the same size as the Isle of Wight and by far the largest in the group, with a population of 40,000. It is a stunningly beautiful place, with an all-year-round temperature in the 80s and regular rainfall. The climate produces lush and colourful jungle vegetation that reaches the fringes of the bleached white beaches edging the clear turquoise sea. Outside of the capitol, Victoria, there were few people, very little traffic and, astonishingly, no predatory insects despite the tropical climate. The only inconvenience of any description was the persistent mouse in our hotel room that defied all attempts at capture, forever scrabbling up and down the curtains and waking our toddler in the middle of the night! Miles was 18 months old and the great wonders for him were the hundreds of tiny fish that used to gather in shoals round our feet whenever we went paddling and the peacocks that strutted about making the 'cwaark' sound that always made him jump.
Despite our hasty exit from the flat in Platt's Lane we'd been lucky enough to rent a small farmhouse in Oxfordshire, overlooking one of the largest village greens in England. I'd loved Oxfordshire when I lived there in the 80s and Trudie felt she'd had enough of London. It was a lovely place to come home to after our holiday in the Seychelles and we both felt confident and rested for the first time in months. It didn't last long.
We were woken at 7.30 the following morning by a hammering on our front door. Two bailiffs had arrived to impound my record and CD collection in lieu of our debt to Bruno, who knew the collection was valuable and intended to sell it off to recover at least some of his money. Apparently the law was on his side. We discovered that technically I no longer owned my records, that it was at the discretion of the bailiffs as to whether I kept them or not and that we had seven days to appeal. 'We suggest you call a lawyer,' they said, as we all sat drinking tea in our kitchen. 'We'll wait while you make the call, otherwise we're instructed to remove the collection.'
It was a desperate situation. Our future depended entirely on my records and my ability to build and broadcast my shows. Without the raw materials – well, God knows what I was going to do. Theresa Mulgrew at Cole and Cole in Oxford had agreed to represent us and issued a stay of execution. After a couple of hastily arranged meetings, we arrived for the High Court hearing in the Strand the following Wednesday morning, a very bleak experience. We tried to explain that I needed my CDs and records to allow me to hand-build my programmes in the way that had become my trademark, that they were my 'tools of trade'. Bruno's contention was that I didn't need them and that as a fellow disc jockey he should know. He never built his programmes and therefore didn't need music at home. It was the job of a producer to choose the tracks and anyway, the BBC library was full of anything I'd ever want. It was only a last-minute plea that persuaded the Master of the Court to allow us a little more time to put some kind of case together. We were due back in court on 15th December. I had 14 days to save my future.
I arrived at BFBS to record my show in a state of shock. I'd come very close to losing my livelihood and I was shaking visibly as acting station manager Marc Tyley took me through to his office for a while to calm down. I sat there, staring out of the window at the Westway traffic, feeling scared and hopeless. It seemed that, despite having managed to keep my career going all these years, sometimes against the odds, this time I really was beaten.
I've always spent hours putting my programmes together, getting the blend and the tempo of the music exactly right. I specifically concentrate on segues, playing two, three or four tracks back to back in a seamless run, integrating a diverse range of musical styles in a 'no boundaries' musical mix. For me, programme building is a labour of love, a wonderfully enjoyable, creative and spontaneous process. I never conform to any set format and follow my instincts completely when it comes to selecting the tracks. I've always had the freedom to express myself in this way and knew that Bruno's solicitor's suggestion that all this could be achieved in somebody's office at the radio station an hour or so before a show was completely unworkable for me.
As I moved through to the BFBS studio to begin my recording session, I had absolutely no idea what I was going to do next. It was almost impossible to concentrate on the broadcast and I was struggling with it all when Andy Lowe, the BFBS librarian, edged his way into the studio. 'I don't want to disturb you,' he said, 'but I wondered if this might be helpful.' He put a letter down on the desk in front of me and waited while I read it through.
He'd written that his job was to oversee the BFBS library, one of the most comprehensive CD and record collections in the world; that in all his time with the station he'd only ever seen me use the facility for the occasional track and that I always delivered the music myself from my own resources. He went on to explain that the concept of 'programme building' was integral to the station's definition of my working relationship with them, that my shows were unique and that the idiosyncratic nature of the musical choice was at the core of their appeal. What's more, he said, he would be prepared to stand up in a court of law and offer this professional observation and opinion under oath. This was the answer. I looked up to see a smile on his face. 'I don't know how to thank you, Andy,' I said with relief. 'I think you might just have saved my life.'
As word of the dispute between two erstwhile colleagues at Radio 1 spread through the industry, people started phoning to offer their support. As well as Andy Lowe, Marc Tyley and producer Phil Ward Large from BFBS, Johnny Beerling, Phil Swern, fellow disc jockey Johnnie Walker and Tim Blackmore headed a number of Britain's top independent radio producers who all wrote affidavits in support of my 'tools of trade' contention. Colin Larkin, editor of the Guinness music reference books, sent a long letter describing the value of album sleeves as a research tool and in all we collected a dozen affidavits to be presented in court. Sky News and the national press were waiting for us as we arrived for the hearing.
Torturously, the matter was not resolved. Bruno's solicitor tried to dismiss the credibility of the affidavits by saying that they were all from friends of mine who 'would say that wouldn't they' and insisted that they should all come into court and testify in person. The next hearing was set for 24th February and everyone turned up for me. It was a bit like _This Is Your Life_ , with everyone offering touching and heartfelt testimony of support, sticking to their guns under vigorous and, at times, unpleasant cross examination. I was on the stand for over two hours myself, a surreal and intimidating experience for me. It was even more difficult for a heavily pregnant Trudie, watching from the spectators' gallery, who was now expecting our second child and thinking she may give birth at any moment! Only agent Tony Fox and fellow disc jockey Liz Kershaw had written letters on Bruno's behalf but neither appeared in court. Not surprisingly, Tony no longer represented me.
The whole process took up so much time that we were instructed to return to court for a fourth hearing in May to enable both sides to deliver their final summing-up, but even then we didn't get a decision. After what seemed an unbearable wait, Cole and Cole finally called us on 12th August to tell us that we'd won, that the court had accepted our 'tools of trade' contention and that my collection was mine once again. It was a moment of enormous relief. Bruno immediately appealed, lost the appeal and had all costs awarded against him, the worst possible outcome as far as he was concerned.
Meanwhile, BFBS had been keeping me going. Since losing my shows on Radio 1, I'd once again had no other source of regular income and, with the court case running, our finances were devastated. When Charles Foster offered me a three-month series of daily BFBS UK shows in the spring of 1994 I jumped at the chance. I was also keeping busy as one of the judges for that year's Sony radio awards, listening to hours and hours of taped programmes from radio stations large and small. But the pressures of the court case and our financial situation were affecting me. I'd developed a frozen shoulder, an inconvenient and horribly painful condition: stress related, my doctor told me. I was aware that, although we'd won the court battles, we hadn't won the war. Bankruptcy was now hanging over us like the sword of Damocles.
Jude Howells, deputy manager of Greater London Radio, had been following the story in the press, and out of the blue, she called me. 'It suddenly occurred to me that maybe you'd like to come in and do some shows for us,' she said. 'We'd love to have you.' It was all very casual and warm. I started broadcasting for the station in the summer of 1994 and it only took me a few programmes to realize that GLR and I were made for one another.
I started by doing a three-hour programme on Saturday nights, but quickly expanded into the weekdays, broadcasting on Monday, Tuesday and Wednesday nights from 8 to midnight in what became the most enjoyable broadcasting experience of my career to that point. The money was absolutely hopeless and did little to ease our financial plight, but I knew instinctively that this was the right place for me to be.
Oddly, a few weeks after starting I got a call from GWR, offering me a berth on their networked late-night 'love songs' show, broadcasting from Swindon, not far from us in Oxfordshire, with a financial package that could have begun to solve our problems. The terms and conditions were that I'd only have one 'free choice' track an hour in among the back-to-back Phil Collins, Simply Red and Mariah Carey records that constituted the bulk of their playlist. It took me a nanosecond to turn it down. I knew I'd hate it and that the programmes would sound completely unconvincing. Twelve months on, when the current generation of Australian middle management people moved on, I'd be out of a job and I wasn't ready to go out to graze just yet. In contrast, GLR offered the opportunity of exposure to a whole blast of fresh new music.
The station's playlist was strongly indie-based, with bands like Oasis, Blur, Dodgy, Red Hot Chilli Peppers and The Lemonheads defining the station's sound, with disc jockey Gary Crowley, in particular, unearthing any number of fantastic new gems. Blues, soul, punk and reggae punctuated many of the daytime shows and it was clear that everyone had a reasonably free choice on air. Peter Curran was doing a dryly intelligent teatime show and Johnnie Walker was sounding as good as ever in the mornings. The lovely Mark Simpson was spreading his gentle bonhomie and the late Charlie Gillett was broadcasting his alchemic mix of world and roots music every Saturday evening. It was a stimulating environment and Jude Howells and station manager Steve Panton were very encouraging, giving me the confidence to push the musical boundaries of my own programmes to the limit.
More and more new names began to pour into the shows as I increasingly sharpened my taste for independent and roots-based music. Leah Andreone, Beth Orton, Audio Sound System, Black Star Liner, Galliano, Lucy Kaplansky and the Afro Celt Sound System rubbed shoulders with the Primitive Radio Gods, Robben Ford, King L, Chris Smither, Eliza Carthy and John Hiatt in a liberating fusion of styles. I was championing teenage guitar sensations Kenny Wayne Shepherd and Jonny Lang, giving first plays to David Gray, Collective Soul and Canadian band Tea Party and playing tracks from Skip McDonald's brilliant _Little Axe_ album.
It was a massive commitment, doing all the listening and building 15 hours-worth of programming every week. I worked four days from around 10 a.m., putting the shows together then driving to London for the broadcasts, getting back home about 1.30 the following morning, then doing the same the following day. With my BFBS shows and the occasional voice-over or writing commission it was a hectic, time-consuming schedule, but worth every minute.
GLR was desperately underfunded and that, in fact, was the _quid pro quo_. Come in and enjoy yourself but we can't afford to pay you very much. The equipment was from a bygone age and the two main studios had both seen better days. Facilities were in such short supply that bartering over an empty tape spool or the use of an editing razor was not uncommon and the station relied heavily on volunteers for programme support, particularly in the evenings, mostly to help out on the phones. I'd inherited a helper called Doug from my predecessor, Simon Barnett, but he was leaving soon, so I needed to build a backup team.
I set up a competition, offering a 13-CD box set of Columbia label classic re-issues and a visit to the studio as prizes. The winner was Alan Watts (Motorcycle Alan), who drove all the way from his home in Southampton to collect it. From then on he made the journey every Tuesday evening to help on the show.
The atmosphere of those programmes was wonderful – very easy and loose, people calling in, live sessions and loads of back-to-back music in carefully crafted segues. People would call us up for dedications and information about the tracks and Doug invited a few of the regular callers into the studio just before he left. So began the formation of my amazing programme team. Hugh (The Man with the Tie) began to sacrifice his spare time between his bank job and drama group rehearsals to come in and help on a Monday night. University student Kirsti Reeve (Clued-in Kirsti) applied her awesome mind and computer skills to setting up a Bob Harris website, further developed by Roy Webber's design company The Works and now a major music resource maintained through all these years by the amazing Les Kneeling. It was Kirsti who taught me basic computer skills and developed the templates I still use for programme building to this day. And there was Backstage Patrick.
Patrick had been caught up in the atmosphere of the show and joined me at GLR almost every night. He was amazingly in tune with what I was trying to do and began to organize sessions for the programme, all done in his spare time. He liaised with the record and promotion companies to get some of my favourite musicians into the studio to talk and play live and organized sessions from the bright and brilliant Dave Matthews and the venerable Dr John. Tom Paxton, Christy Moore, Mary Chapin Carpenter, The Hamsters, Lynn Miles, Bruce Cockburn, The Hellecasters, Dar Williams and Judie Tzuke all did sets on the show, often bringing friends into the studio, joining the team and helping to create a kind of club atmosphere on air. The 'feel' really did communicate to the listeners, who seemed to sense how much we were enjoying it all. It was fabulous to be in the middle of one of those sessions, mixing a two-track sound on the antiquated BBC desk for Fairport Convention, Peter Frampton, Paul Rodgers or Iris DeMent, amazed at how lucky I was to be doing this job. Richard Thompson and June Tabor provided the night that best defined the whole vibe.
Patrick is the biggest Richard Thompson fan I've ever met. He knew every lyric of every song and was visibly nervous on the night Richard came in to play live. Patrick took up a seat just to the right of the microphone and there must have been at least a dozen people in the studio while Richard was performing, warm applause greeting every number. He was midway through 'Beeswing' when he stopped singing, having apparently forgotten the lyrics to the song, repeating the chord a couple of times while he sorted out the next line in his mind. Exactly on cue, Patrick sang it for him, Richard picking up from him again a few words on. The look of pride on Patrick's face was a picture as everyone burst into applause. At the end of the set, everyone moved through to the production room to join June Tabor, who was appearing later that evening. As I watched through the glass, she and Richard began to rehearse together and when she came through to join me, Richard came back in to accompany her for a magical, impromptu performance.
I loved the freedom to be able to spend an hour or so with artists in this way and we subsequently featured Steve Earle, Jackson Browne, Lou Reed, John Hiatt and blues legend Jimmy Rogers in interview and 'unplugged' specials. And it was on air at GLR that I celebrated my twenty-fifth anniversary, the first major milestone in my broadcasting career. _Time Out_ advertised the event as follows:
They reckon his musical tastes make Phil Collins sound like Iron Maiden. They say he lurks somewhere between low cred and no cred. They misread his urbanity as showbiz phoniness. And such stories probably led to his axing from the new, youth-orientated Radio Wonderful. But they're all wrong. Bob Harris arouses irrational affection in these quarters and fortunately for us fans, the Whisperer has found a natural home at GLR. Monday's show marks his 25th year of jockery, his ginger whiskers gently wagging to the usual mix of live session and more new music than he played on 1FM, so don't mention AOR. Happy birthday, Bobby.
My three-year-old son, Miles, sat with me for most of the evening at the broadcast desk, fascinated by everything, behaving impeccably and occasionally munching on the microphone-shaped cake baked specially for the occasion. My daughters Miri and Emily were there, Miri with her new baby daughter, Marnie, my first grandchild, who was four months old. The Team was in, Fish, ex-lead singer of Marillion, turned up and Robyn Hitchcock and James Reyne played live sets. I was particularly pleased that James was there because his song 'Take A Giant Step' was very important to us. Not only had it been one of the great anthems of the Radio 1 overnight shows, but the title had also, in a funny way, been symbolic, an inspiration to Trudie and me as we addressed the ongoing problems in our financial life. Take A Giant Step, then another. Be positive and just keep going.
Two weeks later on 2nd September 1994, our second son, Dylan, was born – our sunny baby – a happy, smiling, loving boy, blessed with the deepest of voices. Before he could speak he would express his general contentment with life with a resonant, growling gurgle.
When we moved into our Oxfordshire farmhouse we did so on the understanding that it was a long-lease arrangement, but shortly after I started on GLR, the landlords changed their minds. Their daughter was getting married and they were giving her the house as a wedding present. We were given two months' notice to leave and had to be out by 4th January 1995, so we began the process of looking at properties day after day, a joyless experience. With virtually no money we couldn't afford anywhere big enough to house the music room that was essential for my work, yet so many of the smaller houses we saw seemed so dark, damp and depressing – and the closer we got to Christmas, the more desperate we became.
Finally, we found the house we live in now, situated in south Oxfordshire, set in the privacy of a large garden and perfect for the children, a world-within-a-world environment. I knew it was exactly right for us and it provided an immediate spur to my determination to work our way out of our financial troubles.
Having failed in his attempt to strip me of my record collection, Bruno was now pursuing a 'divide and conquer' strategy. Trudie and I had both signed the original agreement with him regarding the loan and he now singled out Trudie and hit her for the money. I'm still perplexed as to why he thought we'd ever be able to write him a cheque for £130,000, just like that. The only possible explanation was that maybe he thought the Harrods chairman would fund us. Mohamed had called me in a few times to discuss plans to start a Harrods record label and build a £20-million studio on the roof. I advised him against the idea. He later bought a radio station instead and sank his millions into Fulham Football Club, but he was never going to bail us out. Trudie and I truly didn't have the resources to pay the loan in full and in the spring of 1995, Bruno issued Trudie with a bankruptcy order. Twelve months later I went under too.
In some ways bankruptcy came as a relief. At least we could draw a line and begin again, but it was a bleak and difficult experience, one that profoundly affected the day-to-day running of our life. You have to declare yourself the whole time and it's impossible to get any credit of any description. It took us a while to get even a personal bank account again and the restrictions on us were draconian. We weren't allowed a cheque card or charge card and the account would be closed if we went one penny into the red. Almost everything had to be done in cash and several times we went through periods of up to two or three weeks when we didn't have enough money to go food shopping. It was a strange feeling, heading up to London sometimes, maybe to an important meeting or lunch, knowing that in my pocket I had only the fiver Trudie had somehow managed to squeeze out of the housekeeping money. Avoiding my round became a reluctant art form, new clothes were exclusively for the children, holidays were completely out of the question. But I never doubted that we'd come through it all.
My illness had taught me to take things on, to address the difficult issues and try to overcome them. The tougher our problems became, the more I was determined to fight back. 'Don't you worry, Trudie,' I kept saying to her. 'I've got this really strong feeling everything's going to be alright.'
'Ah ... listen to you, you bloody old hippie,' was her usual reply. 'You don't have to deal with the practicalities of life. You creative people, you're all the same. What's it like on Cloud 9 then?'
Despite my optimism, things did get really bad. The worry of our financial plight caused Trudie to have a miscarriage in the summer of 1996. I was at home looking after the children while she recovered in hospital when a reporter from the _Daily Mail_ turned up on our doorstep, wanting some quotes about my bankruptcy! (I didn't particularly resent him being there. But let's face it, who would ever want to DO that job?) I invited him in and he sat at our kitchen table, bombarding me with questions about our money problems while I tried to pacify toddler Dylan, missing his mummy and crying on my lap. At that very moment Jude Howells phoned from GLR, and was very sympathetic when I described the scene. 'Just tell him to fuck off,' she advised. I think the guy actually took pity on us because the paper didn't carry the story, we were relieved that there was very little coverage in the newspapers of our stigmatized state.
We'd slipped several thousand pounds behind with the rent and were getting really scared about what was going to happen. If we lost the house we knew we'd go under and the landlords were beginning to threaten the possibility. We had only a few days left to raise the money when, out of the blue, a £6000 cheque arrived from the BBC for sales of _Whistle Test_ to distant territories around the world. We couldn't believe it when we opened the envelope. It was the turning point for us.
The first hint of Trudie's impending miscarriage had happened in Somerset, on an otherwise wonderful summer weekend. I'd turned 50 a few weeks earlier and, with her brother Brandon approaching his thirtieth birthday, we decided to pool resources and have a combined 80 years bash, lavish not an option. Family and friends joined us for a most wonderful picnic in lovely evening sunshine, by the lake in Stourhead Gardens, followed by a game of cricket on the local ground on the Sunday afternoon, organized by Trudie's older brother, Justin. My Mum and Dad drove down from Norfolk for the weekend and Miri, her then-partner, Rob, and their daughter, Marnie, arrived from London.
The centrepiece of the picnic spread was a huge cake, made by Trudie's sister Grace, in the shape of a record player, with a big chocolate arm resting on a replica of a 7-inch single. Grace was there with her husband, Lewis, and their children, Max and Agnes. Trudie's little sister Jo was giggling with her gaggle of girlfriends while Robin, Trudie's patient uncle, enjoyed another glass of red wine with grandmother Jane on that peaceful, balmy evening. Trudie's great friend, Fiona Ronaldson, was there and, at the centre of it all, were Trudie's parents, Simon and Angela Myerscough-Walker.
The first thing you notice about Simon is that the thumb and two fingers of his right hand are missing, the legacy of an encounter with a 19-millimetre cannon shell in the post-war Sussex countryside when he was twelve. He'd been exploring near the rusting wreck of a German fighter plane and picked the thing up to have a look. The explosion killed his little brother and detonated bits of shrapnel into his body. He spent the next two years of his life in and out of hospital for surgery and repair, an experience that probably explains his amazing resilience.
His father, Raymond, was the definitive bohemian, living the life of an artist at odds with the real world. A qualified architect and teacher, skilled in the art of 'perspectives' (a rare and valuable ability to create a drawing of a finished building from the plans), he'd turned his back on the prospect of wealth and conformity and decamped to the countryside, where the family lived variously in a marquee in the middle of the Sussex Downs, in a small farmhouse in the middle of a 50,000-acre forest and in a caravan miles from anywhere. Together with his sister and brothers, Simon never attended school, their father preferring the virtues of home education and freedom of spirit. As soon as he was old enough, Simon began working on the local farms.
Simon and Angela met in their teens and have hardly been separated for more than a day since. Angela is one of the most capable women I've ever met and, side by side, she and Simon have invested their life in farming, gradually building up to the dairy business they and Brandon were running when I first met the family. Since then, as for all farmers, times for the Myerscoughs have been very tough.
In our case, there were signs that things were beginning to improve as offers of work slowly started to trickle in. Satellite television music channel VH1 transmitted a _Whistle Test Weekend_ , 48 hours of nonstop studio and film material, to mark the programme's twenty-fifth anniversary, an event promoted by a poster campaign that featured a particularly alluring photograph of my good self, all long hair and faraway smile, emblazoned with the slogan 'The best of the _Whistle Test_ , the worst of Whispering Bob's tank tops'.
Many of the old team gathered to reminisce in front of the cameras with Mike Appleton, Mark Ellen, Andy Kershaw, David Hepworth, Trevor Dann and myself holed up in a studio for a few hours, exchanging stories and anecdotes about our time with the show. Billy Bragg, Robyn Hitchcock and Rick Wright from Pink Floyd added their thoughts during an evening touched by a genuine sense of camaraderie between us all. I put together a 'My Top 10' for the channel and was invited by programme manager Mike Kaufman to present the late-night _Nightfly_ video music show for a few weeks while regular host Tommy Vance was away. Building those programmes was fantastic fun and I really enjoyed being on television again.
VH1 were broadcasting from the old TVAM building near Camden Lock in northwest London, acquired by parent company MTV and transformed from an already radical space into a kind of futuristic pop music amusement arcade, the studios and work areas linked by stainless steel stairs and bridges. I was halfway through a programme one morning when the lights went up and we were all asked to stop filming. Mariah Carey had turned up for an appearance on MTV.
The forecourt had been cleared so she could park her trailer, in which she sat ensconced for almost three hours. She'd insisted that all staff be brought outside to applaud her into the building and there was a lot of 'she's leaving the trailer, everybody get outside' followed by 'er ... no she's not, everyone back in again' going on during that time. Work virtually ground to a stop with the constant interruptions as she kept the staff on tenterhooks. The delay was caused, it transpired, by her desire for canine company.
'I want to be interviewed cuddling a cute little puppy,' she is reported to have said. 'Puppies,' she directed the people from her record company. 'Get me puppies!'
All available pedigree mutts having been corralled from local pet shops and God knows where else, she finally flounced triumphantly from her trailer, through the building and onto the dimly lit studio set. There she arranged herself on the bed where she was to do her 'intimate' interview, pouting provocatively as she stroked the orange puppy nestling on her lap. The demonstration of single-minded star behaviour was awesome, a relentless, self-obsession-fired promotional momentum that later propelled her into the richest recording contract in music business history, reportedly worth £20 million an album.
A few days later I compered the Guildford Festival, somewhat more down to earth. I introduced Big Country, Eddi Reader and the return to the stage of the legendary Peter Green, making only his second appearance in front of an audience after an absence of more than 25 years. At the height of his powers with Fleetwood Mac he'd been one of the most confident, powerful and expressive guitarists in the world, able instinctively to fuse his traditional blues playing with the band's British rock style. He'd written some of the most distinctive and moving songs of the era, a string of hits including the awesome 'The Green Manalishi', which was climbing into the charts when he left the band in 1970. The pressure of fame and expectation was too much for him, however, and the psychological and mental problems that ensued led to him shutting down on music altogether. At one point he grew his fingernails so long that he was unable to play and a pathological reluctance to appear in public had only recently been overcome. Watching him on stage that night he looked bewildered and frightened, like a big, shaggy rabbit in the glare of the spotlights. His voice sounded shot and he was leaning so heavily on the other members of the group that I thought his talent was all but lost. But, as the set dragged towards what seemed likely to be a wearisome close, he located unexpected resources of energy and launched into a version of Don Nix's 'Going Down', good enough to evoke the images of glory days gone by, laced with intuitive licks and a driving groove. He even got a thumbs-up from Eric Clapton, dressed in black and standing almost unnoticed in the shadows at the side of the stage.
I briefly returned to Radio Oxford, in its new guise as Thames Valley FM, to do a three-hour show on Sunday afternoons, Motorcycle Alan and good friend and team member Graham Brown would come in with me most weeks to help out on the phones. Fairport Convention, Sam Brown and local band The Unbelievable Truth did sessions for us and Trudie would often bring Miles and Dylan in for the last half hour so they could get the feel of the studio and see where their dad was doing his work. The children never blinked an eyelid at hearing me on the radio, although Miles would occasionally get frustrated that I was programme building or writing yet again, just at the time he wanted a game of football – all part of the joys of working from home.
I was delighted to discover that my GLR programmes were beginning to find an audience at Radio 2. Some of the programme producers started phoning, telling me they were listening in the car driving home after work and enquiring as to the source of some of the tracks I was playing. It was becoming clear that the station was about to undergo some changes and I was eventually invited to record a pilot programme at Broadcasting House and a _Rock Show_ pilot with producer Robin Valk at Pebble Mill and both tapes were submitted to the Radio 2 controller, Frances Line, at the same time. Both were rejected. 'Bob Harris. Isn't he a Rock Jock?' she queried, but the announcement that Jim Moir was to be Frances's successor gave me renewed hope that there might be a place for me on the network after all.
I'd met Jim a number of times at Television Centre when he was Head of Light Entertainment on BBC1. We'd always got on well and he'd once told me that he was a fan. Soon he was on the phone, inviting me to lunch to talk about doing some programmes for Radio 2 and I asked if I could bring Phil Swern with me. Following our enjoyable partnership at Radio 1, Phil and I had vowed to continue working together whenever we could and this seemed the ideal opportunity to reunite. I also thought that Phil was probably more in tune with the 'sound' of Radio 2 than I was at that time and that he'd be able to smooth off some of the rough edges my musical tastes had acquired.
'What are the boundaries?' I asked Jim as we sat chatting together at the restaurant.
'Just bring in all your lovely music,' he answered, offering us a two-week run through Christmas, starting on 21st December 1996.
My son, Ben, was staying with us for a few days during the lead-up to that first show and couldn't believe the pressure I was putting myself under. 'I've never seen you so stressed,' he observed. 'Why can't you chill about it?'
'If I was going out on Saturday to play at Wembley,' I explained, 'you wouldn't expect me to just jog out onto the pitch. You'd surely expect me to prepare, get myself into the right state of mind. Saturday is my Cup Final. I honestly believe it's the most important radio show I've ever done.'
Two factors informed this opinion. First, Radio 2 seemed the obvious place for me to be, now moving to embrace the very audience that had been with me from the start. Second, I knew that if the station didn't employ me, in the long term I probably wouldn't be working. Dark rumours of a GLR 'repositioning' were in the air and anyway, however much I loved it, they weren't paying me a living wage. Commercial radio was now uniformly computer programmed and there didn't seem any other obvious place for me to go. While most stations were all about 'streaming' and digital jukeboxes, Radio 2 has adamantly remained true to the concept of individual 'programmes' and I knew the station represented my only long-term opportunity to go on air in Britain with the freedom to express myself. So, it had to be Radio 2, or we'd probably be off to America.
Phil and I spent ages putting that first show together and eventually decided to start with The Beach Boys. 'Add Some Music To Your Day' seemed an appropriate choice, followed by 'Dance With Me' by Orleans, Shawn Colvin's 'Sunny Came Home' and tracks from Jann Arden, Jackson Browne, Jackie Wilson, Little Milton, Leann Rimes, Joni Mitchell, Lynn Miles, Van Morrison and The Beatles (George's spine-tingling acoustic version of 'While My Guitar Gently Weeps' from the _Anthology 3_ collection). We ended the show with Steve Winwood's 'Back In The High Life Again', because we really hoped we would be. Jim Moir was on the phone less than a minute after we came off air.
'We need to speak about your future,' he told me. I looked across at Phil.
'YES!!'
_The Bob Harris Show_ began its regular Saturday night slot on Radio 2 in April 1997.
Just over a month later our little Flo was born, Florence Jayne Myerscough-Harris, on 21st May, the eighth and last of the children in my extended family – and I am so proud of her. She is a bright, beautiful, sensitive girl, loved and protected by the big brothers she adores. We are a tight family unit.
I settled in quickly at Radio 2, broadcasting from a new self-op studio on the first floor of Broadcasting House. I was mostly building the programme myself this time, with Phil acting as my support system, and for a while we kept a lid on the volume level of the music and made sure we laced the new stuff with plenty of tracks people knew. But gradually, as people like Johnnie Walker, Jonathan Ross and Mark Lamarr joined and the music policy of the station sharpened up, we gradually took the constraints off.
I think Radio 2 is a 'world-class station', where the range of programming is unique and I'm very proud to work for the most popular radio station in Britain and to be working in an environment of high-level professionalism.
Almost immediately, the listening figures for Saturday nights started picking up and within two years we'd almost trebled the numbers, to me a confirmation that there really is an audience for the kind of music I play. Trace my programmes right back to 1970 and you'll discover they're very consistent, that I've always been true to the music. I've got a lot of faith in my ability to pick good tracks and the management at Radio 2 give me the freedom to play the people I really believe in and I hope my programmes demonstrate what a good time we're in right now. I know you wouldn't know it by following the mainstream charts, but there's a fabulous wealth of music out there, just under the surface. In my case, I've been lucky enough to discover whole new seams of it through my _Bob Harris Country_ show and the music of Nashville and Austin, Texas.
It was a big surprise when Radio 2 first offered me _Bob Harris Country_ late in 1998. I've always enjoyed country music and featured it on my shows, right from the early days of _Whistle Test_ when we were playing Poco, The Eagles, Pure Prairie League, The Flying Burrito Brothers, New Riders of the Purple Sage, Neil Young and Little Feat. I'd featured sessions from Shawn Colvin, Mary Chapin Carpenter, Suzy Bogguss, Jimmie Dale Gilmore and others on my Radio 1 and GLR programmes and have always respected the fact that country music is all about a good song. I've played Steve Earle, Hank Williams, Johnny Cash, Rodney Crowell, Lyle Lovett, The Jayhawks, Buddy Miller and Patsy Cline.
Dave Shannon, the programme's producer at the time, first called me in December 1998. We'd already met, in April 1994, when I was compering an Alexis Korner tribute concert at the Opera House in Buxton, Derbyshire, a wonderfully ornate and intimate old-fashioned theatre and one of my favourite venues. Jimmy Page and Robert Plant topped the bill that night, playing together for the first time in years. I was introduced to Dave backstage and immediately liked him – he was one of the good guys. A Belfast boy, he had terrific knowledge of music, great dedication to it and a fabulous, sometimes wicked, sense of humour. Dave was one of the few people who could make me really laugh. For many years he produced the _Paul Jones Rhythm & Blues Show_ on Radio 2 and later worked with Mark Lamarr on his _Rockabilly_ series, the Sony 'Music Programme of the Year' 2000, and produced the country slot from the days of Wally Whyton in the early 90s.
Dave told me that Jim Moir's decision to ask me to do the show was based on his desire to let the programme explore the fringes of mainstream and unearth the new artists who were going to take the music forward. He was very keen for me to stamp myself on the show, hence the title _Bob Harris Country_ , to demonstrate the personal nature of the musical choice. It felt like a big responsibility. I understand how passionate and protective people can be about the music they love and I wasn't sure the regular listeners would approve of the choice of what must have appeared to them to be an interloper from Planet Rock.
When it became clear that the programme had abandoned the bighat middle ground that had previously been its territory, in favour of Lucinda Williams, Buddy Miller, Steve Earle and other left-of-centre performers, the die-hards reacted with venom. We got so many letters from people who thought they'd been abandoned that I eventually took a load of them onto air with me to discuss grievances. I was at pains to point out that I hadn't slammed the door shut on them, but that if they wanted back-to-back Jim Reeves, why didn't they just pull his _Greatest Hits_ collection off their shelf at home and put it on? I read out a letter from a listener who'd sent me a list of ten names he wanted me to feature as 'core' artists on the programme's playlist. Six of them were dead. It seemed to me that we needed to move on.
The whole idea was to inspire the sort of excitement in the new acts that the older listeners had felt when they had discovered the artists 'of their day'. I didn't abandon the traditionalists, and made a point of playing music, in a range of different styles, by the artists that I believe are loyal, in their own way, to the various traditions, rules and values of country music, even if they might bend them around a bit.
Most people 'got it', thank goodness, and we began to attract a whole new audience. To my astonishment, the programme added over 300,000 to the listening figures, despite my left-of-centre musical tastes. 'God knows what'll happen if you actually play some country on the programme,' joked Lesley Douglas, Jim Moir's No. 2. _Radio Times_ published a couple of complimentary articles about the show. Even Jeremy Clarkson declared himself to be a fan. Writing in his column in the _Sun,_ he rejected the test car he was driving on the basis that the road noise was so loud he couldn't hear me whispering!
Before we started the series, Dave thought I needed to immerse myself in Nashville culture so, in March 1999, we set off to spend time in Music City, meeting and greeting, setting up contacts, going to gigs, listening to the radio and recording sessions. It was the first time I'd been to the States for nearly 20 years, and that month proved to be the most enjoyable of all the times I've ever spent there.
Despite having done so much filming for _Whistle Test_ in America in the 70s, I'd never visited Nashville before and our first stop, on the Monday night, was the Station Inn, the world-famous Mecca of Bluegrass, to see the opening night of a forthcoming tour by Steve Earle and the Del McCoury Band, in support of their album _The Mountain_. The gig was a very big deal and the old, rustic venue was absolutely packed, tables swilling with beer amid the hubbub of conversation, everyone aware of the one suspended silver microphone, highlighted in a shaft of spotlight on an otherwise dark stage.
Bluegrass music is played on traditional instruments and the Del McCoury Band line-up highlighted acoustic guitars, mandolin, banjo and fiddle, with Steve adding lead vocals and guitar. All the members of the band stood around one microphone for the performance with no other amplification, the soloist stepping forward to the microphone to play as others moved aside to give him space, all of them constantly shifting position to produce the best ambient balance in a brilliant exhibition of dextrous choreography.
The microphone was a work of art, a signature microphone, developed over many years by Steve Earle's Twang Trust production partner, Ray Kennedy – in my opinion one of the best studio engineers in the world. Their Room and Board studio is located close to Music Row, and has produced some of the most radical music to come out of Nashville, mostly recorded on the analogue equipment Ray has collected over the years. He has tape machines from Abbey Road, and Beatles memorabilia galore in the beautiful control room environment he's created. The place is regarded as something of a museum, with old 45s, music scripts and Elvis records housed with other sundry bits of fascinating memorabilia in soothingly lit glass cabinets.
Ray mixes on a relatively antiquated 16-track desk and rarely uses e.q. (equalization) or echo. He believes the best sound is located within the relationship between the instrument and the microphone and that's where the time is spent, in pre-production, getting the dynamics of the sound exactly right for every member of the band. He mostly records as live, with no production tricks and the minimum of overdubs, sparingly used for emphasis. Buddy Miller's approach is much the same and if I were producing today, they would be my models.
After having recorded sessions at Gretchen Peters' beautiful woodland home and later with Gillian Welch and David Rawlings, we met Sara Evans on the day she hit No. 1 in the American charts with 'No Place That Far'. RCA Records had hung a huge banner all the way down the side of their building, congratulating her on the achievement.
I interviewed Steve Earle, puffing on his pipe in the middle of the chaos that was his E-Squared label office and Dave and I made our début on Nashville radio on 98 WSIX with Gerry House, host of the most successful breakfast show in town. The power of that programme was awesome – everyone in the business listened. Whenever we were introduced to someone new from then on, the reaction was the same: 'Oh, you're the guys from the BBC. Heard you on the _Gerry House Show_.' We couldn't have had a better calling card.
We visited the Reba McEntire headquarters, a fully self-contained operational building, complete with miniature indoor fountain in the air-conditioned marble reception hall, three-storey office suite, galleries and recording, television and radio studios.
But the highlight of the trip was a visit to Emmylou Harris's house, to record an interview about the forthcoming release of _Return Of The Grievous Angel – A Tribute To Gram Parsons_ , which she had overseen. In all the years I've known her, I've never heard anyone have anything but a good word for her. She is a respected and much-loved figure in Nashville and a genuinely caring person. Emmylou reminisced about her first meeting with Gram Parsons and the recording of the tribute album, and it became clear the extent to which 'chance' has played a significant part in her life. 'If there was a church of serendipity,' she reflected, 'I would be the high priestess.'
The week ended with a session by the admirable Texan songwriter Robert Earl Keen, followed by a raucous gig later the same evening by Robert and his band, supported by an Austin group called Reckless Kelly at the Exit Inn, another well-known venue.
I've discovered that country music people are admirably friendly and accommodating. Highlights included meeting Beth Nielsen Chapman, after she won the Song of the Year award for Faith Hill's _This Kiss_ in 1999, and a conversation at the 2000 event with Tia Sillers, a few moments after she received Song of the Year award as lyricist of 'I Hope You Dance' recorded by Lee Ann Womack. I discovered that the Tia Sillers CV also includes the lyrics for Kenny Wayne Shepherd's 'Blue On Black', a blues-influenced song I played regularly on Saturday nights. I was impressed she'd written it, she was amazed I knew the song, a 'Bob Harris moment' as Richard Wootton put it. But the major coup for us was Shania Twain.
Having swept the board the previous year, Shania attended the 2000 event, punctuating a year-long break from the industry, to pass on her Female Vocalist of the Year crown to Faith Hill and afterwards wandered through to meet us. Artists often come into the studio surrounded by publicists, who rush around telling you you've only got two questions maximum and creating agitation. But Shania arrived on her own, knocking tentatively at the door of our small dressing room studio and asking if it was OK to come in. She stood for a moment, looking like a princess in her purple silk gown, before joining me to record what I was later told was the only interview she'd given all year. She was charming, natural and unpretentious, telling us how much she'd needed to take a break after seven years of solid work and how good it felt to do normal things again for a while. She is a genuinely nice person.
Little could I have known after that first trip the impact that Music City would have on my life. Nashville and I established an excellent relationship. I really enjoy the atmosphere of the place and the fact that I can get at the music easily, through any number of venues and record shops. All the music business infrastructure is packed into Music Row and the surrounding area, with major labels, indies, management companies, venues and equipment hire all on tap, creating an atmosphere that's very conducive to music-making. Steve Earle told me that Nashville has a population of just over a million, 900,000 of whom are songwriters, and that young hopefuls travel from all over America and Canada to plug into the resources.
Because of the competition you have to be good to succeed in Nashville and the smaller labels and emerging fringe artists I support recognize that my show represents one of the few but welcome opportunities to get their music heard in Britain. A number of the people I've introduced on the programme, like Slaid Cleaves and Kevin Montgomery, have subsequently been able to tour the UK on the strength of the plays I've given them, a fact which gives me enormous pleasure. That is precisely my appointed role, to bring good music to people.
NINE
Music City USA
THE FIRST EDITION OF THIS BOOK WAS PUBLISHED TWO DAYS AFTER the most brutally devastating day in modern history. On that fateful morning of 9th September 2001 – 9/11 – I was in a small basement studio at BBC Broadcasting House, recording a major career interview with an artist who was to be more affected than most by the events of that day.
The interview was with Yusuf Islam who, in December 1977, had formerly embraced Islam at the Regent's Park Mosque in his home city of London, changed his name and rejected the life he had formerly known as Cat Stevens, one of the most successful artists of the 1970s, a man whose work virtually defined the concept of the sensitive singer songwriter.
Following a brief career as a 60s pop star, Cat Stevens had released his breakthrough album _Mona Bone Jakon_ in April 1970, with the follow-up _Tea For The Tillerman_ coming out just as I started my broadcasting career on Radio 1 in November that year. It was a stunning and beautiful album, featuring 'Father and Son' and 'Wild World', tracks I played regularly on my _Sounds Of The 70s_ show, alongside 'Morning Has Broken', 'Moonshadow' and 'Peace Train' from his next release _Teaser And The Firecat_. I truly loved those records. He was also a frequent _Whistle Test_ session guest and through the next few years our friendship grew. Like many of his friends from those early days, I'd always known him as Steve.
We chatted and reminisced in that little studio about his life and his music. I recalled to him a time in the mid-1980s, when he came in to my _Nightline_ show on LBC radio, to talk about the Islamia Primary School that he had founded in the borough of Brent in 1983, the first-ever Muslim school in London. The fact that it was the first radio interview he'd done since he adopted the Muslim faith was a story in itself, and my producer, Cathie Louie, and I were excited as we headed down to LBC reception to meet him.
We revisited that moment as we discussed his conversion to faith and his rejection of the rock-star lifestyle in the late 1970s. It was wonderful to spend time with this warm, affable, creative artist and he told me that the turning point had come when he was swimming on the Pacific coast, near the home of Jerry Moss who, with Herb Alpert, owned A&M, Yusuf's American record label. Caught in a strong current, he found himself being pulled further and further out to sea, desperately fighting to save himself from drowning.
'There was no one on this earth to help,' he told me. 'I just called out and said "God, if you save me I will work for you", and at that moment a wave came from behind me and pushed me forward.'
The following year his brother David gave him a copy of the Koran on his birthday and so began a deep devotion to his faith, at first radical and intense, in recent times more mellow, that has seen him become a respected and articulate spokesperson for Britain's Muslim community and a passionate advocate of tolerance and peace in an increasingly divided world.
Our conversation had lasted more than two hours before I finally had to break away to join American country star Gary Allan, who was waiting for me in a nearby studio to record a session for _Bob Harris Country_. As Yusuf and I walked into the control room, the first images of the burning twin towers were appearing on the monitors above the mixing desk. The sound was down and we gave the screens very little attention. I assumed the engineers were watching some kind of disaster movie and I briefly stepped out into the corridor to have some photographs taken with Yusuf, before he left and I returned to join Gary and his band in the studio.
Gary was a big star at the time and I'd been looking forward to meeting him. He'd just received a platinum disc for sales of his third album _Smoke Rings In The Dark_ and was promoting his new record _Alright Guy_ , which contained songs by two of my favourite writers – Todd Snider from East Nashville, who wrote the title song, and Bruce Robison, who had contributed a hilarious track called 'What Would Willie Do', an ode to fellow Texan Willie Nelson '... he loves all the people no matter what their races, hell, he even made a country song with Julio Iglesias!'
It was only when we returned to the control room at the end of the recording that the full horror of the 9/11 attacks began to sink in. Gary had brought his band and representatives from his Nashville record label into the BBC with him and by now they were absolutely traumatized as we stood transfixed, staring at those screens, watching the smoke pouring from the crumbling Twin Towers. Some of them were crying, hugging each other for comfort. None of us knew what to say. Time stood still in a terrible combination of grief and silent panic.
The emotional impact and knock-on effect for all the visiting Americans was horrendous. At the moment they most wanted to get home to be with their loved ones they couldn't leave. All airports were on lock-down for days. It still seems strange to me that exactly at the time the attacks were taking place, I was discussing the Koran and the Muslim faith with Yusuf Islam.
The echoes of that awful day stayed with Yusuf too. On 21st September 2004 it was reported that he and his daughter had been arrested on a flight to America. He was due to meet with some musician friends in Nashville. Instead, the flight was diverted to Maine, where he was taken to a military base and interrogated by the FBI. 'Yusuf Islam barred from the US for suspected potential terrorism-related activities' the story read. A few days after returning to Britain, he appeared on prime-time TV in the States in a transatlantic interview with legendary American talk show host Larry King, who asked him 'Where were you on 9/11?'
'I remember exactly where I was, Larry. I was in a BBC studio again, just down the road from here, having an interview with Bob Harris.'
Yusuf's American ban was rescinded two years later but the fact that he had been heading to Nashville when he was arrested only deepened my sense of coincidence because, by now, my own relationship with Music City had become one of the most important in my life. In total, I have now visited Nashville more than thirty times and I owe a huge debt of gratitude to my former producer Dave Shannon for opening my mind to this incredible place.
Dave died of cancer in February 2013 and I miss him very much. He was a fine musician and a kind, gentle and generous man. I never heard him say a bad word about anyone. He was a true professional, and a humorous, creative and supportive producer. His former production assistant, Sue Welch, wrote a lovely tribute that appeared in the BBC _Ariel_ magazine soon after Dave passed away, saying '... he made the working day fun and everyone had huge respect for this quiet, humble man', sentiments that perfectly express my own feelings about him. He fostered a fantastic team spirit around _Bob Harris Country_ , which exists to this day, and I am now blessed to work with Al Booth and Mark Hagen who have become close friends and partners in the creative process that produces the show. We all love country music and we all love Nashville!
Nashville has become the music capital of the world. In a rapidly changing industry, the traditional music business infrastructure I discovered when I first went there is still flourishing and despite its very high density of well-known stars, the city is relatively paparazzi free. It's a mix of facilities and freedom that is attracting artists from all styles of music. My old mate Joe Brown and his wife, Manon, have just bought a house there; Dave Stewart recorded his two most recent albums at John McBride's famed Blackbird Studio and has made a wonderful and eccentric film expressing his love affair with the city. The Rival Sons travelled from Long Beach, California, to work at the West Nashville studio of producer Dave Cobb, to make the brilliant and edgy _Great Western Valkyrie_ , voted the 2014 _Classic Rock_ magazine album of the year. Ed Sheeran moved to Nashville for several months, the Black Keys relocated from Akro, Ohio, in 2010 and opened the Easy Eye Sound Studio, and Jack White started Third Man Records in the middle of what is an incredibly vibrant and creative scene.
Founded in 1779 and originally called Fort Nashborough, Nashville is also the capital of the state of Tennessee. Located on the Cumberland River in mid-Southern America, it rapidly grew to become a thriving port and eventually a major railroad and transportation hub. It is an important university town, known as the Athens of the South, and is a major medical centre, home to more than three hundred health care companies. Called the 'Buckle of the Bible Belt', it is also deeply religious. My guess is that there are probably more churches per square mile in Nashville than just about anywhere else in the world and it was religion that originally brought music to the city. Printing presses proliferated for Bible production, drawing in the sheet music publishers who put the first structures of the music business in place, bringing in the forefathers of the songwriting community that is a massive part of what makes the city such a friendly and creative place today.
Central to the growth of the music scene was the Ryman Auditorium, a stunning and imposing building situated right in the heart of downtown Nashville, which first opened its doors as a Tabernacle church in 1892. As time went by, the sound of gospel gradually gave way to the twang of country as the Ryman became home to a live-performance radio show called the _Grand Ole Opry_ , the longest-running radio programme in the world, now broadcast from the stage of the iconic, custom-built Grand Ole Opry House near the banks of the Cumberland River.
Founded in 1925, those early Opry shows were blasted across America by the awesome transmitter power of radio station WSM, known as 'The Air Castle Of The South'. It was possible to hear the transmissions right across the States and up into parts of Canada, and the Opry drew fans into town in huge numbers. Honky-tonks and record shops sprang up in the streets around the Ryman as downtown Nashville began to generate the wild vitality that makes it one of my favourite places in the world.
I have a special personal relationship with the Ryman. Known as the 'Mother Church of Country Music', it feels like a sacred place to me, with its hard, polished wooden pews (take a cushion if you're going to a concert!) and stained glass windows, the colours from which bathe the upper-tier balcony in a gentle, coloured light. The auditorium and Confederate Gallery seat more than two thousand people and there is a museum area at the back of the building housing some truly iconic country memorabilia.
In 2009 I was thrilled to narrate a documentary on the Ryman made by Al Booth for Radio 2, and joining one of the many public tours of the place was like walking in the footsteps of giants. Hank Williams, Johnny Cash, Patsy Cline, Elvis Presley and countless other stars have played there. And it was one of the proudest moments of my life when I stepped out onto that stage myself to receive the Trailblazer Award presented on behalf of the Americana Music Association by Emmylou Harris in September 2011. Robert Plant was honoured that year too with _Band Of Joy_ winning in the Album of the Year category. Who would have predicted in the 1970s that the Rock God lead singer of Led Zeppelin and the long-haired hippy host of the _Old Grey Whistle Test_ would be embraced by the Americana community at the Mother Church of Country Music! As he and I reflected on the journey that had brought us both to this wonderful moment, Trudie and Robert's manager, Nicola Powell, joined us side stage, Robert joyfully donning the Wolverhampton Wanderers cap and scarf they had bought for him, before falling to his knees and lifting a hefty glass of red wine in celebration.
The Americana Music Association was founded by Jed Hilly and a small, enthusiastic group of like-minded visionaries in 1999 with the aim of 'helping American roots music secure an elevated and secure place in the artistic and commercial life of the nation' – a lofty ambition they have achieved magnificently. From support for young artists to presentations to the president, the AMA has grown organically year by year to become the hugely influential organization it is today, a movement respected and acknowledged by iconic stars and major media alike. Americana is now one of the best-selling music genres in the States, with younger artists such as Mumford & Sons, Old Crow Medicine Show, The Avett Brothers, The Civil Wars and The Lumineers joining blue-chip stars such as Emmylou, Rosanne Cash, Steve Earle and Lucinda Williams in the _Billboard_ Top-30 album charts.
The first AMA Honours and Awards show took place in 2002, moving to the Ryman three years later, where Al Booth and I have set up a mini studio each year in a tiny office next to the stage, monitoring the performances and speeches and recording the interviews and reactions that form the basis of our coverage of the ceremony on Radio 2. It's a fabulously enjoyable but highly pressured evening, at the end of which Al and I usually head out of the stage door, across the alley and into Tootsie's Orchid Lounge to unwind, soak up the atmosphere and down a couple of well-earned margaritas!
The bar is situated on Lower Broadway, the epicentre of Nashville's raucous nightlife, a loud, exciting cacophony of sound. Call into Tootsie's, Robert's or any of the many downtown honky-tonks and beer joints and I guarantee you'll hear some of the best playing you've ever heard ... by musicians you've probably never heard of performing on the window stage for tips. Those spit-and-sawdust venues are where many of the major stars first learned their trade, playing from early morning to late at night, and that tip jar was what kept their show on the road and paid their rent.
It isn't easy making it in Nashville. The level of musicianship is incredibly high. Chris King, a young, hopeful British musician, recently told me of his own experience on arriving there with his guitar on his back. 'So you think you're a guitarist?' said the cab driver who picked him up from the airport. 'Well, the guy who delivers the pizza to your hotel tonight will be a better player than you are!' It only took a short while before Chris realized that he was right, but he also soon discovered that Nashville has a very supportive music community; that big stars will step forward to help young hopefuls if they believe they have the talent and the work ethic. Most of the musicians who are now household names have played those window stages themselves, devoting their lives to music and hoping to be discovered, and they know how much it means to get a helping hand. I find this spirit of generosity and support hugely attractive and I've been blessed to forge what I know will be life-long friendships with some truly great people in this wonderful music city.
One of the most exciting of the many big personalities in Nashville is Scott Borchetta, known as the 'King Of Music Row'. Having followed his father into the music industry in the mid-1980s, Scott worked his way up from the post room at MTM Records, through stints at MCA and Universal, to become the founder and CEO of Big Machine Records ('we called the label Big Machine, because who the hell's gonna tell us we ain't!'), starting a sales explosion that has seen the company become the biggest independent label in America today.
I like Scott very much. He's a massive rock music fan, particularly the big-hair bands of the late 1980s, and I simply cannot think of anyone else in the world who could've persuaded some of the biggest names in country to turn out for the recording of _Nashville's Tribute to Motley Crue_ , one of the more unexpected compilation albums of recent times. He has an amazing knack of making me feel good and he encourages me to tell stories of my _Whistle Test_ days. He loves to hear about Marc Bolan in particular and told me that he played T. Rex covers in his first band. There's no disputing that he's brought these influences to Music Row.
The predominant sound of Big Machine is a powerful and commercial blend of country music and rock, and like all great label bosses Scott has an unerring instinct for the great opportunity. 'Think about it ... how many massive rock bands have come out in the last ten years?' he asked me. 'Less than a handful. That lane was virtually empty, so we decided to fill it.'
The country traditionalists may shake their heads in disapproval but it's a blend that has taken artists like Florida Georgia Line, Brantley Gilbert, Thomas Rhett and The Cadillac Three to the top of the charts, bringing a new, young, predominantly male audience into the music and selling millions and millions of records in the process. No wonder Scott has been able to build a collection of supercars and vintage automobiles to die for, a garage full of classic American heavy metal.
Central to the growth of Big Machine has been the phenomenal crossover success of Taylor Swift, who Scott signed as a fourteen-year-old in 2005. She is bright, mega-talented, frighteningly focused and is currently the biggest star in the world. When she played the Bridgestone Arena in Nashville on her 'Red' tour in 2013, no less than eighteen equipment trucks pulled up outside, containing the rigs and technology that powered a stunning Cirque du Soleil-inspired extravaganza, one of the best and most spectacular live shows I've ever seen.
Taylor puts concentrated thought and energy into every aspect of her career and connects with her audience in an amazing way. She is a PR specialist and before the show she invited Trudie, Miles and me to join her in a hospitality area she'd set up backstage, where she'd created what looked like a big kids' party room, with a soft-drinks bar, bowls filled with brightly coloured sweets and a Diet Coke dispenser. Taylor is tall, intense and looked absolutely stunning in black shorts and black top, a black hat perched on top of her long blonde hair. I was very impressed that Miles managed to keep a lid on the obvious excitement he was feeling as she walked into the room. With her wide eyes, pale complexion and bright red lipstick, she looked like a porcelain doll.
She introduced us to her mother, the equally driven and almost as famous 'Mama Swift', who, before the doors opened, took us on a tour of the stage and the phenomenal technology and hydraulic wonders it contained, with lifts, pulleys, computer screens and no less than eleven different mini dressing-room areas for Taylor's various costume changes. I've been around rock'n'roll tours for most of my life but I had never seen anything quite like it.
Like many of the artists on the Big Machine roster, Taylor has opened the door to a new audience for country music, including my daughter Flo, who is a massive fan. I am thrilled that Flo loves music as much as she does, taking it with her everywhere and consuming it in bite-sized chunks on her iPhone, from iTunes, YouTube and Vevo. Despite my best intentions, however, she is still somewhat resistant to the wonders of Americana but I am consoled by the fact that Kacey Musgraves is one of her main artists on shuffle, in a mix that also includes 365-days-a-year Christmas songs, Michael Bublé, the Vamps and One Direction. Flo's big dream is to meet One Direction but this is (as I write) an ambition unfulfilled, even though her Daddy is supposed to be able to fix theses things! All attempts have so far failed, despite the best efforts of my friends and fellow Radio 2 DJs Dermot O'Leary, Steve Wright and Sara Cox, but at least Flo did get to meet the Vamps, who were guests at the O2 when Taylor brought her show to London in 2014. And I am happy to report that Flo also loves the music of Beth Nielsen Chapman, a central figure in our lives.
Beth is a truly lovely person and a dynamic and creative force. In addition to winning the Country Music Awards Song of the Year for 'This Kiss', she is a multi-Grammy nominated artist and the writer of songs covered by an amazing array of stars including Bonnie Raitt, Martina McBride, Willie Nelson and Michael McDonald. She is an environmental activist and the creator of a beautiful recent project called _The Mighty Sky_ , a beautifully crafted album of songs about the wonders of astronomy, co-written by Beth, songwriter Annie Roboff and Rocky Alvey, director of the Vanderbilt Dyer Observatory in Nashville. The concept has now been translated into a syllabus for schools and Trudie has been at the heart of the project from the start, helping Beth organize concerts, lectures, lessons and events to take the wonders of the universe into the classroom.
Beth has experienced extreme pain in her life. She lost her first husband, Ernest, to cancer in 1994, an emotional trauma that informed the writing of the songs for her album _Sand And Water_ , released three years later. The title song is so moving yet inspiring that Elton John chose it to replace 'Candle In The Wind' in the set he performed on his world tour in 1997. Three years later, Beth herself was diagnosed with breast cancer, which through sheer will and determination she successfully fought. She has been a source of inspiration to me in my own battle against the disease in recent years.
When I took Miles with me to America for the first time in 2010, Beth organized a welcoming concert for us at her beautiful Brentwood home. House concerts and 'guitar pulls' are a regular feature of life in Nashville but for Miles and me this was a new and very special experience, with an 'A'-list gathering of Rodney Crowell, Siobhan and Ray Kennedy, Keb Mo, Gary Nicholson, Darden Smith and Mary Gauthier swapping guitars, stories and songs in a joyous and spontaneous evening of amazing music.
Three years later, Beth recreated the evening for us with a line-up that this time included Jason Isbell, Amanda Shires, Kim Carnes, Kim Richey, Angel Snow, John Fullbright and two wonderful English singer-songwriters Chris While and Callaghan. This time we took a camera crew with us, capturing the unique atmosphere for a TV special entitled _Back To Beth's_ , made by our production company WBBC. The film was shot by director John Williams, produced by Trudie, edited by Miles, and shown on BBC television in November 2014.
The show also featured Kimmie Rhodes who, to quote Emmylou Harris, 'Has the voice of a beautiful child coming from an old soul. She touches us where the better angels of our nature dwell, and I believe we need that now more than ever.' My family has also been deeply enriched by our friendship with Kimmie.
Miles met Kimmie for the first time when we spent a few days with her and her late husband, Joe Gracey, at their house in the countryside just outside of Austin, Texas, during our time in America together in 2010. Kimmie has a studio there, housed behind the stained glass windows of a beautiful outbuilding at the top of her garden, and had just put the finishing touches to her _Dreams Of Flying_ album, produced by her son Gabe. The album includes a sensitive and touching version of Donovan's _Catch The Wind_ , which she taught Miles to play on the new guitar Ray Kennedy had helped him choose in Nashville a few days earlier.
Kimmie is from Lubbock in Texas, birthplace of Buddy Holly and the great Joe Ely, such a lovely person, who, with Butch Hancock and their wives, joined us that night for Mexican food and a guitar pull. After dinner, Kimmie's daughter Jolie invited Joe to join her on a version of 'True Love Ways', which, amazingly, he said he had never played before. It took him only a few moments to learn the chord sequence before they performed a beautiful version of that classic Buddy Holly song, with Kimmie singing harmonies and Butch playing Miles's new guitar. He said how much he loved the sound and tone of the guitar and sat picking and strumming it for most of the evening, before passing it around for everyone to sign. It was a truly lovely evening, a very happy memory.
The following day, Miles and I borrowed Kimmie's little white two-seater Mazda sports car for a trip into Austin along Interstate 35. The top was down, the sky was blue, the temperature was close to 100°F and old-time country star Ray Price was blasting from the radio. 'Miles,' I said as we sped through the sunshine, 'it really doesn't get much better than this!' Three years later, my son Dylan was sharing a similar experience with Kimmie, driving her to New Orleans on his own American adventure.
A few days after that first magical house concert at Beth's, Miles and I were invited to attend another fabulous evening at the home of our great friend, publicist Kissy Black. Hosted by her husband, Jeff, it was a 'Stage It' internet event, with performances from another top-of-the-range gathering, which this time included Gretchen Peters and Suzy Bogguss (both of whom took part in our _Back To Beth's_ TV show), Matraca Berg and her husband, Jeff Hanna, from the Nitty Gritty Dirt Band, Jessi Alexander and Jon Randall, Grammy-nominated multiinstrumentalist Sam Bush and my Nashville Brother Eric Brace. All played brilliant, heartfelt sets but the revelation of the evening was Mike Farris, who absolutely blew me away. You may not know him, but he is the real thing.
His music is an amazing amalgam of gospel, blues, honky-tonk and Stax-driven soul and his voice is a gift from God. Life for Mike Farris has not been an easy ride. He has battled personal issues and drug addiction that threatened to wreck his world but he has come through them all to emerge as one of the great artists of our time. 'Out of the arms of defeat, he has done a victory lap. He takes people who are hurting, who are broken, who think they are alone and through just the sound of his voice he lets them know they're not ... that's magic,' says Mary Gauthier. Buddy Miller goes further. 'Mike Farris has enough heart, soul and power to light up a city. He mixes up the elements and turns them into something new, beautiful and uniquely his own'.
Shortly before Miles and I saw him play at Kissy Black's house, Mike had enlisted the help of some of Nashville's top musicians to record a charity EP at the historic Downtown Presbyterian church for the victims of the devastating floods that swept through Tennessee in May 2010. When the Cumberland River burst its banks, the music community was hit particularly hard. Parts of the Grand Ole Opry House were completely submerged and water flooded into the basement of the newly built, state-of-the-art Schermerhorn Symphony Center in downtown Nashville, causing the destruction of two Steinway grand pianos, valued at more than two million dollars.
But for many musicians, the damage at the massive Soundcheck storage facility was the most profound. Many of the major country stars stored their tour equipment and personal instruments there. Between them, Vince Gill, Brad Paisley and Keith Urban lost literally millions of dollars worth of gear, including guitar collections they had taken a lifetime to build. Eric Brace took Miles and me on a tour of some of the flood-damaged areas of town. It was a heartbreaking experience to see the extent of the devastation and realize how many lives had been affected.
Eric is one of my closest friends. He and his wife, Mary Ann, have embraced my family into their home, and when we were filming our _Bob Harris: My Nashville_ documentary in 2013, their house became our operational base.
Eric is the boss of Red Beet, an indie record label located across the Cumberland River on the east side of town. East Nashville is very cool indeed. With its rebel musicians, arty vibe, funky venues, trendy coffee shops and vinyl record stores, Eastside is Nashville's very own version of Greenwich Village and the Red Beet catalogue is full of gems by Todd Snider, Elizabeth Cook, Jon Byrd and other free spirits from that colourful, bohemian neighbourhood. While we were there, Eric unveiled his latest project, a folk-opera called _Hangtown Dancehall_ , a three-year labour of love co-produced with Washington writer Karl Straub, which they premiered at a sold-out showcase at 3rd and Lindsley, a 400-seater venue in the centre of Nashville.
Inspired by the traditional song 'Sweet Betsy From Pike', it is a musical tale set in the mid-1850s in the wild days of the California gold rush. The sixteen-piece band that brought it to life onstage that night included Austin vocalist Kelly Willis, one-man orchestra Fats Kaplin and Bluegrass star Tim O'Brien. I was so impressed by the whole idea of it that when we returned home I contacted Sir Tim Rice for advice as to how to realize it into a full-blown musical production. Having listened, he described the project as 'muscular and tuneful' and generously offered to spend some time with Eric, who flew to Britain especially to meet him at his favourite restaurant in Hammersmith by the River Thames, where we had a spirited and laughter-filled lunch that lasted well into late afternoon.
Recently, Eric has been working on a passion project – a soulful new album by Jerry Lawson, the long-time lead vocalist with the legendary _a cappella_ group The Persuasions. Scan through other Red Beet records and you'll come across a tribute to Tom T. Hall, which Eric produced with his main creative partner, writer, historian and musician Peter Cooper, and Lloyd Green, arguably the finest pedal steel guitar player in the world. It's a project I feel connected to in many ways, not least because Tom T.'s unlikely No.1 single 'I Love' was all over the radio when I first arrived in America with _Whistle Test_ in 1974. Entitled _Songs Of Fox Hollow_ , the album contains interpretations of Tom T.'s children's songs, including a new version of 'I Love' by Patty Griffin, 'The Mysterious Fox Of Fox Hollow' by Eric and his band Last Train Home, and a totally wonderful version of the impish 'Sneaky Snake', featuring Buddy Miller on lead vocal and the brilliant and distinctive guitar playing of Duane Eddy, the Titan of Twang.
Over the past few years, Duane and his wife, Deed, have joined our closest circle of friends and it has become a tradition for Mark Hagen, Trudie and I to meet them on our first night in Nashville and go out for a curry! I absolutely love these moments, because they give me a chance to hear Duane's stories. It's like talking to my record collection.
As a young rock'n'roll enthusiast in the late 1950s, I was buying some of the best American records ever made. Elvis Presley, Buddy Holly, the Everly Brothers, Chuck Berry, Bo Diddley, Little Richard, Ricky Nelson – these were absolutely magical and mythical names to me growing up in a small town in England – and Duane knew them all. As my collection grew, Duane's singles became the backbone of it. From 1958–63, he had no less than twenty-one Top-50 singles in the UK and I bought every one of them, first on the London American label, then on RCA. It actually brought a lump to my throat to visit the legendary RCA Studio B with Duane during the filming of the _Bob Harris: My Nashville_ documentary to see Miles sitting at the piano Floyd Cramer had played in his 'slip note' style on countless hits recorded there by Roy Orbison, Patsy Cline, Jim Reeves and Elvis.
In the era of the instrumental, Duane's singles were the template, sounding completely different from anything else I'd heard before. He was the first guitarist to have a signature model guitar and he played his Gretch in the deep lower registers accompanied by a chunky sax and the wild yelling of his group the Rebels. The atmosphere he and producer Lee Hazelwood created on those records was electric, pioneering, totally funky and massively influential, and Bruce Springsteen, Hank Marvin, Neil Young and Mark Knopfler are among many musicians who have acknowledged the role Duane's music has played in their lives. The biggest UK hit 'Because They're Young' was even adopted by my friend and fellow Radio 2 DJ Johnnie Walker as his theme tune.
I first met Duane more than forty years ago when he visited Britain to work with Dave Edmunds, another massive fan. He came in for a live conversation on _Whistle Test_ and it was great to meet this genuinely modest man and talk about those fabulous early days, and it has been wonderful to see how his popularity has remained throughout the decades since. In 1986, Art of Noise recorded a Grammy-winning version of one of his biggest hits 'Peter Gunn', and the following year he made a record with Jeff Lynne, George Harrison and Paul McCartney. On his last trip to the UK in 2011, Duane released the brilliant _Road Trip_ album, produced in Sheffield by Richard Hawley. He also sold out the Royal Festival Hall and played at the Glastonbury Festival. We love Duane in Britain.
In America, he was inducted into the Rock and Roll Hall of Fame in 1994 and the Musicians Hall of Fame in 2008. Recently, he has recorded with Beth Nielsen Chapman and Mary Gauthier, in addition to playing on projects for the Red Beet label. John Fogerty calls Duane 'the first guitar god' and I was deeply honoured to present him with a Lifetime Achievement Award on behalf of the Americana Music Association on the stage of the Ryman Auditorium in 2013.
The Red Beet label office is run by Lindsay Hayes, one of our favourite people in the world. She is truly super-dench! Dylan, in particular, has established a close friendship with Lindsay and her partner, Jesse Lafser, a recording artist and songwriter whose work has been compared to that of Gillian Welch and Mary Gauthier. After Trudie, Miles and Flo had returned to the UK following our 2013 filming trip, they became our East Nashville guides. I'd stayed on to spend a few days with Dylan before he set off on his own amazing three-month adventure across America, which took him to New York, Atlanta and New Orleans with Kimmie Rhodes, and a week in the sunshine at the 30A Music Festival on the northwest coast of Texas with singer-songwriter Callaghan and her husband, Steve Massey.
Steve and I first met when he was working as Head of Events at Cancer Research UK, in charge of a fund-raising project called Sound and Vision (about which more later) and I was massively impressed by his dedication and dynamism. We quickly became good friends and soon he invited Trudie and me to see Callaghan play an acoustic set at a private showcase. It was a difficult gig in front of an unresponsive audience but I thought she handled it brilliantly and I loved the warmth and intelligence of her music. Steve was hugely encouraging and although they had only just become a couple, I could tell how proud he was of her.
As Steve devoted more and more of his time and organizational brilliance to Callaghan's career he would call me on a regular basis for advice and I really enjoyed feeling so connected to them both. She was a huge fan of singer-songwriter Shawn Mullins and sent him some of her demos, asking for advice. To her joy and amazement, he invited her join him in Atlanta to do some recording sessions that led to him producing her album _Life In Full Colour_ , which was released in 2011. And when Shawn asked Callaghan to support him on his forthcoming tour, she and Steve moved to America full-time to build her career there. It was a very brave decision and it has been very hard work but it has paid off. She has done gigs in almost every state of the Union, travelling thousands of miles a month to get her music in front of people, playing tiny venues and house concerts, gradually building an amazing database of fans and reinvesting every dollar earned. Crucially, Callaghan and Steve have retained financial and artistic control of her career. I would suggest to any aspiring artist that this is a template to follow, one that so impressed the editors of _Billboard_ magazine that they ran a four-page article about Callaghan, unprecedented exposure for a relatively unknown artist. As I write, she has just played a series of headline concerts and released a beautiful new record called 'A History Of Now', fan-funded through a successful Pledge Music campaign. She and Steve have now moved from Atlanta to Nashville, where their apartment acts as a house, a studio, an office and a rehearsal space, their centre of operations. It was also where Dylan spent much of his time during his three months in the States.
It is such great fun being with Dylan. He does, as Steve puts it, have 'great energy'. He is gregarious, knowledgeable and charismatic and the few days we spent exploring Nashville together were very special to both of us. As I'd done with Miles three years earlier, I took him to the home of Alan Messer, with his old, black El Dorado parked outside. The house dates back to the turn of the nineteenth century and sits on an avenue a few blocks from the famed Music Row – and is an extraordinary and eccentric building. When he moved in, Alan took a sledge hammer to the place, knocking the whole of the interior back to its original shell before aiming a super-high velocity water jet at the inside walls, plaster and rubble gushing out of the front door and into skips in the street outside. The result of all this aqua-energy is a space stripped back to the bone – wood framing, beams and original brick visible through the bare, unpainted, rough-hewn walls onto which he has hung examples of his magnificent photographic work. The effect is minimalist, somewhat unsettling and unique.
Alan was with me in the studio for the best part of four years during my time presenting _Whistle Test_ in the mid-1970s, taking pictures of all the artists who appeared on the show, in performance, in rehearsal and behind the scenes. He took all of the most stunning stills you see from that time, including Freddie King, Curtis Mayfield, Bob Marley and the Wailers and perhaps the most iconic and well known of them all, a striking black-and-white image of a bandana-wearing Ry Cooder.
Alan began his career as a music photographer working for Dezo Hoffmann in the late 1960s, capturing off-guard moments with The Beatles, the Small Faces, The Rolling Stones and notably Bobbie Gentry, for whom he took the cover photograph for her first album _I'll Never_ _Fall In Love Again_ in 1968. Following his time with _Whistle Test_ , he took his entire archive with him and moved to Nashville in 1978, where he became a close friend and confidant of the late Johnny Cash and his wife June, sharing happy and informal times with them in America and Jamaica, capturing many of the best memories on film. Following their deaths, he staged an exhibition of portraits in tribute to them in Memphis in 2005, to rave reviews.
Leafing through his collection of contact sheets is an amazing experience, a gallery of the recent history of rock and country music. He sees the world in a unique way through the lens of the camera that never leaves his side. He has worked on many album shoots through the years with such as Lucinda Williams, Tia McGraff and Kimmie Rhodes, and in 1988 won a Grammy for his silkscreen for the O'Kanes' album _Tired Of Running_. Despite the fact that he has been in Nashville for more than thirty-five years, Alan has hardly picked up even a trace of an American accent. He is a proud English genius abroad.
The following evening, Dylan and I went to the Bluebird Cafe, where Callaghan was taking part in an 'in the round' songwriters' workshop. Situated in an unassuming strip mall a few miles from Downtown, the Bluebird has become a Nashville institution, an intimate venue holding less than a hundred people where songwriters form a circle in the centre of the floor, playing together and exchanging the stories behind their songs, audience participation encouraged. The selection process is totally democratic, mixing established hit makers with young hopefuls, a place where budding songwriters can cut their teeth. Kathy Mattea was the first major star to be identified with the Bluebird and she still makes regular guest appearances to this day. Country mega-star Garth Brooks was actually discovered there, filling in for a writer who missed the gig, and Taylor Swift played at the Bluebird way before she signed to Big Machine and hit the charts.
With its unique atmosphere and historical significance, the Bluebird has also become one of the main locations for the ABC TV drama series _Nashville_ , the popularity of which has seen sightseers and music fans from all over the world flocking to the venue, creating queues round the block and a demand for tickets they are struggling to cope with. Initially, many of the scenes for _Nashville_ were actually filmed there, but when the disruption became too much, ABC simply built a virtual Bluebird Cafe in one of the two vast hangars that house the film sets. They have perfectly recreated the interior of the cafe and the minute attention to detail is absolutely awesome. Every bulb, bottle and bar stool has been exactly reproduced, as I discovered when Dylan and I were given a tour of the film lot by one of the major stars of the series, Sam Palliado.
Sam is a young Cornish actor and musician who is living the dream. Having appeared on British television in the Sky comedy drama series _Little Crackers_ and with Matt LeBlanc and Stephen Mangan in _Episodes_ , he applied online for a part in _Nashville_ , sending some songs and a short section of dialogue he'd recorded in a couple of hours on the computer in his bedroom. It worked, and within days he found himself on a flight, heading to Los Angeles for an audition. He was nervous and excited but one look was enough. 'Are you Sam Palladio?' asked the casting director when he walked into his office. 'You are _so_ hired!'
Sam is a genuinely modest and lovely person, as we discovered when Mark Hagen invited him to perform a session for _Bob Harris Country_ in 2012 at Audio Productions, our Music Row studio of choice, which is where our friendship began.
In _Nashville_ , Sam plays the part of Texan musician Gunnar Scott, a role that has completely changed his life. The series has become a phenomenon in America, propelling its cast to superstardom and fast-tracking them onto the stages of the Ryman and the Grand Ole Opry. In a town usually blasé about its superstars, Sam is constantly stopped for autographs and selfies everywhere he goes by fans, with whom he is kind, smiling and generous. He says that being asked for pictures and autographs by his country music heroes and superstars such as Brad Paisley and Carrie Underwood completely blows his mind!
During our visit to the _Nashville_ set, Sam took us to meet actor and musician Charles Esten, who plays the character Deacon Claybourne. He was in his trailer, strumming his acoustic guitar and practising a song for a scene he was filming in a few hours' time. The quality of the soundtrack is a key factor in the success of the series: producer T Bone Burnett and musical director Buddy Miller encourage the top writers in town to submit original material and the fact that the actors actually sing and play these new songs themselves, rather than miming to recordings, is crucial to the authenticity and credibility of their performances. As we sat talking on that late-November afternoon, Charles put down his guitar for a few moments to muse on the impact the series was having on his life. 'You'll never guess what I'll be doing on Friday,' he said. 'I'm going to be turning on the Christmas lights at Graceland, fake snow and everything. It's all totally surreal!'
The more I became inspired by the city of Nashville and the people I was meeting, the more I began to talk about them, on my radio programmes and to my friends in Britain. Robert Plant, in particular, was fascinated by my description of the Nashville music community and asked me to make up a few CD compilations of some of my favourite artists.
He told me he'd been driving home through the Worcestershire countryside one July evening, listening to my show on Radio 2, when I played a track by Alison Krauss. He'd never heard her before but was so stunned by Alison's voice that he'd pulled over to the side of the road, turned up the volume, stepped out of his car and stood under the stars listening to her beautiful music drifting into the warm summer air. 'It was', he said, 'like hearing a sound from another planet.'
As well as being blessed with the voice of an angel, Alison is a world-class violin player and a wonderful producer. She is quirky and funny and the warm, gentle sound she creates has won her no less than twenty-seven Grammy awards, as a solo artist and with her band Union Station. She is America's most successful contemporary Bluegrass star.
During the past fourteen years, Alison and I have recorded many sessions and interviews together, and the next time Al Booth and I were at Audio Productions, she joined us to play a new acoustic set, arriving with the surprising and intriguing news that she and Robert had been discussing the possibility of working together. Initially, it seemed an unlikely combination but she explained that her older brother, Viktor, was a massive Led Zeppelin fan and that she had grown up with the sound of Robert's voice echoing round the family home. I felt excited, imagining the blend their vocal styles would create. The album they were planning to make turned out to be one of the most successful of their respective careers, the award-winning _Raising Sand_.
The catalyst for the project was producer T Bone Burnett, with whom Alison had worked on the old-time music soundtrack for the film _O Brother, Where Art Thou?_ Released in 2000, _O Brother_ proved to be an absolute blockbuster, selling more than seven million copies, inspiring and profoundly influencing a whole new generation of young, roots-based musicians like Mumford & Sons and Old Crow Medicine Show to make natural, organic music. 'It was like a depth charge,' T Bone explained to me a few years later. '... and all the bubbles are now coming to the surface.'
Shortly before _Raising Sand_ was released, Robert told me that he and Alison were planning a short promotional tour in America and that he would love me to go to one of the gigs. Looking at the dates, I realized that their proposed appearance at the New Orleans Jazz and Heritage Festival was four days after my wedding anniversary, on 25th April 2008. 'That's it!' said Robert. 'You and Trudie have to be there!' We invited Roy and Karen Webber to join us on what turned out to be an incredible few days.
Robert, his manager, Nicola Powell, and his tour entourage were staying at a hotel in the centre of New Orleans and we arranged to meet them there on the morning of the gig. When we arrived, the receptionist told us that they'd gone to a local cafe a few blocks away for breakfast. As it happened, we didn't need the directions they'd left for us because, as we walked down the street, we could already see the crowd of people gathering outside the cafe, none of them more than twenty-five years old, faces pressed up against the windows.
There is a whole new, young audience for Robert's music in the States, through his work with Alison, with Buddy Miller and the Band of Joy and his latest group, The Sensational Space Shifters. There was even a dedicated Led Zeppelin station on the New Orleans radio dial and when we left the cafe to head for the tour bus he was immediately swamped by excited fans who simply could not believe they were in this moment.
The New Orleans Jazz and Heritage Festival has come a long way since its modest beginnings in the early 70s when Mahalia Jackson and Duke Ellington played in front of no more than a few hundred people. Each year since then it has grown to become more and more important, expanding into the massive and truly eclectic international gathering it is today. Robert and Alison's set was part of a week-long schedule of music and events that pumped more than $300 million into the local Louisiana economy, revenue that was seen as a hallmark of the area's recovery after the devastation of Hurricane Katrina, the scars from which could still be seen in parts of the city – bleak rows of empty, flood-wrecked houses, their contaminated contents piled up in mountains at the end of each deserted block.
The main concert stage was located at the Fair Grounds Race Course and as we pulled into the site it was clear that this was no ordinary festival. The dry, dusty backstage compound was huge, housing the production offices, trailers, dressing rooms, bathrooms, chill-out areas, catering facilities, generators and general infrastructure needed to support an amazing line-up of stars, a bill that featured (among many others) Stevie Wonder, Santana, Randy Newman, Al Green, Diana Krall, Elvis Costello and Billy Joel alongside local Louisiana legends Dr John, Allen Toussaint and the Neville Brothers.
Shortly before Robert and Alison began their set we made our way to the side of the stage where we met Sheryl Crow, who was on later that afternoon. I like Sheryl very much. She is a real trouper, a performer who gives it everything she's got. Over the past few years, she's embraced and been embraced by country music and recently came in to play an acoustic set for _Bob Harris Country_ while on a whirlwind promotional tour of the UK, a moment that also provided a wonderful and unexpected reunion with her accompanying guitarist Audley Freed, whom I'd previously met in the 1990s when he was in the band Cry Of Love. 'I don't want anyone to think I've jumped on the country bandwagon,' Sheryl told me. 'I've always loved the music. The Nashville music community is the best there is.'
We stood talking for a few minutes next to the side-stage sound monitor desk, looking out at the vast festival arena in front of us, and what a sight it was. The crowd seemed to go on forever, a throng of thousands of smiley, happy people in a swirling sea of colour; flags and banners waving, blown by the gentle breeze on that warm, sunny afternoon. It was beautiful to see and as Robert and Alison began their set, Trudie and I made our way out into the crowd and onto the grass bank in front of the stage to soak in the atmosphere.
The previous year, I had recorded an interview with Robert for a documentary I was making with my brilliant editor Neil Myners called _Who Knows Where The Time Goes_ , which won our production company WBBC a prestigious Sony Silver Award. The programme told the story of the life of Sandy Denny and was broadcast on Radio 2 to mark the thirtieth anniversary of her death. Sandy had begun her career in the late 1960s as the lead singer with Fairport Convention, the group that basically invented a whole new genre of music – folk rock. She went on to make a series of sublime solo albums and was voted top female singer in the _Melody Maker_ poll in 1970, the year Robert first won the award for Male Vocalist of the Year, and he was a massive fan.
'I remember how proud I was when we were both voted top vocalists in our field. We ended up on page five of the _Daily Mirror_ , hugging each other and having a great photograph. She and I gravitated towards each other. We were such young souls to be in the middle of it all.'
English folk music was always an important ingredient of the Led Zeppelin sound and Sandy was unique in being the only guest outside of the group ever to have appeared on any of their albums. The track she recorded was 'The Battle Of Evermore' on _Led Zeppelin 4_ and Robert described the thrill he'd felt hearing their voices blending together for the first time.
'When Jimmy and I began writing "The Battle Of Evermore", it was obvious it was a two-voice part. To hear her first vocal response was one of those great moments when you've written something and somebody takes it to a whole new place. We had to get it so that the one voice cascaded over the other one without actually ever dominating. It was beautiful; a spectacular moment for both of us.'
Robert and Alison also touched the heights in New Orleans on that glorious afternoon, playing through the songs on _Raising Sand_ and backed by a band as good as anything I've ever heard – T Bone Burnett and Buddy Miller on guitars, Dennis Crouch on stand-up bass, Stuart Duncan on fiddle, mandolin and banjo and Jay Bellerose on drums, Alison's violin playing weaving patterns across the tapestry of sound. It was both dreamy and funky, and as Trudie and I lost ourselves in the music, thoughts of Robert's work with Sandy Denny flooded into my head and the amazing combination of their voices, a sound he'd found so inspiring. At that exact moment, he announced to the crowd that he and Alison were going to sing a Led Zeppelin classic. When 'The Battle Of Evermore' began, I thought I was going to cry. Trudie and I hugged each other. 'We are blessed to be here,' she said. And she was right.
TEN
A Rocky Road
THE TIME WITH ROBERT PLANT AND OUR FRIENDS ROY AND KAREN IN New Orleans had come as a much-needed boost; a happy moment in the middle of a period in my life that sometimes took me to the edge of despair.
Trudie and I were making our way through the dark, busy streets of Soho, heading towards the Borderline, a music venue just off Charing Cross Road in London, where we were staging a showcase to mark the release of a new Americana CD I'd compiled as part of an on-going _Bob Harris Presents_ series, all packed full of my favourite music. It was 2nd February 2007 (my daughter Emily's birthday), and a very important event for us, one we'd been planning for weeks. Three of the acts on the compilation – Eve Selis, Grayson Capps and Alana Levandoski – were playing live and we'd invited Bob Paterson, Lisa Redford and other friends and key music industry people to join us. The gig was a sell-out, so we knew there would be a great atmosphere, and I couldn't wait to get up onstage and get the evening started.
We were running slightly late and, as we hurried through the rush-hour throng in Soho Square, my mobile phone lit up. It was a call from Miles, who was back at home. He sounded flustered and alarmed. 'The Health Centre just phoned,' he told me. 'They wanted to speak to you. They've given me the number of a hospital and said you have to call straight away to make an appointment.' I could hear how worried he was. 'Are you ill?' he asked me. 'What's going on?' I think I succeeded in sounding reasonably calm and reassuring but my mind was starting to race. I tried to call the hospital from the middle of the street but I couldn't get through, so Trudie and I decided to head straight to the Borderline and use a landline to phone the hospital from there.
We arrived to find a large crowd of people outside the venue, many of them gathered round a big old Volvo that Eve Selis and her band were using as a tour bus. The front window had been smashed and Eve was standing amid the broken glass, stressed and animated, explaining that the car had been broken into during the band's soundcheck and some of their equipment had been stolen. As we stopped to sympathize, I felt totally distracted. I really felt for Eve, it was a horrible thing to happen, but I was absolutely desperate to get inside and make that call to the hospital.
A couple of weeks earlier, I'd noticed a trace of blood in my urine. At the time I didn't think anything of it. I had been feeling tired, but we work very hard, so that's not surprising; other than that I felt well. Sensibly, Trudie had insisted that I get it checked out, so I booked myself in for a routine blood test at my local health centre in Abingdon. It was a decision that probably saved my life.
The manager of the Borderline let me use his office phone but there was no privacy at all, and in the middle of the pre-gig chaos the news from the hospital was not good. My blood test had revealed an abnormally high level of Prostate-Specific Antigen, a protein that is produced by the prostate gland. The level of PSA in the blood is often elevated in men with prostate cancer. A healthy reading is anything below 4.0 ng/mL: mine was 22. The hospital told me that there was no time to lose and that they wanted me there at 9 o'clock on Monday morning to undergo a biopsy to determine the extent of the problem. I was adamant that I would not be attending, that I just had to take a few days to work everything out. It was a deeply uncomfortable conversation and I absolutely was not ready for this.
The Borderline was now packed with people and by the time I put the phone down we were late with the start of the show. People were coming in and out of the office urging me to hurry up. Alana was already at the side of the stage waiting to go on but I was by no means sure that I was even close to being able to do this. How the hell was I going to walk out in front of the crowd and put aside all the worries going through my head?
'You've got to do it,' said Trudie. 'We can't pull out now and let everyone down, just do it! You'll get into it, the gig will take your mind off everything and we can talk about it all later on.'
As always, she was right. I took a deep breath, gathered my thoughts and made my way through the corridors, out onto the stage and into the spotlight, summoning up the smile with which I greeted the audience. The show must go on.
The evening was a blur, to be honest, as were the next few days. I immediately booked myself in to see Michael Robertson, my doctor for the past twenty years. He referred me to a specialist and while I was waiting for the appointment, I had a top-to-toe medical. The readings were frightening. My PSA level had already risen to 34 and I was beginning to feel more and more tired. I was desperately trying to tell myself that basically things were OK, that the biopsy results would be fine, but I was wrong.
A prostate biopsy is not a glamorous experience. It's messy, bloody and extremely painful. The procedure uses Transrectal Ultrasound Imaging to guide ten needles through the lining of the rectal wall and into the prostate. Each needle takes a sample of tissue, each sample is analysed, producing a rating out of 10, known as the Gleason scale: the higher the number, the more threatening the cancer. It was with horror that I discovered mine was a 9 and it was clear that I was in serious trouble. What's more, my consultant told me that I had a particularly aggressive type of cancer and there was a strong chance some cells may have escaped the prostate capsule and got out into my system. If they hadn't, we were talking about cancer management. If they had, we were talking about a few months ...
Trudie was waiting in the hospital reception area and as I emerged, ashen-faced, from the consultant's surgery, she ran towards me. We just held each other there for a few minutes in a state of shock, trying to let it all sink in. Miles, Dylan and Flo were waiting for us when we got back home and we sat down with them in the kitchen to explain, as best we could, what was happening. They listened attentively to everything we said, after which Dylan had a serious question to ask. 'What's for supper?' Children have a great way of putting things into perspective!
It all felt surreal as I paced around our house. I couldn't think what to do with myself, so I decided to head over to my studio and listen to some music. The studio sits under an apple tree at the bottom of our garden and is the centre of my creative world. It houses my CD collection, most of my vinyl albums and is where I do all my writing, my listening and where I build my programmes. I make my radio documentaries there and it's also where Miles and I film our WBBC _Under The Apple Tree_ sessions. It's a very personal space and I must've made that walk across the garden hundreds and hundreds of times. This time, though, it felt completely different. As the studio came into view the enormity of what was ahead of us finally hit me; the uncertainty, the lack of any sense of control of the future. What if we hadn't caught it in time? What if I'd only got a few months left? I broke down, collapsing onto the grass under the weight of it all. I sobbed my heart out, I just couldn't help myself. It felt like my whole world had crashed into bits. I only knew that I was going to have to put every ounce of energy I had into fighting for my life. As my mind began to swirl into panic I suddenly remembered the famous John Lennon quote: 'Life is what happens when you're busy making other plans'. How bloody right he was.
The mood in the house was sombre, to say the least. Trudie told me that she felt completely helpless. 'I can fix most things,' she said, 'but I can't fix this.' But then she had a brilliant idea. She remembered how fastidious Mohamed Al Fayed had been when she worked for him in the early 90s, how he was a stickler for hygiene and always had a medical team on hand. She thought that maybe he'd have a contact who might be able to help us, so she called him and explained my diagnosis. He was instantly sympathetic and massively helpful.
'Give me five minutes,' he said. Exactly five minutes later he called back. 'I've arranged an appointment for Bob with Professor Roger Kirby, one of the top prostate cancer specialists in the world. He's a very busy man, so make sure that Bob is on time for the appointment tomorrow ... And Trudie, be sure to tell him to shave his fucking beard off!!'
The next few days were fraught and hectic as I went in and out of hospitals and clinics for various CTI and MRI scans and blood tests. Finally, with all the images, X-rays and notes in front of us on his desk, Professor Kirby was ready to give me the results. 'You are a very lucky man,' he said. 'We've literally caught it just in time.' I was overjoyed. I knew the next few months would be testing but suddenly we were talking management, not termination.
There were now some difficult choices to be made and we began to discuss the options. I could have what is known as a radical prostatectomy to completely remove the prostate and the cancer with it. This sounded like a comprehensive answer but there can be serious consequences such as incontinence and a loss of sexual feeling. There is a horrible finality about the phrase 'permanent erectile dysfunction', not a great prospect, I decided. Another possibility was brachytherapy, where small radioactive seeds are inserted directly into the tumour, but I didn't want that either. In the end, I opted for eight weeks of radiotherapy, preceded by a course of hormone therapy, which replaces the male hormones in the body with female hormones. It's a process that effectively switches off the production of the testosterone that feeds the cancer, thereby reducing the tumour to a size that can then be zapped by the radiotherapy lasers. The hormone therapy is administered by regular injections into the stomach, first with a small injection to anesthetize the area, then with a needle that, to me, looked large enough to pierce my stomach wall.
The side effects were much more profound than I expected. As my breasts began to grow, my waistline began to thicken and my moods began to change, I realized the extent to which the treatment was mounting a major attack on my sense of my own masculinity. My emotions were all over the place and always much closer to the surface than I wanted them to be. I was suffering random hot flushes, waking up in the middle of the night drenched in sweat ('menopausal' Trudie called it). I was up and down to the loo and constantly worried about being caught short, not a good look! I was starting to feel seriously down, and more and more tired. Even a family holiday at Disneyland Paris didn't lift my mood. All I wanted to do while we were there was sleep.
I was determined to keep working right up to the start of my radiotherapy and everyone at Radio 2 was massively supportive. Lesley Douglas, the network controller, told me to take as much time off as I needed, that I wouldn't lose a penny in wages. Phil Swern, Al Booth and my production team were wonderfully flexible, moving recording and session dates around, sometimes at the last minute, to accommodate my various hospital visits. Johnnie Walker had been through his own extreme cancer experience and regularly called me with words of encouragement, which I really appreciated. I did my last show on 4th August 2007, with Joe Bonamassa playing live in the studio, before I took four months off to get myself well again.
Life became a routine and I surrendered to the process. Monday to Friday I caught the same morning train to London, arriving at the Cancer Clinic at 11.30. External beam radiotherapy has to be carefully planned for it to be as effective as possible and I'd spent a lot of time with my oncologist and guardian angel Heather Payne to make sure everything was right. I had a final CT scan, which took X-rays of the exact area to be treated, and got three tiny tattoos on my torso to enable the radiographers to position me accurately in the machine for the radiotherapy beams to have maximum impact. After all this initial preparation, the sessions themselves only lasted a few minutes, so I was able to leave the clinic just after noon, with the whole of the rest of the day ahead of me. I hadn't had free time like this for years and I began to enjoy the feeling. Heather had told me how much more effective radiotherapy can be if backed up by exercise, so I started walking the two miles or so back to Paddington station each day, making sure to plan the route for emergency toilet stops!
With time on my hands I could see friends for lunch at my favourite tea house, Patisserie Valerie on Marylebone High Street, and I regularly met my first wife, Sue, for a coffee at a sweet cafe overlooking the canal at Little Venice, before catching the train back home. Sue and I have known each other for more than fifty years now and throughout this whole time she has been one of the central and most important people in my life. It was lovely to have these moments to relax and catch up on news about our girls, their partners and their children. Miri's daughters, Marnie and Alana, were now twelve and ten and, following her breakup with their father, Miri had met a new partner, her future husband, Graeme. Emily and her husband, John, had married on 30th June 2004 in a beautiful wedding ceremony held on a windswept Holkham Beach on the North Norfolk coast – one of my favourite parts of the world – and Ems also had two girls: Niamh, who was six, and toddler Ysobel. They all live close to one another in North London and are a tight family unit, with Sue and her partner, Dixie, an integral part of the grandchildren's daily lives.
As I write, Sue is now seventy, but she hasn't retired. She is still doing what she was doing then and has always done: caring for people. She is a social worker at St Mary's Hospital in Paddington, helping elderly patients during their rehabilitation after serious illness, offering advice and support and, if needs be, visiting them at home to check on their welfare and safety. She is a force for good in the world and I always love seeing her.
Despite the rigours of my treatment, I have happy memories of those few weeks. The weather was mostly warm and sunny, I was getting lots of exercise and I was enjoying the freedom from the pressures of work. I couldn't believe I was feeling so well, better than I had for months. I was beginning to feel like a fraud! Gradually, though, the impact of the radiotherapy started to kick in.
The effects were cumulative. The further into the treatment I got, the more bleak and sluggish I felt. As the exhaustion grew, I stopped wanting to see anyone and stopped exercising. All I wanted to do was get home and go to bed. The skin on my stomach was dry and sore, I lost my appetite and energy for life and began to plunge into a horrible depression. I hated myself for being so sluggish, weak and pathetic but all I wanted to do was pull the covers up over my head and shut out the world.
I was feeling particularly gloomy one evening, propped up on my pillows as usual and staring blankly at the TV screen, half-asleep, as Dylan wandered into the bedroom to see me. 'What are you watching?' he asked as he sat down. I wasn't even sure. It turned out to be a Nigella Lawson cookery programme. As we focused on the screen we saw her melt some butter, dark chocolate and golden syrup in a saucepan, stirring in broken biscuits and marshmallows before pouring the thick, bubbling mixture into a foil tray, spooning on a final covering of melted chocolate for good measure.
'Pop it into the fridge for a couple of hours to let it set,' she explained, 'and you have rocky road, the perfect simple snack.'
'Oh wow! That looks amazing!' said Dylan, and he was right. Even with my diminishing appetite, my mouth was watering.
'I'll make you some!' I told him. 'When you get home from school tomorrow, we'll all have rocky road for tea.'
Dylan looked incredulous 'What, seriously?' he smiled. 'You, cooking?!'
I am not known as a chef. I occasionally do a fry-up or make the children sandwiches, but generally I only use the kitchen when Trudie's not around because she gets so irritated with my ineptitude and the general mess I usually make. Nevertheless, the thought of creating a delicious dish for everyone was making me feel genuinely excited and on my way back from the clinic the following day, I called into our local village shop and picked up all the ingredients. When I got in I downloaded the recipe from the internet and set to work and by the time Trudie appeared in the doorway after the school run, there was a tray of rocky road in the middle of the kitchen table, next to a pot of tea, places laid for everyone. It was the best evening we'd all spent together for a long time and I felt so happy that I was able to do something for the family again instead of them having to do everything for me. In retrospect, it seems such a mundane event, but it was a turning point. I realized I could not allow myself to be defeated by my illness, that I had to start to fight.
The first thing I addressed was my fitness. I was determined to work off my lethargy and 'man boobs' and begin to like myself again. I pulled the exercise bike out of the garage, bought a mat and some weights and devised a workout, building up slowly. I climbed up and down our stairs over and over again, using the rails on the landing for push-ups. I made notes in my diary and later bought a fitness app for my iPhone to keep a detailed daily record of my progress. Trudie bought me a free-weights bench for Christmas and by the time I returned to work at Radio 2 at the end of 2007, I was looking and feeling much better, the effects on my radiotherapy receding.
I was still a long way from getting the all-clear, however, so to further help my recovery the late, great Jon Lord recommended that I have a consultation with the naturopath Bob Jacobs, founder of the Society for Complimentary Medicine. The Society was a beneficiary of the annual Sunflower Jam fundraisers – rousing rock concerts featuring Jon, members of Deep Purple and their friends and organized by Jon's wife, Vicky, and her sister Jackie, who's married to Ian Paice, the drummer in the band. Sunflower Jam was set up 'to work towards providing access for all to complimentary and integrated treatments in the fight against cancer and other diseases by funding and supporting research, treatment and education', a noble vision that I have supported as compere of some the events.
The results of the blood tests Bob carried out on me were not great, but I completely bought into the idea that what the radiotherapy had taken out of my system, he could put back in, through minerals and vitamins. He told me to think of every day as a battle in my fight with cancer. 'Win the daily battles and you'll win the war,' he said. I found him sincere and inspiring and a few minutes later I left his office with a bag bursting with jars and containers full of all sorts of supplements and boosters and a bill for almost £500. It was just about the best money I've ever spent. I began to feel the benefits almost immediately and for more than two years Bob Jacobs became a vital part of my recovery regime.
My daughter Mirelle was also a wonderful source of support. She had studied homeopathy for several years, graduating with a degree in 2002 before founding a community practice in Primrose Hill in London, offering alternative therapies and advice on health issues and diet. Unlike conventional medicine, homeopathy takes a holistic view, looking at the physical, spiritual, mental and emotional factors affecting a person, so Miri was very tuned in to what was going on in my head.
A few months after my diagnosis she had told me she was expecting a baby and I was absolutely thrilled to hear the news. She'd had a tough time following the break-up of her relationship with the father of her two daughters, sometimes struggling with the balance between the demands of bringing up Marnie and Alana as a single mother and her restless ambition to establish her career. Now her life had stabilized, anchored by her new partner Graeme, later to be her husband, a man who truly loves her.
Shortly before she'd discovered she was pregnant, Miri had committed her medical skills to the NHS, enrolling on a four-year course of nurse training, initially working in the accident and emergency department of her local hospital, sometimes seven days straight without a break. She was now well into her pregnancy and at the end of one particularly stressful twelve-hour shift, she began to feel seriously ill. She was rushed into an emergency ward at the Elizabeth Garrett Anderson Hospital in central London, where she gave birth to a baby girl on 11th March 2008. Olivia was four months premature and weighed less than 740 grams.
Within moments the tiny baby was put on a ventilator to keep her alive. Seventy-two hours later, she had a massive brain haemorrhage – a Grade 4 intraventricular bleed. The damage was potentially so profound that the doctors warned Miri and Graeme that, even if she survived, Olivia was likely to be severely disabled. The news was terrible but there was worse to come. Shortly after Trudie and I returned from a trip to New Orleans, Olivia was rushed to Great Ormond Street Hospital suffering from Necrotizing Enterocolitis, a life-threatening disease that necessitated a massive operation to remove a part of her bowel. Her condition was so serious that no one expected her even to last the night. Prayers were said at her bedside. Yet, against all the odds, Olivia survived, almost motionless in her incubator, wired up and helpless, hanging on to life by a thread. Miri moved into the hospital to be with her and, over time, she very slowly began to improve and gain strength. For me, in my own battle with illness, her fighting spirit was an inspiration. After three months she came off her ventilator, after six months she was allowed home. The doctors told Graeme that it was unprecedented for a baby to survive what she'd been through, but survive she did.
At exactly this time, I got a call from Steve Massey, in his role of head of special events at Cancer Research UK. He'd heard that I was receiving treatment and wondered if I would be willing to appear at a charity fundraiser he was organizing, an annual event called Sound and Vision, held at the world-famous Abbey Road studios in London, where The Beatles did the bulk of their recordings. He said he'd like me to join the founding patron of the event, Sir George Martin, onstage for a few minutes to talk about the impact of cancer on my life.
Sound and Vision takes the form of a live auction of rock and pop memorabilia donated by some of the world's biggest music stars, photographers and artists and Studio 1 was transformed into a colourful and magnificent art gallery for the event. Striking, iconic images, paintings and photographs of icons such as David Bowie, Jimi Hendrix, John Lennon and Deborah Harry lined the studio walls, alongside gold discs, signed guitars and other unique rock'n'roll souvenirs. The Brand New Heavies and 10cc played storming live sets, there was a champagne bar in the middle of the studio and, as the auction got started and the evening went on, the atmosphere became more and more rowdy. I took to the stage, expecting to struggle for attention, but as I began to speak the room fell silent and I knew my words were having an impact. There is no cause closer to my heart than the work to find a cure for cancer and my emotions were still very raw as I stood up there in the spotlight, urging people to donate. In the end, once the online auction revenue and other donations were added to the total, the event raised more than £165,000 for Cancer Research UK and I was very proud to have been a part of such a worthwhile and wonderful evening.
A few days later Steve was back in touch. He asked if I would consider permanently joining Sir George as co-patron of Sound and Vision and I was honoured to accept his invitation. He also invited Trudie and our production company to be at the centre of the organization of the next event, with specific responsibility for artist recruitment, and we were thrilled to get involved. Being an integral part of such an important initiative was a hugely exciting prospect. Our production company WBBC was about to move into new offices in our village (previously the HQ of our local Truck Festival) and the wonderful Genevieve Wills (now an Ambassador Relations Manager at UNICEF) had joined us to work on some of our bigger projects and we soon set up a meeting with the special events unit at CRUK. Steve Massey was joined by Jacqueline Fitzgerald, Kirsty Jones and Ali Cleveland and we immediately knew that we would love working with this sincere and caring team.
As we began to put together the plans for Sound and Vision 2009 we had lunch with Giles Martin to talk about his dad's involvement; we liaised with Drive, the production company responsible for staging the event; we invited Roy Webber and his design team at The Works to get involved with the look and the branding; and we called our friend Colin Hall in Liverpool to ask him if he could locate some rare Beatles memorabilia for our auction. Colin and his wife, Sylvia, work for the National Trust as custodians of John Lennon's childhood home, Mendips, and 20 Forthlin Road, the small terraced house where Paul McCartney lived as a child and where more than 180 of the Beatles' hits were written.
Both houses have been meticulously restored to the homes that Lennon and McCartney would recognize from their younger years, using photographs and eyewitness accounts to replicate the original fixtures, fittings and furniture – and walking in was like stepping back into another era. There was a picture of John that particularly resonated with my own childhood memories of the 1950s, wearing his school cap, blazer and short trousers, long socks pulled up to his knees, satchel on his shoulder. I've got a picture of me looking exactly the same. All kids looked the same in those days. I loved seeing copies of some of his favourite vinyl 45s, scattered on the bed in his little box room at the top of the stairs. There was 'Baby Face' by Little Richard, 'Tom Dooley' by Lonnie Donegan, and 'Only The Lonely' by Roy Orbison, and positioned on the shelf behind John's bed head, next to a somewhat battered Gallotone Champion Guitar, was a magazine of the time, opened at a colour picture of Elvis. It's giving me shivers just thinking about it. Colin recently told me that when Bob Dylan had visited Mendips he also stood there in silence for several minutes before declaring 'It was cold in my bedroom too'.
Visiting the houses with Colin and Sylvia was a fascinating experience that gave me the inspiration for our award-winning WBBC documentary _The Day John Met Paul_ , broadcast on Radio 2, for which I recorded a major interview with Paul McCartney. The programme told the story of Paul's first encounter with the Quarrymen at a summer fête held in a field next to St Peter's Church in Woolton, a leafy suburb of Liverpool, where they were playing among the fairground stalls and tea tents on a makeshift stage on the back of a flat-bed truck. Paul was only fifteen and he'd ridden down to the fête on his bike especially to see them play and to try and meet their rebellious and charismatic lead singer, John Lennon. After their set, the band invited Paul to hang out and jam with them backstage before their gig at the church hall later that evening. There was a lot of banter but they were knocked out that Paul could play piano and knew all the words to Eddie Cochran's 'Twenty Flight Rock', which he played on John's acoustic guitar. Paul told me that when he handed the guitar back to John he got a whiff of his 'beery breath' and was not impressed – 'They had a gig to do!' – but they hit it off immediately and two weeks later, John invited Paul to join him in the group. Shortly afterwards George Harrison also became a member and the rest, as they say, is history. No one knew it at the time but the events of that day, 6th July 1957, were to change music forever.
It was fascinating hearing Paul tell the stories of his time with John at Mendips. As you approach the house, there is a small, glass-encased vestibule outside the front door where the two of them used to rehearse, with just enough room for them to stand shoulder to shoulder, their guitars pointing in opposite directions as they played and sang. It was a space that gave them a unique and very 'live' sound, their harmonized voices bouncing off the glass surfaces all around them. Paul became more and more animated as he told us how much John loved the sound in there and as I listened a huge penny dropped in my mind. I'd always thought that the slap-echo that John favoured so often (listen to 'Come Together' or almost everything on the _Rock'N'Roll_ album for reference) was his attempt to recreate the vocal sound of 'Be-Bop-A-Lula' by Gene Vincent, one of his favourite records. Not so. It was an attempt to recreate the voice sound he'd experienced with Paul, all those pre-Beatles years ago, in the vestibule at Mendips.
_The Day John Met Paul_ was turning out to be a fantastic project and as well as spending quality time with Paul, Neil Myners and I also recorded a wonderful interview with the surviving members of the Quarrymen in my studio, our conversation underlining to me the significance of Lonnie Donegan's cover of the Leadbelly song 'Rock Island Line', which had hit the UK Top 10 in January 1956. To my mind, it is without doubt one of the most important British records ever made.
'Before then we were listening to things like "How Much Is That Doggie In The Window?" and "The Ballad Of Davy Crockett",' they told me. 'But this record had an energy that was totally different from anything we'd heard before.'
It was a record that changed everything, a pathway into rock'n'roll that inspired the Quarrymen and a whole new generation of post-war teenagers to thrash out a DIY music style called skiffle, the punk of its day. 'We were a garage band without the garage!' they laughed.
We'd also recorded a long conversation with Cynthia Lennon at her son Julian's home in Chelsea; it was the first time she and Trudie had met. We'd taken Miles, Dylan and Flo with us and it was a wonderful family afternoon, the beginning of a friendship between us all that deepens more and more as time goes by. In recent years we have spent holidays with her at her island home in Mallorca (where some of this book was written) and we love her very much. With her strong connections to Abbey Road, we invited Cyn to Sound and Vision and, as we worked with the CRUK team to draw up a shortlist of favourite artists, I composed a letter to Paul McCartney, asking him if he would also like join us for the show.
A lot of things have to come together for an artist to appear. They've got to want to do it – not a given in this charity-saturated age – and they have to be free to do it. The bigger the stars the more in demand they are, constantly being approached to put their names to all sorts of different projects, so diaries tend to be full as much as eighteen months ahead. If they're not touring, they'll probably have to pull a band together and rehearse. With the show on a Thursday evening and full run-through the day before, it's a big commitment, particularly to create the unique performances the event became known for. It's a charity, so who's going to cover for the time and expenses? There are some very big hitters in the room on the night, paying £200 a ticket to be there – will they all be happy with the bill? There were a lot of things to consider, especially as Paul had replied to say the event was during half-term and he would be away with his daughter, but gradually we settled on one name we all agreed we wanted.
I first met Paul Weller when he appeared on _Whistle Test_ with his band The Jam in 1977, and we've remained friends ever since. We'd appeared together at 'Dear Mr Fantasy', a beautiful concert held at the Roundhouse in London in 2007, organized with the help of Trudie by Aninha Capaldi in tribute to her late husband, Jim Capaldi, drummer with the band Traffic. Trudie and I had arrived at the Roundhouse that evening to be greeted by Pete Townshend, who gave me a massive hug. 'I want to apologize for being so rude to you when I was on _Whistle Test_ with Ronnie Lane,' he explained. I was struggling to remember. 'I watched the DVD the other day and I was so aggressive,' he went on. 'But I wasn't angry at you. I hope you didn't take it personally. I was just angry!' I laughed and returned his hug and we shook hands as we made our way through to meet the other artists at the gig.
It was an incredible line-up featuring Yusuf Islam, Jon Lord, Joe Walsh, Steve Balsamo and his wonderful band The Storys, Stevie Lange, Bill Wyman, Gary Moore, Dennis Locorriere, Simon Kirke, Margo Buchanan and, of course, Jim's soulmate Steve Winwood. Steve played a heartfelt version of Traffic's signature song 'Dear Mr Fantasy' and a beautiful interpretation of 'Love Will Keep Us Alive', which Jim had co-written with Pete Vale and Paul Carrack for the Eagles album _Hell Freezes Over_. Trudie took an armful of programmes to the dressing rooms for everyone to sign for an online auction, expecting to encounter some crazy backstage madness, but there was none. Everyone was drinking green tea and behaving impeccably, very un-rock'n'roll!
Paul Weller was fantastic. It was clear how much he respected Jim and he put everything he had into the show, as he always does. He performed 'Paper Sun', 'Pearly Queen' and 'Here We Go Round The Mulberry Bush', my favourite moments of the entire evening and I knew he would be exactly right for Sound and Vision. Luckily, the timing of my call to him was perfect: he'd just pulled into an M6 service station and was sitting his car, taking a break. I explained the ethos of Sound and Vision and he bought into it immediately, promising to do the show and create something really special.
The event turned out to be a triumph. Nashville singer-songwriter Diana Jones played a beautiful showcase at the start of the evening and there were brilliant performances from Newton Faulkner and R&B star Lemar. Cynthia Lennon made her emotional return to Abbey Road, joining me onstage with photographer and performance artist Mike McCartney (Paul's younger brother) to conduct the crowd in a rousing version of 'Yellow Submarine' and my great friend Dermot O'Leary hosted the auction. Finally, Paul Weller appeared, joined by Kelly Jones and backed by a string quartet, reimagining some of his biggest hits, all uniquely arranged for that moment. It was absolutely magical and fabulously successful, raising more than £230,000 for CRUK. The challenge now was to top that figure in 2010!
While all of this was going on, a strange but rather wonderful thing had happened. Out of nowhere, a tiny, scruffy stray kitten had arrived at home. His matted fur was mostly black but he had big white patches under his chin and on his stomach and he had the cutest white-shoed feet. He couldn't have been more than five weeks old and he was traumatized, ragged and frightened, taking shelter under the floorboards of our house, gaining access from outside through a gap in the brickwork and meowing constantly. We already had a handsome black cat called Colby, who was fascinated by this noisy newcomer, catching voles and mice in the garden and leaving bits of them next to the gap in the wall to keep him alive. I've always loved cats. I've had them around me all my life and I think I understand them, but this little kitten wouldn't let any of us get anywhere near him. He was so skinny and small I wondered if he would be able to survive and in my mind I began to connect him to Olivia and her battle for life.
We called him Razz and with time on my hands, he became a 'project'. I was determined to gain his trust, so each time I put food out for him I would stand near his saucer, speaking constantly (almost in a Whisper!), encouraging him to come so that he would get used to the sound of my voice and associate it with a meal. First of all he would rush in, hoover up all the food and rush off again in seconds, but very slowly he got used to me being there and began to relax. I had the strongest feeling that if he let me stroke him everything would be OK and when, after weeks and weeks of patient persuasion, he finally let me touch his back, it was like an electric charge. I can't explain it. His body language transformed completely and as he relaxed he looked up at me with love in his eyes, and began rubbing his body around my legs. From that moment on we became almost inseparable. He was still too frightened to come into the house but would wait near the kitchen door, trotting out from his hiding place to join me as I walked over to the studio, where he would sit contentedly for hours watching me as I got on with my work. It was like having a cat-dog. He was healthy, happy and a bundle of love.
Meanwhile, despite everything she had endured, Olivia was at home and making fantastic progress. The trauma she suffered as a newly born baby has left its mark on her but she has overcome her physical limitations through sheer will and determination, helped by the care and love of her big sisters, Marnie and Alana. It is a wonderful miracle.
My own prognosis was also really good and my cancer was now completely under control. I knew that I would have to take medication for the rest of my life and the side effects were still occasionally debilitating and depressing but I was alive and my vitality had returned. My early diagnosis had been absolutely vital and I would urge any male reader over fifty to have a routine PSA check. If you take anything from this book, take that. A blood test is really no big deal but it could literally save your life the way it saved mine. It's quick, almost painless and you don't even have to give an armful!
By the summer of 2009 my visits to the clinic had been reduced from once a month to once every three months and the August test results were the best yet. 'Carry on doing what you're doing', I was told, 'and we'll still be having this conversation in twenty years' time.' It was fantastic news and the following Saturday Aninha Capaldi joined us as we celebrated by visiting Fairport's Cropredy Convention to spend a day in the warm sunshine, listening to the music. It's a safe and welcoming world within a world, almost a throw-back to the hippy festivals I used to go to in the 1960s and I love soaking in the gentle atmosphere there, sipping one of the many real ales available at the beer tent, the focal point of the entire operation!
The lovely vibe at Cropredy reminded me of my favourite festival experience ever – the glorious annual four-day celebration of Bluegrass music known as MerleFest, staged in the dramatic setting of the forested foothills of the Blue Ridge Mountains in North Carolina, one of the most picturesque and beautiful places I have ever visited. I was there in 2002 with Dave Shannon and Sue Welch to record live music and interviews for _Bob Harris Country_ and to shine a light on an event that is relatively unknown to British audiences – and I am so glad we made the journey. It turned out to be the definitive outdoor music experience, with no less than fourteen stages scattered across the grounds of the local Wilkes Community College, offering a staggering range of roots music, jam sessions and workshops.
The festival was founded in 1988 to honour local legend Merle Watson, who had been killed in a farming accident three years earlier. What began as an informal gathering of home-grown musicians playing on the back of a flat-bed truck to a small gathering of about three hundred people, has grown organically through the years to become one of America's largest music events and a major fundraiser for the entire area, attracting more than 80,000 fans and pumping more than $9,000,000 into the local economy. Not that the infrastructure is exactly set up to accommodate this huge influx of people. There is only one major hotel within a fifty-mile radius, booked at least a year in advance. Other than that, the options are to pitch a tent in one of the many popup campsites or stay, like we did, at a local motel. It was rough-and-ready accommodation but the owner was friendly and obliging when we drew up outside, coming out to greet us carrying a large glass jar full of what looked to me like Calpol, the medicine for children. Wilksboro had been notorious in the past as the 'Moonshine Capital of America', a major distribution point for the sale of illicit whisky throughout the South and this homemade brew was particularly potent. He smiled as he offered us a taste and I could see that there were two peaches floating in the thick, pink liquid. 'Eat them peaches,' he told us, 'and you'll get as drunk as hail!'
The festival had a family atmosphere I found hugely attractive, with all the artists encouraged to mingle with the audience and watch the other acts as they played and with a bill that featured Gillian Welch and David Rawlings, multi-Grammy nominated Bluegrass superstar Sam Bush and the majestic Patty Loveless, the whole experience was an absolute joy. I spent a lot of my time there with Chris Thile, mandolin player with the wonderful Nickel Creek, who provided me with a moment of pure festival magic. As we sat in front of the main stage waiting for the Yonder Mountain String Band to begin their set, a little girl began strumming an out-of-tune guitar just behind us. Chris asked her to pass him the instrument while he tuned it for her, her family looking on amazed. He had his mandolin with him and as we sat there on the grass he began to teach her some basic chords and rhythms. Soon, we were all joining in, her whole family singing, clapping their hands and laughing in the warm sunshine on that lovely April afternoon. It was as spontaneous as it was beautiful.
To my mind, Cropredy is the closest UK equivalent of MerleFest and it is always great to see so many of our friends there. We often meet up with Danny Thompson, who stays with his family in the vast camp site just behind the backstage compound. He is an encyclopaedia of knowledge and I love talking to him about music, reminiscing about the late Alexis Korner or discussing the work he's done with John Martyn and many other great musicians across a broad range of styles. 'It was a musical conversation with John,' he told writer Martin Chilton in a recent interview, 'taking in all strands. I've done a lot of what you might call more commercial music – with Kate Bush, Rod Stewart and the like – and I don't play any different than when I'm down Ronnie Scott's or in a folk club. It's all free form. Someone like Kate is just a fantastic singer and a lovely lady, too, and it's as interesting working with her as with Tubby Hayes.'
As we stood chatting, Richard Thompson and Yusuf Islam joined us just as Ralph McTell went onto the stage to play a brilliant set to the bank of 20,000 people chilling on the grass in the evening sunshine. Life felt good.
Later that evening, Trudie and I talked to organizer Gareth Williams and Stevie Horton and Andy Farquarson from Iconic Media about ways of getting Cropredy across to an even wider audience. I'd established a great working relationship with Sky Arts and had been curator and presenter of programmes on the channel for the previous two years, beginning with a _Bob Harris Night_ takeover in 2007 and a concert series called _Centre Stage_ the following year, broadcast every weekday evening at nine. It was great fun being at the centre of this vibrant new television channel and I particularly enjoyed working with producer Dan Bougourd, whom I'd met through Celia Quantrill, now a close friend and confidant of Cynthia Lennon. Dan and I worked together on a number of arts shows made at the Serpentine Gallery in Hyde Park and a programme made in tribute to Frank Zappa, filmed at an exhibition and concert held at the Roundhouse to mark what would have been his 70th birthday in 2010. I'd just signed a contract to present a series of _Songbook_ programmes with Kelly Jones, KT Tunstall and Diane Warren, so the time seemed right to talk to the channel about the idea of them broadcasting WBBC-produced coverage of the festival the following year. Trudie and I were excited as we discussed the possibilities during the car ride home.
We all had a late start the following morning. The weather was beautiful and I was doing my daily workout on the lawn in the sunshine when Trudie set off to our local shop to buy the ingredients needed for a slap-up Sunday lunch. A few moments later she was running back into the house, screaming that one of our cats had been killed. She thought it was Colby but when I ran to the gate with Miles, Dylan and Flo we discovered it was Razz. He'd been run over and was lying at the side of the road. I was devastated. He'd been my constant companion through my cancer recovery and I was so grateful to him. I couldn't believe he was dead. If he'd run into the road a split second earlier or later the vehicle would have missed him. Miles gently picked him up and we put him into a cardboard box and buried him under the apple tree outside my studio. I still miss him very much and to this day I believe he was sent as some kind of angel to see Olivia and me through the worst times of our fight to get well, and when his job was done he left us.
I felt so sad about Razz but there was little time to dwell on all of this because, as always, we were so busy. I was leaving for Nashville for the Americana Music Awards three weeks later and in the meantime had a WBBC documentary to make, another Colin Hall-inspired programme called _The Songs The Beatles Gave Away_ , featuring an interview with Sir George Martin, which we recorded the following Monday.
If you count 'The Best Things In Life Are Free' by Johnny Gentle, to which John contributed the middle eight in 1960, there are 27 numbers written by either John, Paul or George and that were covered by other artists during the lifetime of the band but never recorded by The Beatles themselves. Running in chronological order from 1960–1970 they are:
1. 'The Best Things In Life Are Free' Johnny Gentle
2. 'I'll Be On My Way' Billy J. Kramer with The Dakotas
3. 'Bad To Me' Billy J. Kramer with The Dakotas
4. 'Tip Of My Tongue' Tommy Quickly
5. 'Hello Little Girl' The Fourmost
6. 'Love Of The Loved' Cilla Black
7. 'I'll Keep You Satisfied' Billy J Kramer with The Dakotas
8. 'I'm In Love' The Fourmost
9. 'A World Without Love' Peter & Gordon
10. 'One And One Is Two' The Strangers with Mike Shannon
11. 'Nobody I Know' Peter & Gordon
12. 'Like Dreamers Do' Applejacks
13. 'From A Window' Billy J. Kramer
14. 'It's For You' Cilla Black
15. 'I Don't Want To See You Again' Peter & Gordon
16. 'That Means A Lot' P. J. Proby
17. 'Woman' Peter & Gordon
18. 'Love In The Open Air' George Martin & His Orchestra
19. 'Cat Call' Chris Barber
20. 'Step Inside Love' Cilla Black
21. 'Thingumybob' John Foster & Sons Ltd. Black Dyke Mills Band
22. 'Goodbye' Mary Hopkin
23. 'Sour Milk Sea' Jackie Lomax
24. 'Badge' Cream
25. 'Penina' Carlos Mendes
26. 'Come and Get It' Badfinger
27. 'Penina' Jotta Herre
It's a fascinating list and much of the material we used in the programme was priceless. It was an absolute delight to talk to Mary Hopkin and reminisce with her about the childhood days we spent together in Pontardawe in South Wales. We never dreamed then that Mary would become the first artist signed to the Beatles' record label, replacing them at the top of the charts with her cover of a Russian gypsy song called 'Those Were The Days' and taking over at No. 1 from 'Hey Jude', the first-ever release on the Apple label in 1968. Paul had seen her on a hugely popular talent show called _Opportunity Knocks_ , the _X-Factor_ of its day, and Apple sent a telegram inviting her to London to sing for Paul.
'I sang a couple of folk songs and a Donovan song,' she told me. 'Then Paul took my mum and me out to lunch to the Angus Steak House, I think it was ... the one in Oxford Street.' She laughed as she remembered. 'I was in awe of Paul. I'd been a Beatles fan since I was 13, but I didn't feel nervous meeting him.'
As their friendship grew, Paul began to take this sweet, shy girl under his wing and after the huge success of 'Those Were The Days' sent a new song for her to consider.
'I felt privileged that he wrote a song especially for me,' she said. 'Apparently he wrote it in a delightful little Italian restaurant that everyone from Apple used to go to. He was there with some friends one evening, they'd had a meal, he had his guitar with him and came up with this idea. He thought "Mary needs a song", so he wrote "Goodbye" in a matter of minutes, which only he can do – write a great song in minutes.' The single was released as the follow-up to 'Those Were The Days' and took Mary to No. 2 in the UK charts in April 1969.
Billy J. Kramer was not so lucky. Although he'd been the first artist to take a Beatles' song to No.1 with 'Bad To Me' in 1963, he'd then rejected one of the most successful titles in music history. 'I remember going to the ABC in Blackpool and asking Paul for a song. He played me "Yesterday" before anyone else had heard it. I thought it was too mamby-pamby and told him I wanted a rocker. I turned it down.' Ouch!
Olivia Harrison gave us a quite brilliant acoustic demo of 'Sour Milk Sea' for the show that Jackie Lomax had recorded with Olivia's late husband, George, in Esher in 1968 and we discovered some great BBC archive footage of George explaining the reason for the title of the last hit single in the chart career of Cream, the band that featured one of the best guitarists in the world ever – George's best friend Eric Clapton.
'He was round at my house and we'd worked out the chords to the song,' George explained. 'I was writing down the lyrics on a piece of paper and Eric was sitting opposite me. When it got to the middle part I wrote down "bridge". Well, I think we'd had a few bottles of wine or something and he looked at the paper upside down and just broke up laughing thinking the word was "badge", so he called the song "Badge".'
Alcohol also played an hilarious part in the creation of the accidental hit 'Penina', as Paul told us with some mirth. 'I was on holiday in Portugal and ended up one night at a bar in a golf club. There was a lounge band playing and, not being in full possession of my senses, I got on the drum kit, grabbed a mike and started making up this awful drunken song about the name of the golf club. Someone must've recorded it and passed it on to Carlos Mendes because the next thing I knew it was released as a single!' Unbelievably, there was also a cover version by Dutch band Jotta Herre, released just as The Beatles were breaking up.
Making radio documentaries is a wonderfully enjoyable thing to do. We record all the interviews, usually on location, before taking them back to my studio to be reviewed and edited. I always have a good idea of where I want a programme to go but I like to have enough flexibility to let the interviews guide my direction, so as we assemble the material we look for the most fluent way to tell the story. I source the tracks we need and I script and record the links before the mixing begins. Weaving the threads of a documentary together is my favourite part, a truly creative process; cross-fading the music into a flow and finding exactly the right space for each voice is an instinctive art and I could not have anyone more dedicated by my side than my editor, Neil Myners. We are perfectionists.
_The Songs The Beatles Gave Away_ went out on BBC Radio 2 on 28th November 2009 and was the fifth major documentary to be broadcast on the network made by WBBC. Trudie and I founded the company in 2005 on the advice of the then Radio 2 controller Lesley Douglas and our first commission was a two-part series called _The Maple Leaf Revolution_ , reflecting the history and development of Canadian music, the making of which took Neil Myners and me to another of my favourite cities – Toronto.
ELEVEN
Still Whispering ...
IT WAS HOT AND SUNNY WHEN NEIL MYNERS AND I ARRIVED IN Toronto and we spent a fabulously enjoyable week in this vibrant, multi-cultural metropolis, mostly in the company of Larry LeBlanc, one of the world's greatest music authorities. Described as 'the glue that holds the Canadian music industry together', Larry has been at the centre of the scene in Toronto for almost fifty years, a penetrative, fearless and sometimes bombastic writer and broadcaster with whom I have forged a deep friendship.
He took us to visit Sunrise Records and the Sam The Record Man store in downtown Toronto, where I was recognized by Jann Haust, producer of the recent _Bob Dylan Basement Tapes_ box set. He introduced me to Suze Rotolo, Dylan's former girlfriend, who is seen walking with him in the photograph on the cover of _The Freewheelin' Bob Dylan_ album, released in 1963. Larry also provided me with my first (and so far only) experience of live, major league baseball, when the Toronto Blue Jays took on the mighty Boston Red Sox at the Rogers Centre stadium, where Alannah Myles sang the National Anthem before the game began. It turned out to be an unexpectedly hilarious evening, as Larry reminded me in a recent email.
I was trying to explain baseball to you, then something I've never seen happen, happened. A player hit a home run but twisted his ankle around second base and couldn't make it home to score. They had to send a cart out to pick him up. I have never ever witnessed that before and I'm not sure you can find another incident of it in baseball.
It was also wonderful to reacquaint with Larry's wife, Anya, who I'd known in the early 70s when she was running the Acme Plug Company, handling press and publicity for Marc Bolan and David Bowie. She moved to Toronto a few years later, heading the promotion team at Cachet Records and working with the great Johnny Cash. Now, she runs her own radio promotion and publicity agency and is, like her husband, a perceptive communicator and commentator on the ways of the music industry.
Larry is currently the senior writer of the weekly American entertainment trade database CelebrityAccess, overseeing the authoritative online profile series 'In The Hot Seat', but at the time of our visit he was Bureau Chief for _Billboard_ magazine in Toronto and through his many contacts had organized several days of artist interviews for us, recorded at the headquarters of FACTOR, the Foundation to Assist Canadian Talent on Record.
FACTOR is a non-profit-making organization dedicated to providing assistance towards the growth and development of the music industry in Canada, an enviable initiative that offers programmes of financial support to recording artists, songwriters, managers, labels, publishers, event producers and distributors. It is a wide mandate but the existence of FACTOR and other funding bodies is a constructive force, contributing to the tangible and very attractive sense of community that exists within the culture of the music scene in Canada.
I've always had a strong affinity with Canadian artists, who provided me with two significant firsts – 'Diana' by Paul Anka (born in Ottawa) was the first single I ever bought and 'Cinnamon Girl' by Neil Young (born in Toronto) was the opening track on my debut show on Radio 1 in 1970 – and through the years I have always heavily featured Canadian music on all my programmes, from The Band, Leonard Cohen, Bruce Cockburn and Joni Mitchell in the 1970s through Rush, Bryan Adams and Sarah McLachlan to the new generation of artists who were also represented in the 'Maple Leaf Revolution'.
I was particularly keen to talk to singer/songwriter Kathleen Edwards, described at the time as 'the new "it girl" of alt country', whom I'd discovered through her debut album _Failer_ in 2003, a recording made possible through government funding. 'I would not be here talking to you today had it not been for that support,' she told us.
Bright and self-assured, Kathleen is also fiercely patriotic. 'I think people assume that whatever's happening in Canada is just happening off the back of America,' she observed, 'but there is a great sense of community here. There's no New York or LA of Canada, with that whole "I'm gonna make it big" mindset, we don't have that whole pop thing. We have long winters, so we play a lot of music inside and we all face similar challenges, so there's a lot of bonding.'
We also talked to Kathleen's guitarist, Jim Bryson, who had contributed so much to the raw, edgy sound that made _Failer_ so striking, and we recorded interviews with Sam Roberts, members of Nickelback, Ron Sexsmith, Gordon Lightfoot, Steven Page from Barenaked Ladies, the Sadies, Michael Timmins from the Cowboy Junkies, the Trews, Sue Foley, producer Colin Linden, Luke Doucet, Todd Clark from emerging band Pilot Speed and Heather Ostertag, the head of FACTOR. It was a packed schedule but all the artists brought a refreshing atmosphere of thoughtful creativity into our makeshift studio and the success of the programmes paved the way for the Radio 2 coverage of the annual North By Northeast Music Festival in Toronto the following year, during which I bumped into Centro-matic, one of my favourite bands. They are from Denton, Texas (home of the also magnificent Midlake) and enthusiastically told me about a fan who had turned up at one of their local gigs a few days earlier, having been introduced to them on my weekend show on Radio 2.
'He only lives about five miles away from where we are in Denton but had never even heard of us before,' they told me. 'He discovered our music listening to your radio show, broadcasting from six thousand miles away!' The power of the internet!
I was particularly pleased to spend time in Toronto with Jim Cuddy, founding member of the multi-Juno award-winning band Blue Rodeo. They are one of the best-loved acts in Canada and had just released their tenth album _Are You Ready_ , featuring the track 'Finger Lakes', which was on repeat on my CD player at the time. Like every artist through that whole week, Jim arrived for his interview spot on time, accompanied Susan de Cartier, with whom I struck up an immediate friendship.
Susan is the founder of the artist management company Starfish Entertainment, working with Blue Rodeo, Oh Susanna, the Sadies and the Skydiggers. Sharply intelligent, witty and generous, she has a calm, gentle authority and is much loved by the artists whose careers she helps to shape. She stayed on in the studio to chat after my interview with Jim and we resolved to meet again at the Americana Music Awards in Nashville, where she introduced me to her best friend Shauna de Cartier (no relation), boss of Six Shooter Records in Toronto, whose motto 'life is too short to listen to shitty music', brilliantly encapsulates her strength of spirit, integrity and wonderful sense of humour.
Running an independent record label is a massive challenge, particularly when the music industry is going through an intensive period of rapid change – and, at times, Shauna has had to put her whole life on the line to keep the label afloat – but she believes in her artists, has never compromised her ideals in the name of commercialism and her determination has paid off. Six Shooter has established a peerless reputation with a vibrant catalogue of artists that regularly feed into the playlists on my radio shows including Mary Gauthier, Melissa McClelland, Trampled By Turtles, Amelia Curran and the mournful but beautiful Deep Dark Woods.
Three years ago, with Susan's help, Shauna launched the Interstellar Rodeo, a major three-day summer festival in Edmonton, the success of which has seen her branch out into a new event, staged in Winnipeg for the first time in August 2015 and she richly deserves all the good things that happen. Shauna, Sue and I are very tuned into one another and I am very proud of our friendship. I deeply respect these two amazing women.
My close relationship with Canada has led to me appearing on the prestigious _Q_ radio show on CBC in Toronto (with the Great Lake Swimmers) and at the East Coast Music Awards where, in March 2010, I was the keynote speaker in a two-hour Q&A session with Larry LeBlanc. The event was held in Sydney, Nova Scotia, a small, windswept town situated at the northern tip of Canada on the east coast of Cape Breton Island, which, despite the onset of spring, was without doubt the coldest place I had ever been to. With a temperature of –10 and the island engulfed by an ice storm, it was almost impossible to walk between venues without getting almost sliced in two by the ferocity of the freezing temperature, so most of the musicians and delegates gathered in one of the town's two main hotels for the daily showcases, which began at breakfast time and lasted until the early hours. After the showcases the bands transferred to the rooms and corridors throughout the hotel for the impromptu jam sessions and thrashes that provided a twenty-four hour cacophony of continuous sound, sleep not an option.
Some of the performances were absolutely stunning. It was where I discovered the beautiful and sensitive music of Catherine MacLellan, who is the daughter of Gene MacLellan, writer of the song 'Snowbird', made famous by Ann Murray. I also saw sets from singer/songwriter Dave Gunning, local Indie band The Novaks and a brilliant concert from the sharp and clever Joel Plaskett, who was the big winner at the awards show with six trophies across all categories. The level of musicianship was phenomenal and I felt fortunate to be among such a warm and closely knit musical community.
I have been blessed to meet some truly great characters and personalities through the years but few people have touched our lives as profoundly as the late and much loved Ali Booker.
Trudie met Ali first in 1996, at the playgroup at St James C of E Primary School in Hanney, where our son Miles, her son Douglas and daughter Joanne were pupils. I was introduced to Ali shortly afterwards and as we all stood chatting in the playground it was clear that this wonderful woman was very special. Modest, warm and wickedly funny, she was also one of the brightest people I've ever met. She had a rare and instinctive ability to make everyone around her feel good, fabulous attributes to take into broadcasting. She told us she'd just begun news-reading duties at BBC Radio Oxford, having moved from the West Country, where she'd been working at BBC Radio Devon.
'Oh no, not another DJ!' laughed Trudie.
Within a few months Ali took over the Radio Oxford morning show and I was in awe of her ability to make it all sound so easy. She was sincere, touching and funny and the listeners absolutely loved her. The show was an immediate success and soon she transferred to the early afternoon slot that became her own. I was always on the end of a line if Ali ever needed an emergency interviewee and I loved the times we spent on air together.
In 2002, Ali was diagnosed with breast cancer and had to undergo a double mastectomy and an intensive course of chemotherapy, beginning a fight with cancer that lasted for the rest of her life. She dealt with her illness with astonishing bravery and humour, once joking to a doctor who needed to examine her that she never took her clothes off for anything less than a couple of really good meals and a bunch of flowers! By now she'd met her future husband Andrew (to whom she proposed live on air during the _Children In Need_ broadcast in 2005) and he and Trudie formed a strong alliance of support and friendship.
We were thrilled when Ali joined us at WBBC for a while, co-producing a documentary with Trudie for Radio 2 entitled _Who Breaks A Butterfly On A Wheel_ , which told the story of The Rolling Stones' traumatic summer of 1967. The programme looked at the events and effects of a highly publicized drugs bust at a party held at Redlands, the Sussex home of the Stones' guitarist Keith Richards, and took its name from the headline of a leading article by William Rees-Mogg, the then-editor of _The Times_ , which questioned the outcome of the resulting court case. As a result of the bust, organized by the _News of the World_ , Keith Richards was given a twelve-month prison sentence and Mick Jagger was given a jail term of three months, sentences which, Rees-Mogg argued, were more severe than 'any purely anonymous young men' would have received. The culture of pop celebrity had begun.
By the time we began work on the documentary, Ali's cancer had spread to her lungs, forcing her to retire from the BBC. Although increasingly encumbered by the equipment she needed to help her breathing, she 'got bored with sitting around at home and waiting to die' and, following her work on the documentary, had resumed her broadcasting career as a newsreader at Oxfordshire station Jack FM, sounding as bright and articulate as she always did. Before she died she made a series of audio diaries documenting her life with cancer, recordings so moving that they deservedly won her two major radio awards in 2010, a Sony Silver in 'The Best Community Programming' category and a Radio Academy Gold Arqiva, the biggest award in Commercial Radio. The diaries were also featured in _The Sunday Times_ and there was even a tribute to Ali in the House of Commons, when Wantage MP Ed Vaisey made a speech in her honour. 'The way she fought cancer,' he said, 'made it seem like she was indestructible.'
At no point during her long ordeal did I once hear Ali complain. Throughout, she was a caring and constant source of inspiration to me in my own battle with cancer and a true and loyal friend to Trudie, who describes her as being her soul sister. Just before she passed away, Ali wrote, 'I have a wobbly moment, silently in my head while no one else notices, and I turn into a frightened little girl who's changed her mind about having terminal cancer now, and would like someone to make it stop.'
Ali Booker died at the Sobell House Hospice in Oxford on 1st July 2010 and we all miss her very much.
Our friendship with Ali and my own health issues had underlined to Trudie and I the importance of the work done by Cancer Research UK, and had focused our minds on our Sound and Vision event, held at Abbey Road a few months before Ali passed away, the planning of which had begun almost two years earlier in Nashville, in the week of the 2008 Americana Music Awards, where Robert Plant and Alison Krauss were the big winners with their Album of the Year Award for _Raising Sand_. I'd spoken to Beth Nielsen Chapman about the possibility of her being involved in the event and we'd been trying to meet up for the entire week to talk about it but I'd been so busy covering the Awards for Radio 2 and compiling material for _Bob Harris Country_ that I'd had no free time.
I'd recorded sessions and interviews with country star Suzy Bogguss, John Peel protégé Laura Cantrell, the frightening and intense James McMurtry and Kentucky musician and writer Chris Knight, who had just released his sixth album _Heart Of Stone_ produced by Dan Baird of the Georgia Satellites. Chris also works regularly with Ray Kennedy, one of my favourite producers, and is a major talent. Honest, gritty and uncompromising, he should be right up there with Bruce Springsteen and John Mellencamp.
My work schedule had literally filled every minute of the week but finally, on Friday, a window appeared. Beth phoned me to say she was free that afternoon and would collect me at 3 o'clock at the end of my final session and take me for a beer at Bobby's Idle Hour, an old-style drinking house near Music Row, about a block away from the Audio Productions studio.
'The only problem is that I haven't got a lot of time,' she warned. 'I've got a really important meeting with my agent Paul Fenn and whatever happens, I must be away by four.'
A few moments after we finished our conversation my phone rang again. This time it was Robert Plant's manager, Nicola Powell, who had called with a lovely invitation. She and Robert were free that night and would like to take me out to dinner. She was thrilled when I mentioned Beth. 'Robert will love to meet her, he's a big fan.' She told me that Robert had a photoshoot organized for five o'clock at Buddy Miller's house and suggested that we meet up at 4.30 outside a vintage bookshop on the high street at Hillsborough Village, just outside of Nashville, not far from Buddy's house. I agreed, of course, and immediately phoned Beth.
'You're going to have to cancel your meeting,' I told her.
Beth was astonished. 'I can't possibly do that, Bob! It's much too important. We're talking about a UK tour!'
'Beth,' I explained. 'We're having dinner tonight with Robert Plant.'
There was a short pause.
'My dinner is _so_ cancelled!' she said.
Beth and I arrived at the bookseller's a few minutes early and sat for a while outside a nearby coffee shop, chatting and chilling in the sunshine as we watched the people go by. Nicola soon joined us and as we sat sipping our coffees we saw Robert pull into the parking lot opposite. He waved as he got out of his car but instead of crossing the street to join us, he turned left and strode up the sidewalk, disappearing into the crowd. We sat waiting for him for ages, to the point where Nicola was getting worried, so I set off to find him, soon discovering him in a little instrument shop about two blocks away. He'd noticed a harmonica in the window as he'd driven past and was playing it as I walked in, lost in the moment.
As we headed back down the high street together, I noticed a couple of boys in baseball caps, probably in their early twenties, skateboarding on the pavement opposite, weaving their way in and out of the pedestrians. At the moment I looked across one of them glanced up and spotted Robert and in a split second an extraordinary thing happened. The boys seemed to lose all sense of reason and control as they sprinted, skateboards flying everywhere, straight into the busy traffic towards us, self-preservation forgotten in the rush. One of them lost his flip-flops in the middle of the road, cars and pick-ups swerved to avoid them, people were pointing and shouting and suddenly it was like being in a slow-motion movie. By the time we joined Beth and Nicola at the coffee shop, we were swamped by a crowd of excited people, all desperate for an autograph or a picture with Robert, exhilarating as well as being a little scary.
'Well,' said Beth to Robert later. 'If you must stride round Nashville looking like a lion, what do you expect?!'
We eventually made it to Buddy Miller's house for the photo session before heading out to dinner at a sweet, quiet Italian restaurant in the centre of downtown Nashville, where we surrendered to a magical evening of good food, red wine, conversation, memories and laughter. I told Robert of the passion I was feeling for the Sound and Vision project and he immediately promised to get involved but only on one condition – that he was given the freedom to create a performance that was absolutely unique. Boy, did he keep his promise.
As we began to formulate the line-up, I called David Gray, who also generously offered his time. I was probably the first person to play him on UK radio and I still have fond memories of the broadcasts we did together when I was at GLR in London in the 90s. David is a big Manchester United fan and one of his first sessions for my show exactly coincided with a Wednesday night Champions League game. For about the only time ever, I'd left the monitor on in the studio and however much we tried we could not help being drawn to the screen. David was about halfway through his first live number when United scored their first goal. Session forgotten, we were both out of our seats, fists pumping, high fiving in the middle of the studio.
His commitment to Sound and Vision 2010 was really appreciated and the event turned out to be an absolute triumph. Newton Faulkner began the evening with a characteristically funky and rhythmic performance and after David had played, Beth performed a truly beautiful set accompanied by multi-instrumentalist Maartin Allcock. But the focus of the night was Robert. I knew he'd put everything he had into the rehearsals for this moment and when I introduced him to the room, the sense of anticipation was awesome. He and hurdy gurdy player Nigel Eaton were surrounded onstage by the seventy-strong London Oriana Choir, performing a set comprising of songs by one of Robert's great heroes – Scott Walker. It was quite simply one of the best musical moments I have ever witnessed, Robert bending and blending his vocals with the voices of the choir, Beth adding her heavenly harmonies. It was beautiful. Not only that, when the auction proceeds and online bids had been totalled up, we had all raised more than £260,000 for Cancer Research UK.
It was hard to imagine that we would ever top that figure but the following year we did. Essential to the success of the 2011 event was the incredible energy of our auctioneer Al Murray who, in his role as pub landlord, was down from the stage, bantering with the crowd and whipping up bids for the money-can't-buy auction items on display. Nicky Campbell and Jon Briggs helped me with the compering duties, Giles Martin addressed the audience on behalf of his father Sir George, and the music was once again amazing, with perfectly pitched sets from Eve Selis, the perennial Newton Faulkner, Liam Bailey and The Feeling, all setting the tone for Tom Jones to take to the stage to deliver a performance of incredible power and professionalism. Between us all, we raised £340,000 at Abbey Road that night, taking the Sound and Vision total to well over £1,000,000. Finally, to complete what was a truly special moment, Robin Gibb appeared onstage from nowhere to present me with a UK Heritage Award. It was an amazing honour but it wasn't the first time that Robin had brought unexpected joy into my life.
Early in 2003, I'd received a call from Phil Hughes, my executive producer at Radio 2. He told me that the network was making a Bee Gees documentary and that he would like me to record a career interview with Robin at Broadcasting House for the programme.
'It's a major project and we'll be filming it too,' he told me.
The idea of having cameras in the studio didn't surprise me. The BBC was in the early stages of developing its digital service BBCi (later rebranded as The Red Button) and had begun to look for ways of visualizing as much of its radio output as possible, an on-going process that now sees multi-camera shoots for _In Concert_ programmes, interactive coverage of the _The Chart Show_ and _Sounds Of The 80s_ and Go Pro-like technology attached to every microphone in every on-air studio at Radio 1.
I was thrilled by the whole idea of the Bee Gees project but amazed by how uncharacteristically flat and disinterested Trudie appeared to be when I told her the news. This was not like her at all and to be truthful, she hadn't seemed herself for several weeks. She seemed to be drifting away from me, becoming distant and disconnected, constantly disappearing to various parts of the house with her mobile phone or standing out by the washing line in the garden (her favourite private spot), to hold furtive conversations I knew she didn't want me to hear. She seemed reluctant to look me in the eye and was dismissive when I asked her if there was anything wrong.
We had been invited to a Radio Academy Awards event at the Shaw Theatre a few days later and I was hoping this would give her a chance to relax and enjoy herself but we hardly spoke as we drove to London as my worries about our relationship intensified. Thankfully, she seemed to unwind as we took our places in the auditorium to settle in for what became an amazing evening.
I was particularly pleased to see Robin Gibb arrive on stage to collect the Scott Piering Award on behalf of the Bee Gees, receiving a standing ovation as he made an impassioned speech extolling the virtues of UK musicianship.
'I'd like to see British music dominate the American charts again,' he said. 'It's very important British songwriters are supported here at home. We can do it. We've got great writers and talent and we've got originality and innovation in this industry.'
I knew that Steve Harley was going to be one of the main presenters and I had with me a valuable white label copy of the first Cockney Rebel album, which I planned to give him later to auction for charity. Steve is a tireless campaigner, raising money for the Mines Advisory Group and working with several schools for disabled children, projects that in recent years have seen him lead two fundraising treks, one in Cambodia and another across the formidable Death Valley in Eastern California. Soon, he took the microphone to hand over the PRS award for Outstanding Contribution to Music Radio, and as he started his introduction I was speculating as to whom the recipient might be.
'This fellow has the right attitude to rock music,' he began. 'He started his career on Radio 1 on _Sounds Of The 70s_ in August 1970 ...'
I lost the rest of his speech in the excitement of the moment, engulfed by the realization that the recipient was me! It was a total surprise and as Steve recited a roll call of my career highlights, I turned to look at Trudie.
'Did you know about this?' I asked. As she smiled, I began to feel a whole lot better.
'Of course you did!'
Suddenly, the last few weeks of Trudie's covert conversations and whispered phone calls made some sense and I was as much relieved that this was the explanation for her distant behaviour as I was thrilled to get the award itself. I strode onto the stage clutching my Cockney Rebel white label.
'eBay!' said Steve as I handed him the record.
I felt so happy. I'd been acknowledged by the Radio Academy, everything was good with Trudie and we were celebrating a wonderful evening surrounded by people who were special in our lives. Amanda Beel had booked a table at the Four Lanterns in Cleveland Street, one of her favourite restaurants, where we were joined by Radio 2 controller Lesley Douglas and my producer Phil Swern.
Amanda has been part of our world since my early days back on Radio 1 in the 1990s, when she was part of the promotion team for Sony Records, delivering music to my desk from such as Shawn Colvin, Mary Chapin Carpenter, Bruce Springsteen and Jeff Buckley. She was a colleague of the late and much missed Stuart Emery before founding her own company, All About Promotions, in 2003, representing a roster of artists which currently includes Paul Carrack, Fiona Bevan, Red Sky July, Midge Ure and Callaghan. I love spending time with Amanda. She knows the music industry like the back of her hand and truly cares for the artists she represents. Like Susan de Cartier and Shauna de Cartier in Toronto, she is a dedicated and phenomenal woman surviving and thriving in the male-dominated world of the music business.
The atmosphere on the journey home with Trudie was in total contrast to the silent drive to London earlier that evening and, as we spilled laughing into our house, we were met with a hug from our beautiful friend Marie, who had been babysitting for us. We'd first met Marie, her husband Mark and their boys Toby and Ben in the playground at Hanney School, soon after meeting Ali Booker and our families have been close right through the nearly twenty years that have passed since then.
'How was your evening?' she asked me.
'It was fabulous,' I replied. 'Steve Harley did this whole career retrospective before he gave me the award. It felt a bit like being on _This Is Your Life_!'
She nearly spat out the champagne she was drinking. There was a silent pause before a now flustered Marie unexpectedly explained that Mark and the boys were waiting for her and she really had to get home. Seconds later she'd grabbed her coat, was out of the door and gone.
Trudie and I stayed up celebrating until the early hours and I was so pleased things between us would now settle back to normal. Alarmingly, however, the reassurance did not last long. The furtive phone calls picked up again and I knew she was concealing something. The more it became clear that the Radio Academy evening wasn't the answer after all, the more suspicious I became of these furtive, half-heard conversations.
'Oh, it was the parent/teacher association again,' she would unconvincingly explain.
All these worries were rumbling around in my head as I got to Broadcasting House a few days later for the big recording with Robin Gibb. My friend Roy Webber had called to tell me that he'd be in London that day, so I'd invited him to be there too. I'd built myself up for this moment and when Roy and I arrived to discover a full film crew in the studio and a control room packed with people I realized Phil Hughes was right; this interview really was a very big deal. Robin arrived shortly after and I complimented him on his brilliant Radio Academy speech as he and I took our places under the studio lights. Soon we were reminiscing about the amazing and memorable day we'd spent together twenty-five years earlier at the Criteria Sound Studios in Miami, where he and his brothers Barry and Maurice had given me a private and exclusive live performance of their much anticipated new album _Spirits Having Flown_ , months before its release, still one of the absolute highlights of my musical life.
As he always was, Robin was sensitive, enthusiastic and engaging and we were well into a really enjoyable interview when I heard someone push open the big soundproofed door behind me. There is a strict protocol preventing anyone entering a studio when a recording is taking place and it was with some irritation that I turned to see who was interrupting us. The first thing I saw, as I squinted through the haze of the television lights, was a big red book, held by a smiling Michael Aspel who was walking across the studio towards us. I leaned back, expecting him to address Robin but instead, he turned to me.
'Pardon the invasion into your studio, Bob. Robin Gibb, you know that you're not just here to be interviewed by Whispering Bob, because you know I'm here to say ... Bob Harris, This Is Your Life!'
I absolutely could not believe it. I'd been a fan of the programme for many years, going right back to the Eamonn Andrews days of the 50s and 60s but I never dreamed I would ever be the subject. This was a huge honour and I was thrilled and excited, but how naive had I been? All those weeks of suspicion, Trudie's secret phone calls, Marie's reaction, Radio 2's deception and (now I began to think about it) a thousand other little signs ... I looked at Roy and Robin, who burst out laughing as they stepped forward to give me a big hug. More and more people spilled into the studio, slapping my back and shaking me by the hand, Phil Hughes tapping his nose with a knowing look.
Soon, the programme production team were pulling Roy and I away and escorting us out of Broadcasting House and into a waiting Mercedes. Roy explained that he was my designated chaperone and, of course, he was not going to breathe a word of what was about to happen. Months of planning had gone into all of this.
We were whooshed across London to the Thames Television studios, to be met by a welcoming committee that quickly escorted us to the far side of the main building and into a stylish but windowless dressing room.
'We're going to have to lock you in here,' they told us. 'We don't want you to see any of the guests and ruin the surprise.'
If this was going to be our prison for the next few hours it was fine; bright, airy and beautifully furnished, with a table groaning under the weight of sandwiches, crisps, fruit, biscuits, a large and beautiful bunch of flowers and enough alcohol for Roy and I to have got seriously drunk. With several hours to kill, there was a brief temptation to pour ourselves a couple of large glasses of red but I wanted to keep a completely clear head. I didn't want anything to get in the way of total recall.
Shortly before the show, Roy was called to take part in the final rehearsals, leaving me to choose what I was going to wear from the many different options Trudie had left in the wardrobe for me. My favourite jacket was there, a new pair of shoes ... she really had thought of everything.
Alone for the first time that day, I paced around the dressing room in a state of suspended animation, thinking back over my life, trying to anticipate what the evening might bring, until finally came the expected knock on the door and I was led through what seemed like an endless maze of corridors to join Michael Aspel, who was waiting for me in a quiet corner of the studio, out of sight of the audience and guests, ready for the start of the show. My heart was beating so hard I could actually hear it and the feeling of nervous excitement was almost overwhelming as we stood there waiting for our cue, but Michael was calm and kind.
'You don't have to worry about anything,' he smiled. 'It's all been rehearsed and I'll take care of everything. This is your night, Bob, all you have to do is enjoy it!'
I really appreciated the reassurance and his words were ringing in my ears as the familiar theme music struck up and we stepped through the famous doors together.
Trudie gave me a knowing smile as she came forward to hug me and, as the applause died down and we took our seats, I looked around at all the familiar faces. My Mum and Dad were at the front, sitting next to my wonderful and stout-hearted Aunt Margaret, who is still alive today, a proud 100 years old. Sue, Jackie and Val were all there too, introduced by Michael Aspel who noted, 'To prove this is a rock'n'roll show and, I think, for the first time in _This Is Your Life_ history, we have a record three ex-wives on the set with us!'
Much was made of the size of my family, as my children Miri, Emily, Charlie, Ben, Jamie (wearing a 'Who's the Daddy?' T-shirt), Miles, Dylan and Flo all burst through the doors, alongside my granddaughters Marnie and Alana and, the youngest of all, little Niamh, her face covered in chocolate, carried by her father John. Trudie's entire family was also in attendance and there were friends and colleagues spanning every era of my life.
My great friend Jeff Griffin, producer of my first-ever radio programmes, talked about the Radio 1 audition he supervised in 1970.
'I liked the sound of his voice,' he said. 'It was a bit unusual, and he was knowledgeable, so we set up a pilot programme a few weeks later and he did that very well. I then put that forward to the audition panel for DJs and he passed that. But of course the trouble was, having told him that he passed it, he then wouldn't stop phoning me to find out when he could get a proper job!'
It's true. I pestered Jeff unmercifully throughout the entire ten months I had to wait before I finally made it on air, Jeff booking me to sit in for my great hero John Peel on _Sounds Of The 70s_ in August 1970.
My former Radio 1 controller Johnny Beerling spoke warmly of my return to Radio 1 in 1989, when I took over on Sunday evening from the late Roger Scott – huge boots to fill. There was much laughter as _Whistle Test_ producer Mike Appleton told the story of the two of us hobbling off a plane together at JFK airport for the first of our many working trips to New York. Just before leaving Los Angeles earlier in the day, I'd bought a pair of tight brown leather boots which, for comfort's sake, I'd taken off for the duration of the flight, a bad decision as it turned out. As we came into JFK and I tried to put them back on again, I realized that the left boot just wouldn't fit. No matter how hard I tried, I couldn't lever my foot back into it. I had managed to force the other one on but it hurt like hell and was so tight I couldn't get it off again. I know that feet tend to swell when you're flying but I must've bought boots that were at least one size too small. I'm not sure how I got them on in the first place. It was comical. Mike had a bad back and was limping with a walking stick while I was clumping up and down on one Cuban heel, holding my other boot like hand luggage as we disembarked from the plane. It was not, as Mike observed, the coolest way for these two supposed rock'n'roll dudes to arrive in New York!
As the evening went on fellow broadcasters Tony Blackburn, Paul Gambaccini, Dave Lee Travis, Nicky Campbell and John Inverdale all appeared onstage to tell stories of times we spent sharing microphones or at cricket grounds together. Roy Webber reminisced about our recording days with his band Wally at Morgan Studios in London, and George Nicholson described the notorious night at the Speakeasy with the Sex Pistols.
Suzi Quatro told the story of a visit we'd made to her house. 'I invited Bob and Trudie over for Christmas a couple of years ago and we had a nice cheese and wine evening planned. Nice evening. Not only did they arrive about two hours late, but this man arrived in leather trousers. Now, how dare you come to my house wearing leather?' she chuckled.
The warmth of the evening was incredible and it was particularly lovely to hear Judie Tzuke talk with great affection about our long-time friendship. She and I were first introduced by Marc Bolan's wife June at the time that Jude signed to Elton John's Rocket record label in 1977 and we've been close friends ever since. I had no idea, of course, that Elton himself was about to appear onscreen.
As I later learned, the planning of all of this had begun months earlier, when Trudie was putting together a promotion campaign for the release of a forthcoming _Bob Harris Presents ..._ compilation. She had asked Amanda Beel for advice as to how to promote the album and, in addition to helping line up some radio and press interviews, Amanda suggested calling her friend Deborah Cohen, one of the _This Is Your Life_ producers, who loved the idea of me being a subject for the show. Plans were now underway and gradually, over the next few weeks, Trudie, Amanda, Deborah and her co-producer Sue Green began building the guest list. The first person they approached was Robert Plant, with whom Amanda was working on the extraordinary 'Festival In The Desert' project. He immediately agreed to take part, filming this wonderful message.
'Hi Bob!' he said. 'You are an institution,' [or, as Trudie says, I should be in one!]. Your presentations and interviews on the _Whistle Test_ were imaginative, informative and focused, while dealing with so many egos and so many loonies back then. I know because I was one of them! Your consistency down the years is second to none and you, like me, have an insatiable appetite for hunting out beautiful, challenging music way to the left side of that High Street fluff. You bring fresh, alternative music to me, and many like me. So thanks to you, and I'll see you soon.'
As always, Robert's words were thoughtful and considered and I was particularly struck by the word 'consistency', a huge compliment.
David Gray came on screen to thank me for the support I gave him at the beginning of his career (United games notwithstanding!) and Nanci Griffith appeared on film from Nashville, clutching a Ken Bruce-branded radio and suggesting to the BBC that I should have one too! It was an amusing and lovely moment and I was thrilled to be able to reciprocate when I presented Nanci with a Lifetime Achievement Award at the Radio 2 Folk Awards in February 2010.
But perhaps the most touching contribution to the programme came from Elton John who, at the time, was in the middle of a huge 'Face To Face' American tour with Billy Joel. Through a combination of luck and detective work, Trudie had tracked down Elton's manager Frank Presland on a Friday afternoon at the tour hotel in Philadelphia (obviously!) and was delighted to find him friendly and receptive.
'We'll put it to Elton and we'll see what he says,' Frank said. 'Call us again on Monday.'
It was just the reaction Trudie had been hoping for and Deborah Cohen was impressed that contact had been made. 'Tell them we can organize it all,' she told Trudie. 'We'll get a crew out there to film him and provide them with everything they'll need.'
It was a big call for the programme and when Trudie finally got through again on the Monday afternoon, she couldn't wait to explain what the _This Is Your Life_ team were offering.
'There's no need for you to do anything,' Frank Presland told her.
'Oh. Does this mean he doesn't want to do it?' asked Trudie.
'No, it means he's already done it. He really wanted to do it for Bob, so he pulled out all the stops, hired a crew over the weekend and filmed it here. I just need to know where to send it!'
The production team were blown away by how generous and accommodating Elton and Frank had been; unprecedented, they said. The tape arrived a few days later and it was a very moving moment when, towards the end of the show, Elton's film came up on the studio monitor screens.
'Why I wanted to do this was to say thank you to you for all the wonderful support you gave me early on in your career. People should never forget who helped them when they first started out and you were such a big supporter of mine. I did many an _Old Grey Whistle Test_. We had a lot of fun in those days. It's still a lot of fun but it's not as nice as it used to be, but you know, there are not people like you around anymore. So I hope you have the best evening. Thank you so much for supporting me early in my career. It meant so much to me and it still does. Thank you.'
It was such a beautiful message. I'm actually feeling quite emotional about it as I type this, but there was still one more fantastic surprise to come on that magical evening, as Michael Aspel explained.
'Finally, Bob, let's rewind to your youth. As a teenager you tuned the family radiogram in to your favourite shows and on Saturday nights the big date for you and millions of other kids was _Pick Of The Pops_. You were such a fan that for your fifteenth birthday your mother wrote in to the show for a dedication.'
As if the evening had not been amazing enough, now here was David Jacobs, my original inspiration. 'I was delighted to give you your first-ever mention on the radio, Bob,' David said as he joined us on the stage, my mother waving from the audience. It was such a huge moment for her and she just could not contain herself in the excitement of it all. As the applause died down, her voice came ringing across the studio like a bell. 'Oh, David, I'm your greatest fan!'
'The Harris's are a bit of an item in your life,' commented Michael Aspel.
'Well, really I know his mother better than I know Bob,' David replied. 'You see, she's been one of my regular correspondents. But it wasn't until you joined Radio 2, Bob, that I realized that your mother was _my_ Mrs Harris. I'm sure she is very proud of you, as should all of your family be, because your dedication to music and radio is absolutely incredible. So for heaven's sake just keep on doing what you do so well and always let us have "Whispering Bob" with us.'
After he had read out that first dedication all those years ago my Mum had written to David again, thanking him for mentioning me and complimenting him on the music he was playing on his show. Like the gentleman he was, David wrote back, exchanging thoughts about music and the radio, which my Mum loved so much, and that triggered a correspondence between the two of them that had spanned more than four decades. Yet, despite the longevity of their relationship, this was the first time they had actually met. It was a dream come true and my most vivid memory from that glorious evening is of my Mum looking as happy and animated as she had for years, sitting with my Dad, chatting with David at the after-show party. And what a party it was, lasting way into the early hours, a gathering of all the people who were special in my life. I felt so happy that my parents were able to be there to share the evening with me.
It was particularly poignant for the fact that my Dad's health was beginning to fade. It was, as it turned out, the last major event he was able attend. He died a few months later, at the Queen Elizabeth Hospital in King's Lynn. I was with him when he passed away. It's so hard to think about it now, remembering those final hours as I sat watching him at his bedside, listening to his shallow breathing getting weaker and weaker as life slowly drained from him. We had become very close in his later years and I knew he was very proud of me. I was certainly proud of him. He was a lovely man; contented, relaxed, intelligent and philosophical, with a calm strength and a generosity of spirit I deeply admired.
His death was a devastating blow to my Mum, from which she never really recovered. She had built her whole life around him and she found it almost impossible to cope on her own. She felt so isolated, lonely and unhappy it was heart breaking. I regularly drove from Oxfordshire to Norfolk to see her, staying at the sweet Le Strange Arms Hotel just outside of Hunstanton, overlooking the sand banks on the North Norfolk coastline. I got to know the hotel and the staff there very well and the visits provided me with welcome breaks, suspending me from my always busy schedule. It was lovely to walk with my Mum along the windswept promenade at Hunstanton or sit in her garden and talk but I never felt I was able to be with her for long enough and I hated leaving her alone.
Eventually she, Trudie and I decided it would be best if she came to live with us, and the children were all in agreement, particularly my daughter Emily, who was always very close to her Nana and Papa. The move was a massive upheaval but for a while Mum rallied, enjoying the hustle and bustle of our busy lives. I was installing my new studio at the bottom of the garden with help from my former wife Sue's partner Dixie and Mum would occasionally wander down to see us, sometimes bringing us egg and bacon sandwiches and cups of tea to keep us going as we laid the carpet, put up the shelving and sorted my CD and vinyl collection back into alphabetical order. She even briefly joined Miles, Dylan and Flo one afternoon for a game of tennis on the lawn. But the Indian summer didn't last. She was missing my Dad terribly and, as her health deteriorated, I knew it was the worst possible sign when she stopped listening to her beloved radio. A short time later she was admitted to the John Radcliffe Hospital in Oxford, where she died on 27th September 2005. She was buried next to my Dad in the Northampton cemetery on 11th October, two days before what would have been her ninetieth birthday.
My links with my home town have lessened since my parents passed away and I rarely go back there now (apart from very occasional visits to Sixfields Stadium to watch the Northampton Town football team navigate the ups and downs of Division 2), so imagine my delight and amazement when, out of the blue, I was invited to receive an Honorary Fellowship by the University of Northampton, joining 2,000 students for a week of graduations in the summer of 2007. Trudie, Miles, Dylan and Flo all came with me and the ceremony was also attended by flamboyant fashion designer Zandra Rhodes, who collected an honorary doctorate wearing an outfit of vibrant pink and orange, a glorious distraction as I began my acceptance speech.
'This is somewhat ironic,' I observed as I addressed the students. 'It's a very happy surprise to be here considering I left school under a large cloud. I was spotted by one of my teachers drinking half a lager shandy at a pub during the summer holidays and was sent to see the head teacher. I was seventeen and a half and it felt like I was being unfairly treated. I just handed in my books and stormed out, without really thinking what I was going to do after that. Today is testament to the support I got from my parents, who really backed me when I walked out of school with virtually no qualifications.'
I received the Fellowship in the middle of a run of accolades that has become both mind-blowing and humbling. In 2002 I was awarded a Gold Badge by the British Academy of Composers and Songwriters. Twelve months later, the UK Radio Academy acknowledged my 'outstanding contribution to British radio'. In 2004 I was voted 'International Broadcaster of the Year' by the Country Music Association in Nashville, a massive honour that was repeated when I was presented with the award again in 2013 by the wonderful Little Big Town in the full glare of the television crews lining the red carpet at the CMA Awards. I also received the 'Wesley Rose International Media Achievement Award' from the Country Music Association in 2012, following Taylor Swift onto the podium. I was inducted into the British Country Music Association Hall of Fame in 2012, the Radio Academy Hall of Fame in 2009 and our WBBC documentaries _The Day John Met Paul_ and _The Sandy Denny Story_ both won Silver at the Sony's, in 2008 and 2009 respectively.
Then, in 2014, I received perhaps the greatest accolade of all when I was chosen to join Kirsty Young as a castaway on _Desert Island Discs_ on BBC Radio 4, a major ambition realized. I gave great consideration to my musical choices, eventually settling on a list of tracks that resonated most closely with important moments in my life. The list is as follows.
1. Mark Germino 'Rex Bob Lowenstein' from the album _Caught In The Act Of Being Ourselves_ , a brilliant song about a free-form DJ, first played on the radio by the late Roger Scott
2. Robert Plant & Alison Krauss 'Gone Gone Gone' from the _Raising Sand_ album, so important in my life
3. Paul Anka 'Diana', my first-time buy
4. Love 'Alone Again' from the _Forever Changes_ album, given to me by John Peel
5. Neil Young 'Cinnamon Girl', the first track I played on the radio, on _Sounds Of The 70s_ in August 1970
6. Dick Stratton 'Music City USA', the first song on the soundtrack of the film _Bob Harris: My Nashville_
7. Kacey Musgraves 'Merry Go Round' from her album _Same Trailer, Different Park_ , chosen to represent the refreshing surge of young energy that has burst into the country music scene
8. Ben E. King 'Stand By Me', my all-time favourite record
For my book choice, I managed to persuade Kirsty and the production team to allow me to take a massive file of cricket statistics onto the island with me and for my luxury item I chose a greenhouse, in which to indulge my passion for gardening, a neglected pursuit I wish I had more time for.
I am a notorious workaholic but I am fortunate in that I absolutely love what I do. My professional world is a very creative place and I am extremely motivated to establish WBBC as a self-sufficient and successful production house able to provide a secure future for Trudie and my family, an ambition that has become a priority and a driving force in my life. Running a family business is not always easy, particularly in the ultra-competitive environments of radio and television. Our schedule is sometimes relentlessly demanding and holidays are a rarity but we are an amazingly productive team, willing to push ourselves to the limit. We set very high standards but I am a great believer that you get back what you put in. 'And in the end, the love you take, is equal to the love you make' as the Beatles put it.
Nevertheless, there are times when even I am amazed at our ability to sustain our high-intensity schedule, as a quick glance at my diary for early 2011 demonstrates; an awesome mix of work and pleasure.
My first studio session of the year was on the 4th January at Western House, pre-recording my Radio 2 weekend show, containing a beautiful, mellow session with a band called The Low Anthem from Providence, Rhode Island, whose album _Oh My God, Charlie Darwin_ was one of my favourites at the time. It was the first of fourteen shows I built and broadcast that month. The following morning I was back in London to do some location filming with Sky Arts before returning to Western House to pre-record the first of a new series of programmes for the three-hour Friday night slot I had just inherited from Mark Lamarr. Starting a new series is always a special moment and I'd spent hours crafting a diverse playlist of UK artists with tracks ranging from vintage Pink Floyd and Deep Purple to Kate Rusby, Lonnie Donegan, Cherry Ghost, Paul Weller and The Damned. Once the show was in the can, I walked to Wardour Street where I ended my working day in a voiceover studio recording an ad for Virgin Atlantic.
A couple of days later, Miles and I drove to Manchester to link up with our friend Clive Tyldsley, who was commentating on the United versus Liverpool third round FA Cup tie for ITV. We'd been really looking forward to this and made sure we arrived in time to sit in on a fascinating early morning production meeting before Clive took us backstage at Old Trafford to meet some of the United legends, a very cool experience indeed. It was an absolute pleasure to be introduced to the warm and sincere Paddy Crerand, with whom Miles chatted for maybe fifteen or twenty minutes, and we were briefly in the same room as Sir Bobby Charlton, my all-time sporting hero. We even stood in the tunnel watching Sir Alex Ferguson and Kenny Dalglish give their pre-match television interviews although, judging by the looks he kept giving us, Sir Alex was not best pleased to see us in this hallowed place, particularly when the Liverpool assistant manager Sammy Lee came over to tell me how much he enjoyed my country show!
Then, a few moments later, we were walking in the footsteps of giants, as Clive took us out of the tunnel into the stadium and onto the edge of the pitch, a tingle running down my spine as we took in the awesome pre-match atmosphere generating from the stands all around us. With the fans of both teams in full voice, the decibel level was higher than a rock concert and we were happy to take some sharp, shouted banter as we walked past the managers' dug-out in front of the crowd before climbing the flight of steps that leads into the heart of the South Stand and right up into the roof of the building, where we negotiated our way across the narrow, precarious little walkway that drops down into the television gantry situated high above the 76,000 crowd. The view up there was absolutely incredible, taking in the panorama of the entire ground and beyond, a privileged vantage point from which to watch United's hard fought 1–0 win secured by a third minute Ryan Giggs penalty.
I love watching football and I still enjoy the simple pleasure of kicking a ball around in the garden with Miles and Dylan but cricket is also a major sporting passion and I was honoured to take part in the glorious _Voices Of Summer_ programme on BBC Radio 5-Live, celebrating the work of some of the greatest broadcasters of all time, and to be invited to Lords as a lunchtime 'View From The Boundary' guest on _Test Match Special_ on the first Saturday of the Test series against the West Indies in May 2012, joining the peerless Jonathan Agnew in the commentary box. Miles was with me there too, and it was a pleasure to introduce him to David Gower, whom I'd not seen for many years. We also bumped into Mark Butcher who, as well as being an outstanding international batsman, is also a fine musician. He's even played a session on my radio show.
Everyone was keen for Miles and I to stay on and join them for lunch – and I couldn't imagine anything more enjoyable – but we had to leave immediately after the broadcast. As coincidence would have it, our friends Sara and Saul were getting married later that same afternoon, way on the other side of Oxfordshire, and Miles was due to be filming the ceremony. We legged it out of Lords, jumped into the car, hurtled down the M40 and somehow made it to the church on time, just as the first guests were beginning to arrive. One or two of the old boys in the congregation were amazed to see me there. 'Didn't we just hear you on _Test Match Special_?' they asked, incredulously.
We'd also had to leave Old Trafford in a hurry too, after our day with Clive Tyldsley. Trudie and I had two important meetings in London early the following morning, the first of which was at Cancer Research UK. Tom Jones had just confirmed his appearance at the 2011 Sound and Vision evening and additionally we were planning a huge Race Day event at Silverstone, working with the endearing and charismatic Stephanie Moore, widow of the former England football captain Bobby Moore. Bobby died of bowel cancer in 1993 since when Stephanie has tirelessly dedicated her life to the Bobby Moore fund, a charity that has raised nearly £19m and funded more than fifty research programmes into the disease that killed her husband at the age of just fifty-one. I have huge respect for Stephanie and the important work she does. She is a truly special person and it was an honour to become part of her team.
Our second meeting of the day was with my producer Mark Simpson and editor Neil Myners to discuss what proved to be one of the most enjoyable projects I have ever been involved with. Entitled _OGWT 40_ , it was a major WBBC series for Radio 2 marking the fortieth anniversary of the _Old Grey Whistle Test_.
The first _Whistle Test_ was broadcast on BBC 2 in September 1971, running from then until 1987, and we were working to recreate the ethos of the programme across sixteen one-hour shows, each one celebrating a year of _Whistle Test_ history. The organization was a massive undertaking and Trudie and Miles were joined in our WBBC office by the indispensible Steph Punfield and Miles's beautiful girlfriend Catherine Snell, who worked with us through most of the twelve months it took to put it all together.
To help us capture the original atmosphere, we commandeered the famous Maida Vale Studio 3, the BBC equivalent of Abbey Road, where we hosted more than 120 artists and bands. The tone was set at the beginning of the first programme with original archive appearances by David Bowie, who performed 'Five Years', 'Keep On Keeping On' by Curtis Mayfield, introduced by the first _Whistle Test_ presenter Richard Williams and 'Under My Wheels' by Alice Cooper, with whom I reminisced about that first-ever UK television performance and our subsequent meeting in LA in 1974, where he took Mike Appleton and I into the weird and rather wonderful world of a private room at the Rainbow Bar and Grill, a notorious late-night hang out on Sunset Strip. Alice was in full make up and garb, the place was absolutely rocking and I couldn't believe the crazy madness of the West Hollywood night-lifers who surrounded him.
'It was the lair of the vampires,' he recalled. 'Bernie Taupin was there that night, Keith Moon also, probably Harry Nilsson. It was a last-man-standing drinking club and you did very well, Bob, as I recall! The first thing I learned when I got to LA was how to drink all night, because when you were out with Jim Morrison and those guys you had to know how to drink! But then Jim, Janis Joplin, Hendrix ... all the guys we used to hang out with were all dying aged 27 years old. What it said to me was if you're going to have an image as strong as Alice Cooper you can't live that image off-stage, because that's what killed all those guys.'
The first _OGWT 40_ also featured a beautiful new acoustic session with Yusuf Islam, who played 'Trouble' and 'Road Singer' and a heartwarming interview with Elton John. 'It was the show to do,' he told me. 'The forerunner of _Later ... With Jools Holland_ and having looked again at the DVDs it was archive, historic footage. It was part of a pantheon of great television music shows – _Oh Boy!_ , _Ready Steady Go!_ , _The Old Grey Whistle Test_ ... those programmes stand the test of time.'
It was exciting to record new interviews and 'in the round' sessions for the series with a cast-list of artists and friends that reads like a who's who of rock'n'roll history. In addition to Elton and Alice, Brian May, Peter Frampton, Emmylou Harris, Jackson Browne (who brought Dawes and Jonathan Wilson to Maida Vale with him), Roger Daltrey, Rab Noakes, Jim Kerr, Mark Knopfler, Kiki Dee, Joan Armatrading, John Ottway, John Hiatt, Thomas Dolby, Robin Hitchcock, Andy Partridge, Rod Argent, Russ Ballard, Colin Blunstone, Thijs van Leer, Iain Matthews, Andy Roberts, Steve Harley, Greg Allman, Greg Lake, Steve Hackett, Deborah Harry, Chris Difford and Glenn Tilbrook, Gordin Giltrap, Ralph McTell, Randy Newman, Billy Bragg, Hazel O'Connor, Wilko Johnson, Thin Lizzy, Bob Geldof, Judie Tzuke, Ian Anderson, Chuck Prophet, Jack Bruce, Fish, Loudon Wainwright, Gang of Four, Clare Grogan, Roger Hodgson, Paul Rodgers, Paul Young, Nick Lowe, Midge Ure, Chris Rea, Dave Stewart, Robert Plant and many more joined us for this amazing reunion, as did _Whistle Test_ producer Mike Appleton, film-maker Ian Emes and almost all of the presenters of the original show – Mark Ellen, David Hepworth, Andy Kershaw, Richard Skinner and Ro Newton. It's a sensational list. Eric Brace recorded a new version of the theme tune 'Stone Fox Chase' for us in East Nashville with his band Last Train Home, featuring the original harmonica player Charlie McCoy, and the announcement of the series even made the front page of _The Times_.
I will always be grateful to _Whistle Test_ for catapulting me into the centre of the music world I love and creating a legacy I am proud of to this day. Of the many incredible experiences it brought into my life, perhaps the most exciting of all was the three days Mike Appleton and I spent with John Lennon in New York in 1975 to record an interview for a _Whistle Test_ special, for which he filmed exclusive versions of 'Slippin' and Slidin'' and my all-time favourite song 'Stand By Me'. John saw the moment as a way of sending a postcard from America to his estranged young son, who he knew would be watching back home in the UK, so it was an honour to close the series with an emotional full-circle performance of the song by Julian Lennon, particularly poignant for the fact that his mother Cynthia was in the studio with us too, her husband Noel Charles at her side. It was a wonderful and fitting moment, in keeping with the four months we spent at Maida Vale making the _OGWT 40_ series, one of the most fulfilling and creative times of my career. But 2011 wasn't over yet.
On 7th May, the postman delivered his usual sack full of post – a handful of letters wrapped with an elastic band among the mountain of parcels and packages that had arrived from across the Globe. I receive approximately 200 CDs every week from artists, managers and record labels and it is a source of stress to me that I receive far more than I have ever got time to listen to. I know that whoever has sent me this latest recording is counting on me to listen to it and maybe play it on the radio, but there are only twenty-four hours in a day and it is literally impossible to keep up with the expectation.
Selecting the music to listen to from the never-ending supply is a tried and trusted mix of intuition and subjectivity. Not surprisingly, I prioritise releases from artists I like and I also look at the sleeve credits to check the names of producers and backing musicians. I'll take more notice of a record sent by someone whose opinion I value and there are certain labels I always trust, like Bella Union, Six Shooter, New West, Nonesuch, Sugar Hill and Rounder. I know that anything on Big Machine is going to have huge mainstream potential, and so it goes on. I'll follow links to downloads too, but that's a much less personal route. It is impossible to replicate the 'feel' of a physical copy and sometimes I just get a vibe from the look of an album, something about the design or the atmosphere that compels me to put it in the machine.
It was with all this in mind that I was sorting through the parcels when one of the small batch of letters caught my eye. It looked official and interesting and when I opened it I could scarcely believe what I was reading.
'The Prime Minister has asked me to inform you, in strict confidence, that he has in mind, on the occasion of the forthcoming list of New Year's honours to submit your name to the Queen with a recommendation that Her Majesty may be graciously pleased to approve that you be appointed an Officer of the Order of the British Empire for services to music broadcasting.'
An OBE! I had to go through the letter again to make sure I hadn't misread it and to say I was flabbergasted is an understatement. To this day I'm still in the process of trying to connect it with me, because I still have a feeling of not being worthy in any way. It is a massive honour, one that came to me as a result of doing something I love.
I replied immediately accepting the invitation and soon received a follow-up letter from St James's Palace which began: 'I am commanded to inform you that an Investiture will be held at Windsor Castle on Thursday 20th October 2011 at which your attendance is requested. You may bring three guests to watch the ceremony.'
Obviously, one of the guests would be Trudie but who else should I take? However much I wished to have all my children there with me, only two could attend. It was a tough call and I didn't want anyone to feel disappointed, so I knew that the selection process had to be totally democratic. After much thought, I decided on an FA Cup-style draw. I typed out the names Miri, Emily, Charlie, Ben, Jamie, Miles, Dylan and Flo in capital letters onto separate squares of identically sized paper, each of which I folded several times out of sight of anyone before putting them all into the large gold Himalayan cowbell (a present from our friend Sara), which I keep in the studio. Before Neil Myners and I began our _OGWT 40_ editing that day, I filmed him as he closed his eyes, reached into the bell and pulled out two pieces of paper, which we carefully unfolded on to the mixing desk. The first name we saw was CHARLIE, the second name was MILES.
The lead up to the investiture was busy and exciting. Four days earlier I'd been in Nashville, where I'd become only the third ever recipient (following Nanci Griffith and Lyle Lovett) of the prestigious Trailblazer Award at the Americana Music Awards, presented to me by Emmylou Harris, an honour that was almost as important to me as my OBE, as I explained in my acceptance speech. 'To get such an award on the stage of the Ryman Auditorium, the Mother Church of Country Music, is amazing,' I said. 'Being accepted and acknowledged by the music community I love and respect so much is very special.'
I'd got back from Nashville absolutely buzzing and had pitched straight back into work. Neil and I were still editing _OGWT 40_ programmes the day before the investiture and while we were in the studio, Trudie and our WBBC film director Luke Jeans were attending an important appointment at Sky Arts, a meeting that confirmed our coverage of the Cropredy Festival for the channel the following summer. So I was in celebratory mood, if slightly jet-lagged, when Charlie arrived later that afternoon to prepare for the big day that followed. She was pregnant and I was so happy to see her looking glowing and radiant.
The next morning we were all up at the crack of dawn to get ourselves ready before the arrival of the chauffer-driven car Trudie had organized for the day. The journey along the M4 was mercifully smooth, so we arrived at Windsor in good time to take in the sights. The setting was absolutely perfect: the sky was a cloudless blue and the castle looked imposing and magnificent in the shimmering autumn sunshine as we walked up the long drive and into the quadrangle in front of the state apartments, seeing the Queen's private residence to the right. On entering the castle, I was separated from Trudie, Charlie and Miles, who were taken to the grand Waterloo Chamber to await the ceremony while I was led to a vestry deep in the heart of the building, joining the other recipients to await instructions. The Central Chancery of the Orders of Knighthood, which is a branch of the Lord Chamberlain's Office, is responsible for the staging of each investiture, and the organization was an awesome timetable of pomp and precision.
After a detailed briefing, all the recipients were escorted through the ornate and opulent state rooms to the door of the Waterloo Chamber, where we formed an orderly queue to wait for the ceremony to begin at eleven o'clock sharp. Her Royal Highness the Princess Royal was conducting the Investiture and I felt a huge surge of excitement as the orchestra from the Household Division struck up the National Anthem, announcing her arrival in the Chamber. I'd been playing this scene through in my head for months and the sense of anticipation was almost overwhelming as I stepped forward into the Chamber, trying to remember all the instructions I'd been given. As I approached the dias on which the Princess Royal was standing I stopped and bowed my head then stepped forward and stood in front of her while she put the medal into the clip that had been pinned to my lapel. I'd been told not to speak until spoken to, but as I stepped back she looked at me and smiled.
'I thought you were in Nashville,' she said. I was stunned that she even knew.
'I was, Your Royal Highness,' I replied. 'I've just got back!'
'You were there for the Americana Awards,' she added. I looked at her quizzically, thinking that maybe she'd been briefed. 'I listen to your country show,' she explained.
This was amazing news and as I relaxed, we talked for a few moments about the Tennessee stud, of all things. Then she stood back, shook my hand and the moment was over. I left the Waterloo Chamber almost bursting with pride, imagining what my parents would have thought if they could have been there to witness one of the most beautiful and important events of my life.
I couldn't wait to be reunited with Trudie, Charlie and Miles for the photographs and interviews that followed. Charlie told me afterwards that as Princess Anne presented me with my insignia, she had felt her baby kick for the first time – an amazing moment. I didn't want us to break away from this incredible experience but finally we made our way back to the car and headed to our favourite restaurant, The White Hart in Fyfield in Oxfordshire, where I was engulfed by my family and my friends for one of the best parties ever.
Trudie is probably the greatest party organizer in the world. Three years after the spectacular _This Is Your Life_ evening, she had staged a sixtieth birthday bash for me at Lains Barn in the Oxfordshire countryside, a party so enjoyable that it is still talked about and fondly remembered by everyone who attended. Larry LeBlanc had flown over from Toronto, Alan Messer had made the journey from Nashville, as had Tia McGraff and her husband Tommy Parham. Johnnie Beerling was there, sharing memories with Jeff Griffin, his wife Rita and radio producer Kevin Howlett. Miles had his best mates Ben Granville and Doug Booker with him, Dylan and Flo pretended to play giant inflatable guitars, messing around with their friends Toby and Ben Barnard on the lawn outside the venue, while The Storys played an acoustic set for the people who were arriving. The music set the tone perfectly and it was wonderful to see everyone looking so happy.
The party was 60s themed and, with two major exceptions, everybody had come dressed in appropriately fab gear. Trudie and Marie were wearing identical Mary Quant mini-dresses, Trudie sporting a black wig, Marie a blonde wig. There were Mods, Beatle outfits, outrageous leopard skin prints and, notably, a 1966 full England World Cup-winning football strip, worn by Neil Myners. Janice Long, Sally Boazman, PR boss Gabby Green and my friend and agent June Ford-Crush were flower girls, Steve Wright and Johnnie Walker looked like something from the _Sgt. Pepper_ album sleeve, songwriter Gary Osborne was wearing a flamboyant silver velvet jacket and Trudie's long-time friend Fiona Ronaldson wore crushed velvet. I went in character as an old hippie. Wearing beads, bells, purple loons and a stupid long blond wig, I looked like a cross between Jerry Garcia and Willie Nelson.
Trudie had commissioned a specially designed cake with an exact reproduction of my original 78 rpm version of 'Diana' by Paul Anka etched into icing that was beginning to melt from the heat of the lighted candles. As I bent over to blow them out, a flame touched my wig, setting it on fire, briefly threatening disaster before a handily placed soda siphon came to my rescue. It was a ridiculous moment, captured brilliantly in a stand-up speech by comic and broadcaster Mark Lamarr: 'I always thought the 60s was the promiscuous decade, the era of free love,' he joked. 'But how any of you ever got a fuck looking like that is beyond me!'
Mark was one of the two people not in fancy dress that night. The other was Robert Plant. It was my fault, I'm afraid. I'd forgotten to tell them! Not that it mattered, as Robert got up onstage to add the sound of his stunning electric guitar playing and vocals to the beat of the massive blues jam session that rounded off the evening with a lineup that additionally featured Steve Balsamo and The Storys, Belfast singer songwriter Brian Houston, Thea Gilmore and her husband Nigel Stonier, the great Bernie Marsden from Whitesnake and Martyn Joseph, who had bought me a beautiful SXI Panther cricket bat as a sixtieth birthday present.
Martyn and I have known each other now for almost a quarter of a century and our friendship continues to grow. He is a true artist, recognized worldwide as a performer of rare talent, courage, warmth and dedication, and I was very proud when he invited me to become Patron of his Let Yourself Trust, a project-based initiative that he founded with his charismatic partner Justine. The Trust is a labour of love, designed to pull together the threads of his humanitarian endeavours, work for which he was given an Amnesty International award in 2002. Martyn is a genuine force for good in the world and the warmth between us somehow sums up my feelings as I come towards the end of writing this book. I have been massively fortunate that my work and my life have taken me to places that most could only dream of, yet, underpinning all of those experiences, has been the sharing of them with the people who made them so special.
Central to so much of what has happened over the past few years has been my country producer Al Booth, now Head of Specialist Music at Radio 2. We began to get to know each other at approximately the same time as the first edition of this book was published, when Dave Shannon took her to Nashville to work with us on the coverage of the CMA Awards in 2001, and she has been one of the most important people in my life ever since. She is strong, funny and incredibly perceptive and I would trust her with my life. She is part of the superb and professional team at Radio 2 that oversee my programmes and I am indebted to Bob Shennan, Mark Simpson, Mark Hagen and Janine Mayer-Smith for the fantastic support they give me and to Maria Byrne for adding to the soundtrack of our lives.
However, although my work is still very important to me, my family is my stability and it is impossible to adequately express the love I have for them.
My son Miles is now twenty-two and I am in awe of him. His drive and work ethic are second to none and he has a skill set I can only envy. We work together in my studio, producing the acoustic _Under The Apple Tree_ sessions we post on our website and YouTube channel, and Miles is cameraman, lighting engineer and sound mixer, creating the beautiful films he edits so skilfully. He has recently worked on videos with Mollie Marriott, Deborah Rose and Scott Matthews and is a go-to filmmaker for Cancer Research UK. He was also the editor of the much-praised _Back To Beth's_ house concert shown on BBC 4 in November 2014. Miles is still with his beautiful girlfriend, Catherine Snell, who we all adore. She has a warm and happy spirit and brings light and laughter into our lives.
Dylan's three-month stay in America and his exciting multi-country European adventure in 2014 have further fuelled his desire to see as much of the world as possible and he is currently saving for his next major project, an animal conservation trip to South Africa and Botswana in the summer. He is a people person, a knowledgeable and engaging conversationalist, and I love the chats we have together. His warm and sunny disposition is wonderful to behold. 'You have a gift,' Cynthia Lennon told him recently. 'Make sure you use it.' I know he will.
Flo loves her music and has been to more than twenty gigs and festivals in the past year, including The Radio 1 Big Weekend in Glasgow, One Direction at Wembley Stadium (she still hasn't met them yet!), Taylor Swift at O2, Paulo Nutini and Ed Sheeran in the Live Lounge and Justin Timberlake at the BBC Radio Theatre, where I introduced her to Sara Cox and Scott Mills. Flo and I have also forged a great friendship with Radio 1 DJ Greg James, a genuinely lovely person and one of the brightest and most naturally talented broadcasters I've heard for many years. Flo and I are very alike and we always seem to be in sync with one another, a lovely feeling.
Miri and her family are about to move to Brighton, where she will continue her nursing work. Her husband Graeme runs a garden landscaping company, which he plans to transport to East Sussex with them. Marnie is currently pondering the options of University, Alana is approaching her A level exams and Olivia is a bright, thriving, feisty seven-year-old, absolutely doted on by her proud dad.
Emily is the Harris organizer. She is the one everybody in the family calls upon because she is kind, sympathetic and caring. Like her mum, she devotes much of her life to looking after others and is a care worker at a special needs school in Camden. She lives in North London with her husband John and their three daughters Niamh who is now fourteen, Ysobel who is eleven and Eliza who is four.
Charlie followed me into the music industry and after two years at MTV was head hunted across into PR, working with Midas, Omnibus Press and Music Sales, looking after authors and organizing their promotion and publicity schedule, so she knows exactly where I am in my writing process right now. A few months after she came to my Investiture at Windsor Castle she gave birth to a beautiful little girl, the adorable Lola Mae, who is now three years old. So, I have seven grandchildren, all of them girls, and my eldest granddaughter, Marnie, is older than my youngest daughter, Flo, who is her auntie. It's a mind-boggling thought.
Ben also tried the music industry for a while, co-hosting a brilliantly eclectic cutting-edge radio show called _Beltdriven_ with Paul McCarthy for Radio Reverb in Brighton, before following his mother Valentina's footsteps and becoming a chef, founding a catering company called 'Bepino's'. Like his mother, Ben can also write and I have a feeling that one day he will make writing his passion. Meanwhile, Jamie is busy working with Miri's husband Graeme, applying his awesome physical strength and natural athleticism to the heavy demands of a landscape gardening business.
I have a close-knit family and Trudie is the foundation of everything, the rock upon which my whole life is built, and I am so fortunate she has chosen to spend her life with me. She is an incredible, dynamic force – a loving, loyal wife, mother, manager, company director ... it's a hell of a lot of relationships to keep together and sometimes I wonder how she does it all but my absolute certainty is that I love her more than words can say. When everything is good with Trudie, everything is good with the world.
The most important thing to me is that everyone is well. I am healthy too and I still maintain the fitness regime that helps me sustain the busy pace of my life. As I write, _Bob Harris Country_ has just been nominated in the 'Best Radio Show' category at the _Music Week_ Awards and I am just about to launch the digital radio service 'BBC Radio 2 Country', which runs for the four days of the spectacular 'Country 2 Country' Festival at the O2, where I will be multi-tasking. As well as hosting our WBBC _Under The Apple Tree_ sessions that will showcase Kimmie Rhodes, Ward Thomas and Katie Armiger, I will be compering on the main stage and joining my Radio 2 colleagues Patrick Kielty, Alex Lester and Jo Whiley to broadcast live backstage interviews and sessions with all the major stars, after which I join Eric Brace and his wife Mary Ann for a seven-day break in North Carolina, which I think I'm going to need!
My brush with cancer has taught me to live in the moment and despite the fact that I am seventy next year I still have the energy to put my heart and soul into everything I do. You can follow my daily life via Twitter, a social medium I have enthusiastically embraced @WhisperingBob and we also have a WBBC account @WBBCOfficial.
I am still driven by my work, am surrounded by people who care and I love the life I live. I am very lucky and blessed to be still whispering after all these years.
ACKNOWLEDGEMENTS
Heartfelt thanks to Louise Dixon and everyone at Michael O'Mara Books for their fantastic support and belief in me; to Cynthia Lennon, Eric Brace and Mary Ann Werner for allowing me the space to complete some of the writing; to the Nashville music community for the joy you bring; to Radio 2 for giving me the freedom to play the music I love; to my listeners for sharing it all with me; and to my family for being the bedrock of my life. I love you very much.
PICTURE CREDITS
All photographs courtesy of the author, except:
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Image here
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\- Alan Messer/REX
Image here
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\- Dezo Hoffmann/REX
Image here, Image here
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\- Alan Messer/REX
Image here
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\- Alan Messer/REX
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Image here, Image here, Image here, Image here
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\- Miles Myerscough-Harris
Image here
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\- Chris Ison / WPA Pool / Getty Images
INDEX
Unattributed subheadings refer to Bob Harris
4 x 4 Theatre Company, Wallingford ref1
9/11 ref1
Abbey Road Studios ref1, ref2, ref3, ref4, ref5
Agnew, Jonathan ref1
'Air Castle Of The South, The' ref1
Airforce Academy ref1
Al Fayed, Mohamed ref1, ref2, ref3, ref4, ref5
Aladdin, Las Vegas ref1
Aldridge, Alan ref1
'All My Words Were Taken Away' (John Golding) ref1
'All Right Now' (Free) ref1
Allan, Garry ref1
_Alright Guy_ (Garry Allan) ref1
America (band) ref1, ref2, ref3
_American Bandstand_ ref1
Americana Music Association (AMA) ref1, ref2, ref3, ref4, ref5
Amsterdam ref1
Andrews, Bernie ref1, ref2
Anger, Kenneth ref1
Anka, Paul ref1, ref2, ref3
Anthony, Dee ref1, ref2
Appel, Mike ref1, ref2
Apple records ref1
Appleton, Mike ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, ref10, ref11, ref12, ref13, ref14
Area Code 615 ref1
Argent ref1, ref2, ref3
_Ariel_ magazine ref1
Aspel, Michael ref1, ref2, ref3
Astor Park, Birmingham ref1
_At The Beeb_ (CDs) ref1
Atlantic Records ref1, ref2, ref3, ref4
Aubrey Small ref1
Audio Productions ref1, ref2
Augarde, Tony ref1
Austin, Texas ref1
Average White Band ref1, ref2
_Back To Beth's_ (WBBC) ref1, ref2, ref3
Baez, Joan ref1
Bailey, Andrew ref1
Baines, Sue ref1
Bakewell, Joan ref1
Band, The ref1, ref2
Band of Gypsys ref1
Bannister, Matthew ref1, ref2
Barber, Chris ref1
Bates, Simon ref1, ref2
'Battle of Evermore, The' (Sandy Denny and Robert Plant) ref1
BBC ref1, ref2 _see also_ Radio 1; Radio 2
Beach Boys, The ref1, ref2, ref3
_Beach Boys Story, The_ (Radio 1) ref1, ref2
Bearsville Picnic ref1
Beatles, The ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9
'Be-Bop-A-Lula' (Gene Vincent) ref1
Bee Gees, The ref1, ref2, ref3, ref4
Beel, Amanda ref1, ref2
Beerling, Johnny ref1, ref2, ref3, ref4, ref5, ref6, ref7
_Being There_ (Hal Ashby) ref1
Bel-Air ref1
Bell, Madeleine ref1
Bernard, Ralph ref1
Berry, Chuck ref1
_Best Of In Concert_ (Radio 1) ref1
_Best Of The Eagles_ (The Eagles) ref1
Betts, Dickie ref1
Beverly Rodeo Hotel, Los Angeles ref1, ref2
Bibury ref1
Big Machine Records ref1
_Billboard_ ref1, ref2, ref3, ref4, ref5, ref6
Bird, Jon ref1, ref2
Bird's Nest, Chelsea ref1, ref2
Bishop, Elvin ref1
Black, Alan ref1, ref2, ref3
Black, Kissy ref1, ref2
_Black and Blues_ (British Forces Broadcasting Service) ref1
'Black Pearl' (Sonny Charles and the Checkmates) ref1
Blackheath ref1
Blackhill Enterprises ref1
Blackmore, Tim ref1, ref2
Blackwell, Chris ref1
Blondie ref1
Blue Mink ref1, ref2
'Blue On Black' (Kenny Wayne Shepherd) ref1
Blue Rodeo ref1
Bluebird Cafe, Nashville ref1
bluegrass ref1, ref2
Blues and Barrelhouse Club ref1
Blues Incorporated ref1
_Bob Harris Country_ (Radio 2) ref1, ref2, ref3, ref4, ref5, ref6
_Bob Harris Music Show_ (Radio Broadland) ref1
_Bob Harris: My Nashville_ ref1
_Bob Harris Presents_ ref1, ref2
_Bob Harris Show_ (Radio 2) ref1
Bolan, June ref1, ref2, ref3, ref4, ref5
Bolan, Marc ref1, ref2, ref3, ref4, ref5, ref6, ref7
Bon Jovi, Jon ref1
Bonamassa, Joe ref1
Bonham, John ref1
Booker, Ali ref1
Booth, Al ref1, ref2, ref3, ref4
Borchetta, Scott ref1
Borderline club, London ref1, ref2
_Born To Boogie_ (Ringo Starr) ref1
_Born To Run_ (Bruce Springsteen) ref1
Bowie, Angie ref1
Bowie, David ref1, ref2
Brace, Eric ref1, ref2
Branson, Richard ref1, ref2, ref3
_Breakfast Show_ (Radio 210) ref1
Bridge House, Paddington ref1
Bridgestone Arena ref1
Briggs, Jon ref1
Bright, John ref1
Brill Building, New York ref1
Bristol ref1, ref2
British Forces Broadcasting Service (BFBS) ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9
British Schools ref1, ref2, ref3
Broadcasting House ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9
Broadway ref1
Brook, Danae ref1
Brook, John ref1
Brookes, Bruno ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9
Brown, Arthur ref1, ref2
Brown, Graham ref1
Brown, Pete ref1
Bruce, Jack ref1
Bryson, Jim ref1
Burnett, T Bone ref1, ref2, ref3
Butler, Keith ref1
Byron, David ref1
Caledonia Orchestra ref1
Callaghan ref1, ref2
Campaign for Nuclear Disarmament (CND) ref1
Campbell, Nicky ref1
Canada ref1
cancer ref1, ref2, ref3
Cancer Research UK ref1, ref2, ref3, ref4, ref5
Capaldi, Aninha ref1, ref2
Capaldi, Jim ref1, ref2
Capital Gold ref1
Capital Radio ref1, ref2, ref3
Capitol Records ref1
Capricorn Records ref1
Capris, The ref1
Captain Beefheart ref1
Carey, Mariah ref1
Carpenters, The ref1
Carson, Jenny ref1, ref2, ref3
Carson, Phil ref1, ref2, ref3
Carter, Jimmy ref1
Cash, Johnny ref1, ref2
Cassie (dog) ref1, ref2
_Catcher in the Rye_ (J.D. Salinger) ref1
_Cathy Come Home_ (BBC Television) ref1
'Cats In The Cradle' (Harry Chapin) ref1
Centipede ref1
Central School of Art, Holborn ref1
Centre 42 (theatre) ref1
Century 21 ref1
Chamonix ref1
Chapin, Harry ref1
Chapman, Beth Nielsen ref1, ref2, ref3, ref4
Chapman, Roger ref1
Chinnery, Derek ref1
Chislehurst Caves ref1
_Circuit_ (magazine) ref1
Cirque du Soleil ref1
Clapton, Eric ref1, ref2, ref3, ref4, ref5
Clark, Dick ref1
Clarkson, Jeremy ref1
Clash, The ref1
Cleaves, Slaid ref1
Cochran, Eddie ref1, ref2
Cohen, Deborah ref1, ref2
Cohn, Marc ref1
Cold War ref1
Cole and Cole solicitors ref1, ref2
_Colour Me Pop_ (BBC2) ref1
Coltrane, John ref1
Columbia Records ref1, ref2
Comic Relief ref1
_Coming Out_ (Manhattan Transfer) ref1
Compass Point Studio, Nassau ref1
Con C (Radio 1) ref1, ref2
Conteh, John ref1
Continental Hyatt House Hotel, Los Angeles ref1, ref2, ref3
Cooder, Ry ref1
Cooke, Sam ref1
Cooper, Alice ref1, ref2
Corcoran, Tom ref1
'corner chords' ref1
Coronation (Elizabeth II) ref1
Cosker, Pete ref1, ref2, ref3
Country Club, Hampstead ref1
Country Music Association Awards ref1
Cousins, Dave ref1
Cramer, Floyd ref1
cricket ref1, ref2, ref3, ref4, ref5
Criteria Sound ref1
Croce, Jim ref1
Crook, Max ref1
Cropredy ref1, ref2, ref3
Crosby, David ref1, ref2
Crow, Sheryl ref1
Crowley, Gary ref1
Crozier, Steve ref1, ref2, ref3, ref4, ref5
Cry Of Love ref1, ref2
Cuba ref1
Cumberland River ref1
Curran, Peter ref1
Curry, Steve ref1
_Daily Mail_ ref1, ref2
Damned, The ref1
Dansette record players ref1
_Dark Side of the Moon_ (Pink Floyd) ref1
_Dave Lee Travis Show_ ref1
Daventry ref1
David, Simeon ref1
Davies, Cyril ref1
Day, Aidan ref1, ref2
_Day That John Met Paul, The_ (Bob Harris) ref1
de Cartier, Shauna ref1
de Cartier, Susan ref1
Decca ref1, ref2, ref3
Dee, Dave ref1
Dee, Kiki ref1
Del Amitri ref1
Del McCoury Band ref1
Denny, Sandy ref1, ref2
_Desert Island Discs_ ref1
Dexter, Jeff ref1, ref2, ref3, ref4, ref5
Diamond, Jim ref1
'Diana' (Paul Anka) ref1, ref2, ref3
Dick Clark Nostalgia Show ref1
Diddley, Bo ref1
Dingwalls ref1
Dire Straits ref1
_Disc and Music Echo_ ref1
_Discarded Verse_ (John Golding) ref1
_Disco 2_ ref1
Disneyland, Paris ref1
Donovan, Jason ref1
Doors, The ref1
Douglas, Lesley ref1, ref2, ref3
Dowdall, Jim ref1
Downtown Presbyterian Church, Nashville ref1
Dr Hook ref1
Dr John ref1, ref2
_Dreams of Flying_ (Kimmie Rhodes) ref1
Drifters, The ref1
Driscoll, Julie ref1
_Drive Time_ (BFBS) ref1
_Drive Time_ (Radio 210) ref1
_Drive Time Show_ (Radio Oxford) ref1, ref2
Duke of Edinburgh awards ref1
Duncan-Smith, David ref1
Dunn, John ref1, ref2
Dylan, Bob ref1, ref2, ref3, ref4
E Street Band ref1, ref2
Eagles, The ref1, ref2
Ealing Rhythm and Blues Club ref1
Earle, Steve ref1, ref2, ref3
Eastside, Nashville ref1
Eddy, Duane ref1
Edinburgh, Duke of ref1
Edmunds, Dave ref1
Edwards, Kathleen ref1
Egton House ref1, ref2, ref3, ref4
Elephant's Memory ref1
Elizabeth II, Queen ref1, ref2
Elizabeth Garrett Anderson Hospital ref1
Ellington, Duke ref1
Elliott, Tony ref1, ref2, ref3, ref4
_Elton John_ (Elton John) ref1
Ely, Joe ref1
Emerson, Lake and Palmer ref1
_Emotional Rescue_ (The Rolling Stones) ref1
Empson, Hetta ref1
Ertegun brothers ref1
Essex Road, Islington ref1
Esten, Charles ref1
Evans, Sara ref1
Everett, Kenny ref1, ref2, ref3, ref4
Everly Brothers ref1, ref2
Everyman Cinema, Hampstead ref1
Exit Inn ref1
Exploding Galaxy, The ref1
_Fabref1_ (Radio London) ref1
Faces, The ref1
FACTOR (Foundation to Assist Canadian Talent on Record) ref1
Fair Grounds Race Course, New Orleans ref1
Fairfield Parlour ref1
Fairport Convention ref1, ref2
Falcon, Billy ref1
Family (band) ref1, ref2, ref3
_Fanfare For The Common Man_ (Emerson, Lake and Palmer) ref1
Farris, Mike ref1
Fataar, Ricky ref1, ref2
Fellini, Federico ref1
Ferrin, Roger ref1
ffrench-Blake, Neil ref1, ref2
Fieger, Doug ref1
Finn, Mickey ref1
Fleetwood Mac ref1
Fogerty, John ref1
'Fooled Around And Fell In Love' (Elvin Bishop) ref1
Ford, Gerald ref1
_Forever Changes_ (Love) ref1
Forte Di Marmi, Italy ref1
Foster, Charles ref1, ref2, ref3, ref4
Fowler, Bill ref1, ref2
Fox, Barry ref1
Fox, Samantha ref1
Fox, Tony ref1, ref2, ref3
'Frankenstein' (Edgar Winter) ref1
Franklin, Aretha ref1
Free (band) ref1, ref2
Freed, Audley ref1, ref2
Freeman, Alan ref1, ref2
Freeman, David ref1
_Friends_ (magazine) ref1
'From Me To You' (Lennon and McCartney) ref1
Fulham FC ref1
Garden Cricket Club ref1, ref2
Garland, Judy71
Geffen, David ref1
Geldof, Bob ref1
Gentry, Bobby ref1
Germino, Mark ref1, ref2
_Gerry House Show_ ref1
'Get Together' (Jesse Colin Young) ref1
Gibb brothers ref1, ref2, ref3 _see also_ Bee Gees, The
Gibraltar ref1, ref2
Gillett, Charlie ref1
Gilmour, Dave ref1
_Glasgow Herald_ ref1
Glass, Dave ref1
Gleason scale ref1
Godard, Jean-Luc ref1
_Godspell_ ref1
'Going Down' (Don Nix) ref1
Golding, John ref1
Good, Jack ref1
'Good Time' (The Beach Boys) ref1
'Goodnight My Love' (Jessie Belvin) ref1
Gorton, Ted ref1, ref2
Gotch, Tarquin ref1, ref2
Gough Square ref1
Gower, David ref1, ref2
Graceland ref1
Gracey, Joe ref1
_Grand Ole Opry_ ref1, ref2, ref3
Grant, Peter ref1
Gray, David ref1
Great Ormond Street Hospital ref1, ref2
_Great Western Valkyrie_ (The Rival Sons) ref1
Greater London Radio (GLR) ref1, ref2, ref3, ref4
Green, Derek ref1
Green, Jonathan ref1
Green, Peter ref1
'Green Manalishi' (Fleetwood Mac) ref1
Greenwich Village ref1
Greyhound pub, Fulham ref1
Griffin, Jeff ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, ref10, ref11, ref12, ref13, ref14
Grossman, Albert ref1
Grundig tape machines ref1
Grundy, Stuart ref1, ref2, ref3
_Guardian_ ref1
Guildford Festival ref1
Gulf War ref1
GWR (commercial radio station) ref1, ref2
Haddon Hall ref1
Hagen, Mark ref1, ref2, ref3
Hall, Colin ref1, ref2
Hall, John ref1, ref2
Hall, Tom T. ref1
Hammersmith Hospital ref1
Hammersmith Odeon ref1, ref2, ref3
Hampstead ref1, ref2, ref3
Hancock, Butch ref1
_Hands Across The Water_ ref1
_Hangtown Dancehall_ (Eric Brace) ref1
Harley, Steve ref1
Harley Davidsons ref1, ref2
Harper, Roy ref1
Harriman, Ed ref1
Harrington, Dee ref1
Harris, Ben (son) ref1, ref2, ref3, ref4, ref5, ref6
Harris, Bob _see also_ Myerscough-Harris, Trudie (wife), plus children
EARLY YEARS: buying records ref1, ref2; cinema visits ref1; John Peel interview ref1; listening to the radio ref1, ref2; music clubs ref1; parents ref1, ref2, ref3, ref4; ref1, ref2, ref3, ref4, ref5, ref6; Police Cadets ref1; Radio London ref1; school ref1; _Time Out_ ref1, ref2; Tiranti's ref1, ref2; writing for magazines ref1
ESTABLISHING HIMSELF: disc jockeying ref1; filming ref1; first radio programme ref1; Marquee ref1; _Melody Maker_ article ref1; _Monday Programme_ ref1; playlist ref1; Radio 1 research project ref1; recording for the first time ref1; _Roundtable_ ref1
FAMILY: _see_ individual family members
HEALTH: legionnaire's disease ref1; prostate cancer ref1, ref2, ref3
MISCELLANEOUS: 9/11 ref1, ref2; 60th birthday bash ref1; Ali Booker ref1; Aunt Margaret ref1; awards ref1, ref2; ref1, ref2; bankruptcy ref1; cricket ref1, ref2, ref3, ref4, ref5; _Desert Island Discs_ ref1; grandchildren ref1, ref2, ref3, ref4, ref5, ref6; Italy ref1; LSD trip ref1; obsessive fan ref1; pet cats ref1, ref2; pet dog ref1; Roger Scott, in praise of ref1; _This Is Your Life!_ ref1
MUSICIANS: _see also_ Bolan, Marc; John, Elton; Plant, Robert Beach Boys ref1; Bee Gees ref1, ref2, ref3; Beth Nielsen Chapman ref1; Bruce Springsteen ref1; Cat Stevens ref1; Duane Eddy ref1; Elton John ref1; Emerson Lake and Palmer ref1; Harry Chapin ref1; John Lennon ref1; Led Zeppelin ref1; ref1; Paul McCartney ref1, ref2, ref3, ref4; Queen ref1; Wally ref1
NORTH AMERICA: Jimmy Carter ref1; Las Vegas ref1; Los Angeles ref1, ref2; Memphis ref1; MerleFest ref1; Miami ref1 ref1; Nashville ref1, ref2; New Orleans ref1; New York ref1; Toronto ref1
OLD GREY WHISTLE TEST: _see_ Old Grey Whistle Test
PUNK ERA: criticisms ref1, ref2; relations with Jackie ref1, ref2; Sex Pistols incident ref1
RADIO WORK: _see also_ British Forces Broadcasting Service; Radio 1; Radio 2 Greater London Radio ref1, ref2, ref3 GWR ref1, ref2; Hereward Radio ref1; LBC ref1, ref2; putting programmes together ref1; Radio 210 ref1, ref2, ref3; Radio Broadland ref1; Radio London ref1; Radio Oxford ref1, ref2; The Super Station ref1; VH1 ref1
Harris, Bryn (father) ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9
Harris, Charlotte (daughter) ref1, ref2, ref3, ref4, ref5, ref6
Harris, Doria (mother) ref1, ref2, ref3, ref4
Harris, Emily (daughter) ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9
Harris, Emmylou ref1, ref2, ref3, ref4
Harris, Jackie (partner) ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8
Harris, Jamie (son) ref1, ref2, ref3, ref4
Harris, Mirelle (daughter) ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, ref10, ref11, ref12, ref13
Harris, Sue (first wife) ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, ref10, ref11, ref12, ref13
Harris, Val (second wife) ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9
Harrison, George ref1, ref2, ref3, ref4
Harrison, Olivia ref1
Harrods ref1, ref2, ref3
Harry, Deborah ref1
Hawley, Richard ref1
Hayes, Brian ref1
Hayes, Lindsay ref1
Hayward, Justin ref1, ref2
Hazelwood, Lee ref1
headphones ref1
'Heartbreaker' (Dionne Warwick) ref1
Heckstall-Smith, Dick ref1
_Help!_ (The Beatles) ref1
Hendrix, Jimi ref1, ref2
Henry, Stuart ref1
Hensley, Ken ref1
Hereward Radio ref1
High Court ref1
Hill, Faith ref1
Hilly, Jed ref1
'History of Now, A' (Callaghan) ref1
_History of Rock, The_ (television production) ref1
Hit Disc ref1
Hodson, Philip ref1
Hoffmann, Dezo ref1
Holiday Inns ref1
_Holland_ (Beach Boys) ref1
Holly, Buddy ref1, ref2
Hollywood Hills ref1
Holme, Christopher ref1
Holmes, Jonathan ref1, ref2
Hookfoot ref1
Hopkin, Mary ref1, ref2
Horne, Nicky ref1
'Horse With No Name' (America) ref1
House, Gerry ref1
'House Of the Rising Sun' (The Animals) ref1
'How Sweet It Is' (James Taylor and Carly Simon) ref1
Howe, Steve ref1
Howells, Jude ref1, ref2, ref3
Hughes, Phil ref1, ref2
Hunter, Rachel ref1
Hurley, Michael ref1
Hurricane Katrina ref1
Hutchins, Chris ref1
Hyde Park ref1, ref2, ref3, ref4
Hyland, Mike ref1
Ibiza ref1, ref2
_In Concert_ (Radio 1) ref1
_Independent_ ref1
Independent Radio News ref1
_International Times_ ref1, ref2, ref3, ref4
Islam, Yusuf (Cat Stevens) ref1
Islamia Primary School ref1
Island Records ref1
Isle of Wight ref1
_Italian Regional Cooking_ (BBC TV) ref1
Italy ref1, ref2
Jackson, Jack ref1
Jackson, Mahalia ref1
Jacobs, Bob ref1
Jacobs, David ref1, ref2
Jagger, Mick ref1, ref2, ref3, ref4
Jambco Reocrds ref1
James, Greg ref1
Japan (country) ref1
Jardine, Al ref1, ref2, ref3
Jeans, Luke ref1, ref2
Jenkinson, Philip ref1
Johansen, David ref1
John, Elton ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, ref10
Jones, Brian ref1
Jones, Mair ref1
Joseph, Martyn ref1
'Just For Me And You' (Poco) ref1
'Just Like A Woman' (Bob Dylan) ref1
Katon, Michael ref1, ref2
Katrina (hurricane) ref1
Kaufman, Mike ref1
Keeler, Paul ref1
Keen, Alan ref1
Keen, Robert Earl ref1
Kennedy, Ray ref1
Kershaw, Liz ref1
Kihn, Greg ref1
King, Ben E. ref1, ref2
King, Chris ref1
King, Larry ref1
King's Road, Chelsea ref1
Kingsbury, Jimmy ref1
Kirby, Professor Roger ref1
Knack, The ref1
Knebworth Festival ref1
Kneeling, Les ref1
Kool & The Gang ref1
Kooper, Al ref1
Koran, The ref1, ref2
Korner, Alexis ref1, ref2, ref3, ref4, ref5, ref6, ref7
Kossoff, Paul ref1
Krauss, Alison ref1, ref2
_La Flute Indienne_ (Los Kalchakis) ref1
La Tambura, Italy ref1, ref2, ref3
Labelle ref1
Lafser, Jessie ref1
Laine, Brian ref1, ref2, ref3
Laing, R.D. ref1
Lake, Greg ref1
Lamarr, Mark ref1, ref2, ref3, ref4
Landau, Jon ref1
Langham Place ref1
Langham Studios (BBC) ref1
Large, Phil Ward ref1
Larkin, Colin ref1
Las Vegas ref1
_Late Night Line Up_ (BBC2) ref1
_Late Show_ (Radio 1) ref1
_Late Show, The_ (Radio 210) ref1
_Later, With Jools Hollandref1_
Lawson, Jerry ref1
LBC ref1, ref2
Le Brock, Kelly ref1
'Leader Of The Pack' (The Shangri-Las) ref1
Leaver, John ref1, ref2
LeBlanc, Larry ref1, ref2
Led Zeppelin ref1, ref2, ref3, ref4, ref5\- _see also_ Page, Jimmy; Plant, Robert
_Led Zeppelin 4_ (Led Zeppelin) ref1
Legend, Bill ref1
Leicester ref1
Lennon, Cynthia ref1, ref2, ref3, ref4, ref5
Lennon, John ref1, ref2, ref3, ref4
Lennon, Julian ref1, ref2
Let Yourself Trust ref1
_Life in Full Colour_ (Callaghan) ref1
Line, Frances ref1
_Little Axe_ (Skip McDonald) ref1
Live Aid ref1
'Live At The Lyceum' (concert) ref1
Loggins, Kenny ref1
London Music Festival ref1
London Radio Productions ref1
London School of Economics ref1
'Loner' (John Golding) ref1
Lord, Jon ref1
Los Angeles ref1
Los Kalchakis ref1
Louie, Cathie ref1, ref2, ref3, ref4
Louisiana ref1
Love (band) ref1
Love, Mike ref1, ref2, ref3
_Love Beach_ (Emerson, Lake and Palmer) ref1
Lowe, Andy ref1
Lower Broadway, Nashville ref1
LSD ref1
Lubbock, Texas ref1
Lulu ref1
Lycett, Chris ref1
Lynott, Phil ref1, ref2
Macon, Georgia ref1, ref2
_Made_ (John Mackenzie) ref1
Madison Square Garden ref1, ref2
Mahe, Seychelles ref1
Maida Vale Studio 3 ref1, ref2
Mallett, Timmy ref1
Mallorca ref1
Manchester United FC ref1, ref2
Manhattan ref1
Manhattan Transfer ref1
Manson, Charles ref1
_Maple Leaf Revolution, The_ (Bob Harris and Trudie Myerscough-Harris) ref1
Margaret Street, London W1 ref1
Marie (friend) ref1, ref2
Marillion ref1, ref2
Marine Offences Bill ref1
Marley, Bob ref1, ref2
Marquee ref1, ref2
Marsh Baldon, Oxfordshire ref1
Martha's Vineyard ref1
Martin, George ref1
Martin, Giles ref1
Martin, Gregorio ref1
Martyn, John ref1, ref2
Massey, Steve ref1, ref2
Mathis, Johnny ref1
Mattea, Kathy ref1
May, Brian ref1
Mayfield, Curtis ref1
McCartney, Paul ref1, ref2, ref3, ref4, ref5
McDonald, Skip ref1
McEntire, Reba ref1
McGovern, James ref1
McGowan, Cathy ref1
Meatloaf ref1
Medalla, David ref1
Melly, George ref1
_Melody Maker_ ref1, ref2, ref3, ref4, ref5, ref6
'Melting Pot' (Blue Mink) ref1
Memphis ref1
Mendips (John Lennon) ref1
Mercer's Row, Northampton ref1
Mercury, Freddie ref1
MerleFest ref1, ref2
Messer, Alan ref1
Miami ref1, ref2, ref3
Middle Earth (club) ref1, ref2
Middleton, Paul ref1, ref2
'Mighty Quinn' (Manfred Mann) ref1
_Mighty Sky, The_ (Beth Nielsen Chapman) ref1
Miller, Buddy ref1, ref2, ref3, ref4, ref5
Miller, Frankie ref1
Ministry of Defence ref1
Mitchell, Joni ref1, ref2, ref3
Modern Jazz Quartet ref1
Moir, Jim ref1, ref2, ref3, ref4
Monaghan, John ref1
_Monday Programme, The_ (Radio 1) ref1, ref2, ref3, ref4, ref5
Montgomery, Kevin ref1
Montreal ref1
'Mood I'm In, The' (Wally) ref1
_Moody Blues Story, The_ (London Radio Productions) ref1
Moon, Keith ref1, ref2
Moran, Johnny ref1
Morgan studios, Willesden ref1, ref2, ref3, ref4
Morrison, Van ref1
Moss, Jerry ref1
MTV ref1, ref2, ref3
Muir, John F. ref1
Mulgrew, Theresa ref1
Mullins, Shawn ref1
Munich ref1
Murray, Pete ref1
Music Row, Nashville ref1, ref2, ref3, ref4
Musicland, Berwick Street ref1, ref2
Mussolini, Benito ref1, ref2
Myerscough-Harris, Dylan (son) ref1, ref2, ref3, ref4, ref5, ref6
Myerscough-Harris, Flo (daughter) ref1, ref2, ref3, ref4, ref5
Myerscough-Harris, Miles (son) ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, ref10
Myerscough-Harris, Trudie (wife) ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, ref10, ref11, ref12
Myerscough-Walker, Angela (mother-in-law) ref1
Myerscough-Walker, Brandon (brother-in-law) ref1, ref2
Myerscough-Walker, Raymond ref1
Myerscough-Walker, Simon (father-in-law) ref1
Myerscough-Walker family ref1
Myners, Neil ref1, ref2, ref3, ref4
NASA Headquarters ref1
Nashville ref1, ref2, ref3, ref4
_Nashville_ ref1
Nassau ref1
Necrotizing Enterocolitis ref1
Nelson, Willie ref1
Nelson Mandela Tribute Concert ref1
'N-E-R-V O-U-S' (Ian Whitcomb) ref1
New Orleans ref1, ref2, ref3
'New Rose' (The Damned) ref1
New Wave ref1, ref2
New York ref1
New York Dolls ref1
Newsdesk ref1
'Nez Percé' (Wally) ref1
_NME_ ref1, ref2, ref3
Nicholson, George ref1, ref2, ref3, ref4
Nico ref1
Night Assemblies Bill ref1
_Night That Made America Famous, The_ (Harry Chapin) ref1
_Nightfly_ ref1
Nightingale, Annie ref1
_Nightline_ (LBC) ref1, ref2
Nilsson, Harry ref1, ref2
Nix, Don ref1
'No Place That Far' (Sara Evans) ref1
Northampton County Police Cadets ref1
Northwold, Norfolk ref1
_O Brother, Where Art Thou_ (Coen Brothers) ref1
OBE ref1
O'Connor, Hazel ref1
_Ogden's Nut Gone Flake_ (The Small Faces) ref1
_Oh Boy!_ (ITV) ref1
_Old Grey Whistle Test_ (BBC2) ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, ref10, ref11, ref12, ref13, ref14, ref15, ref16
_Oldies Show_ (Radio 210) ref1
O'Leary, Dermot ref1
'Once In A Lifetime' (Talking Heads) ref1
One Direction ref1
Opera House, Buxton ref1
Orbis Books ref1
Orbison, Roy ref1
O'Reilly, Ronan ref1
Osborne, Gary ref1, ref2
_Oxford Dictionary_ ref1
_Oxford Mail_ ref1, ref2, ref3
Oxfordshire ref1, ref2, ref3, ref4
Page, Jimmy ref1, ref2, ref3, ref4
Palladio, Sam ref1
Palmer, Carl ref1
Pang, May ref1
Panton, Steve ref1
Paris ref1
Paris Theatre ref1
Parks, Van Dyke ref1
Parsons, Gram ref1
Patisserie Valerie ref1
Patterson, Ottilie ref1
Patto ref1
Payne, Heather ref1
Pebble Mill ref1
Peel, John ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, ref10, ref11, ref12, ref13, ref14
Peel, Sheila ref1
_Perfect Pasta_ (Val Harris) ref1
_Perfumed Garden, The_ (Radio London) ref1, ref2
Perry, Roger ref1, ref2
Peters, Gretchen ref1
Petty, Tom ref1, ref2
_Photographs_ (John Golding) ref1
Piccadilly Theatre ref1
Pinewood Studios ref1
Pink Floyd ref1
pirate radio ref1, ref2
Plant, Karac ref1
Plant, Robert ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, ref10
Platt's Lane, Hampstead ref1, ref2, ref3, ref4, ref5
Player, Alma ref1
Pleasure Tree, The ref1
Police, The ref1, ref2
Pontardawe ref1, ref2
pop music ref1
Portland Hospital, London ref1
Powell, Andy ref1
Powell, Nicola ref1, ref2, ref3
'Power Windows' (Billy Falcon) ref1
Presentation B ref1
Presland, Frank ref1
Presley, Elvis ref1, ref2
'Prettiest Star, The' (David Bowie) ref1
_Pretty Blue World_ (Billy Falcon) ref1
Pretty Things, The ref1
Previn, Dory ref1
Price, Ray ref1
Primrose Hill ref1
Princedale Road ref1
Princess Royal ref1
Proby, P.J. ref1, ref2
Procol Harum ref1
prostate cancer ref1, ref2
Punfield, Steph ref1
punk music ref1
Putney ref1
Pyrah, Gill ref1, ref2
Quarrymen, The ref1
Queen ref1, ref2
Queen Mary's Hospital, Roehampton ref1
Quinn, Mike ref1
Racoon (record label) ref1
radio ref1
Radio 1 ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, ref10, ref11
Radio 2 ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, ref10, ref11, ref12, ref13, ref14, ref15
Radio 210 ref1, ref2, ref3, ref4, ref5
Radio Broadland ref1
radio documentaries ref1
Radio London ref1, ref2, ref3
Radio Luxembourg ref1, ref2, ref3, ref4
Radio Oxford ref1, ref2, ref3
_Radio Times_ ref1
Radio West ref1
Rainbow Bar and Grill, Los Angeles ref1, ref2
Rainbow Theatre, London ref1
_Raising Sand_ (Robert Plant and Alison Krauss) ref1, ref2
Ralphs, Mick ref1
Raven, Dave ref1
Read, Mike ref1, ref2
_Read and Wright Show_ (Radio 210) ref1
Reading Hexagon ref1
_Ready, Steady, Go!_ ref1, ref2, ref3
_Record Mirror_ ref1
records ref1
Red Beet records ref1
Red Button, The ref1
Redding, Otis ref1
Reddington, Joe ref1
Reed, Lou ref1
Rees-Mogg, William ref1
Reeve, Kirsti ref1
Reeves, Jim ref1
Regent's Park Mosque ref1
Reid, Terry ref1, ref2
Release ref1
_Return Of The Grievous Angel-A Tribute To Gram Parsons_ ref1
'Rex Bob Lowenstein' (Mark Germino) ref1, ref2
Reyne, James ref1
Rhodes, Kimmie ref1, ref2
Rice, Tim ref1
Richard, Cliff ref1
Richards, Keith ref1, ref2
Ringwood, Mark ref1
Ritz Hotel, Paris ref1
_Road Trip_ (Duane Eddy) ref1
Roberge, Philip ref1
Robertson, Michael ref1
Robison, Bruce ref1
_Rock and Pop Mastermind_ (Bob Harris) ref1
'Rock Island Line' (Lonnie Donegan) ref1
_Rock On_ (Del Shannon) ref1
_Rock Show_ (Radio 210) ref1
_Rockdate Diary, The_ ref1, ref2
_Rolling Stone_ ref1
Rolling Stones ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8
Ronaldson, Fiona ref1, ref2
Ronchi, Italy ref1, ref2, ref3
Rosko ref1
Ross, Phil ref1
Rough Diamond ref1
Roundhouse, Chalk Farm ref1, ref2, ref3, ref4
_Roundtable_ (Radio 1) ref1
Roxy Club, Los Angeles ref1, ref2, ref3
Royal College of Art ref1
Rugby Union ref1, ref2
'Runaway' (Del Shannon) ref1
Rundgren, Todd ref1
Rushton, Willie ref1
Ryman Auditorium, Nashville ref1, ref2, ref3, ref4
Sage, Paul ref1, ref2
_Sand And Water_ (Beth Nielsen Chapman) ref1
Sandilands, Jo ref1
_Saturday Night Fever_ (John Badham) ref1
Sayer, Leo ref1
Scafell Pike ref1
Scarfe, Gerald ref1
_Scene and Heard_ (Radio 1) ref1
Schermerhorn Symphony Center, Nashville ref1
Scott, Howard ref1, ref2, ref3
Scott, Roger ref1, ref2, ref3, ref4, ref5
Scott, Valentina _see_ Harris, Val
Sebastian, John ref1
Selector ref1
Selis, Eve ref1
Sellers, Peter ref1
_Seven Types of Ambiguity_ (William Empson) ref1
Sex Pistols, The ref1, ref2, ref3
Seychelles ref1
Sforza, Nick (brother-in-law) ref1, ref2, ref3
Sforza family ref1, ref2
_Sgt. Pepper's Lonely Hearts Club Band_ (The Beatles) ref1, ref2
Shangri-Las, The ref1
Shannon, Dave ref1, ref2, ref3, ref4
Shannon, Del ref1, ref2
Sharp, Richard ref1
Shepherd, Kenny Wayne ref1
Shepherd's Bush Theatre ref1
Shepperton ref1
Sheraton Four Ambassadors, Miami ref1
Shirelles, The ref1
_Silk Torpedo_ (The Pretty Things) ref1
Sillers, Tia ref1
Simon, Carly ref1
Simon, Paul ref1
Simpson, Mark ref1
Sinclair, Jill ref1
singles ref1
'Singles Cavalcade, The' (Radio Oxford) ref1
_Six-Five Special_ (BBC) ref1, ref2
Six Shooter Records ref1
Skinner, Richard ref1, ref2
Sky Arts ref1, ref2
Sky News ref1
Slough ref1
Small Faces, The ref1
Smith, Dr Mike ref1
Snell, Catherine ref1, ref2
Snider, Todd ref1
_Song Remains The Same, The_ (Led Zeppelin) ref1
_Songs The Beatles Gave Away, The_ ref1, ref2
Sonny Charles and the Checkmates ref1
Sound and Vision ref1, ref2, ref3, ref4, ref5
_Sounds_ magazine ref1
_Sounds of the 70s_ (Radio 1) ref1, ref2, ref3, ref4, ref5, ref6, ref7
Southcote, Berkshire ref1, ref2
_Space Oddity_ (David Bowie) ref1
Speakeasy Club ref1, ref2, ref3, ref4, ref5
Spector, Phil ref1, ref2, ref3, ref4
_Spirits Having Flown_ (The Bee Gees) ref1, ref2
_Sports Show_ (Radio 210) ref1
Springsteen, Bruce ref1, ref2
Squire, Chris ref1
St Mary's Hospital, Paddington ref1
Stafford, Jim ref1
'Stand by Me' (Ben E. King) ref1, ref2, ref3, ref4
Starr, Ringo ref1, ref2, ref3
Station Inn, Nashville ref1
Stein, Chris ref1
Stevens, Cat ref1
Stewart, Ian ref1
Stewart, Rod ref1, ref2
Stockton, Peter ref1
'Stone Fox Chase' (Area Code 615) ref1
Stourhead Gardens ref1
Strawbs, The ref1
Stringfellow, Peter ref1
Strong, Colin ref1, ref2, ref3
_Sun_ ref1
_Sunday Sport_ ref1
Sunnyland Jazz Club ref1
Sunset Strip ref1, ref2, ref3, ref4
Super Station, The ref1, ref2
_Surf's Up_ (The Beach Boys) ref1
Swan Song label ref1
_Sweet Baby James_ (James Taylor) ref1
'Sweet Betsy From Pike' (trad.) ref1
Swern, Phil ref1, ref2, ref3, ref4, ref5, ref6, ref7
Swift, Taylor ref1, ref2
Swindon ref1
Symonds, David ref1, ref2, ref3
T. Rex ref1, ref2, ref3
T2 ref1, ref2
Tabor, June ref1
'Take A Giant Step' (James Reyne) ref1
Talking Heads ref1
Taupin, Bernie ref1
Taylor, Del ref1
Taylor, James ref1, ref2, ref3
Taylor, Rod ref1
Taylor, Roger ref1
TC5 (Television Centre) ref1
telestrators ref1
television music shows ref1
Thain, Gary ref1
Thames Valley FM ref1 _see also_ Radio Oxford
Thatcher, Margaret ref1, ref2
'There's A Moon Out Tonight' (The Capris) ref1
Thin Lizzy ref1
_This Is Your Life!_ ref1
Thompson, Danny ref1
Thompson, Richard ref1
'Those Were The Days' (Mary Hopkin) ref1
Tiles Club ref1
_Time Out_ ref1, ref2, ref3, ref4, ref5
Tippett, Keith ref1
Tiranti's, Charlotte Street ref1, ref2
Tomelty, Frances ref1
_Today_ (newspaper) ref1
_Tonight_ (BBC) ref1
Tootsie's Orchid Lounge, Nashville ref1
_Top Gear_ (Radio 1) ref1
_Top of the Pops_ ref1, ref2, ref3
Toronto ref1
Tower Records ref1
Townshend, Pete ref1
Traffic ref1
Trailblazer Awards ref1
Transrectal Ultrasound Imaging ref1
Travelling Wilburys, The ref1
Travers, Kieran ref1
Travis, Dave Lee ref1, ref2, ref3
Tregurtha, Paul ref1, ref2
Trinity High School, Northampton ref1
'True Love Ways' (Buddy Holly) ref1
Truffaut, François ref1
_Tube, The_ ref1
_Tubular Bells_ (Mike Oldfield) ref1, ref2
Turner, Ted ref1
Turner, Tina ref1
Tuscany ref1
TVAM building, Camden ref1
Twain, Shania ref1
Twang Trust ref1
Twitter ref1
Tyley, Marc ref1
'Under My Wheels' (Alice Cooper) ref1
_Under The Apple Tree_ (Bob Harris and Miles Myerscough-Harris) ref1, ref2, ref3
_Unit_ ref1, ref2
Upchurch, Phil ref1
Uriah Heep ref1
Valk, Robin ref1
_Valley Gardens_ (Wally) ref1
Vance, Tommy ref1, ref2, ref3, ref4, ref5
Vauxhall Crestas ref1
Velvet Underground ref1
Venice Beach, Los Angeles ref1
Vertigo (record label) ref1
VH1 ref1
Vicious, Sid ref1
Vincent, Gene ref1
vinyl ref1
Virgin ref1
Visconti, Tony ref1
Wainwright, Loudon ref1
Wakeman, Rick ref1, ref2, ref3
Walden, Phil ref1, ref2
Walker, Johnnie ref1, ref2, ref3, ref4, ref5, ref6, ref7
'Walking In Memphis' (Marc Cohn) ref1
Wally (band) ref1
Walmsley, Pete ref1, ref2
_War Of The Worlds_ (Gary Osborne and Jeff Wayne) ref1
Warner Brothers ref1, ref2, ref3, ref4
Warwick, Dionne ref1
Waters, Muddy ref1, ref2
Watson, Merle ref1
Watts, Alan ref1
Watts, Charlie ref1
Watts, Michael ref1, ref2, ref3
Wayne, Jeff ref1
Webber, Karen ref1, ref2
Webber, Roy ref1, ref2, ref3, ref4, ref5, ref6
Welch, Sue ref1, ref2
Weller, Paul ref1
Wesker, Arnold ref1
West Hampstead ref1
Weston, Mike ref1
Wexler, Jerry ref1
'Whatever Gets You Through The Night' (Elton John and John Lennon) ref1
'While My Guitar Gently Weeps' (George Harrison) ref1
_Whistle Test Weekend_ (VH1) ref1
Whitcomb, Ian ref1
White, Carol ref1
White, Jim ref1
Whiteladies Road, Bristol ref1
_Who Breaks A Butterfly On A Wheel_ (Ali Booker and Trudie Myerscough-Harris) ref1
_Who Knows Where The Time Goes_ (Bob Harris) ref1
'Whole Lotta Love' (CCS) ref1
Whyton, Wally ref1
Wight, Mark ref1, ref2
Wilkes Community College ref1
Williams, John ref1
Williams, Richard ref1
Wills, Genevieve ref1
Wilson, Brian ref1, ref2, ref3
Wilson, Carl ref1, ref2, ref3
Wilson, Dennis ref1, ref2, ref3, ref4
Wilson, Elizabeth ref1
Wilson, Marilyn ref1, ref2, ref3
Windsor, Duchess of ref1
Windsor, Duke of ref1
_Wings Over America_ (Wings) ref1
Winter, Edgar ref1
Wishbone Ash ref1, ref2
'Wishing Well' appeal (Great Ormond Street Hospital) ref1
Wogan, Terry ref1, ref2
Womack, Lee Ann ref1
Wonder, Stevie ref1
Woodcock, Stuart ref1
Woodstock ref1
Woollcott, Tony ref1
Wootton, Richard ref1
Wootton Bassett ref1
Works, The ref1, ref2
World Cup 1982 ref1
Wright, Steve ref1, ref2, ref3, ref4
Yates, Chris ref1
Yes ref1, ref2, ref3, ref4
'You Can't Sit Down' (Phil Upchurch) ref1
'You Turn Me On (The Turn On Song)' (Ian Whitcomb) ref1
Young, Jesse Colin ref1, ref2
Young, Suzi ref1
_Your Mother Wouldn't Like It_ (Radio Luxembourg) ref1
'Your Own Way' (Wally) ref1
Zappa, Frank ref1, ref2, ref3
List of Illustrations
1. My first-ever record, Paul Anka's 'Diana', now framed and on my studio wall.
2. Summer 1947, on holiday with my parents in Mablethorpe. Most often we would spend summer holidays in Pontardawe, surrounded by blue-grey mountains. My parents didn't own a car until I was eight, so each year they would save up to hire the little Austin 7 in which we undertook the eight-hour journey across the Brecon Beacons from Northampton to south Wales.
3. Marc Bolan and I backstage on the first T.Rextasy tour in 1971.
4. A letter Marc sent me after publication of the first edition of _Time Out_ magazine.
5. The working hub of the _Old Grey Whistle Test._ Director Colin Strong (left), myself and producer Mike Appleton put final touches to the show in the gallery of Presentation B studio at Television Centre.
6. A rare photograph of the whole _Whistle Test_ team, captured in the studio in 1976.
7. A memorable and very difficult interview with Van Morrison in my early days on _Whistle Test_.
8. The Wailers preparing to perform 'Concrete Jungle' and a hypnotic version of 'Stir It Up' in our tiny studio in 1973 – a wonderful image by Alan Messer, our resident _Whistle Test_ photographer, now living in Nashville.
9. A lot of rock 'n' roll stars came into the _Whistle Test_ studio, among them Del Shannon, The Everly Brothers, Duane Eddy and Bill Haley (pictured).
10. A recent shot of Robert Plant and I in my studio 'under the apple tree'.
11. _Old Grey Whistle Test_ producer Mike Appleton and I lifting the cup at Wembley.
12. With Gary Lineker, Fred Rumsey, David Gower and Nick Cook at the launch of a pro-celebrity Quick Cricket tournament in 1985.
13. 'Kill the hippy!'
14. The early 1980s and I begin to rebuild my life.
15. My sons Jamie (left) and Ben (the newspaper caption put them the wrong way round) meeting Jason Donovan at Harrod's sale.
16. My friend Emmylou Harris who presented me with my AMA Trailblazer Award in Nashville in 2011.
17. The woman of my dreams. Trudie and I have been together since September 1989 and were married on 24th April 1991.
18. With Beth Nielsen Chapman at her home in Nashville. A still from our _Back To Beth's_ television programme, shown on BBC4 in November 2014.
19. Trudie with Robert Plant at Robert's sixtieth birthday party.
20. Trudie and Paul McCartney at the recording of an interview for _The Day John Met Paul_.
21. I have massive respect for Rosanne Cash, with whom I'm pictured in Nashville in 2014.
22. From the recordings for our _OGWT 40_ series for BBC Radio 2, marking the fortieth anniversary of _The Old Grey Whistle Test._ Jackson Browne and Brian May, Steve Harley, Alice Cooper and Yusuf Islam.
23. With Elton John at the Electric Proms at the Roundhouse, London in 2010.
24. Presenting the great Duane Eddy with a Lifetime Achievement Award, onstage at the Ryman Auditorium in Nashville in 2013.
25. Trudie and Miles joined me backstage with Taylor Swift on her Red Tour in 2013.
26. My Mum with her great radio hero, David Jacobs, at my _This Is Your Life_ recording in 2003.
27. A family picture, clockwise from left, Miles, Dylan, Flo, Catherine, Trudie, Aunt Margaret (now 100 years old) and Mr Monk Monk!
28. Charlie, Jamie, Ben and Mum at Emily's wedding on Holkham Beach, Norfolk.
29. Miles looking across the Cumberland River at the Nashville skyline.
30. Emily's wedding, Holkham Beach, Norfolk, 2004.
31. Catherine and Flo in our 'Under the Apple Tree' session.
32. Miri, Ben, Dylan and his friend Abi Blain at Miri's 21st birthday party.
33. left to right: Flo, Dylan, Trudie, Miles, Niamh, Emily, Me, Eliza, Olivia, Miri, Alana, Ysobel, Graeme, Sue and Marnie.
34. Just some of my beautiful granddaughters: Marnie, Alana, Olivia and Lola Mae.
35. Onstage at the O2, compering the 2015 Country 2 Country festival.
36. Broadcasting backstage at C2C for BBC Radio 2 Country with Jo Whiley.
37. With Charlie, Trudie and Miles at Windsor Castle, following my investiture in 2011.
1. My first-ever record, Paul Anka's 'Diana', now framed and on my studio wall.
2. Summer 1947, on holiday with my parents in Mablethorpe. Most often we would spend summer holidays in Pontardawe, surrounded by blue-grey mountains. My parents didn't own a car until I was eight, so each year they would save up to hire the little Austin 7 in which we undertook the eight-hour journey across the Brecon Beacons from Northampton to south Wales.
3. Marc Bolan and I backstage on the first T.Rextasy tour in 1971.
4. A letter Marc sent me after publication of the first edition of _Time Out_ magazine.
5. The working hub of the _Old Grey Whistle Test._ Director Colin Strong (left), myself and producer Mike Appleton put final touches to the show in the gallery of Presentation B studio at Television Centre.
6. A rare photograph of the whole _Whistle Test_ team, captured in the studio in 1976.
7. A memorable and very difficult interview with Van Morrison in my early days on _Whistle Test_.
8. The Wailers preparing to perform 'Concrete Jungle' and a hypnotic version of 'Stir It Up' in our tiny studio in 1973 – a wonderful image by Alan Messer, our resident _Whistle Test_ photographer, now living in Nashville.
9. A lot of rock 'n' roll stars came into the _Whistle Test_ studio, among them Del Shannon, The Everly Brothers, Duane Eddy and Bill Haley (pictured).
10. A recent shot of Robert Plant and I in my studio 'under the apple tree'.
11. _Old Grey Whistle Test_ producer Mike Appleton and I lifting the cup at Wembley.
12. With Gary Lineker, Fred Rumsey, David Gower and Nick Cook at the launch of a pro-celebrity Quick Cricket tournament in 1985.
13. 'Kill the hippy!'
14. The early 1980s and I begin to rebuild my life.
15. My sons Jamie (left) and Ben (the newspaper caption put them the wrong way round) meeting Jason Donovan at Harrod's sale.
16. My friend Emmylou Harris who presented me with my AMA Trailblazer Award in Nashville in 2011.
17. The woman of my dreams. Trudie and I have been together since September 1989 and were married on 24th April 1991.
18. With Beth Nielsen Chapman at her home in Nashville. A still from our _Back To Beth's_ television programme, shown on BBC4 in November 2014.
19. Trudie with Robert Plant at Robert's sixtieth birthday party.
20. Trudie and Paul McCartney at the recording of an interview for _The Day John Met Paul_.
21. I have massive respect for Rosanne Cash, with whom I'm pictured in Nashville in 2014.
22. From the recordings for our _OGWT 40_ series for BBC Radio 2, marking the fortieth anniversary of _The Old Grey Whistle Test._ Jackson Browne and Brian May, Steve Harley, Alice Cooper and Yusuf Islam.
23. With Elton John at the Electric Proms at the Roundhouse, London in 2010.
24. Presenting the great Duane Eddy with a Lifetime Achievement Award, onstage at the Ryman Auditorium in Nashville in 2013.
25. Trudie and Miles joined me backstage with Taylor Swift on her Red Tour in 2013.
26. My Mum with her great radio hero, David Jacobs, at my _This Is Your Life_ recording in 2003.
27. A family picture, clockwise from left, Miles, Dylan, Flo, Catherine, Trudie, Aunt Margaret (now 100 years old) and Mr Monk Monk!
28. Charlie, Jamie, Ben and Mum at Emily's wedding on Holkham Beach, Norfolk.
29. Miles looking across the Cumberland River at the Nashville skyline.
30. Emily's wedding, Holkham Beach, Norfolk, 2004.
31. Catherine and Flo in our 'Under the Apple Tree' session.
32. Miri, Ben, Dylan and his friend Abi Blain at Miri's 21st birthday party.
33. left to right: Flo, Dylan, Trudie, Miles, Niamh, Emily, Me, Eliza, Olivia, Miri, Alana, Ysobel, Graeme, Sue and Marnie.
34. Just some of my beautiful granddaughters: Marnie, Alana, Olivia and Lola Mae.
35. Onstage at the O2, compering the 2015 Country 2 Country festival.
36. Broadcasting backstage at C2C for BBC Radio 2 Country with Jo Whiley.
37. With Charlie, Trudie and Miles at Windsor Castle, following my investiture in 2011.
|
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By Percival Everett
Published: Graywolf Press - June 13th, 2017
Percival Everett gives us the story of Kevin Pace, an artist working on a giant secret canvas, during three key times in his life: his adventures in El Salvador in 1979, an affair he had in France, and dealing with his pregnant daughter and secret painting in the present time. Everett develops each of these stories and for the most part lets the reader's draw their own conclusions of how they fit together. This is one of the finest novels written by a true American master.
Mothering Sunday: A Romance (Vintage International) (Paperback)
By Graham Swift
This is the perfect novel for the Downton Abbey crowd. A servant from one household has a fling with the heir of the neighboring house. The action of this novel mostly takes place on one day in 1924 England. It's the day before the heir is to marry and the illicit lovers treat each other with tenderness as they try not to say the words good bye.
Night at the Fiestas: Stories (Paperback)
By Kirstin Valdez Quade
Published: W. W. Norton & Company - March 7th, 2016
These short stories take place in Northern New Mexico and show us communities that are struggling with their traditional religions and the modern world. In one a pregnant girl is the receptionist for the Catholic Church in another tale a town recreates the passion and the man playing Jesus decides that he is willing to suffer as much as Jesus did. Quade writes with great compassion and drama.
The World's Wife: Poems (Paperback)
By Carol Ann Duffy
Published: Farrar, Straus and Giroux - April 9th, 2001
Duffy rewrites history, mythology and fairytales with women as the focal point in this remarkably diverse collection of poems. Whether Shakespeare's wife is using a sonnet to get her story told or Darwin's wife is skewering him with a rhyming couplet, you can be assured that Duffy's nimble style will amaze and amuse you.
‹ Bookseller Recommendations up Brad's Recommendations ›
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Q: Why do I generally see real solutions to recurrence relations? I haven't worked very much with recurrence relations, but for the ones I have worked with I always get real solutions, which is strange to me because looking briefly at the procedure for solving (linear) recurrence relations, it seems that we try to "find the roots that fit the polynomial". Why should this necessarily give real solutions, or is that just what intro discrete math books do- choose the coefficients to the recurrence relations to yield real solutions?
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Q: Kotlin: invoke function in companion object (via reflection) I am trying to notify a central class on startup about the existence of some classes that will be used during runtime. My idea is to use reflection: scan for annotation (or interface implementation) and call a method from the companion's object of those classes.
As suggested in [1] I am using classgraph but I'm totally open to alternatives.
package com.test
import io.github.classgraph.ClassGraph
import io.github.classgraph.ClassInfo
import io.github.classgraph.ScanResult
import kotlin.reflect.KFunction
import kotlin.reflect.jvm.kotlinFunction
@Target(AnnotationTarget.FUNCTION)
@Retention(AnnotationRetention.RUNTIME)
annotation class OnStartup
// a class that will be instantiated a lot of times during runtime
data class SomeClass(val name: String) {
companion object {
@OnStartup
fun onStartup() {
// notify someone at startup about our existence
}
}
}
fun main() {
val scanResult: ScanResult = ClassGraph().enableAllInfo().acceptPackages("com.test").scan()
scanResult
.getClassesWithMethodAnnotation(OnStartup::class.java.name)
.filter { it.isStatic }
.flatMap { findStartupMethods(it) }
.forEach { it.call() }
}
private fun findStartupMethods(classInfo: ClassInfo): List<KFunction<*>> {
return classInfo.methodInfo.filter { function ->
function.hasAnnotation(OnStartup::class.java)
}.mapNotNull { method ->
method.loadClassAndGetMethod().kotlinFunction
}
}
The problem is, that the code exits with
Exception in thread "main" java.lang.IllegalArgumentException: Callable expects 1 arguments, but 0 were provided.
From reading the Kotlin Docs and [2] my guess is that I should hand over the companionObjectInstance as a parameter. But I have absolutely no idea how to get it...
Any help is really appreciated.
[1] Getting a list of annotated functions in Kotlin using reflection
[2] Kotlin invoke companion function with reflection
A: Maybe it looks ugly, but it works...
it.call((it.parameters[0].type.classifier as KClass<*>).objectInstance)
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{"url":"http:\/\/mathoverflow.net\/revisions\/22584\/list","text":"2 added 165 characters in body\n\nThe reason is simple: There are many non-unital rings which appear quite naturally.\n\nIf $X$ is a locally compact space (in the following every space is assumed to be hausdorff), then $C_0(X)$, the ring of continous complex-valued functions on $X$ vanishing at infinity, is a $C^*$-algebra which is unital if and only if $X$ is compact. If $X = \\mathbb{N}$, this is just the ring of sequences converging to $0$. Gelfand duality yields an anti-equivalence between unital commutative $C^*$-algebras and compact spaces, and also between (possibly non-unital) commutative $C^*$-algebras (with \"proper\" homomorphisms) and locally compact spaces (with proper maps). In a very similar spirit ($\\mathbb{C}$ is replaced by $\\mathbb{F}_2$), there is an anti-equivalence between unital boolean rings and compact totally disconnected spaces, and also between boolean rings and locally compact totally disconnected spaces. One-point-Compactification on the topological side corresponds here to the unitalization on the algebraic side. Perhaps we have the following conclusion: As locally compact spaces appear very naturally in mathematics (e.g. manifolds), the same is true for non-unital rings.\n\nIf $A$ is a ring (possibly non-unital), its unitalization is defined to be the universal arrow from $A$ to the forgetful functor from unital rings to rings. An explicit construction is given by $\\tilde{A} = A \\oplus \\mathbb{Z}$ as abelian group with the obvious multiplication so that $A \\subseteq \\tilde{A}$ is an ideal and $1 \\in \\mathbb{Z}$ is the identity. Because of the universal property, the module categories of $A$ and $\\tilde{A}$ are isomorphic. Thus many results for unital rings take over to non-unital rings.\n\nEvery ideal of a ring can be considered as a ring. Important examples also come from functional analysis, such as the ideal of compact operators on a Hilbert space.\n\n1\n\nThe reason is simple: There are many non-unital rings which appear quite naturally.\n\nIf $X$ is a locally compact space (in the following every space is assumed to be hausdorff), then $C_0(X)$, the ring of continous complex-valued functions on $X$ vanishing at infinity, is a $C^*$-algebra which is unital if and only if $X$ is compact. If $X = \\mathbb{N}$, this is just the ring of sequences converging to $0$. Gelfand duality yields an anti-equivalence between unital commutative $C^*$-algebras and compact spaces, and also between (possibly non-unital) commutative $C^*$-algebras (with \"proper\" homomorphisms) and locally compact spaces (with proper maps). In a very similar spirit ($\\mathbb{C}$ is replaced by $\\mathbb{F}_2$), there is an anti-equivalence between unital boolean rings and compact totally disconnected spaces, and also between boolean rings and locally compact totally disconnected spaces. One-point-Compactification on the topological side corresponds here to the unitalization on the algebraic side. Perhaps we have the following conclusion: As locally compact spaces appear very naturally in mathematics (e.g. manifolds), the same is true for non-unital rings.\n\nIf $A$ is a ring (possibly non-unital), its unitalization is defined to be the universal arrow from $A$ to the forgetful functor from unital rings to rings. An explicit construction is given by $\\tilde{A} = A \\oplus \\mathbb{Z}$ as abelian group with the obvious multiplication so that $A \\subseteq \\tilde{A}$ is an ideal and $1 \\in \\mathbb{Z}$ is the identity. Because of the universal property, the module categories of $A$ and $\\tilde{A}$ are isomorphic. Thus many results for unital rings take over to non-unital rings.","date":"2013-05-21 23:57:11","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9585553407669067, \"perplexity\": 204.13766490896523}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2013-20\/segments\/1368700871976\/warc\/CC-MAIN-20130516104111-00096-ip-10-60-113-184.ec2.internal.warc.gz\"}"}
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Q: Completion of normed space Let $(X,\|\cdot\|_X)$ be a Banach space and $S$ a subspace of $X$ (not necessarily closed).
Consider a linear (not neccesarily bounded) operator $T:S \rightarrow X$ and equip $S$ with the norm $\|u\|_S := \|u\|_X + \|T(u)\|_X$, which makes $T$ continuous.
Denote $S'$ the completion of $S$ with respect to the norm $\|\cdot\|_S$.
1) Can we assure that $S'$ i contained in $X$ (obviously, the notion of contained is in the sense of the Cauchy classes of equivalence). I think so, because $\|\cdot \|_X \leq \|\cdot\|_S$ in $S$ and therefore every pair of equivalent Cauchy sequences in $(S,\|\cdot\|_S)$ are also equivalent Cauchy sequences in $(X,\|\cdot\|_X)$.
2) Can we extend $T$ in some way to $T': S' \rightarrow X$? Would it be something like $T'(s') = \lim_n T(s_n)$, where $s_n$ is a sequence in $S$ converging to $s'$ in the extension of the norm $\|\cdot\|_S$?
3) In case 2) is true, does it hold that $\operatorname{Ker}(T') = \operatorname{Ker}(T)$?
In case you're wondering why I'm asking this, the answer is that I'm trying to know if what holds in Sobolev Spaces can also be extended in some way for more general settings. I mean, if we consider $\Omega \subset \mathbb R$ an open interval and $X = L^2(\Omega)$, $S = C_c^\infty(\overline\Omega)$ and $T$ the derivative operator we know that 1)-2)-3) hold, being $S' = H^1(\Omega)$ and the Kernels the space of constant functions.
A: I'll answer the second of your questions first. Yes, we can extend $T$ to $S'$, and what you wrote is one of the standard ways of describing the extension. That is a special case of a more general theorem. If $E$ is a normed space, $F$ a Banach space, and $\tilde{E}$ the completion of $E$, then every continuous linear map $L \colon E \to F$ has a unique continuous linear extension $\tilde{L} \colon \tilde{E} \to F$. Also this is a special case of a more general theorem, we don't need the norms, the same (mutatis mutandis) holds if $E$ is a topological vector space, $\tilde{E}$ its completion and $F$ a complete topological vector space. And the vector space structure is also irrelevant, we can take $E$ as a uniform space with completion $\tilde{E}$, $F$ a complete uniform space, and $L \colon E \to F$ a uniformly continuous function. (If you don't know uniform spaces yet, take metric spaces.)
The answer to your first question is more involved. While indeed equivalent Cauchy sequences in $S$ correspond to equivalent Cauchy sequences in $X$, it may be the case that classes of non-equivalent Cauchy sequences in $S$ correspond to classes of equivalent Cauchy sequences in $X$.
I find it more transparent to identify $S$ with the graph of $T$, that is to consider
$$Y = \{(u, T(u)) : u \in S\} \subset X \times X.$$
Endowing $X\times X$ with the norm $\lVert (x,y)\rVert_{X\times X} = \lVert x\rVert_X + \lVert y\rVert_X$ makes it a Banach space (this norm induces the product topology) and the projection $\pi_1 \colon (x,y) \mapsto x$ induces an isometry $\iota \colon Y \to S$ when $Y$ is normed by the restriction of $\lVert\,\cdot\,\rVert_{X\times X}$ and $S$ is normed by $\lVert\,\cdot\,\rVert_S$. This gives an identification of $S'$ with $\overline{Y}\subset X \times X$. And the natural interpretation of "$S'$ is contained in $X$" is that the restriction of $\pi_1$ to $\overline{Y}$ provides that inclusion, i.e. that $\pi_1\lvert_{\overline{Y}}$ is injective. That is easily seen to be equivalent to saying that $\overline{Y}$ is the graph of a linear map (with domain $\pi_1(\overline{Y}) \subset X$), and to the condition $(0,v) \in \overline{Y} \iff v = 0$. Thus in this sense $S'$ is contained in $X$ if and only if $T$ is a closable operator. There may be continuous injections $S' \hookrightarrow X$ also in other cases, but the extension of the natural inclusion $S \hookrightarrow X$ to $S'$ is injective if and only if $T$ is closable.
To sum up: in general we cannot assure that $S'$ is contained in $X$, but modest niceness conditions on $T$ suffice.
The short answer to the third question is also "in general, no". If $\ker T$ is not a closed subspace of $X$, then we trivially have $\ker T \subsetneqq \overline{\ker T} \subset \ker T'$ (well, if $T$ isn't closable the inclusions need to be interpreted appropriately). But we can also have $\ker T \subsetneqq \ker T'$ if $\ker T$ is closed in $X$, even if $T$ is continuous. Consider in $X = \ell^2(\mathbb{N})$ the subspace $S$ of sequences with only finitely many nonzero terms, and $T(u) = u - \langle u \mathop{\vert} \xi\rangle\cdot \xi$ where $\xi$ is a unit vector with infinitely many nonzero terms. Then $T$ is injective, $S'$ can be naturally identified with $X$, and $\ker T' = \mathbb{C}\cdot \xi$.
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| 3,279
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Concussion dangers still not fully accepted
by Paul Gardner on Apr 28, 3:39 PM
If ever proof were needed that the English style of refereeing is a bad model for American referees, it was provided in abundance this past weekend. Of course, I am of the opinion that no such added proof was needed anyway, so skewed is the English view of officiating.
The Greatest. Remembering Richie Benaud, 1930-2015
I'll need to switch sports for a moment here. But it's important. The greatest of television sports commentators died last week. Richie Benaud, the Australian cricket commentator.
Stars? Bah, says Mourinho. The team -- meaning the coach, that is ME, is the one who matters
by Paul Gardner on Apr 13, 11:46 AM
Coaches, of course, can be relied on to say something. Without doubt they are the most frequently quoted contingent in the sport of soccer. They can also be relied on to make themselves highly visible during games by frequently throwing histrionic fits -- it wouldn't amaze me to learn that we actually see more of the coaches during a telecast than we do of any individual player.
Hallelujah! A terrible diving call gets rescinded!
by Paul Gardner on Apr 10, 11:56 PM
Regularly, at least once per season, I announce, with indignant protestations of disgust, that I have just witnessed the worst-ever diving call.
Lalas & Balboa agree -- breaking the rules is fine
by Paul Gardner on Apr 6, 6:02 PM
We all remember Alexi Lalas and Marcelo Balboa, don't we. The stalwart double act at the heart of the U.S. defense in the 1994 World Cup. A rather rustic pair. That's right -- those two. That was over 20 years ago, and they've moved on, of course.
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SNC-Lavalin chief warns Canadian job losses possible amid scandal
The head of the Montreal-based construction giant at the centre of a political firestorm warned the company remains undervalued, is vulnerable to a takeover and at risk of shedding jobs in Canada.
"Justice is upside down on this," Bruce said in a BNN Bloomberg television interview. "We've apologized for the behaviour of the previous management, and ultimately, I firmly believe the prosecution service should hold those responsible to account and stop damaging the innocent people."
SNC-Lavalin once had 20,000 workers in Canada and now has 9,000, he added. "If we can't put some of this behind us, it's highly likely that we'll have less," he said.
Bruce's comments are the latest twist in a saga over whether his company will get a deferred prosecution agreement, a negotiated fine that would end prosecution and help it avoid a ban on bidding for federal contracts that would come with a potential conviction. Trudeau's former attorney general alleges the prime minister and several staff pressured her to help SNC.
Political scandal
The scandal is dominating political debate in Canada, coinciding with a drop to second place in opinion polls for the governing Liberal Party. Trudeau, whose finance chief delivered his final budget this week before an election this fall, has lost two cabinet minister, one of his top political aides and Canada's top bureaucrat to the controversy.
Bruce said Wednesday he never spoke with Trudeau directly about job losses or a deferred prosecution agreement, but that his company lobbied through normal channels.
"We put forward in our submissions what the public interest case is," he said. "We've never asked for charges to be dropped, we've never asked for this to be circumvented in any way. We'll follow the rule of law, whether it's the court process or a remediation agreement."
He said he never threatened to move the company headquarters from Montreal: "This is where we want to be, in terms of our base." But the chief executive also signalled the company could pivot its focus elsewhere.
"We are a proud Canadian global champion — one of the few, actually," Bruce said. "We're a global company, we've got over 50,000 people. We can dial up, dial down, where we work. And if we are not in a position to do federal contracts, then that's really clear. We don't do that, we do something else."
He said the company is looking at all its options and that it remains undervalued. "It's always a possibility, but no, we haven't" been approached recently about a takeover, he said. Asked if he was considering spinning off parts of the business, he said "every option is open."
Bruce added: "Ultimately, this uncertainty just makes it very, very difficult to surface the true value." The prosecution could take another three or four years, he said.
Saudi Arabia and Scheer
The legal case wasn't the only thing Bruce singled out as hurting SNC's business. He also cited uncertainty in Saudi Arabia, saying "it's not of our making, in terms of the intergovernmental relationships there." Trudeau's government clashed with Saudi Arabia last year over human-rights issues, prompting the kingdom to restrict Canadian investment.
Bruce criticized political leaders for the current scandal, likening it to an "unacceptable" hockey game between Trudeau's team and that of his rival, Conservative Leader Andrew Scheer, with his employees caught in the middle.
"It's politics, it's not actually anything to do with us. We've gone through the right channels, we've been really transparent and we've been clear," Bruce said, adding that he's spoken to Scheer on social occasions. "He seemed pro-business and seemed supportive, so I'm sort of puzzled by the reaction," he said.
Lavalin
Conservative Leader Andrew Scheer
David Olive: David Olive: The SNC-Lavalin 'scandal' lies entirely with the Trudeau government
What the mob thirsts for is not good government in itself, but the merry chase of a definite exponent of bad government. — H.L. Mencken Canada cannot afford the damage...
Troubled SNC-Lavalin to net $3.25B after partial exit from 407 highway
Troubled SNC Lavalin Group Inc. said it is selling a 10.01 per cent stake in Highway 407, a key artery in Ontario, to The Ontario Municipal Employees Retirement System, or OMERS....
SNC-Lavalin Group slashes dividend by 65 per cent and reports a $1.6-billion fourth-quarter loss
MONTREAL—Amid an ongoing scandal that has rocked the Liberal government in Ottawa, the head of SNC Lavalin Group Inc. said he's tired of seeing his employees "used as a puck in...
Why SNC's 407 highway sale may do little to turn around its fortunes
SNC Lavalin Group Inc. will pocket about $2.8 billion after selling a 10 per cent stake in Highway 407, but the price is slightly less than analysts were expecting and is...
David Olive: SNC-Lavalin blamed a teenage refugee for its poor performance. Here's the real story
In a controversial conference call with stock market analysts on Monday, Neil Bruce, CEO of Montreal based engineering and construction giant SNC Lavalin Group Inc., appeared to deflect blame for his company's woes...
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This nicely presented 3 bedroom family home is a must to inspect. Featuring 3 light and spacious bedrooms with built in robes, separate lounge room with reverse cycle air conditioning, large kitchen and dining area, bathroom with separate toilet, external laundry, double garage with one side drive thru access to backyard plus a huge fully fenced yard. Polished timber floorboards through the living rooms and bedrooms and timber laminate flooring in kitchen and dining rooms. Quiet cul de sac location but close to local schools, shops and public transport. AVAILABLE NOW.
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{"url":"http:\/\/arxiv-sp.directory\/2018\/01\/08","text":"# High-frequency spicule oscillations generated via mode conversion\n\nSpicule oscillations involve high-frequency components with a typical period approximately corresponding to $40-50$ s. The typical time scale of the photospheric oscillation is a few minutes, and thus, the origin of this high-frequency component is not trivial. In this study, a one-dimensional numerical simulation is performed to demonstrate that the observed spicule oscillations originate from longitudinal-to-transverse mode conversion that occurs around the equipartition layer in the chromosphere. Calculations are conducted in a self-consistent manner with the exception of additional heating to maintain coronal temperature. The analyses indicate the following features: (1) mode conversion efficiently excites high-frequency transverse waves; (2) the typical period of the high-frequency waves corresponds to the sound-crossing time of the mode conversion region; and (3) simulated root-mean-square velocity of the high-frequency component is consistent with the observed value. These results indicate that the observation of spicule oscillation provides direct evidence of mode conversion in the chromosphere.\n\nOriginal Article: http:\/\/arxiv.org\/abs\/1801.01254\n\n# The Instruments and Capabilities of the Miniature X-ray Solar Spectrometer (MinXSS) CubeSats\n\nChristopher S. Moore (1, 2 and 3), Amir Caspi (4), Thomas N. Woods (2), Phillip C. Chamberlin (2 and 5), Brian R. Dennis (5), Andrew R. Jones (2), James P. Mason (2 and 5), Richard A. Schwartz (5 and 6), Anne K. Tolbert (5 and 6) ((1) Department for Astrophysical and Planetary Science, University of Colorado, (2) Laboratory for Atmospheric and Space Physics, University of Colorado, (3) Harvard-Smithsonian Center for Astrophysics, (4) Southwest Research Institute, Boulder, CO, USA, (5) NASA Goddard Space Flight Center, (6) American University)\n\nThe Miniature X-ray Solar Spectrometer (MinXSS) CubeSat is the first solar science oriented CubeSat mission flown for the NASA Science Mission Directorate, with the main objective of measuring the solar soft X-ray (SXR) flux and a science goal of determining its influence on Earth\u2019s ionosphere and thermosphere. These observations can also be used to investigate solar quiescent, active region, and flare properties. The MinXSS X-ray instruments consist of a spectrometer, called X123, with a nominal 0.15 keV full-width-half-maximum (FWHM) resolution at 5.9 keV and a broadband X-ray photometer, called XP. Both instruments are designed to obtain measurements from 0.5 \u2013 30 keV at a nominal time cadence of 10 seconds. A description of the MinXSS instruments, performance capabilities, and relation to the Geostationary Operational Environmental Satellite (GOES) 0.1 \u2013 0.8 nm flux are discussed in this article. Early MinXSS results demonstrate the capability to measure variations of the solar spectral SXR flux between 0.8 \u2013 12 keV from at least GOES A5 \u2013 M5 (5 $\\times$ 10$^{-8}$ \u2013 5 $\\times$ 10$^{-5}$ W m$^{-2}$) levels and infer physical properties (temperature and emission measure) from the MinXSS data alone. Moreover, coronal elemental abundances can be inferred, specifically Fe, Ca, Si, Mg, S, Ar, and Ni, when there is sufficiently high count rate at each elemental spectral feature. Additionally, temperature response curves and emission measure loci demonstrate the MinXSS sensitivity to plasma emission at different temperatures. MinXSS observations coupled with those from other solar observatories can help address some of the most compelling questions in solar coronal physics. Finally, simultaneous observations by MinXSS and Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) can provide the most spectrally complete soft X-ray solar flare photon flux measurements to date.\n\nOriginal Article: http:\/\/arxiv.org\/abs\/1801.01261\n\n# Synchronized Observations of Bright Points from the Solar Photosphere to Corona\n\nEhsan Tavabi\n\nOne of the most important features in the solar atmosphere is magnetic network and its rela- tionship with the transition region (TR), and coronal brightness. It is important to understand how energy is transported into the corona and how it travels along the magnetic-field lines be- tween deep photosphere and chromosphere through the TR and corona. An excellent proxy for transportation is the Interface Region Imaging Spectrograph (IRIS) raster scans and imaging observations in near-ultraviolet (NUV) and far-ultraviolet (FUV) emission channels with high time-spatial resolutions. In this study, we focus on the quiet Sun as observed with IRIS. The data with high signal to noise ratio in Si IV, C II and Mg II k lines and with strong emission intensities show a high correlation in TR bright network points. The results of the IRIS intensity maps and dopplergrams are compared with those of Atmo- spheric Imaging Assembly (AIA) and Helioseismic and Magnetic Imager (HMI) instruments onboard the Solar Dynamical Observatory (SDO). The average network intensity profiles show a strong correlation with AIA coronal channels. Furthermore, we applied simultaneous observations of magnetic network from HMI and found a strong relationship between the network bright points in all levels of the solar atmosphere. These features in network elements exhibited high doppler velocity regions and large mag- netic signatures. A dominative fraction of corona bright points emission, accompanied by the magnetic origins in photosphere, suggest that magnetic-field concentrations in the network rosettes could help couple between inner and outer solar atmosphere.\n\nOriginal Article: http:\/\/arxiv.org\/abs\/1801.01307\n\n# Solar Flares and the Axion Quark Nugget Dark Matter Model\n\nAriel Zhitnitsky\n\nWe advocate the idea that the nanoflares conjectured by Parker long ago to resolve the corona heating problem, may also trigger the larger solar flares. The arguments are based on the model where emission of extreme ultra violet (EUV) radiation and soft x-rays from the Sun are powered externally by incident dark matter particles within the Axion Quark Nugget (AQN) Dark Matter Model. The corresponding annihilation events of the AQNs with the solar material are identified with nanoflares. This model gives a very reasonable intensity of EUV radiation without adjustments of any parameters in the model. When the same nuggets enter the regions with high magnetic field they serve as the triggers igniting the magnetic reconnections which eventually may lead to much larger flares. Technically, the magnetic reconnection is ignited due to the shock wave which inevitably develops when the dark matter nuggets enter the solar atmosphere with velocity $v\\sim 10^{-3}c$ which is much higher than the speed of sound $c_s$, such that the Mach number $M=v\/c_s\\gg 1$. These shock waves generate very strong and very short impulses expressed in terms of pressure $\\Delta p\/p\\sim M^2$ and temperature $\\Delta T\/T\\sim M^2$ in vicinity of (would be) magnetic reconnection area. We find that this mechanism is consistent with x -ray observations as well as with observed jet like morphology of the initial stage of the flares. The mechanism is also consistent with the observed scaling of the flare distribution $dN\\sim W^{-\\alpha}dW$ as a function of the flare\u2019s energy $W$. We also speculate that the same nuggets may trigger the sunquakes which are known to be correlated with large flares.\n\nOriginal Article: http:\/\/arxiv.org\/abs\/1801.01509\n\n# Solar polarimetry in the K I $D_2$ line: A novel possibility for a stratospheric balloon\n\nOf the two solar lines, K I $D_1$ and $D_2$, almost all attention so far has been devoted to the $D_1$ line, as $D_2$ is severely affected by an O$_2$ atmospheric band. This, however, makes the latter appealing for balloon and space observations from above (most of) the Earth\u2019s atmosphere. We estimate the residual effect of the O$_2$ band on the K I $D_2$ line at altitudes typical for stratospheric balloons. Our aim is to study the feasibility of observing the 770 nm window. Specifically, this paper serves as a preparation for the third flight of the Sunrise balloon-borne observatory. The results indicate that the absorption by O$_2$ is still present, albeit much weaker, at the expected balloon altitude. We applied the obtained O$_2$ transmittance to K I $D_2$ synthetic polarimetric spectra and found that in the absence of line-of-sight motions, the residual O$_2$ has a negligible effect on the K I $D_2$ line. On the other hand, for Doppler-shifted K I $D_2$ data, the residual O$_2$ might alter the shape of the Stokes profiles. However, the residual O$_2$ absorption is sufficiently weak at stratospheric levels that it can be divided out if appropriate measurements are made, something that is impossible at ground level. Therefore, for the first time with Sunrise III, we will be able to perform polarimetric observations of the K I $D_2$ line and, consequently, we will have improved access to the thermodynamics and magnetic properties of the upper photosphere from observations of the K I lines.\n\nOriginal Article: http:\/\/arxiv.org\/abs\/1801.01655\n\n# Spatial Inhomogeneity In Solar Faculae\n\nIn this paper, we investigate the inhomogeneous spatial distribution of solar faculae. The focus is on the latitudinal and longitudinal distributions of these highly localised features covering ubiquitously the solar surface. The statistical analysis is based on white light observations of the Solar and Heliospheric Observatory (SOHO) and Solar Dynamics Observatory (SDO) between 1996 and 2014. We found that the fine structure of the latitudinal distribution of faculae displays a quasi-biennial oscillatory pattern. Furthermore, the longitudinal distribution of photospheric solar faculae does not show homogeneous behaviour either. In particular, the non-axisymmetric behaviour of these events show similar properties as that of the active longitude (AL) found in the distribution of sunspots. Our results, preliminary though, may provide a valuable observational constrain for developing the next-generation solar dynamo model.\n\nOriginal Article: http:\/\/arxiv.org\/abs\/1801.01716\n\n# Ghost Images in Helioseismic Holography? Toy Models in a Uniform Medium\n\nDan Yang\n\nHelioseismic holography is a powerful technique used to probe the solar interior based on estimations of the 3D wavefield. Porter\u2013Bojarski holography, which is a well-established method used in acoustics to recover sources and scatterers in 3D, is also an estimation of the wavefield, and hence it has the potential to be applied to helioseismology. Here we present a proof of concept study, where we compare helioseismic holography and Porter\u2013Bojarski holography under the assumption that the waves propagate in a homogeneous medium. We consider the problem of locating a point source of wave excitation inside a sphere. Under these assumptions, we find that the two imaging methods have the same capability of locating the source, with the exception that helioseismic holography suffers from \"ghost images\" (i.e., artificial peaks away from the source location). We conclude that Porter\u2013Bojarski holography may improve the current method used in helioseismology.\n\nOriginal Article: http:\/\/arxiv.org\/abs\/1801.01759","date":"2019-02-22 16:14:42","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6175196170806885, \"perplexity\": 2259.2135775929282}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-09\/segments\/1550247518497.90\/warc\/CC-MAIN-20190222155556-20190222181556-00565.warc.gz\"}"}
| null | null |
\section{Introduction}
Undulatory locomotion is a common way for animals to move in various environments (e.g. spermatozoa in water \cite{gray1955propulsion}, sandfish in sand~\cite{maladen2009undulatory}, snakes on land~\cite{hu2009mechanics,guo2008limbless}, and fish in water~\cite{wardle1995tuning}, for reviews, see \cite{lauga2009hydrodynamics,cohen2010swimming,alexanderbook} ) and a popular mode of locomotion for bio-inspired robots~\cite{tesch2009parameterized,crespi2008online,maladen2011undulatory}. This type of locomotion consists of bending the body or some portion of the body to form a traveling wave in the direction opposite to the motion direction to generate propulsion. For organisms in environments dominated by resistive forces, such as spermatozoa swimming at low Reynolds numbers (Re) and snakes slithering on the ground, how the propulsive forces from the environments are generated is quite well understood~\cite{cohen2010swimming,goldman2010wiggling}.
To bend the body and generate propulsion, internal torques (bending moments) are required to overcome both the restoring forces and damping forces of the body and the external forces from the resistance of surrounding media. For macroscopic animals such as eels and snakes, the internal torques are generated by muscle forces acting on the body. Therefore, in previous theoretical and computational studies, spatio-temporal torque patterns were used to explain and predict muscle activation patterns~\cite{cheng1994bending,cheng1998continuous,hess1984fast}. Ongoing interdisciplinary research over the past several decades has provided a general overview of the torque and muscle activation: they both exhibit traveling wave patterns from head to tail. However, the waves of the muscle activation and the torque travel faster than the wave of the curvature, which is a phenomenon known as neuromechanical phase lags~\cite{wardle1995tuning,butler2015consistent}. Consequently, muscles activate after they begin to shorten in the anterior part of the body, and muscles begin to activate before they begin to shorten in the posterior part of the body.
By imposing kinematics and considering contributions from the resistance of the environment and the passive body properties of fish (e.g. saithe and lamprey), qualitative agreements between predicted torque patterns and muscle activation patterns have been achieved~\cite{cheng1994bending,cheng1998continuous,hess1984fast}. For the relatively simple case of the sandfish lizard swimming in sand, where resistive forces dominate and the body is nearly uniform, a quantitative agreement has been obtained using resistive force theory (RFT)~\cite{ding2013emergence}. However, how the torque pattern is formed and whether the pattern is always a traveling wave are still open questions.
\begin{table}
\caption{\label{tab1}Wave numbers observed in nature}
\resizebox{0.5 \textwidth}{!}{%
\begin{tabular}{| c | c | c | c |c |c|c|}
\hline
Organism & Spermatozoon & Nematode & Snake & Eel & Scup & Sandfish \\ \hline
Wave number \footnote{When only amplitude and wavelength are given in the reference, we assume that the motion is sinusoidal and approximated the wave number as $\xi=L/\int_0^\lambda{\sqrt{1+B^2\sin^2{x}}\mathrm{d}x}$, where $L$ is the body length, $B$ is the undulation amplitude, and $\lambda$ is the wavelength.}& 1.25-1.4 &0.55-1.31 & 1.60 (on ground), 3.5 (in sand) & 1.7 & 0.65 & 1.0 \\ \hline
Source & \cite{gray1955propulsion,brokaw1965non} & \cite{fang2010biomechanical,berri2009forward} & \cite{hu2009mechanics,sharpe2015locomotor} & \cite{wardle1995tuning} & \cite{wardle1995tuning} & \cite{maladen2009undulatory} \\ \hline
\end{tabular}
}
\end{table}
Another approach for studying the mechanics of undulatory locomotion is to start with the internal forces/torques and observe the kinematics as a result of the couplings between the internal drives, passive body properties and external environments. Two closely related kinematic parameters are the wavelength and the wave number (the number of wavelengths on the locomotor's body), which, in reality, vary in different species and for the same species in different environments (Tab.~\ref{tab1}). For example, the wavelength decreases as the viscosity increases in nematodes and spermatozoa~\cite{fang2010biomechanical,brokaw1966effects}. By imposing a neuron activation pattern, muscle forces, or a relationship between internal shear force and curvature, previous studies showed the trend of decreasing wavelength in spermatozoa and fish swimming when the relative strength of the external resistance to the internal driving forces/torques is reduced~\cite{johnson1979flagellar,tytell2010interactions,mcmillen2008nonlinear}. However, how the variations in internal torque, kinematics and other components interact with each other is still not well understood.
In robots using undulatory gaits, torques are generally generated directly by motors (e.g., \cite{choset2000design}), although new actuation mechanisms are emerging~\cite{yan2012novel,chu2012review,nguyen2009c}. Torque is also a convenient way for detecting unexpected forces and avoiding damage to robots~\cite{de2005sensorless}. A deep understanding of the features of torques such as their magnitudes, power output, and phase relationships with curvature in various configurations and environments is useful for designing driving systems~\cite{liljeback2012review,wright2007design}.
Here, we consider steady forward undulatory locomotion in resistive-forces-dominated media with simple kinematics and body shape. We show the basic torque pattern and its transitions to new patterns as the wave number increases. Further analysis reveals the formation of the torque pattern and the underlying mechanism of the transitions.
\section{Model}
We consider an undulatory locomotor bending its slim and uniform body as a traveling serpentine wave in a plane (Fig.~\ref{fig:model}). We use body length as unit length and one undulation period $T_p$ as unit time. The curvature is prescribed as $\kappa=A \xi \sin[2\pi (\xi s+ t)]$, where $s \in [0\,\, 1]$ is the arc length measured from the tail, $A$ controls the undulation amplitude relative to the wavelength, $\xi$ is the wave number, and $t$ is the time. The speed of the curvature wave becomes $v_\kappa=1/\xi$. $A$ is set to $7.54$, which gives an amplitude-to-wavelength ratio ($\approx$0.24) that is close to experimentally observed ratios~\cite{hu2009mechanics,maladen2009undulatory,gray1955propulsion}. For every time instant, we use a body frame in which the tail end is at the origin and pointing toward the $x-$ axis. The tangent angle of a segment at $s$ to the $x+$ axis can be computed by integrating the curvature along the body: $\theta(s) = \int_0^s \kappa \mathrm{d}l$. The position of the segment can be computed as $\mathbf{r}(s)=(x,y)=( \int_0^s \cos(\theta) \mathrm{d}l,\int_0^s \sin(\theta) \mathrm{d}l)$. By taking the time derivative, the velocity $\mathbf{v}_b$ of a segment relative to the tail end can be computed. Assuming that the tail end is moving at velocity $\mathbf{v}_\mathrm{tail}$ and rotating at angular velocity $\omega$, the velocity at the body position $s$ in the lab frame becomes $\mathbf{v}=\mathbf{v}_b+\mathbf{v}_\mathrm{tail}+\omega \mathbf{e}_z \times \mathbf{r}$.
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.45\textwidth]{./model2.eps}
\caption{Diagram of the model. The black curve represents the body, the magenta arrows represent velocities, and the green arrows represent forces from the medium. The black dot is a representative point on the body at which the internal torque ($T$) is calculated from the forces in the dashed box. The sign and arrow indicate the direction of the torque. $\xi=1.5$, $A=7.54$, and $t=0$.}\label{fig:model}
\end{center}
\end{figure}
To determine the motion of the body and the distribution of the force on the body, we use an RFT model similar to those in \cite{ding2013emergence,hu2009mechanics}. In the RFT model, the body is divided into infinitesimal segments. Assuming that the force ($\mathbf{F}(s)$) experienced by one segment is independent of other segments, the force can be calculated based on the geometry, orientation, and velocity of the segment. The perpendicular and parallel components of the force on a segment can be written as $F_\perp(v_\perp,v_\parallel)$ and $F_\parallel(v_\perp,v_\parallel)$, respectively, where $v_\perp$ and $v_\parallel$ are the perpendicular and parallel components of the segment velocity $\mathbf{v}$. We first consider the simplest case, in which the head drag is negligible and the forces are from viscous drag: $F_\perp=C_\perp v_\perp$ and $F_\parallel=C_\parallel v_\parallel$, where $C_\perp=2$ and $C_\parallel=1$ are the drag coefficients for a very thin cylinder~\cite{rodenborn2013propulsion}. The total external torque on the body can be computed as $\mathbf{F}_\mathrm{total}=\int_0^1 \mathbf{F}(l) \mathrm{d}l$ and $T_\mathrm{total}=\mathbf{e}_z\int_0^1 \mathbf{r}(l) \times \mathbf{F}(l) \mathrm{d}l$. We assume that inertia is negligible, which is a good approximation for micro-swimmers in fluids, crawlers on land, and swimmers in granular materials~\cite{gray1955propulsion,hu2009mechanics,maladen2009undulatory}. Under this assumption, the resultant net force $\mathbf{F}_\mathrm{total}$ and the net torque $T_\mathrm{total}$ related to the tail (reference) frame are both zero, from which $\mathbf{v}_\mathrm{tail}$ and $\omega$ can be determined. The motion and force distributions on the body are shown in Supplementary Video S1, and the MATLAB scripts of the computation are provided in the Supplementary Materials.
To compute the internal torque ($T$) required to overcome the external forces at a point on the body, we analyze the torque balance on the anterior side of the body at that point and simply find that $T(s)=-T^e(s)=-\int_{s}^1 [\mathbf{r}(l)- \mathbf{r}(s)]\times \mathbf{F}(l)\mathrm{d}l$ (see Fig.~\ref{fig:model} for an example), where $T^e$ is the total external torque from the anterior side of the body. Integrating over the posterior side of the body gives the same results. To compute the wave speed of the torque, we use the fitting function $\sqrt{2}\langle T(s) \rangle \sin[2\pi(s/\lambda_T+t)+\phi_T]$, where $\langle T(s) \rangle$ is the standard deviation of the torque at $s$, $\lambda_T$ is the wavelength of the torque wave along the body, and $\phi_T$ is a fitting parameter for the phase. The $\langle T(s) \rangle$ term is used to capture the variation in torque amplitude and the prefactor $\sqrt{2}$ comes from the ratio between the maximum and the standard deviation of the sine function. The fitting parameters $\lambda_T$ and $\phi_T$ are obtained from the best fitting of the torque. The speed of the torque wave is defined as $v_T=\lambda_T/T_p=\lambda_T$ and the speed ratio of the torque wave to the curvature wave is $v_T/v_\kappa=\lambda_T \xi$.
\begin{figure*}
\begin{center}
\includegraphics[width=0.9\textwidth]{./torque2png.eps}
\caption{The internal torque as a function of body position and time for different wave numbers. The magnitude of the torque is normalized by the maximum torque and represented by color. The solid and dashed lines indicate the maximum and minimum curvatures, respectively. The red dotted box in (e) indicates the torque pattern that appears similar to the pattern in (b). The green and blue arrows indicate the local waves traveling posteriorly and anteriorly, respectively. $A=7.54$}\label{fig:torque}
\end{center}
\end{figure*}
\section{Results}
To focus on the torque pattern, we normalize the torque by its maximum value for each wave number $\xi$. We find that the torque exhibits a traveling wave pattern for $\xi<1.8$ (Fig.~\ref{fig:torque}a-d). In this regime, the amplitude of the torque is smaller near the ends and greater in the middle. As in previous studies, the torque wave travels faster than the curvature wave, and different phase lags between the curvature and the torque along the body are observed. When $\xi$ approaches 2, the magnitude of the torque in the middle of the body suddenly decreases, and a pattern of two apparently separated traveling waves forms (Fig.~\ref{fig:torque}e); each wave is similar to a wave with $\xi= 1$ and takes half of the body. For $\xi> 2$, the two waves merge as the wave direction near the middle of the body becomes the opposite direction of the curvature wave. The torque pattern is no longer one or two traveling waves (Fig.~\ref{fig:torque}f). Up to at least $\xi=11$, similar transitions occur by adding one additional traveling wave pattern near the middle of the body when $\xi$ reaches integer numbers. See Supplementary Video S2 for torque patterns with smaller $\xi$ increments.
The speed of the torque wave normalized to the speed of the curvature decreases from 5.2 to 1.3 as the wave number increases from 0.5 to 1.8 (Fig.~\ref{fig:power}a). This result is consistent with the results of previous studies, namely, the muscle activation is nearly synchronized for short wavelengths~\cite{wardle1995tuning}. The fit of a single traveling wave is poor when $\xi>1.8$; therefore, the wave speed is not defined and shown in Fig.~\ref{fig:power}a.
The energy output per cycle required to overcome the external force at each point on the body is computed by integrating the power over a cycle, i.e., $W=\int_0^1 T \dot{\kappa}\mathrm{d}t$. The decrease in the phase difference between $T$ and $\dot{\kappa}$ and the decrease in the amplitude of $T$ at the middle as $\xi$ increases result in a more uniform distribution of the energy output over the body (see the blue line in ~\ref{fig:power}b). When $\xi=2$, the instantaneous power and energy output of the middle segment are zero. As $\xi$ further increases to 2.3, the power of the middle segment becomes negative, which means that the energy generated by other parts of the body is transferred to this part.
\begin{figure}
\begin{center}
\includegraphics[width=0.48\textwidth]{./power4.eps}
\caption{The speed of the internal torque wave normalized by the speed of the curvature wave as a function of the wave number (a) and the energy per cycle required as a function of the body position for different wave numbers (b).} \label{fig:power}
\end{center}
\end{figure}
A few variation are tested to evaluate the influences of the external forces and kinematics on the torque pattern and transitions. First, two additional types of resistive force laws obtained in previous experiments are considered: forces for granular media are described by $F_\perp=C_n \sin[\arctan(\gamma \sin(\phi))]$ and $F_\parallel=[C_f \cos(\phi) + C_l(1-\sin(\phi))]$, where $C_n=5.57$, $C_l=-1.74$, $C_f=2.30$, $\gamma=1.93$, and $\phi=\arctan(v_\perp/v_\parallel)$~\cite{maladen2011mechanical}. These force laws are empirical fitting functions for an aluminum cylinder dragged with different orientations in 3mm glass beads. For anisotropic frictional forces, $F_\perp=\mu_t v_\perp/|\mathbf{v}|$ and $F_\parallel=[\mu_f H(v_\parallel)+\mu_b(1-H(v_\parallel))]v_\parallel/|\mathbf{v}|$, where $\mu_f=0.3,\mu_b=1.3\mu_f$ and $\mu_t=1.8\mu_f$ are the friction coefficients in the forward, backward, and normal directions, respectively~\cite{hu2009mechanics}. $H(x)$ is the Heaviside step function. Since we focus on the torque pattern and normalize the torque by its maximum value, the absolute magnitudes of the forces are irrelevant here. These force laws and coefficients are obtained by measuring the frictional forces while unconscious snakes slide on clothes at different orientations. The torque pattern is qualitatively the same when the force laws are replaced by those for granular and frictional environments, and only subtle differences are observed (Fig.~\ref{fig:var}a\,\&\,b). We also compute the force distribution using Lighthill's elongated body theory (EBT) where only the lateral inertial forces from the fluid are considered (the derivation is provided in the Supplementary Information)~\cite{lighthill1960note}. The inertial forces considered in the EBT give a torque pattern that is similar to that from the RFT, albeit with a phase shift of $+\pi/2$ (1/4 period) (Fig.~\ref{fig:var}d).
To study the effect of undulation amplitude, we increase the amplitude to $A=12.57$, at which the segments nearly overlap. Surprisingly, we find that the torque pattern is insensitive to amplitude (see Fig.~\ref{fig:var}d and Supplementary Video S9). When the amplitude increases linearly toward the tail, similar transitions occur, albeit at a greater wave number (Fig.~\ref{fig:var}e). Since interactions between segments through the medium are neglected, the results from the amplitude variations only include the geometric effects. An example case with head drag is also examined (Fig.~\ref{fig:var}f). Based on an experiment on bull spermatozoa, the head is approximated as a sphere with isotropic drag, and the drag coefficient is chosen such that the head drag is 58\% of the body drag when the body is straight and moving perpendicular to its axis~\cite{friedrich2010high}, i.e. $\mathbf{F}_h=0.58C_\perp \mathbf{v}(1)$. The resulting torque is significantly larger for the anterior half of the body and the transition of torque to the two-wave pattern occurs at a smaller wave number.
\begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{./tor_vary.eps}
\caption{Torque pattern variation for different force laws, kinematics and geometry. Torque pattern with (a) frictional, (b) granular (b), and (c) inertial force laws. $A=7.54$ in (a-c).(d) Large amplitude $A=12.57$. (e) Increasing amplitude toward the tail. $A=7.54(1-s)$. (f) With a large head. Insets in (d-f) are schematic diagrams of the corresponding models. The head is not drawn to scale. See Supplementary Videos S3-8 for the respective torque patterns as a function of $\xi$ for (a-f).}\label{fig:var}
\end{center}
\end{figure}
To elucidate the mechanism underlying the transition of the torque, we analyze the phases of the torque at the middle point of the body and at a point infinitely close to the head as examples (Fig.~\ref{fig:forcedis}). In a previous study~\cite{ding2013emergence}, the torque at the middle point was roughly decomposed into three parts to explain the neuromechanical phase lag. Here we use a more quantitative tool--phasor diagram--to visualize and analyze the relationships among the phases of curvature, force and torque.
Further simplification is needed prior to the analysis. Since the torque pattern is not sensitive to amplitude, a small amplitude ($A=0.6$) is used such that the locomotor is nearly a straight line on the $x$ axis undulating in place. In this case, only the lateral displacement ($y$) and lateral forces ($F_y \approx F_\perp $) need to be considered and the longitudinal forces ($\approx F_\parallel$) are negligible. Then the equation for computing the torque at position $s$ can be simplified as $T(s)=-\int_s^1 (l-s) F_y \mathrm{d}l$. Prior to the analysis, we also note that the spatio-temporal patterns of the lateral force are affected by the requirements of force and torque balances. For $\xi=0.5$, a wave number less than 1, the phase difference between the lateral forces at the head and at the middle point is greater than $\pi/2$, which is the phase difference of the curvatures at these two points (Fig.~\ref{fig:forcedis}). This result can be understood by considering the balance of the lateral forces and the torque: zero total lateral force requires both negative forces and positive forces to be present at any time; the zero torque condition further requires that the negative forces be distributed on both sides when the force in the middle is positive (a similar argument was made by Gray \cite{gray1946mechanism}). Nonetheless, the phase differences of the forces between the middle point and the end points increase with increasing wave number.
\begin{figure*}
\begin{center}
\includegraphics[width=0.9\textwidth]{./forcedisall2png.eps}
\caption{Composition of the torque at the middle and phasor diagrams. (a) The lateral force $F_y$ distribution as a function of body position ($s\approx x$) and time. (b) Phasor diagrams. The blue arrows represent the contribution of the force on the anterior part of the body to the torque at the middle of the body when the force at the middle is maximum. The integration regions are marked by the thick blue lines in (a). $T^e_\mathrm{mid}$ and $T^e_\mathrm{head}$ represent the torque at the middle and the head, respectively, and the corresponding forces are marked by green and red dots in (a). The black arrows represent the curvature phasors. The lengths of the force, torque, and curvature phasors are drawn to reflect only their relative magnitudes for the same value of $\xi$.}\label{fig:forcedis}
\end{center}
\end{figure*}
In phasor diagrams, a variable is represented by a phasor (vector), whose projection on the horizontal axis is the instantaneous value of the variable and the rotation of the phasor corresponds to the time evolution. Since $T$ and $T^e$ only have a sign difference, we examine the phasors of the external torque $T^e$ and first focus on the phasor of $T^e$ at the middle point of the body ($T^e_\mathrm{mid}=T^e(s=0.5)$ in Fig.~\ref{fig:forcedis}b). The force contribution to $T^e$ at the middle point (i.e. $(l-0.5)F_y$ for $l>0.5$) is discretized and visualized using phasors in Figure \ref{fig:forcedis}b. The integrative nature of the torque at the middle point makes the phase of $T^e$ between the phases of the forces. Interestingly, the torque $T^e$ at the middle point is precisely either out of phase (for $\xi<2$) or in phase (for $2<\xi<2.3$) with the force at the middle point. This alignment can be understood by considering the symmetry and torque balance when the force at the middle is zero (this case is similar to the one shown in Fig.~\ref{fig:model} with the fore-aft forces ignored): the lateral displacement is symmetric about the middle point while the lateral velocity and force distributions are antisymmetric. The antisymmetric force distributions generate torque about the middle point with the same sign but the total torque on the body must be zero. Therefore, the torque from each half of the body (i.e. $T^e(0.5)$) at this time instant must be zero. When $\xi$ approaches 2, one full wavelength appears on each side of the body, the torque contributions cancel out, and $T^e_\mathrm{mid}$ becomes zero. As $\xi$ continues to increase, the $T^e_\mathrm{mid}$ becomes in phase with the local force $F_\mathrm{mid}$. This situation corresponds to a breakdown in the torque pattern of a single traveling wave and a reversal of the local torque wave at the middle.
To understand the speed variation of the torque wave (Fig.~\ref{fig:power}a), we compare the phase differences of the torque, force and curvature at the middle point and at the head ($s=1$). At a point infinitely close to the head, the torque $T^e_\mathrm{head}$ is simply in phase with the local force at the head ($F_\mathrm{head}$). Therefore, the phase difference between the torques at the middle point and at the head (the angle between $T^e_\mathrm{mid}$ and $T^e_\mathrm{head}$ in Fig.~\ref{fig:forcedis}b) is considerably smaller than the phase difference between the forces (the angle between $F_\mathrm{mid}$ and $F_\mathrm{head}$ in Fig.~\ref{fig:forcedis}b) and the phase difference between curvatures (the angle between $\kappa_\mathrm{mid}$ and $\kappa_\mathrm{head}$ in Fig.~\ref{fig:forcedis}b). As $\xi$ increases from 0.5 to 1.8, the phase of $T^e_\mathrm{mid}$ remains the same, but $T^e_\mathrm{head}$ increases at the same rate of $F_\mathrm{head}$. Therefore, the phase difference of torque increases from a smaller number (approximately $0.25\pi$ for $\xi=0.5$) to nearly $\pi$. Since such an increase is greater in proportion compared to the increase in curvature, which is from $0.5\pi$ to $1.8\pi$, the speed of the torque wave relative to the curvature wave decreases.
As shown in the above analysis, the torque pattern is primarily determined by the phase distribution of the forces modulated by distance. This picture can also help explain the observed torque variations (Fig.~\ref{fig:var}). When the force laws are changed to granular or frictional ones, the phase distributions of the forces on the body are similar; therefore, similar torque patterns are observed. The phase of the reactive force is proportional to the time derivative of the velocity and is hence ahead of the phase of the resistive force by $\pi/2$; therefore, the phase of the torque is shifted by the same amount. When the curvature amplitude increases toward the tail, the motion and forces on the head are relatively small; thus, the effective phase range from the head to tail is smaller than the nominal one indicated by $\xi$, and the two-wave transition is delayed (greater $\xi$). For the case with a head, because the head force is nearly out of phase with the total torque from other parts when the two-wave transition occurs (see the red and magenta arrows in Fig.~\ref{fig:forcedis}b, $\xi=1.8$), the enhancement of the head drag causes the cancellation and reversal of the torque to occur earlier (smaller $\xi$).
\section{Discussion}
\begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{./SBT.eps}
\caption{Torque pattern computed using slender body theory for viscous fluids. (a) \& (b) are the torque patterns for different wave numbers. See Supplementary Video S10. $A=7.54$. (c) Comparison of the lateral force along the body using resistive force theory and slender body theory. $t=0$, and $A=0.6$.}\label{fig:SBT}
\end{center}
\end{figure}
In the resistive force theory for viscous fluids, the assumption that the force on one segment is independent of the movement of other segments might introduce significant errors in the forces~\cite{rodenborn2013propulsion}. Such error can be alleviated by using slender body theory~\cite{lighthill1976flagellar}. In slender body theory, the body of the swimmer is assumed to be slender, and the ratio between the radius of the body and body length $a/L$ is much smaller than 1. Singularity solutions of point forces and dipoles are arranged along the body centerline ,and the velocity at a point is computed as the superposition of the singularity solutions to include the effect of the interaction between segments (see \cite{rodenborn2013propulsion} for the details of the explanation and implementation). Here, we use a biologically relevant body shape $1/L=1/30$~\cite{moore2013wormsizer} and the same kinematic parameters in RFT. We found that the transition of the torque pattern from slender body theory is qualitatively the same as those from resistive force theory but the transition to the two-wave pattern occurs at smaller $\xi$ ($\approx$1.8) (Fig.~\ref{fig:SBT}a\,\&\,b). The wave speed ratio from SBT is also slightly smaller than the result from RFT (e.g., 3.0 vs. 3.3 at $\xi=1$). Examination of the force distribution for a small amplitude reveals one mechanism for the early transition: forces at the head and tail are larger because at the ends, the segments experience greater drag force as less segments are nearby to ``help'' induce the flow. Similar to the case with a head (Fig.~\ref{fig:var}f), the head and tail forces are nearly out of phase with the total torque from other parts and the enhancement of the drags and the ends causes the cancellation and reversal of the torque to occur earlier.
\begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{./internalplus.eps}
\caption{Torque pattern variation when the elastic or viscous body forces are included. The four subfigures represent combination of two kinds of forces and two the wave numbers. See Supplementary Videos S11-12
for the respective torque patterns as a function of $\xi$ for (a,b) and (c,d).}\label{fig:elast}
\end{center}
\end{figure}
The resistance to the bending from the body can also contribute to the torque, therefore, we further discuss the effects of elastic and viscous forces in the body in a general way. We assume that the elastic force requires an additional torque $T_s=C_e\kappa$ and that the viscous force requires an additional torque $T_v=C_v\dot{\kappa}$. Since when these torque dominates, the torque pattern just coincides with the curvature pattern, a traveling wave, we consider the case in which these torques are significant but smaller compared to the torque from external forces. Therefore, the coefficients $C_e$ and $C_v$ are chosen such that maximal values of these torques are 20\% of the maximal values of the torque from external forces, i.e. $T=T^e/\max(T^e)+0.2 \dot{\kappa}/\max(\dot{\kappa})$ and $T=T^e/\max(T^e)+0.2 \kappa/\max(\kappa)$. For $\xi<1.8$, the inclusion of elastic force causes the wave speed of the torque in the middle part to decrease (Fig.~\ref{fig:elast}a). For example, $v_T/v_\kappa= 2.9$ for $\xi = 1$. The inclusion of viscous force causes the wave speed of the torque in the middle part to decrease. For example, $v_T/v_\kappa= 1.8$ for $\xi = 1$.
In this study, we also adopted a highly simplified locomotion gait, but organisms adopt gaits different from a single-mode sinusoidal curvature wave during turning and other maneuvers~\cite{padmanabhan2012locomotion,saggiorato2017human}. The torque pattern and neural control required for these maneuvers may be quite different and warrant further study.
As shown in our variation study and previous studies, inertia, body elasticity, interactions between body parts, and complex body geometry may all affect the torque and muscle activation patterns. Therefore, the predicted torque from our simple model probably cannot match the muscle activation of a particular organism in detail. However, the torque predicted by our model is certainly an important part of the total torque that needs to be overcome by many organisms.
Our results predict that muscle activation is no longer a traveling wave when the dominant forces that the animal must overcome are external resistive forces and the wave number is greater than two (e.g., the snake in \cite{sharpe2015locomotor}). However, to our knowledge, muscle activation and neural control in animals with wave numbers greater than 2 have not been studied. From another perspective, our results predict that muscle activation of a traveling wave cannot produce a uniform bending wave for more than two wavelengths if external forces significantly contribute to the torque. For robotic systems, our results show that the distributions of torque magnitude and energy output along the body can be adjusted by varying the wave number; this information may guide the design of driving systems and the use of passive materials.
In summary, our study provides a general picture of the torque pattern from resistive forces in undulatory locomotion, including new and complex patterns that have not previously been observed. By introducing the phasor diagram for undulatory locomotion, we show that the torque pattern can be understood from the integration of distance-modulated force phasors and that the rapid transitions occurring near integer numbers are the result of the cancellation of the force phasors. The phasor diagram method may be a useful tool to further investigate the interplay between torque, passive body forces, body shape, and external forces in undulatory locomotion.
\section{Acknowledgments}
Funding for Y.D. and T.Y.M. was provided by NSFC grant No. 11672029, NSAF-NSFC grant No. U1530401, and the Recruitment Program of Global Young Experts.
\bibliographystyle{apsrev4-1}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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Artistic practice: Adriana Sa is a transdisciplinary artist, musician, performer/ composer and researcher. In the 1990s she started using sensor technologies to explore music connected to light, movement, architecture and weather. Currently she explores disparities between human perception and digital analysis as creative material. With John Klima she developed 3D software that operates based on her custom, acoustic zither input. Between 1995 and 2009 she worked full-time on her artistic projects, with grants, supports and commissions. Her work was presented in Europe, USA, Japan and Brazil. Adriana performed and exhibited in venues such as Calouste Gulbenkian Foundation, Culturgest, Serralves, Teatro Maria Matos, Museu do Chiado and Rivoli (Portugal), Experimental Intermedia Foundation and PS1/ MoMa (US), Caixa Forum and Arteleku (Spain), Kampnagel and T-U-B-E (Germany) ICA – Institute of Contemporary Arts (UK), Aomori Contemporary Art Center (Japan). She also performed in non-conventional contexts, such as a codfish-drying factory and a chapel (Portugal), or an active textile mill (UK). She was equally invited to festivals such as LEM (Spain), Ultrasound and Atlantic Waves (UK), Luzboa Biannual, Bons Sons (Portugal), Sonorities (Irland), Novas Frequências (Brasil) and Version Beta (Switzerland), among others. Academic practice: After more than a decade dedicated to artistic practice, Adriana entered the academic world. In 2016 she was awarded a PhD in Arts and Computing Technologies at Goldsmiths, University of London, funded by the FCT. Her research bridges creative practice and perception science. She published with the MIT (Leonardo Almanac 2013 and Leonardo Transactions 2015), with the Journal Of Science And Technology Of The Arts (2015), with XCoAX 2014 and XCoAX 2017, as well as with NIME 2014. She chaired the ICLI – International Conference on Live Interfaces 2014 and was the main editor of its e-book. She was a scientific committee member of CHI 2013 – Conference on Human-Computer Interaction, ICMC – International Computer Music Conference (2015, 2016 & 2017), ICLC – International Conference on Live Coding (2015 & 2017), ICLI 2016 & 2018, Invisible Places – Sound, Urbanism and Sense of Place (2014 & 2017), xCoAx – Conference on Computation, Communication, Aesthetics & X (2017 & 2018). She also evaluated submissions for the Leonardo Journal (MIT) and the Digital Creativity Journal (Routledge). Currently she teaches at University of Coimbra, at ESAD – Upper School of Arts and Design/ IPL and at Lusofona University.
2016: Doutoramento. PhD. Arts and Computing Technologies at Goldsmiths.
|
{
"redpajama_set_name": "RedPajamaC4"
}
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Kalel, 15 (stilizzato come KALEL, 15) è un film del 2019 diretto da Jun Robles Lana.
Trama
La vita del giovane Kalel è piena di segreti che devono restare tali: è figlio illegittimo di un prete, sua madre ha una relazione con un uomo sposato e sua sorella ha avuto un aborto in giovane età. Insicuro per natura e cresciuto sentendosi che deve vergognarsi per peccati che non ha commesso, il ragazzo finisce per cercare incautamente l'amore con perfetti sconosciuti che ha conosciuto su internet. Quando, all'età di 15 anni, gli viene diagnosticata l'AIDS, la sua già fragile esistenza viene completamente sconvolta.
Riconoscimenti
2019 - Tallinn Black Nights Film Festival
Miglior regia
2019 - FAMAS Awards
Nomination Miglior montaggio
2020 - Gawad Urian Awards
Miglior attore a Elijah Canlas
Miglior sceneggiatura
Nomination Miglior film
Nomination Miglior regia
Nomination Miglior fotografia
Nomination Miglior montaggio
Nomination Miglior colonna sonora
Nomination Miglior suono
Nomination Miglior scenografia
2020 - FAMAS Awards
FAMAS Award al Miglior attore a Elijah Canlas (vinto ex aequo con Kristoffer King per Verdict)
FAMAS Netizens' Choice al Miglior attore a Elijah Canlas
Nomination Miglior film
Nomination Miglior regia
Nomination Miglior sceneggiatura
Nomination Miglior fotografia
Nomination Miglior scenografia
Nomination Miglior colonna sonora
Nomination Miglior suono
2020 - Asian Film Festival Rome
Miglior attore a Elijah Canlas
Note
Collegamenti esterni
Film drammatici
Film per ragazzi
Film a tematica gay
Film sull'omosessualità adolescenziale
Film sull'AIDS
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
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The Army–Navy lacrosse rivalry is an intercollegiate lacrosse rivalry between the Army Black Knights and the Navy Midshipmen. The two programs, historical rivals in other sports like football and soccer, have a fierce and nationally-relevant rivalry in lacrosse as well. With 25 national championships, 10 Final Fours in the NCAA era, and 190 consensus first team All-Americans, the two teams have been integral to the game's history. The rivalry carries a different spirit than many others in collegiate lacrosse, described by former Navy goalie Ryan Kern as: "t's the same camaraderie that you had in the fall with the football game and it kind of comes out again in the spring with the lacrosse game," Navy junior goalie Ryan Kern said. "No doubt, all the other sports are important, but just the sheer number of people that come to this game is crazy — just like the football game. You see 16,000 people come to a regular season lacrosse game, and that's not happening at other lacrosse programs." After 101 meetings, Navy leads the series 62–36–3 through 2021.
Series History
Pre-NCAA Era (1924 to 1970)
The teams first met in 1924, with the Midshipmen shutting out Army 5–0 in West Point. The rematch occurred the next year in Annapolis, the second of four consecutive Navy victories to begin the series. A tie in 1928 was part of the Midshipmen's first national championship season and 7–1–1 record. That game was followed by a three goal Army win five years later, their first in the rivalry; the series has been played annually since. The 1940s were a high point for the rivalry, as Army would capture national championships in the 1944 and 1945 seasons, sharing the '45 title with the Midshipmen. Navy campaigns in 1943, 1946, and 1949 also resulted in titles during this period.
Another crucial period began in the late '50s, as either Army or Navy won at least a share of the Wingate Memorial Trophy every year from 1958 to 1970. The lone exception during this stretch was 1968, when Johns Hopkins won the national championship outright. Navy's dominance over the sport was only checked by the Black Knights, the only team from the 1959 to 1966 to defeat the Mids. '61 and '63 victories in Annapolis by the Cadets were the only by a collegiate program during this period. Both teams entered the 1964 game with identical 8–0 records, with Navy pulling off their first win of four straight victories.
Navy Dominance (1970s to 2010)
1970 ended with a three-way split of the national title between Navy, Hopkins, and Virginia. In the final game, Navy prevailed over Army to complete its undefeated season and secure a share of its 17th national title. The following year, the first NCAA Division I Men's Lacrosse Championship was held. The 1971 edition featured both the Cadets and Midshipmen, who both fell in the Final Four. Beginning in 1973, the Naval Academy would win its first of nine consecutive against Army, including a 16–13 victory in the 1978 NCAA tournament. The quarterfinals matchup was led by two Mids players, Mike Hannan and Mike Buzzell, with 6 and 5 goals respectively. In 1981, the Black Knights would halt the streak with a one goal victory in Annapolis. However, a postseason rematch would go the way of the Midshipmen. Outscoring Army nine to three in the second half, Navy would prevail 16 to 10.
In 1991, Army would join the Patriot League and relinquish its previous status as an independent program. The Midshipmen would abstain from conference membership until 2000, when it joined the ECAC Lacrosse League. Despite being a full member of the Patriot League since 1991, Navy would finally move its lacrosse program to the conference in 2004. That season would be the best for the Mids since the 1970s, as they captured both the regular season and conference tournament championships. That included an 18–10 victory over #9 Army in their first conference meeting. In the 2004 NCAA Championship, Navy would earn the 2 seed and make a run to the title game against the Syracuse Orange. A Michael Powell game winner capped a 3–1 Syracuse run in the final five minutes to deny the Mids their first NCAA title.
Subsequent years would generally not be kind for the Cadets. From 1973 to 2009, Navy would go 34–8 against Army, including a 13 game winning streak spanning 1998 to 2007. While Army would snap that streak in 2008 with a nine to six victory, the Cadets would not win more than two consecutive games until 2010.
Recent Years (2010 to Present)
In 2010, Army won their first of six straight games against Navy, their longest streak in the rivalry's storied history. A 2011 victory in Annapolis was the Cadets' first since the 1997 campaign. Since 2015, the series has been relatively balanced, with the Midshipmen taking four of seven matchups. This has included two overtimes games, a 2016 victory for the #9 Mids to clinch the league title and a 2019 win for #20 Army, the 100th game in the rivalry's history. In the Patriot League tournament, the teams have split six meetings, three of which came in the final. After the 2020 game was cancelled due to the COVID-19 pandemic, the teams met again in 2021, with #16 Navy pervailing over #10 Army 9–4.
Rival Accomplishments
The following summarizes the accomplishments of the two programs.
Game results
References
College lacrosse rivalries in the United States
Army Black Knights men's lacrosse
Navy Midshipmen men's lacrosse
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
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package com.huawei.esdk.demo.gen;
import javax.xml.bind.annotation.XmlAccessType;
import javax.xml.bind.annotation.XmlAccessorType;
import javax.xml.bind.annotation.XmlRootElement;
import javax.xml.bind.annotation.XmlType;
/**
* <p>Java class for anonymous complex type.
*
* <p>The following schema fragment specifies the expected content contained within this class.
*
* <pre>
* <complexType>
* <complexContent>
* <restriction base="{http://www.w3.org/2001/XMLSchema}anyType">
* <sequence>
* <element name="resultCode" type="{http://www.w3.org/2001/XMLSchema}int"/>
* <element name="alarmEvent" type="{esdk_ivs_professional_server}AlarmEvent" minOccurs="0"/>
* </sequence>
* </restriction>
* </complexContent>
* </complexType>
* </pre>
*
*
*/
@XmlAccessorType(XmlAccessType.FIELD)
@XmlType(name = "", propOrder = {
"resultCode",
"alarmEvent"
})
@XmlRootElement(name = "getAlarmEventInfoResponse")
public class GetAlarmEventInfoResponse {
protected int resultCode;
protected AlarmEvent alarmEvent;
/**
* Gets the value of the resultCode property.
*
*/
public int getResultCode() {
return resultCode;
}
/**
* Sets the value of the resultCode property.
*
*/
public void setResultCode(int value) {
this.resultCode = value;
}
/**
* Gets the value of the alarmEvent property.
*
* @return
* possible object is
* {@link AlarmEvent }
*
*/
public AlarmEvent getAlarmEvent() {
return alarmEvent;
}
/**
* Sets the value of the alarmEvent property.
*
* @param value
* allowed object is
* {@link AlarmEvent }
*
*/
public void setAlarmEvent(AlarmEvent value) {
this.alarmEvent = value;
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
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William Cramer FRSE (2 June 1878 – 10 August 1945) was a German-born British pathologist and physiologist, best known for his work with the Imperial Cancer Research Fund.
Biography
William Cramer was born in Germany on 2 June 1878. He received his first tertiary education at the University of Munich, and received his Ph.D. at the University of Berlin in 1901. He achieved his D.Sc. at the University of Edinburgh in 1908, during which time he had worked under Swale Vincent. Cramer took the English Conjoint qualification after nine years as a chemical physiology lecturer at Edinburgh. He had worked briefly for the Imperial Cancer Research Fund in 1904; he rejoined the organisation in 1914.
In 1907 he was elected a Fellow of the Royal Society of Edinburgh. His proposers were Sir Edward Albert Sharpey-Schafer, Francis H A Marshall, Alexander Crum Brown and James Cossar Ewart.
Shortly after the outbreak of World War I, Cramer became a naturalised British citizen. He was elected a Foreign Member of the German Society for the Investigation of Cancer. In 1933, he was an official British delegate at the International Cancer Congress in Madrid, and again in 1934 at the International Cancer Research conference in Paris. In 1939, after 25 years with the Imperial Cancer Research Fund, Cramer relocated to St. Louis, Missouri, where he was head pathologist at the Barnard Skin and Cancer Hospital, and a research associate at Washington University.
Throughout his career, Cramer authored numerous papers on cancer, physiology, and biochemistry. His textbook, Practical Course in Chemical Physiology, had reached its fourth edition by 1920. Cramer belonged to the Physiological Society, the Pathological Society, and the Biochemical Society.
References
1878 births
1945 deaths
Ludwig Maximilian University of Munich alumni
Humboldt University of Berlin alumni
Alumni of the University of Edinburgh
British pathologists
German emigrants to the United Kingdom
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
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It's a familiar story seen and heard in mountain towns all over the West. People from all over the country discover their wanderlust and passions for outdoor adventure, often chasing those dreams to the crags, peaks, and powder of the American West. Often, these dreams are pursued as a way of life, with the comforts and material possessions of modern life forsaken so that the individual may spend as much time pursuing the passions to satisfy the soul.
Author Luke Mehall presents an often hilarious, sometimes contemplative, but also spot-on collection of tales and essays in his pursuit of climbing Nirvana, relocating from the flatlands of Illinois, to the lofty environs of Colorado so that he may live the "dirtbag" existence in his twenties and thirties. Mehall's definition of a "dirtbag" will ring true as being "she or he who spends their days in the outdoors, engaged with some recreational activity, and works just enough to pay for their basic necessities of a dirtbag existence." Sound familiar?
Mehall details his upbringing in the flat Midwest, and his use of any and almost all mind-altering substances as being his main recreational pursuits. He eventually discovers climbing and pursues his passion to his adopted home of Colorado, and spins tales of adventure, misfortune, and discovery to all of the best places to pursue climbing in the west including Yosemite, Red Rocks, Southern Utah, Joshua Tree and south of the border to Mexico.
Mehall recollects on his early days of climbing with childhood friend "Two Tent Timmy," a fearless and strong climber who gave him inspiration only to see the friends drift apart and reconnect later in life over climbing.
The essential road trip stories that he undertakes in his "Freedom Mobile" a 1998 Mazda he has painted with the stars and stripes ("do you get pulled over a lot? Asks a gas station attendant) are recounted with the fond recollections of wanderlust, cautionary tales, interesting people, and funny tales that are sure to accompany any extended venture when traveling by car around the West.
Mehall's easy style makes the book hard to put down, as almost everyone can relate to his words in someway. The ending is all too familiar to most of us however, and Mehall provides the inevitable disclaimer in the introduction. "Eventually I changed my ways and was drawn back into a more domestic middle class existence, with a bed to rest my head upon, and a desk to write on." Often true- but his memories will surely spark you to recall your dirtbag existence whether it for a one summer or winter, or a way of life for several years.
September 10, 2014 in Climb.
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{
"redpajama_set_name": "RedPajamaC4"
}
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\section{Introduction}
\label{sec:introduction}
\begin{figure}[hb!]
\centering
\includegraphics[width=0.95\textwidth]{model.pdf}
\caption{Active Speakers in Context (ASC) uses feature representations of face crops and audio provided by short-term encoders (STE). Through a pairwise analysis of feature representations of different speakers at distinct time steps made by a self-attention module (SAT) and the subsequent temporal refinement made by a long short-term memory (LSTM), ASC classifies an active speaker. By adding a face-voice association module (FV), FaVoA supports the classification of active speakers in challenging scenarios where the context does not provide enough information. The face-voice association module is combined with the output of ASC via a gated bimodal unit (GBU). Modules and layers in yellow are pretrained and fixed, those in violet are pretrained but are also updated during fine-tuning, and the ones in blue are trained from scratch.}
\label{fig:model}
\end{figure}
The task of active speaker detection (ASD) consists of determining from which individuals in an audiovisual footage a given speaking activity originates. The combined use of auditory and visual modalities is fairly common in multimodal learning, including tasks like speech enhancement~\cite{hou2018}, speaker diarisation~\cite{chung2020}, speech reconstruction~\cite{qu2019}, and active speaker detection~\cite{alcazar2020b}. ASD is closely related to other audiovisual multimodal learning tasks, and a high-performing ASD model might help in paving the way for better models for those tasks to emerge. Related tasks include speech enhancement~\cite{hou2018} and speech separation~\cite{chung2020,qu2020}.
Recent solutions to the problem of detecting speaking activity in the wild involve the use of 3D convolutions~\cite{chung2019,zhang2019b}, information from other individuals in the same scene~\cite{alcazar2020b} and the optical flow of facial movements~\cite{huang2020}. Although being very powerful, those models still face some difficulties depending on the resolution or the inclination of a person's face~\cite{alcazar2020b,huang2020,roth2020}. Most of them also struggle when working with medium- to long-term time spans~\cite{chung2019,huang2020,roth2020,zhang2019b}.
In cases where faces are not clear enough, ASD must rely mainly on the auditory modality. However, in scenes where there are two people talking to each other and their faces are not clear enough -- due to a low resolution or to a high yaw inclination of their faces --, neither the visual nor the auditory modalities can provide enough information on their own. The existence of a module capable of retrieving a frontal face representation from the speaker's voice might provide information useful for speaker disambiguation in such challenging scenarios. Face-voice association applications show that it is actually possible to retrieve a frontal face representation from a speaker's speech signal~\cite{kim2018,oh2019}. The retrieved frontal face can be useful in cases in which the voice of the person speaking does not match the face of the person being classified for any of several reasons, e.g., difference in gender, ethnicity, age and so on. Additional information obtained via the crossmodal aspect of face-voice association, where one can relate one speech signal with a person's face, can help determining some clear cases that can be challenging for other models. For instance, if the mouth of the actual speaker in the scene is not seen for some reason, and no mouth movement is detected from any other participant in the scene. A non-speaking person whose face does not match the actual speaker's voice would be classified as not speaking. The actual speaker can also be properly classified if the face of no other scene participant matches the voice.
The contributions of this paper include the creation of FaVoA (\textbf{Fa}ce-\textbf{Vo}ice Association \textbf{A}mbiguous Speaker Detector), a model (depicted in Figure~\ref{fig:model}) capable of detecting speaking activities in scenarios in which the context does not provide enough information, e.g., several people speaking simultaneously. We furthermore provide a quantitative evaluation on how much face-voice association actually contributes to the detection of speaking activity.
The remainder of the paper is structured as follows. Section~\ref{sec:related} presents the approaches that have been proposed to tackle the active speaker detection task, as well as applications of face-voice association. Section~\ref{sec:model} introduces the model used in this research to address the task of active speaker detection. The model performance was assessed and compared with state-of-the-art architectures. The details on the experimental setup as well as its results are presented in Section~\ref{sec:experiments}. That section also offers a discussion on those results, as well as an analysis on how much importance face-voice association plays in ASD. Finally, Section~\ref{sec:conclusion} summarises the findings of this research and offers possibilities for future works.
\section{Related Works}
\label{sec:related}
\subsection{In-the-wild active speaker detection}
\label{sec:asd}
AVA-ActiveSpeaker~\cite{roth2020} was the first dataset built for in-the-wild active speaker detection. It was composed of videos in different resolutions with actors speaking in various distinct languages. Labels were provided for some speakers in selected frames of those videos depending on their speaking activity. The labels could be ``not speaking'', ``speaking audible'' and ``speaking not audible''. The dataset was built as part of a task at the 2019 ActivityNet Challenge. The task used mean average precision (mAP) as its evaluation metric and the audibly speaking activity as the positive class for that matter. Two competitors~\cite{chung2019,zhang2019b} achieved a higher mAP than the baseline provided by Roth et al.~\cite{roth2020}. Both models depended on a lip synchronisation preprocessing step, and could only achieve a high performance when working with short-term time spans and usually in scenarios in which there was only one person speaking~\cite{alcazar2020b,chung2019,zhang2019b}.
To address the shortcoming of previous models, Alc\'{a}zar et al.~\cite{alcazar2020b} propose Active Speakers in Context (ASC), a model whose main intuition is to leverage active speaker context from long-term inter-speaker relations. It differs from previous approaches by using not only the information of the face of the target individual and of the audio input, but also that of the faces of other individuals detected at the same timestamp~\cite{alcazar2020b}. The addition of the information from the context in which a speaking activity happens grants ASC an mAP higher than that of Zhang et al.~\cite{zhang2019b}, but still lower than that of the ensemble models of Chung~\cite{chung2019}. Even though the context aids in some challenging scenarios, it may not prove useful in scenarios in which the mouth of the speaker is not seen due to low resolution or for the speaker not facing the camera, and when there are several people speaking simultaneously.
Dense optical flow is also used for ASD, as a means to strengthen facial motion visual representation and this way avoid confusions that happen to audiovisual fusion-based models due to factors such as non-speaking facial motion, varied lighting and low-resolution footage~\cite{huang2020}. The inclusion of the dense optical flow grants the model a performance higher than the baseline model of Roth et al.~\cite{roth2020} in two distinct metrics~\cite{huang2020}, yet no mAP comparison is offered. No comparison with any other architecture is provided either. Similar to other models, the performance of that approach degrades when dealing with faces in low resolution or that are highly tilted.
\subsection{Learning of face-voice association}
\label{sec:facevoice}
Learning of face-voice relations results from continuous and extensive exposure to audiovisual stimuli~\cite{gaver1993}. Psychology studies with infants indicate that the ability to make arbitrary face-voice associations emerge in humans between two and four months of age~\cite{bahrick2005}. In the area of active speaker detection, the advantage of matching visual and auditory representations was shown via the use of contrastive loss by some models~\cite{huang2020,zhang2019b}. Those implementations, however, do not explicitly make use of the advantages face-voice associations can provide.
Applications of face-voice association in audiovisual crossmodal representation learning include the assembling of models capable of generating human faces from speech inputs~\cite{choi2020,oh2019}, as well as of models that can retrieve or match inputs from one modality given inputs of the other modality~\cite{kim2018,nagrani2018}. The performance of active speaker detection models degrades in cases where faces have a very small resolution or a large yaw angle~\cite{huang2020}. The ability to retrieve frontal facial embeddings from speech embeddings might provide additional information capable of helping with those challenging cases.
\subsection{Gated bimodal unit}
\label{sec:gmu}
\begin{figure}[ht!]
\centering
\includegraphics[width=0.65\textwidth]{GBU.pdf}
\caption{GBU inner structure}
\label{fig:gbu}
\end{figure}
To determine if face-voice association presents an actual contribution to the task of ASD and in which cases it contributes the most, one should be able to evaluate its contribution quantitatively. Gated multimodal units (GMUs)~\cite{arevalo2017} are modality fusion mechanisms capable of providing quantitative values on the contribution of a given modality to the classification of a dataset entry. The gated bimodal unit (GBU) is a special case of the GMU oriented for the case where there are only two modalities to be fused. GMUs incorporate ideas from feature and decision fusion~\cite{arevalo2017}. The model architecture is based on the flow control of gated neural networks, e.g., gated recurrent units (GRUs)~\cite{cho2014}. Given embeddings $\mathbf{e}_1, \mathbf{e}_{2} \in \mathbb{R}^{d}$ from different modalities, the GBU outputs a fused embedding $\mathbf{z} \in \mathbb{R}^{d}$. As indicated in Figure~\ref{fig:gbu}, the GBU architecture is similar to the update gate of a GRU. In that sense, the GBU fused modality $\mathbf{z}$ is given by
\begin{align}
\mathbf{z} &= \mathbf{p} \odot \mathbf{h}_1 + (\mathbf{1} - \mathbf{p}) \odot \mathbf{h}_2, \label{eq:gbuz} \\
\mathbf{p} &= \sigma \left( \mathbf{W}_p \left( \mathbf{e}_1 \mathbin\Vert \mathbf{e}_2 \right) + \mathbf{b}_p \right), \label{eq:gbup} \\
\mathbf{h}_i &= \mathrm{tanh} \left( \mathbf{W}_i \mathbf{h}_i + \mathbf{b}_i \right), \label{eq:gbuhi}
\end{align}
where $\odot$ denotes the Hadamard product, $\sigma$ the sigmoid function, $\mathbin\Vert$ vector concatenation and $\mathbf{1} \in \mathbb{R}^{d}$ an all-one vector. It is worth noticing from Equations~\ref{eq:gbuz} and~\ref{eq:gbup} that $\mathbf{p}$ can be interpreted as a vector of probabilities $p_1, p_2, \ldots, p_d$ that indicate the relevance of each modality in every element $z_i \in \mathbf{z}$. In other words, $z_i \in \mathbf{z}$ is composed of a linear combination of $h_{1, i} \in \mathbf{h}_1$ and $h_{2, i} \in \mathbf{h}_2$. The contribution of $h_{1, i}$ in $z_{i}$ is given by $p_{i}$ and that of $h_{2, i}$ is given by the complement of $p_{i}$, i.e., $1 - p_{i}$. Besides the case in which $p_{i} = 0.5$, one of the modalities will provide a major contribution to $z_{i}$ while the other will deliver a minor contribution.
\section{Model Architecture and Training Method}
\label{sec:model}
\subsection{Input data, Active Speakers in Context, and FaceVoice}
\label{sec:input_data}
FaVoA incorporates the context information of Active Speakers in Context (ASC)\hspace{0pt}~\cite{alcazar2020b} and the face-voice association provided by FaceVoice~\cite{kim2018}. And as such, the proposed model requires input data that can be fed to both models. Figure~\ref{fig:model} shows the architecture of the model, how it receives the input data and how it processes it. For the part imported from ASC, given a frame and a person in that frame, the model receives that person's face as a $144 \times 144$ image, as well as the audio input from that particular part of the video, which is converted to a MFCC spectrogram. Both inputs are sent to a short-term encoder, denoted as STE in Figure~\ref{fig:model}, which outputs a vector $\mathbf{u} \in \mathbb{R}^{1024}$. The STE is composed of two ResNet-18 CNNs~\cite{alcazar2020b}, one for each modality, which output vectors of 512 dimensions, which are then concatenated to produce $\mathbf{u}$~\cite{alcazar2020b}. The STE was pretrained with the weights provided by Alc\'{a}zar et al.~\cite{alcazar2020b} and kept fixed during training. From FaceVoice, only its voice subnetwork was used, which is denoted as FV in Figure~\ref{fig:model}. It requires 10 seconds of continuous speaking activity as input. However, it is not common for datasets built for active speaker detection to have the same person speaking for such a long time. To work around this restriction, the same audio input sent to STE was replicated until the repeated input had the length of 10 seconds. This approach was taken because the semantics of what is being said was irrelevant for this task and only the speaking activity was of interest. Given a 10-second audio input, FV then outputs a vector representation $\mathbf{a} \in \mathbb{R}^{128}$. FV was pretrained with the weights provided by Kim et al.~\cite{kim2018}, but unlike STE its weights were not kept fixed.
In order to make use of the context in which a given speaking activity takes place, the vector representations $\mathbf{u}$ provided by the STE are combined and organised in a tensor $\mathbf{C}$. Tensor $\mathbf{C}$ is built in such a way that it may contain information from the time steps before and after the given speaking activity as well as from other speakers in the same scene. $\mathbf{C}$ has dimensions $L \times S \times 1024$, where $L$ is the number of frames used for the context and $S$ is the number of speakers. Those $L$ frames are defined according to a specific time step $t$, in which the speaking activity to be classified happens. The frames must be selected in a way that time step $t$ lies at the centre of the frame sequence. A sequence of $L$ frames should contain every frame from time step $t - \lfloor L / 2 \rfloor \tau$ to $t + \lfloor L / 2 \rfloor \tau$ with hops of $\tau$ units of time between each selected frame. It is worth noticing that the sequence of frames does not need to be contiguous. Given the frame of interest at time step $t$, a set of $S$ speakers in that frame is selected. If there are only $S^{\prime} < S$ speakers on the frame of interest, then information of some of those $S^{\prime}$ may be used more than once when working with that frame of interest. In a similar fashion, if some selected speaker appears only in a part of the frame sequence, its foremost activity is replicated all the way until the first frame of the sequence, and analogously its last activity is also replicated all the way until the last frame of the sequence. A more detailed explanation on the selection of frames and speakers can be found in the ASC original paper~\cite{alcazar2020b}. Tensor $\mathbf{C}$ is then subjected to a self-attention unit (SAT in Figure~\ref{fig:model}) and a single-layer LSTM for the sake of context refinement. The LSTM produces outputs $\mathbf{c^{\prime}_{i}} \in \mathbb{R}^{128}, 1 \leq i \leq L \times S$, which are concatenated into a vector representation $\mathbf{s} \in \mathbb{R}^{L \times S \times 128}$. SAT and LSTM were pretrained with the weights provided by Alc\'{a}zar et al.~\cite{alcazar2020b} and were subjected to updates during training.
\subsection{Fusing speaking context and face-voice association}
\label{sec:fusion_architecture}
By combining the embedding $\mathbf{a}$, provided by FaceVoice, with $\mathbf{s}$, provided by ASC, it is expected that the benefits of face-voice association might aid the active speaker detection model even in cases in which the context is not enough, e.g., when there are several people speaking simultaneously, or when the faces of the speakers are either in low resolution or very tilted. The fusion of those embeddings is made by a GBU unit, but since it requires both modality embeddings to have the same dimension, embedding $\mathbf{a}$ is presented to a ReLU and a linear layer, which outputs a vector representation $\mathbf{a}^{\prime} \in \mathbb{R}^{L \times S \times 128}$. Both $\mathbf{a}^{\prime}$ and $\mathbf{s}$ are then fused by the GBU unit, which produces a fused vector representation $\mathbf{z} \in \mathbb{R}^{L \times S \times 128}$.
The probability $q \! \left( \mathbf{x} \right)$ of a given input $\mathbf{x}$ being classified as ``speaking audible'' is obtained by projection from $\mathbf{z}$ with a linear layer and then the application of a softmax operation over the two classes.
FaVoA was trained on a single NVIDIA GeForce RTX 2080 Ti GPU with 11 GB GDDR6 memory. A single cross-entropy loss $\mathcal{L}$ was used to train it using PyTorch. The loss is given by
\begin{equation}
\mathcal{L} = - y \log \! \left( q \! \left( \mathbf{x} \right) \right) - \left( 1 - y \right) \log \! \left( 1 - q \! \left( \mathbf{x} \right) \right),
\end{equation}
where $y$ represents the expected label, which should be $1$ if there is audible speaking activity, and $0$ otherwise. The model weights were updated through a backpropagation algorithm, by trying to minimise the cumulative loss in every training mini-batch. Data was sent to the model via mini-batches of size 16. Similar to ASC, the model optimisation was done with the ADAM optimiser with an initial learning rate $\gamma = 3 \times 10^{-6}$ and learning rate decay $\eta = 0.1$ every $10$ epochs.
\section{Experiments}
\label{sec:experiments}
\subsection{Dataset}
\label{sec:dataset}
The AVA-ActiveSpeaker dataset is the first dataset intended for the task of active speaker detection that can be considered to be ``in the wild''. Prior to its publication, datasets crafted for this task were mainly composed of high resolution videos with the speakers facing the camera~\cite{roth2020}. AVA-ActiveSpeaker contains videos spoken in very distinct languages, with some of them with low resolution and with video and audio not well synchronised. Speakers may also appear in different video depths, which may cause facial information to be less clear for a learning system, and usually they are not looking at the camera.
The AVA-ActiveSpeaker dataset contains 153 videos, split into 120 for training and 33 for validation. The training dataset is composed of 29,723 speaking/\hspace{0pt}non-speaking streams, ranging from 23 to 304 annotated entries, performed by a total of 10,156 distinct actors, some of them appearing in up to 2,165 dataset entries. The validation dataset has 8,015 streams of speaking/non-speaking activity that range from 14 to 305 dataset annotated entries. Those streams are captured from the performance of 2,515 distinct actors, with some of them having up to 2,143 entries of activity stored in the validation dataset. Table~\ref{tab:label_distribution} displays the label distribution among those datasets.
\begin{table}[ht!]
\caption{Label distribution of training and validation splits of the AVA-ActiveSpeaker dataset.}
\label{tab:label_distribution}
\centering
\def\arraystretch{1.5}\tabcolsep=6pt
\begin{tabular}{@{} l c c c @{}}\hline
& \emph{Not Speaking} & \emph{Speaking Audible} & \emph{Speaking Not Audible} \\ \hline
Training & $1,969,134$ & $682,404$ & $24,776$ \\
Validation & $567,815$ & $192,748$ & $7,744$ \\ \hline
\end{tabular}
\end{table}
\begin{table}[hb!]
\caption{Comparison with state-of-the-art models on the validation subset.}
\label{tab:comparison}
\centering
\def\arraystretch{1.5}\tabcolsep=6pt
\begin{tabular}{@{} l c c c @{}} \hline
& \textbf{mAP} $\uparrow$ & \textbf{AUC} $\uparrow$ & \textbf{Balanced accuracy} $\uparrow$ \\ \hline
ASC~\cite{alcazar2020b} & $0.871$ & N/A & N/A \\
TC-LSTM Ensemble + Wiener~\cite{chung2019} & $0.878$ & N/A & N/A \\
Multi-Task Learning~\cite{zhang2019b} & $0.840$ & N/A & N/A \\
V+O+A VCE-CL~\cite{huang2020} & N/A & $0.932$ & $0.869$ \\
AV-GRU-f2~\cite{roth2020} & $0.821$ & $0.910$ & $0.814$ \\ \hline
\textbf{FaVoA} & $0.847$ & $0.928$ & $0.846$ \\ \hline
\end{tabular}
\end{table}
\subsection{Experimental results}
\label{sec:results}
To evaluate FaVoA, its performance was compared with AV-GRU-f2, the baseline model provided by Roth et al.~\cite{roth2020}, ASC (Active Speaker in Context)~\cite{alcazar2020b}, Chung's TC-LSTM Ensemble + Wiener smoothing~\cite{chung2019} and Zhang et al.'s Multi-Task Learning model~\cite{zhang2019b}. Following the indications on the 2019 ActivityNet challenge, mAP is employed as the metric for this comparison. Table~\ref{tab:comparison} presents the achieved performance of state-of-the-art models and compares them with that of the model described in Section~\ref{sec:model}.
Comparisons were also made with Huang and Koishida's F+O+A VCE-CL (Facial Image, Optical Flow and Audio Signal Visual-Coupled Embedding with Contrastive Loss)~\cite{huang2020}. It, however, does not offer performance values using the mAP metric. Because of this, a comparison is here provided using other metrics instead, namely the area under the ROC curve (AUC) and the balanced accuracy. Those metrics were also published for AV-GRU-f2~\cite{roth2020}. Performance results of those models, as well as FaVoA's, are also offered by Table~\ref{tab:comparison}. Table~\ref{tab:comparison} shows that not only FaVoA outperformed AV-GRU-f2 in every metric, but it also presents an mAP considerably higher than that of the multi-task learning approach~\cite{zhang2019b}, which was the runner-up in the 2019 ActivityNet challenge. Its AUC is also close to that obtained by V+O+A VCE-CL~\cite{huang2020}.
\subsection{Contribution of face-voice association to active speaker detection}
\label{sec:contribfacevoice}
Ablation studies are performed to determine whether a given addition to a model makes an actual difference in its performance. However, they do not offer quantitative measures of how much that addition contributes to the classification. For multimodal classification, this is an important issue if one wants to better understand whether some modality contributes more than another to a given task. The use of GBU for crossmodal integration allows to determine if a given classification favours one modality or another. In the case of this study, the interest lies in determining if the classification is mostly due to context information (from ASC) or to face-voice association (from FaceVoice).
In order to quantify the contribution of each modality, one can use the vector $\mathbf{p}$ produced by the GBU sigmoid unit (see Figure~\ref{fig:gbu} and Equation~\ref{eq:gbup}). For every entry of the dataset, a vector $\mathbf{p}$ can be extracted. This vector contains elements $p_i$, whose values range from $0$ to $1$. Each element $p_{i}$ represents a degree of contribution of modality input $\mathbf{e}_{1}$ (see Figure~\ref{fig:gbu}) to element $z_{i} \in \mathbf{z}$. In turn, the degree of contribution of modality input $\mathbf{e}_{2}$ to element $z_{i} \in \mathbf{z}$ is $1 - p_{i}$. By taking the fraction of elements of $\mathbf{p}$ whose value is greater than $0.5$, one can determine the fraction of elements of $\mathbf{z}$ that favours modality input $\mathbf{e}_{1}$ rather than $\mathbf{e}_{2}$. This way, one can get a quantitative measure of the contribution of modality input $\mathbf{e}_{1}$ to the classification and consequently, the contribution of $\mathbf{e}_{2}$ is simply one minus the contribution of $\mathbf{e}_{1}$. In our case modalities $\mathbf{e}_{1}$ and $\mathbf{e}_{2}$ correspond to the resulting vector representation of the FaceVoice module and the one of ASC.
The graph of Figure~\ref{fig:contribution_graph} presents a histogram of the degree of contribution of face-voice association to the detection of speaking activity in entries of the validation set. The horizontal axis of the graph represents the degree of contribution of face-voice association, ranging from $0$ to $1$. The vertical axis represents the number of entries in the dataset for which the face-voice association had a particular degree of contribution. It can be noticed in the graph that context has a greater contribution to the classification than face-voice association in the entries of the validation set. Nevertheless, context is never favoured by all elements of the GBU output. Besides, face-voice association has a degree of contribution greater than $0.15$ for nearly $40\%$ of the entries, and for $303$ entries this degree of contribution can get higher than $0.3$.
\begin{figure}[hb!]
\centering
\subfloat[Number of entries per degree of contribution.\label{fig:contribution_graph}]{
\raisebox{-.5\height}{
\includegraphics[width=0.5125\textwidth]{contribution_trimmed.png}
\rule[-1pt]{0pt}{50pt}
}
}\hfil
\subfloat[Face-voice association has a much higher degree of contribution for the man marked in green than for the other actors.\label{fig:gbucontribution_example}]{
\raisebox{-.5\height}{
\includegraphics[width=0.375\textwidth]{gbu_contribution.png}
\rule[-18pt]{0pt}{50pt}
}
}
\caption{Degree of contribution of face-voice association in entries of the validation set.}
\label{fig:contribution}
\end{figure}
The contribution graph has three modes. The highest peak and its surrounding values correspond mostly to active speakers whose faces are clearly visible, or to silence. The region surrounding the leftmost peak corresponds to dataset records where there is some sound activity and the face of the active speaker is not entirely clear or the face being analysed is clearly not from the active speaker. The rightmost part of the graph, with degrees of contribution greater than $0.275$, corresponds to entries in which there are very loud sounds. Figure~\ref{fig:gbucontribution_example} depicts a scene in which the GBU assigns a reasonably higher degree of contribution of face-voice association for the man in the foreground ($0.198$) than for the other actors ($0.098$ for the woman in the foreground, and $0.129$ and $0.132$ for the actors in the background). This happens due to the presence of a male voice in the scene and the higher resolution of the face of the man in the foreground.
\subsection{Comparison with Active Speakers in Context}
The integration of FaceVoice into FaVoA offers the capability of classifying some instances of speech activity in which ASC failed. Figure~\ref{fig:examples} presents three cases in which the context information may be ambiguous and face-voice association proves useful. This may happen when actors are facing sideways and a facial feature may be mistaken for an open mouth. In Figure~\ref{fig:example_wrong_gender}, ASC wrongly classifies the facial hair for an open mouth, and classifies the man as speaking and the woman as not speaking. Face-voice association prevents this misclassification by recognising the female voice and associating it to the woman.
ASC can also mistakenly classify speaking people as not speaking if the mouth of every person in the scene cannot be clearly seen due to low resolution (Figure~\ref{fig:example_low_resolution}) or if people are speaking simultaneously (Figure~\ref{fig:example_multiple_speakers}). ASC classifies every person in both figures as not speaking. Face-voice association can aid with correctly classifying the speaker of Figure~\ref{fig:example_low_resolution} due to the age difference. Regarding the scene depicted in Figure~\ref{fig:example_multiple_speakers}, ASC tends to classify a person as not speaking if someone in the same scene context seems to be already speaking. Thus ASC classifies both speaking women as not speaking, since the speaking activity of one of them triggers ASC to classify the other as not speaking and vice versa. Given the presence of female voices, FaVoA presents a less hesitant behaviour in classifying both women whose faces are not partially hidden as speaking.
\begin{figure}[ht!]
\centering
\subfloat[Wrong gender.\label{fig:example_wrong_gender}]{
\includegraphics[width=0.3125\textwidth]{performance_wrong_gender.png}
}\hfil
\subfloat[Low resolution.\label{fig:example_low_resolution}]{
\includegraphics[width=0.3125\textwidth]{performance_low_resolution.png}
}\hfil
\subfloat[Multiple speakers.\label{fig:example_multiple_speakers}]{
\includegraphics[width=0.3125\textwidth]{performance_multiple_speakers.png}
}
\caption{Examples of cases in which the context does not provide enough information and face-voice association is required for a correct active speaker detection. In the subfigures, people who are not speaking are marked with a red bounding box and those speaking with a green bounding box.}
\label{fig:examples}
\end{figure}
FaVoA presents some difficulties in comparison to ASC in scenes where the person is not speaking, but his/her voice can be heard narrating something. It also makes some mistakes in case there is some chanting and the voice of the person who is chanting somehow resembles that of the person being classified. Finally, ASC tends to more precisely classify some speaking activities (model outputs are mostly either close to $0$ or to $1$), whereas the outputs of FaVoA vary reasonably in the range between $0$ and $1$.
\section{Conclusion}
\label{sec:conclusion}
This paper offers a study on the role of face-voice association in the task of active speaker detection. FaVoA provides a better classification in some challenging scenarios, such as low-resolution faces and several simultaneous speakers. Crossmodal learning models integrate the information from different modalities as a means to better tackle tasks in which one or more of those modalities do not provide enough useful information for some reason. By considering a person's characteristics by his/her voice, FaVoA makes use of the benefits of crossmodality in order to better determine the active speakers in a scene even in cases where the mouth of a speaker cannot be seen. The use of GBU for modality fusion allowed for determining quantitatively the contribution of face-voice association in ASD. By analysing that contribution, some cases of non-speaking activity can be immediately identified, which can help preventing the misclassification of some person as actively speaking. Cases in which there are several speakers can also be identified based on the degree of contribution of face-voice association. In future work, face-voice association may be used to support tackling other crossmodal tasks that involve conversational datasets in which speaker faces may not be clear. Additional directions for improvement in active speaker detection include the addition of other modalities, e.g., gaze and face keypoints.
\bibliographystyle{splncs04}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 8,048
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Q: Parrondo's Paradox game using frequency instead of probability Given the following probabilities :
*
*Game A : coin flip (p1 = 0.49)
*Game B1 : coin flip (p2 = 0.09)
*Game B2 : coin flip (p3 = 0.74)
Given the following game :
Initial balance = 0
Runs = 100000
Heads adds 1, tails adds -1 to the balance.
Do a coin flip (p1 = 0.50) (doesn't add anything to the balance yet).
If Heads :
Then play game A
Else :
If Balance is a multiple of 3, Then play game B1
Else, play game B2
The result of this game tends to more or less 6000. That's Parrondo's Paradox.
But if I change the game by replacing this part
:
Do a coin flip (p1 = 0.50) (doesn't add anything to the balance yet).
If Heads :
...
Else :
...
By :
If current_run%2:
...
Else :
...
Then the result tends to more or less -13000.
My question : why is that ?
I don't understand why since :
*
*coin flip == heads probability = 0.50
*current_run%2 == 1 frequency = 0.50
So the frequency of A, B1 and B2 games run should be the same.
A Jupyter Notebook of the Python implementation of this game can be found here :
https://www.kaggle.com/tomsihap/notebook478df90ec5, and here is a shortened version :
def coinFlipEven():
return 1 if random.random() <= 0.5 else -1
def coinModulo(i):
return 1 if i%2 == 1 else -1
def coinFlipA():
return 1 if random.random() <= 0.49 else -1
def coinFlipB1():
return 1 if random.random() <= 0.09 else -1
def coinFlipB2():
return 1 if random.random() <= 0.74 else -1
n = 1000000
balance1 = 0
balance2 = 0
# Try with even coin flip
for i in range(n):
whichGame = coinFlipEven()
if whichGame == 1:
balance1 += coinFlipA()
else:
if balance1 % 3 == 0:
balance1 += coinFlipB1()
else:
balance1 += coinFlipB2()
# Try with modulo
for i in range(n):
whichGame = coinModulo(i)
if whichGame == 1:
balance2 += coinFlipA()
else:
if balance2 % 3 == 0:
balance2 += coinFlipB1()
else:
balance2 += coinFlipB2()
A: This is a gambler's fallacy, balance counts will not balanced out over trials but they will grow, here decrease because of -1 rewards. See other questions Regression to the mean vs gambler's fallacy.
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
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Fear seems insurmountable for Americans
by Erin Ghere
Since the United States began bombing Afghanistan over a week ago, I have heard many television and radio commentators asking experts if Americans are scared. The answer is obvious – of course we are.
With one fell swoop, the Sept. 11 terrorist attacks took away Americans' confidence in the safety of their day-to-day lives. Prior to the attacks, we felt secure in our homes, at our workplaces, in shopping malls and on vacations. Unsafe areas were thought to be obvious – the crime-ridden parts of town or dark alleys. But after that fateful Tuesday, it is difficult to feel secure no matter where we are.
As news programs air video from Osama bin Laden's al-Qaida terrorist network, which promises continued attacks against innocent American civilians until the United States stops its bombing raids, President George W. Bush and other government officials are telling citizens to get back to their daily lives, go about their business and boost the economy by taking airline flights. This is a challenge Americans cannot be expected to live up to. With images of the initial attacks still very fresh in our minds, and terrorists threatening future attacks, Americans are rightly taking a better-safe-than-sorry perspective on decisions.
A new Federal Airport Administration report released Friday revealed many airports are not fully complying with new FAA safety regulations since the attacks. Newspapers commonly report stories of journalists passing knives, laptop computers, microphones, and other electronic devices through airport security without being detected.
Flights are often cancelled, diverted or landed with F-16 escorts after security breaches or passenger disruptions. There are armed National Guard members stationed at airports throughout the country. The FBI announced Friday the Mall of America was looked at as a possible target by the terrorists, along with Disney World and Disneyland theme parks. And cases of anthrax are popping up all over the United States at media organizations and, most recently, a Microsoft office in Reno, Nevada.
How do government officials expect us to feel safe? We can't feel secure when every day we find more reasons to feel scared. The nation's citizens and law enforcement officials are reacting strongly to every incident, from the Science Museum of Minnesota closing for two days because of a suspicious briefcase and jelly-like substance, to bomb squads and health officials being called in to inspect suspicious packages at businesses and residences across the nation. While necessary, the massive responses to small incidents heighten the public's fear for their safety.
If the president and other officials want Americans to feel secure again, they need to start taking real action to make sure we truly are safe. A Band-Aid cannot fix this situation. Airports and other large public facilities that could attract terrorists' attention need to be safe, and they are not.
I have two plane trips in my near future. The sight of armed soldiers at airports does nothing to calm my nerves. Although President Bush thought it would boost confidence in air travel, it does not encourage me; it makes me feel like I live in another part of the world, where there is constant civil war or restricted freedoms, not the United States of America.
And even with these unnerving institutions of supposed protection, airports are still not secure. No airline employee can tell me absolutely when I step onto a plane there will not be another person with a weapon on board. Despite increased security and armed guards, New York Daily News reporters were able to get a variety of dangerous items past security at 10 major airports last week.
An article in the New York Daily reports, "One news reporter carried a razor-blade cutter, similar to the weapons used in the Sept. 11 hijackings, aboard a flight from LaGuardia to Washington. Another News reporter cleared security at Newark Airport toting pepper spray, a utility knife and scissors. Guards at Kennedy Airport failed to catch a camping knife with a 2 1/2-inch steel blade."
To bring it a little closer to home, local newspapers recently reported only three airports nationally are worse than the Minneapolis/St. Paul International Airport at finding bombs before they are brought onto airplanes. I would rather wait in line for two hours at the airport than seriously risk my life each time I get on a plane.
But it is not only flying on airplanes that makes me nervous. Since U.S. military officials have "credible evidence" there will likely be more terrorist attacks against Americans or our foreign interests, I've continued to question my safety on the ground. I haven't gone crazy – there are no gas masks or anthrax antibiotics in my house. But the events of Sept. 11 have made me question for the first time if I'm safe living in a metropolitan area. I'm hoping there are other more obvious targets than the Minneapolis-St. Paul area, but even that doesn't give me much comfort. I have friends and relatives living in New York City, Washington, D.C., Chicago, and London – all the cities that could rank high on the list for the next terrorist attack.
The government cannot cure the fear Americans have by simply making us more confident in air travel. A psychological mark has been seared on this country's psyche. We are fearful of an enemy we can't see, who plots attacks while living on our own soil, and who strikes at us in the places we feel the safest. How do we overcome that?
Erin Ghere's column usually appears alternate Mondays. She welcomes comments at [email protected] Send letters to the editor to [email protected]
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 5,955
|
Bat Masterson: gun-slinger turned sports reporter
January 17, 2023 | By Jim Stovall | Filed in: reporters, reporting, sports, writers, writing.
The world today knows him as one of the Old West's most famous gunslingers, fearless associate of the famous lawman, Wyatt Earp.
But in 1921, the world knew Bat Masterson as a world-class sports writer for the New York Morning Telegraph and one of the foremost experts on the second most popular sport of the day, boxing. (Baseball was the most popular sport, and professional football was hardly thought about.)
Bat Masterson was indeed a gunfighter in Dodge City and elsewhere in the West during his younger days. He was also a buffalo hunter, Indian fighter, and scout for the U.S. Army. But that phase of his life was finished by the mid-1880s when he was in his thirties. Moving to Denver, he became a "sporting man" and gambler and developed himself as a leading authority on prizefighting, which was growing in popularity with the public and with newspaper sports writers.
Masterson was a personal friend of people such as Gentleman Jim Corbett, Jack Johnson, John L. Sullivan, and Jack Dempsey, all legends of the boxing ring. He attended just about every major fight of that era, and his expertise on the sport was unsurpassed.
In 1902 he moved to New York to become a sports reporter and columnist for the Morning Telegraph and did that until his death in 1921. On the way, he became a personal friend of President Theodore Roosevelt and accepted a federal appointment as a U.S. marshal from him. He died at his sports writing desk of a massive heart attack on October 25, 1921. In the late 1950s, a television series loosely based on his life and starring Gene Barry was broadcast for several seasons.
He was writing a column when he died as his desk, and his final written words were:
"There are many in this old world of ours who hold that things break about even for all of us. I have observed, for example, that we get about the same amount of ice. The rich get it in the summer—and the poor get it in the winter." New-York Historical Society http://sports.nyhistory.org/bat-masterson/
Masterson's friend, Damon Runyan, named his lead character in Guys and Dolls Sky Masterson after the old gunfighter.
DeArment, Robert K. Gunfighter in Gotham: Bat Masterson's New York City Years. Norman: University of Oklahoma, 2013.
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« The Tylenol murders
Setting a standard for the police procedural, how we got the Smithsonian, and the love of American football: newsletter, January 20, 2023 »
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 8,579
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Q: 'Rotate' data in a WinForms datagrid Using Winforms .NET 2.0, my client has requested that data in a Datagrid be displayed vertically rather than horizontally. The data layer of the app is built upon NHibernate, so I generally avoid writing raw SQL in favor of HQL. However, this scenario may lend itself to utilizing the 'crosstab' functionality of SQL Server 2005.
So for example, the current gridview layout (which mirrors the table design) is bound to an IList(of ClaimGroup) as such:
GroupName | ClaimType | PlanCode | AgeFrom | AgeTo | AgeSpan
BHFTConv 1| P | CC | 6 | 12 | Years
needs to become:
GroupName | BHFTConv 1
ClaimType | P
PlanCode | CC
AgeFrom | 6
AgeTo | 12
AgeSpan | Years
The grid currently has, and will still require, an 'Apply' button that will save any changes made to the rotated grid.
So what would you do? Use raw SQL to crosstab the data, thereby breaking the NHibernate law of avoiding db specific queries? Or is there some mechanism built into a DataSet that would allow the data to be rotated? Or just use brute force to rotate the data?
thanks in advance
A: I would use the virtual mode of the datagridview.
Property VirtualMode = True
When you have fethed the data as normal
Create the 2 columns and prepare the datagridview
DataGridView.Columns.Add("colGroup", "Group");
DataGridView.Columns.Add("colBVH", "BVH");
DataGridView.Rows.Clear();
DataGridView.Rows.Add(6);
DataGridView.CellValueNeeded +=
new DataGridViewCellValueEventHandler(NeedValue);
Now implement the "CellValueNeeded" event..
private void NeedValue(object sender, DataGridViewCellValueEventArgs e)
{
e.Value
e.ColumnIndex
e.RowIndex
}
Use rowindex and columnindex to set the value that needs to be shown.
You know which property based on rowvalue and which row based on the columnvalue.
A: I have the same requirement to rotate a Grid as I'm replicating the QueryWizard in ASP.NET and the data is more manageable flipped on its side.
My prototype consisted of a Repeater that dumped the row out vertical rows, but formatting is a bit messy if you have unpredictable data lengths as the tables need to have set line-height, width and an overflow:hidden to appear uniformed. - but I guess a simple nobr would suffice.
<HeaderTemplate>
<table>
<tr><td>
<table>
<tr><td>ColumnName1</td></tr>
<td><td>ColumnName2</td></tr>
</table>
</td>
</HeaderTemplate>
<ItemTemplate>
<td>
<table>
<tr><td><%# Eval("Column1") %></td></tr>
<tr><td><%# Eval("Column2") %></td></tr>
</table>
</td>
</ItemTemplate>
<FooterTemplate>
</tr>
</table>
</FooterTemplate>
My plan of attack for Monday was to override the GridView render method and then loop the Rows to have them render as required. I will post back to let you know my progress
Pseudocode - something like
for(int c=0; c < columns.Count; c++)
{
writer.Write("<tr>");
writer.Write("<td>" + columns[c].Title + "</td>");
for(int r=0; r < rows.Count; r++)
{
rows[r].Cells[c].render(writer);
}
writer.Write("</tr>");
}
By letting the Cell handle the rendering you shouldn't need to do anything different with Binding or the ViewState.
A: Have you considered using DataList instead of DataGridView?
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Een inode is een manier om bestanden op te slaan op een harde schijf. De naam komt van index-node. Aangezien grote bestanden in kleine blokjes (zogenaamde sectoren) moeten worden verdeeld, is er een administratie nodig die bijhoudt welke sectoren door een bestand in gebruik zijn. De meest eenvoudige vorm is de File Allocation Table-structuur, die binnen Windows wordt toegepast. Maar voor Unix en later ook Linux werd een complexer systeem gehanteerd.
De eerste 10 blokken staan in een lijst.
Als een bestand langer is dan 10 blokken staat er een "eerste-niveau-i-node". Dit is een verwijzing naar een sector met 170 verwijzingen.
Als een bestand langer is dan 10 + 170 blokken staat er een "tweede-niveau-i-node". Dit is een twee-dimensionale structuur die verwijst naar eerste-niveau-i-nodes.
Als een bestand langer is dan 10 + 170 + (170 * 170) blokken staat er een "derde-niveau-i-node". En dit is een drie-dimensionale structuur die verwijst naar tweede-niveau-i-nodes.
Dit is een complex systeem, maar het had als voordeel dat bestanden bijzonder groot konden worden. Het is voor grote systemen efficiënter dan de File Allocation Table. Een bestand kon een omvang van 2,5 GB hebben. Tegenwoordig worden 32-bits systemen gehanteerd.
Het inode-nummer van een bestand onder Linux of Unix is opvraagbaar met het commando:
ls -i bestandsnaam
Zie ook
File Allocation Table (FAT)
Bestandssysteem
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Q: How to split a column by a delimiter, while respecting the relative position of items to be separated Below is my script for a generic data frame in Python using pandas. I am hoping to split a certain column in the data frame that will create new columns, while respecting the original orientation of the items in the original column.
Please see below for my clarity. Thank you in advance!
My script:
import pandas as pd
import numpy as np
df = pd.DataFrame({'col1': ['x,y,z', 'a,b', 'c']})
print(df)
Here's what I want
df = pd.DataFrame({'col1': ['x',np.nan,np.nan],
'col2': ['y','a',np.nan],
'col3': ['z','b','c']})
print(df)
Here's what I get
df = pd.DataFrame({'col1': ['x','a','c'],
'col2': ['y','b',np.nan],
'col3': ['z',np.nan,np.nan]})
print(df)
A: You can use the justify function from this answer with Series.str.split:
dfn = pd.DataFrame(
justify(df['col1'].str.split(',', expand=True).to_numpy(),
invalid_val=None,
axis=1,
side='right')
).add_prefix('col')
col0 col1 col2
0 x y z
1 None a b
2 None None c
A: Here is a way of tweaking the split:
max_delim = df['col1'].str.count(',').max() #count the max occurance of `,`
delim_to_add = max_delim - df['col1'].str.count(',') #get difference of count from max
# multiply the delimiter and add it to series, followed by split
df[['col1','col2','col3']] = (df['col1'].radd([','*i for i in delim_to_add])
.str.split(',',expand=True).replace('',np.nan))
print(df)
col1 col2 col3
0 x y z
1 NaN a b
2 NaN NaN c
A: Try something like
s=df.col1.str.count(',')
#(s.max()-s).map(lambda x : x*',')
#0
#1 ,
#2 ,,
Name: col1, dtype: object
(s.max()-s).map(lambda x : x*',').add(df.col1).str.split(',',expand=True)
0 1 2
0 x y z
1 a b
2 c
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"redpajama_set_name": "RedPajamaStackExchange"
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{"url":"http:\/\/math.stackexchange.com\/questions\/97979\/total-boundedness-an-equivalent-expression","text":"# Total boundedness, an equivalent expression\n\nI'm trying to show that a metric space $(X,d)$ is totally bounded iff every sequence in $X$ has a Cauchy sub-sequence. This is a point that rose up the other day in another topic and it seemed like very nice thing to know.\n\nThe definition of total boundedness that I'm working with is that for every $\\varepsilon >0$ there exists a finite collection $x_{1},...,x_{k}\\in X$ so that $X=\\cup_{n=1}^{k}B(x_{n},\\varepsilon)$.\n\nWhat I think I solved out so far is the proof from left to right, but I'm having trouble finishing the latter claim. Here's what I got from the first direction:\n\nSuppose that $X$ is totally bounded and choose a sequence $(x_{n})_{n=1}^{\\infty}$ of elements from $X$; we want to show that it has a Cauchy sub-sequence. Since $X$ is totally bounded there exists a collection $y_{1},...,y_{k_{1}}\\in X$ such that $X=\\cup_{n=1}^{k_{1}}B(y_{n},1)$, so there must exist an index $j_{1}\\in\\{1,...,k_{1}\\}$ so that $x_{n}\\in B(y_{j_{1}},1)=:A_{1}$ with infinitely many $n\\in \\mathbb{N}$. Total boundedness is hereditary so $A_{1}=\\cup_{n=1}^{k_{2}}B(z_{n},\\frac{1}{2})$ for some $z_{1},...,z_{k_{2}}\\in A_{1}$. Again there exists $j_{2}\\in \\{1,...,k_{2}\\}$ such that $x_{n}\\in B(z_{j_{2}},\\frac{1}{2})=:A_{2}$ for infinitely many $n\\in \\mathbb{N}$, and we will continue this process indefinitely. For each $i\\in \\mathbb{N}$ we find $A_{i}\\subset X$ such that: $A_{i}=B(w_{i},\\frac{1}{i})$ for some $w_{i}\\in X$, $x_{n}\\in A_{i}$ for infinitely many $n\\in \\mathbb{N}$ and $A_{i+1}\\subset A_{i}$. For each $i\\in \\mathbb{N}$ we choose $x_{n_{i}}\\in A_{i} \\cap \\{x_{n}\\}_{n=1}^{\\infty}$, which results a Cauchy sub-sequence $(x_{n_{i}})_{i=1}^{\\infty}$. Adding few details and giving a more rigorous support for the last sentence, this should be fine?\n\nI already tried several different things for the other direction, so I'd appreciate some fresh ideas there. Thanks for all the input in advance.\n\n-\nWhat about an indirect proof: Suppose $X$ is not totally bounded. This means there is an $\\varepsilon>0$ such that there is no finite $\\varepsilon$-net. Choose arbitrary $x_1$. Since $\\{x_1\\}$ is not an $\\varepsilon$-net, there is $x_2$ such that $d(x_2,x_1)>\\varepsilon$. Can you continue and construct a sequence $(x_n)$? Can you show that this sequence is not Cauchy? Can you show that no subsequence is Cauchy? \u2013\u00a0 Martin Sleziak Jan 10 '12 at 22:23\nYeah, that seems to work. Continuing from there I would find $x_{3}$ so that $d(x_{3},x_{i})>\\varepsilon$ for both $i\\in \\{1,2\\}$, and for each $i\\in \\mathbb{N}$ I find $x_{i}\\in X$ such that $d(x_{i},x_{j})> \\varepsilon$ whenever $i\\neq j$? This sequence can't be Cauchy, and the same property goes down to all of its sub-sequences. I think I can work from here, thanks alot! \u2013\u00a0 Thomas E. Jan 10 '12 at 22:33\n\nYour proof that $X$ totally bounded$\\implies$ all sequences in $X$ have Cauchy sub-sequences looks fine (it should only take 1 line to verify that the sequence you've constructed is Cauchy). To get the other direction, assume that $X$ is not totally bounded, and so we have some $r>0$ such that no finite collection of open balls $B_r(x),x\\in X$ covers $X$. Thus we can create a sequence $x_n,n\\in\\mathbb{N}$ which has no Cauchy sub-sequence by taking $$x_0\\in X, x_1\\in X\\setminus B_r(x_0), x_2\\in X\\setminus (B_r(x_0)\\cup B_r(x_1)),\\ldots$$ which we are allowed to do because $B_r(x_0)\\cup\\cdots\\cup B_r(x_n)\\neq X$. To see that this has no Cauchy subsequence, observe that for any $m\\geq n$ we have $x_m\\notin B_r(x_n)$ so $d(x_m,x_n)\\geq r$.","date":"2015-09-04 19:34:51","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9363118410110474, \"perplexity\": 86.80996367522906}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-35\/segments\/1440645359523.89\/warc\/CC-MAIN-20150827031559-00302-ip-10-171-96-226.ec2.internal.warc.gz\"}"}
| null | null |
Q: mass mv using find? there are a bunch of filename.gif scattered in /home/ directories. I want all the filename.gif replaced by a /home/shared/filename_default.gif.
I tried something like
find /home/ -name "filename.gif" | xargs <cmd>
but I have no idea to reference what I want to. Wasnt sure to ask this here or stackoverflow
Edit:
This works exactly like I explained it, except I not only wanted the data from filename_default to replace filename.gif, but also for filename.gif to be renamed filename_default.gif. So I did mv {} filename_default.gif and mv'ed all the files from their directories to /root/ under the name filename_default.gif ... lol. is there anyway to reference the changing variable in a directory..
for example find /home/ -name "filename.gif" was actually located like this...
/home/brian/dir/1/2/3/filename.gif
/home/beth/dir/1/2/3/filename.gif
/home/andrea/dir/1/2/3/filename.gif
How can I reference brian, beth, andrea... like a wildcard *.
cp /home/shared/filename_default.gif /home/*/dir/1/2/3/filename_default.gif
A: How about this?
find /home/ -name filename.gif -exec mv -f /home/shared/filename_default.gif {} \;
The -exec flag has find execute a command on every found object. The {} indicates the name of the found file. You then have to terminate the shell command with \;. You could arguably use ln -s to symlink those .gifs. That might be easier if you ever want to change your shared .gif without redoing this sort of find and move.
EDIT Good points by Denilson below. Despite the question involving mv, it'll only work once, before the source file is gone. (moved) His advice on the echo command is a good way to double check what's going to happen, before it does.
find /home/ -name filename.gif -exec cp -p /home/shared/filename_default.gif {} \;
--Christopher Karel
A: find /home -name filename.gif -type f -printf "%h\0" | xargs -0 --max-args 1 cp -l /home/shared/filename_default.gif
This isn't the wildcard you asked for, but it does accomplish the first part of your task, namely putting "filename_default.gif" in the target directories. If that works the way you want, you can then replace the 'cp -l /home/shared/filename_default.gif' portion of the command with 'rm', and replace '-printf "%h\0"' with '-print0' to remove the original file.
This presumes you want to take the contents of /home/shared/filename_default.gif and put those contents in a file named 'filename_default.gif' in all of the directories that contain 'filename.gif', removing 'filename.gif' (and thus effectively replacing 'filename.gif' named files with an identical image in a file named 'filename_default.gif')
If you want to replace 'filename.gif' but leave the name the same, then replace '-printf "%h\0"' with '-print0' and omit the rm step.
A: # find -type f -name 'filename.gif' -exec cp -v /home/shared/filename_default.gif {} \;
This will replace all your "filename.gif" files with the contents of "filename_default.gif"
but won't rename "filename.gif" to "filename_default.gif"
To rename use following command
# rename 's/filename.gif/filename_default.gif/' $(find -type f -name 'filename.gif')
HTH
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Il Fokker F.III era un aereo da trasporto passeggeri di linea monomotore, monoplano ad ala alta, sviluppato dall'allora azienda tedesca Fokker-Flugzeugwerke nei tardi anni dieci del XX secolo ma avviato alla produzione in massa dopo il trasferimento dell'azienda nei Paesi Bassi e, costruito su licenza in Germania su iniziativa di Karl Grulich, responsabile tecnico della compagnia aerea Deutsche Aero Lloyd, identificato come Fokker-Grulich F.III.
Sviluppato sulle basi del precedente F.II, del quale manteneva l'impostazione generale ma con una riorganizzazione degli spazi destinati a pilota e passeggeri, riuscì ad imporsi sul mercato dell'aviazione commerciale entrando in servizio dai primi anni venti con la compagnia aerea olandese KLM, con diverse compagnie tedesche, tra cui la Deutsche Aero Lloyd, diventata in seguito Deutsche Luft Hansa, ed altre in Danimarca e Regno di Ungheria.
Storia del progetto
Con la conclusione della prima guerra mondiale, il cui termine avverso all'Impero tedesco comportò lo smembramento dei suoi territori e la creazione della Repubblica di Weimar, l'aviazione tedesca venne pesantemente ridimensionata come previsto dalle clausole imposte dal Trattato di Versailles. I modelli militari vennero quasi interamente distrutti ed i sopravvissuti furono smilitarizzati e, con opportune modifiche, ricondizionati per un uso esclusivamente civile, tuttavia i modelli che permettessero il trasporto di un sostanziale numero di passeggeri erano quasi inesistenti. In quest'ambito alcune aziende tedesche avviarono lo sviluppo di modelli specifici progettati fin dall'inizio per poter essere utilizzati in questo ruolo.
Anthony Fokker, proprietario della Fokker-Flugzeugwerke con sede a Schwerin, incaricò Reinhold Platz, che era a capo del suo ufficio tecnico, di progettare un modello concettualmente moderno da poter proporre alle emergenti compagnie aeree nazionali. Platz, che aveva già disegnato i caccia triplano Dr.I, il biplano D.VII ed il monoplano D.VIII, sfruttò l'esperienza acquisita nel realizzare ali strutturalmente robuste per avviare nel 1919 lo sviluppo dell'F.I, progetto poi abbandonato in favore dell'F.II che ne manteneva le caratteristiche generali: velivolo realizzato in tecnica mista, monomotore, monoplano ad ala alta a sbalzo con cabina di pilotaggio aperta, scompartimento passeggeri chiuso e carrello d'atterraggio fisso.
L'F.II fu il modello con cui si sviluppò la compagnia aerea KLM, cioè Koninklijke Luchtvaart Maatschappij (in italiano Compagnia Reale d'Aviazione), tuttavia Albert Plesman, il proprietario della KLM, benché soddisfatto del velivolo, chiese a Fokker di avviare lo sviluppo di un modello ancora più veloce e confortevole. L'F.II difatti aveva uno scompartimento chiuso per soli quattro passeggeri mentre il quinto si accomodava nell'abitacolo aperto a fianco del pilota e quindi non aveva alcuna protezione dalle intemperie. Inoltre la visuale del pilota poteva essere migliorabile.
Per ottenere ciò Platz disegnò il velivolo spostando il quinto posto all'interno della cabina passeggeri
Il prototipo venne costruito nello stabilimento di Schwerin, in Germania, e portato in volo per la prima volta il 20 novembre 1920.
Tecnica
L'impostazione tecnica del modello, che poi verrà riproposta nell'iniziale serie di modelli civili Fokker, prevedeva una cellula che abbinava un'ala a sbalzo costruita in legno, completamente ricoperta in pannelli di compensato, dotata di alettoni che si estendevano oltre le estremità alari ad una larga fusoliera a sezione quadrata, realizzata con struttura in tubo di acciaio saldato rivestita in tela trattata, sufficiente a fornire una buona stabilità direzionale senza ricorrere a pinne addizionali. Lo scompartimento viaggiatori, dotato di cinque posti a sedere, era ricavato dietro la cabina di pilotaggio aperta monoposto destinata al solo pilota.
Il carrello era un semplice biciclo fisso costituito da un castello tubolare dotato di ruote collegate tra loro da un assale rigido ed integrato posteriormente da un pattino d'appoggio.
La propulsione era inizialmente assicurata da un motore BMW IIIa, un 6 cilindri in linea raffreddato a liquido in grado di esprimere una potenza pari a 185 PS (138 kW) che però dimostrò di avere problemi di raffreddamento. La compagnia aerea olandese KLM che fu tra i primi ad adottarlo, così come fece con il precedente F.II, lo sostituì con il britannico Armstrong Siddeley Puma da 230 hp (171 kW). Risultano comunque diverse motorizzazioni adottate, tutte comunque raffreddate a liquido ed abbinate, a seconda del propulsore, ad eliche bi e quadripala in legno a passo fisso.
Impiego operativo
Il primo F.III consegnato alla KLM, immatricolato H-NABH, venne utilizzato per operare sulla riaperta rotta Amsterdam - Londra via Rotterdam (Aeroporto di Waalhaven) dal 14 aprile 1921, il cui volo inaugurale venne pilotato da Gordon Olley all'andata e dall'asso dell'aviazione britannico Ray Hinchliffe al ritorno.
Lo stesso giorno un secondo F.III, ai comandi del pilota tedesco Gnädig, inaugurò la rotta che univa Rotterdam ad Amsterdam proseguendo per Brema ed Amburgo. Dopo tre settimane, grazie ad un accordo commerciale stipulato con la compagnia belga SNETA (Syndicat national pour l'étude du transport aérien) e quella francese Compagnie des messageries aériennes (CMA), la KLM inaugurò la tratta Amsterdam – Rotterdam – Bruxelles – Parigi, con la particolarità che, dato che non erano stati ancora ratificati trattati di utilizzo dello spazio aereo tra Paesi bassi e Francia, i passeggeri giunti nella capitale belga, dovevano trasferirsi su un velivolo operato da SNETA o CMA per raggiungere Parigi.
Utilizzatori
Det Danske Luftfartselskab
Deutsche Aero Lloyd/Deutsche Luft Hansa
Deutsche Luft-Reederei
Deutsche Aero Luft
Sud-deutsche Luft Hansa
Germania-Unione Sovietica
Deutsch-Russiche Luftverkehrs Gesellschaft (Deruluft)
KLM
Malert
Note
Bibliografia
Pubblicazioni
Altri progetti
Collegamenti esterni
Aerei civili olandesi
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#ifndef DirectoryReader_h
#define DirectoryReader_h
#include "bindings/v8/ScriptWrappable.h"
#include "modules/filesystem/DOMFileSystem.h"
#include "modules/filesystem/DirectoryReaderBase.h"
#include "wtf/PassRefPtr.h"
#include "wtf/RefCounted.h"
#include "wtf/text/WTFString.h"
namespace WebCore {
class EntriesCallback;
class EntriesCallbacks;
class ErrorCallback;
class DirectoryReader : public DirectoryReaderBase, public ScriptWrappable {
public:
static PassRefPtr<DirectoryReader> create(PassRefPtr<DOMFileSystemBase> fileSystem, const String& fullPath)
{
return adoptRef(new DirectoryReader(fileSystem, fullPath));
}
void readEntries(PassRefPtr<EntriesCallback>, PassRefPtr<ErrorCallback> = 0);
DOMFileSystem* filesystem() const { return static_cast<DOMFileSystem*>(m_fileSystem.get()); }
private:
DirectoryReader(PassRefPtr<DOMFileSystemBase>, const String& fullPath);
};
}
#endif // DirectoryReader_h
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Кэмп () — в неклассической эстетике специфический изощрённый эстетский вкус и лежащая в его основе специально культивируемая чувствительность. Кэмп также понимается как социальные и культурные стиль и чувственность, и при таком рассмотрении обычно связывается с гей-субкультурой. Для кэмпа характерны повышенная театральность, любовь к искусственности, преувеличенность до гротеска, некоторая вульгарность, эстетизм, антиномичное сочетание игры и серьёзности. Эстетика кэмпа является примером того, как в культуре постмодерна приобретают новое содержание классические категории возвышенного и низменного, прекрасного и безобразного: если высокое искусство предполагает красоту и ценность, то кэмп нуждается прежде всего в смелости, живости и динамике, противопоставляет себя удовлетворенности, имея целью вызов.
Кэмп начал приобретать популярность в 1960-е. К нему относятся такие режиссёры как Джордж и Майк Кучары, Джек Смит, Энди Уорхол, Джон Уотерс («Розовые фламинго», «Лак для волос», «Полиэстер»). Известные исполнители, использующие эстетику кэмпа — Барри Хамфрис (в образе дамы Эдны Эверэйдж), Дивайн, Ру Пол и Либераче. Широко распространился в 1980-х с приятием постмодернистских взглядов на искусство и культуру.
Происхождение термина
Camp происходит от французского se camper, означающего «принимать позу чрезмерной манерности». Оксфордский словарь английского языка приводит первое определение camp 1909 года:
«показной, преувеличенный, деланный, театральный; женоподобный или гомосексуальный; принадлежащий, характерный для гомосексуалов. В качестве существительного — это кэмп как поведение, манерность и т. д.; человек, демонстрирующий такое поведение».
Этимология остаётся всё же до конца неясной.
Позднее слово использовалось для обозначения эстетических предпочтений и поведения гомосексуальных мужчин рабочего класса. В конце концов, с проникновением обозначаемых словом явлений в культурный мейнстрим оно стало самостоятельным определением, зафиксированным американским художественным критиком Сьюзен Зонтаг в «Заметках о кэмпе».
Постмодернизм превратил кэмп в некий общий тип чувствительности, не приписывавшийся какой-либо узкой группе. Изначально же кэмп был отличительной чертой мужских гей-сообществ эпохи, предшествовавшей Стоунволлским бунтам. В основе этой чувствительности — восприятие гомосексуальности как женственности (социальные роли, в которых она воплощается). Два ключевых компонента кэмпа представляли собой паттерны женского поведения, обозначаемые на сленге swish (плавная женственная походка, мягкие жесты, фальцет, характерная лексика) и drag (ношение одежды, устойчиво ассоциируемой с определённой гендерной ролью лицом другого гендера). Для этих компонентов характерно использование элементов женственности в преувеличенной до неестественности, гротескной степени, что открыло путь для более широкого понимания кэмпа — теперь в него включаются образы и некоторых голливудских актрис, явно обладающие теми же чертами (Кармен Миранда). Именно в таком понимании кэмп становится частью концептуального аппарата художественной и литературной критики 60-х.
Специфика кэмпа
Кэмп как особый тип чувствительности характеризуется определённым соотношением эстетических категорий красоты и уродства, серьёзного и фривольного, наивности и маньеризма, стиля и содержания.
Доминанты кэмпа — фривольность (игра), излишество формы, подчеркнутая сознательная ориентация на искусственность и эстетизм, отодвигающий, затемняющий содержание.
Трёхчастное деление Сьюзен Зонтаг в «Заметках о кэмпе» позволяет очертить контуры этой чувствительности. Если первая, классическая чувствительность (высокая культура: «Илиада», комедии Аристофана, Рембрандт, «Божественная комедия», Сократ, Христос) подчиняет эстетическую сторону морали (её дилеммам, противоречиям и т. д.), вторая, «авангардная» существует в напряжении между эстетической страстью и моралью, воспевая безобразное, безнравственное (Сад, Рембо, Кафка, Арто), то третья чувствительность — кэмп — исключает моральную сторону, любую серьёзность, трагедию, оставляя эстетическую сторону, и следовательно, становится развлекательной.
Неотъемлемы в кэмпе его искусственность, манерность, пышная форма. Произведению не удаётся стать артефактом кэмповской эстетики, если оно хорошо, удачно, серьёзно, лишено маргинальности. «Кэмп — это последовательно эстетическое мировосприятие. Он воплощает победу стиля над содержанием, эстетики над моралью, иронии над трагедией».
Отступая от серьёзности, от содержания, сосредотачиваясь на эстетической стороне, кэмп является такой чувствительностью, которая не есть стиль, но способность воспринимать другие стили, видеть всё в кавычках цитации: вещь как «исполнение роли». Кэмп — наслаждение эстетической стороной, искусственностью, доходящей до вульгарности, по известному определению Зонтаг — «дендизм в век массовой культуры». Часто иллюстрацией кэмпа служат образы музыкальных исполнителей и актёров, отличающиеся преувеличенными сексуальными характеристиками, когда женственность и мужественность становятся набором акцентированных черт — за ними теряется сам носитель, и это их обессмысливает; примеры — Джина Лоллобриджида, Стив Ривз.
Различие между кэмпом и китчем
Кэмп и китч ставят близко. Как основания для сходства китча и кэмпа указываются свойственные обоим отступание от трудного, глубокого, тяга к более легкоусвояемому, дурной вкус. Однако с последним кэмп связывается не всегда.
Часто китч употребляется в качестве синонима дурного вкуса. Кэмп же понимается как намеренный китч, китч в кавычках — это эстетизация дурного, отталкивающего и в таком виде получение от него удовольствия. Кэмповские вещи для не разделяющего к нему любви, серьёзного взгляда — в сущности китчевые. Поэтому о кэмпе говорят как о восприятии какого-либо эстетического объекта или жизненном стиле, тогда как китч относится к самому объекту, его исполнению. Кэмп нельзя замыслить или исполнить — но это возможно с китчем, и такой объект может быть воспринят как кэмповский.
Кэмп в культуре
Эстетика кэмпа может быть обнаружена во многом из того, что составляет багаж современной популярной культуры. Это прежде всего телесериалы: «Семейка Аддамс», «Звездный путь: Оригинальный сериал», «Бэтмен», «Мстители», «Ангелы Чарли», «Напряги извилины», «Остров Гиллигана», «Остров фантазий» привлекают зрителя 21-го века именно тем, что им интерпретируется как кэмп-аспекты этих продуктов. В ранние 60-е, время перехода к цветному телевидению, телеэфир стремились наполнить развлекательным контентом, который бы использовал преимущества нового медиума. Так появились телевизионные сериалы с отличительной эстетикой: яркие цвета, высокая степень стилизации (мыльные оперы, шоу «Бэтмен»). Шоу «Cheap Seats» — пример использования кэмпа: двое представителей Поколения X, братья, делают юмористические обзоры спортивных событий 70-х, интересных в 2000-е именно своими кэмповскими чертами (попытки соединить балет с катанием на лыжах, игра известной баскетбольной команды в тюрьме штата Нью-Йорк, региональный реслинг). Дэвид Линч и Марк Фрост в «Твин Пикс» часто сознательно — посредством образов героев и различных ситуаций — создают атмосферу кэмпа.
Яркий представитель кэмпа в кино — кинорежиссёр Джон Уотерс, популяризовавший его в своих кинолентах «Розовые фламинго», «Лак для волос», «Female Trouble», «Polyester» и других.
Как отражение кэмпа в дизайне иногда рассматриваются некоторые дворовые декорации, распространенные в пригородах Америки, к примеру, пластиковый розовый фламинго, садовый гном, жокей, фигурки белохвостого оленя, а также торт-мороженое от Carvel.
В музыке иконой кэмпа считается английская певица Дасти Спрингфилд за разработанный ею имидж; южнокорейский рэпер PSY использует эстетику кэмпа в своих музыкальных видеоклипах, так же в своих выступлениях используют её популярные исполнители Mika и Кайли Миноуг. К кэмпу относится стиль мюзик-холла и английской пантомимы, декор входов парижского метро Эктора Гимара.
См. также
Китч
Дрэг-квин
Примечания
Литература
Стиль кэмп // История уродства / под ред. Умберто Эко. — М.: Слово / Slovo, 2007. С. 408—418
Ссылки
Susan Sontag, Notes On «Camp» Published in 1964.
Категории эстетики
Постмодернизм
ЛГБТ в культуре и искусстве
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{"url":"http:\/\/me1065.wikidot.com\/micro-scale-heat-exchangers","text":"Micro Scale Heat Exchangers\n\nOperating Principles:\n\nMicro-scale heat exchangers or micro structured heat exchangers are heat exchangers in which a fluid flows in a lateral direction in a confined area such as a tube or small cavity that dimensions are below the size of 1mm. Typically the fluid flows through a cavity which is called a mirochannel. This technology exploits enhanced heat transfer resulting from structurally constraining streams to flow in microchannels, which reduces resistance to transferring heat. Fluid flowing through the channels on a plate evaporates or condenses, and heat is transferred. Micro heat exchangers have been demonstrated with high convective heat transfer coefficients ranging form 10,000 to 35,000 watts\/m2-\u00b0C, or about one order of magnitude higher than typically seen in conventional heat exchangers with very low pressure drops, typically 1 or 2 psi. The basic operating principle of these devices goes back to the convective heat transfer within the flows of the microchannels. The convective heat transfer equation is:\n\n(1)\n\\begin{align} \\ h = N_{u }({k\\over d})\\ \\end{align}\n\nIn this equation h is the heat transfer coefficient of the microscale heat exchanger, Nu is the Nusselt number which is about 3.65, k is the thermal conductivity of the working fluid and d is the diameter of the microchannel which the fluid flows through. From this equation one can tell see how the size of the channel directly affects the heat transfer coefficient of the heat exchanger, as the diameter is decreased the heat transfer coefficient increases.\n\nDifferent Types of Microscale Heat Exchangers:\n\nThe different types of microscale heat exchangers are the same as the different classifications of conventional heat exchangers. They have either one or two passages for the fluid to flow through.\n\n\u2022 One fluid:\n\nWhen there is only one fluid and one passage in the heat exchanger the fluid is used to transfer the heat to another location. Application of this kind of heat exchangers is usually found in electronics to transfer heat into the fluid and out of the electronic device.\n\n\u2022 Two Fluids:\n\nWhen there are two fluids and two passages they are usually classified by the direction in which the fluids flow by each other. Microscale heat exchangers can either be cross flow or counter flow heat exchangers.\n\n\u2022 Counter Flow\n\nCounter flow micro scale heat exchangers work the same way as macro-scale counter flow heat exchangers. In a counter flow heat exchanger the two fluids flow in opposite directions of each other. The fluids enter the heat exchanger at opposite ends. The cooler fluids exits the counter flow microscale heat exchanger at the end where the hot fluid enters therefore the cooler fluid will approach the inlet temperature of the hot fluid. Counter flow microscale heat exchangers are more efficient than cross flow microscale heat exchangers.\n\nFigure 1: Schematic of Counter Flow Heat Exchanger\n\nFigure 2: Counter Flow Microscale Heat Exchangers\n\n\u2022 Cross Flow\n\nCross Flow microscale heat exchangers work the same way as cross flow macro-scale heat exchangers. In a cross flow heat exchanger one fluid flows perpendicular to the second fluid. One fluid flows through tubes or channels and the second fluid passes around the tubes or channels at a 90\u00b0 angle. Cross flow micro heat exchangers are usually found in applications where one of the fluids changes state therefore having a two-phase flow.\n\nFigure 3: Schematic of a Cross Flow Heat Exchanger\n\nTo concurrently achieve the goals of high mass flow rate, low pressure drop, and high heat transfer rates, the microscale cross flow heat exchanger comprises numerous parallel, but relatively short microchannels. The performance of these microscale heat exchangers is superior to the performance of previously available macro-scale heat exchangers. Typical channel heights are from a few hundred micrometers to about 2000 micrometers, and typical channel widths are from around 50 micrometers to a few hundred micrometers. The use of microchannels in a cross flow microscale heat exchanger decreases the thermal diffusion lengths, allowing substantially greater heat transfer per unit volume or per unit mass than has been achieved with other heat exchangers. The cross flow microscale heat exchangers have performance characteristics that are superior to state of the art macro-scale heat exchanger designs.\n\nFigure 4: Cross Flow Microscale Heat exchanger\n\nSubstantially better performance\n- Improves heat transfer coefficient with large number of smaller channels\nSize\n- Smaller size allows for an increase in mobility and uses\nLight Weight\n- Lower weight reduces the structural and support requirements\nCost\n- Lower costs due to less material being used in fabrication\n\nOne of the main disadvantages of microchannel heat exchangers is the high pressure loss that is associated with a small hydraulic diameter. This prevents the uniform flow of the cooling material along the channel. Microchannels are sometimes fairly long and absorb most of the heat along the first section of the channel. This makes them less able to absorb heat along later sections. In order to get the maximum performance out of a microchannel heat exchanger, there needs to be a balance between the desirable high heat transfer coefficient and the undesiarable pressure loss. Due to the small scale of microchannel passages, wall roughness can be very important in determining how high the heat transfer coefficient is.\n\nApplications of Microscale Heat Exchangers:\n\nMicroscale heat exchangers are being used to help along the development of fuel cells. The compact microchannel fuel vaporizer (CMFV), which is a microscale heat exchanger, is a main component of a microchannel fuel processor that will hopefully enable fuel cell powered vehicles. Conventional heat exchangers are too large to be used in this application, nor can they deliver the kind of performance needed in this application. The microscale heat exchanger is also making possible a portable fuel cell power supply. This power supply could make batteries obsolete. It will have a longer run time than a battery of comparable weight. It could also be used in place of portable generators that operate with an internal combustion engine. These fuel cells would operate more quietly and with a greater efficiency than an engine driven generator. Problems with refueling a generator in a remote location could also be solved be this new portable fuel cell.\n\nCurrently used in these Industries:\n\n\u2022 Automotive\n\u2022 Commercial and Residential Heating\/Cooling\n\u2022 Aircrafts\n\u2022 Manufacturing\n\u2022 Cooling Electronics\n\nCreated by Josh Wood, James Coyne and Scott Bassano\n\nReferences:\n\nMadou, Marc. Fundamentals of Microfabrication: The Science of Miniaturization. CRC, 2002.\n\nKiwi-Minsker, L. and Renken, A., \u201cMicrostructured reactors for catalytic reactions\u201d, www.sciencedirect.com, 2005.\n\nBrenchley, David, \u201cApplications for Micro Chemical and Thermal\nSystems\u201d, 2001.\n\nKennedy, Sheila, \u201cThe incredible shrinking heat exchanger\u201d, http:\/\/www.plantservices.com\/articles\/2007\/069.html, 2004.\n\n\"System For Configuring The Geometric Parameters For A Micro Channel Heat Exchanger\", World Intellectual Property Organization. http:\/\/www.wipo.int\/pctdb\/en\/wo.jsp?IA=US2004030377&DISPLAY=STATUS, March 2005.\n\npage revision: 2, last edited: 06 Dec 2007 17:32","date":"2019-12-12 15:46:48","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 1, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5724167227745056, \"perplexity\": 1539.3740655715962}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-51\/segments\/1575540544696.93\/warc\/CC-MAIN-20191212153724-20191212181724-00011.warc.gz\"}"}
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Sterling é uma cidade localizada no estado americano de Illinois, no Condado de Whiteside.
Demografia
Segundo o censo americano de 2000, a sua população era de 15.451 habitantes.
Em 2006, foi estimada uma população de 15.347, um decréscimo de 104 (-0.7%).
Geografia
De acordo com o United States Census Bureau tem uma área de
12,6 km², dos quais 12,1 km² cobertos por terra e 0,5 km² cobertos por água. Sterling localiza-se a aproximadamente 205 m acima do nível do mar.
Localidades na vizinhança
O diagrama seguinte representa as localidades num raio de 20 km ao redor de Sterling.
Personalidades
Paul John Flory (1910-1985), prémio Nobel da Química de 1974
Ligações externas
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\section{Introduction}
In the last thirty years, precision cosmology has achieved important goals through measurements of the Cosmic Microwave Background (CMB) radiation such as its spectrum \cite{0004-637X-473-2-576}, the anisotropies \cite{refId01}, the E--mode component of the polarization \cite{refId0}, and the B--mode component of the polarization due to gravitational lensing from dark matter structure \cite{0004-637X-833-2-228}. Yet, the B-mode power spectrum from inflation and the spectral distortions still remain elusive as well as the spectroscopic measurement of the Sunyaev--Zel'dovich (SZ) effect.
The OLIMPO experiment \cite{Coppolecchia2013} is aimed at measuring the SZ effect which is a CMB anisotropy in the direction of galaxy clusters, due to the inverse Compton scattering of low energy CMB photons by the high energy electrons of the hot gas present in the intra--cluster medium. SZ effect measurements represent an interesting tool to study the morphological and dynamical state of clusters, to probe the CMB temperature evolution with the redshift, to constraint cosmological parameters, and to search for previously unknown clusters by looking at their SZ signature in the microwave sky \cite{1475-7516-2018-04-020, 1475-7516-2018-04-019}.
OLIMPO measures SZ signals with a technique so far unattempted in this kind of obervations: it performs a spectroscopic map of the SZ effect with a differential interferometric instrument, working above the atmosphere, and provides efficient and unbiased decontamination of the SZ and CMB signals from all the foregrounds along the same line of sight \cite{deBernardis}, thus increasing the accuracy on the estimate of the astrophysical quantities involved in the physics of the effect.
The OLIMPO experiment has been, therefore, designed as a large balloon--borne mm--wave observatory, with a \SI{2.6}{m} aperture telescope, equipped with a room--temperature differential Fourier transform spectrometer (DFTS) \cite{schillaci2014}, and four low--temperature detector arrays, centered at 150, 250, 350, and \SI{460}{GHz}, exploring the negative, zero, and positive regions of the SZ spectrum. The detector arrays, consisting of horn--coupled lumped element kinetic inductance detectors (LEKIDs), are cooled to about \SI{300}{mK} by a $^{3}$He fridge, accomodated inside a wet N$_2$ plus $^{4}$He cryostat. The detector arrays are fed and read out coupled by means of two independent bias--readout lines and two FPGA--based electronics.
Kinetic inductance detectors are superconductive photon detectors, where the radiation is detected by sensing changes of the kinetic inductance. A superconductor, cooled below its critical temperature $T_{c}$, presents two populations of electrons: quasiparticles and Cooper pairs, bound states of two electrons with binding energy $2\Delta_{0}=3.528\:k_{B}T_{c}$. If pair-breaking radiation ($h\nu>2\Delta_{0}$) is absorbed in a superconducting film, it breaks Cooper pairs, producing a change in the population relative densities, and thus in the kinetic inductance. For these reasons, in the lumped element configuration, a superconducting strip is properly shaped and sized in order to perform like a radiation absorber, and this structure, which is an inductor as well, is coupled to a capacitor to form a superconductive high quality factor resonator. In this way, the change in kinetic inductance, due to the incident radiation, produces a change in the resonant frequency and in the quality factor, which can be sensed by measuring the change in the amplitude and phase of the bias signal of the resonator, transmitted past the resonator through a feedline.
The KID design and readout scheme are intrinsically multiplexable for large--format arrays, provided that the resonant frequencies of the individual resonators coupled to the same feedline are adjusted to unique values, for instance by changing the capacitor size. In this way, entire arrays can be fed and read out thanks to an electronics chain made of \emph{cold components}, including low noise amplifiers (LNAs), dc--blocks, coaxial cables, and power attenuators; and a \emph{room--temperature stage}, where an FPGA-based electronics, coupled to an ADC/DAC board, is used to generate one bias tone per resonator. This solution allows to feed and monitor the amplitude and phase of the bias signals of all the resonators at the same time, while physically connecting the cold stage to the room--temperature with one cable only.
KID technology has been already proven in ground--based experiments \cite{Ritacco}, and for its features seems to be the optimal solution for next--generation space--borne CMB experiments \cite{1475-7516-2018-04-014,1475-7516-2018-04-015}, but it still needs to be demonstrated in a representative environment for space applications. OLIMPO, which was operated from the stratosphere, is therefore a natural testbed for KIDs in space--like conditions.
\section{Detectors and \emph{cold electronics}}
The first constraint in the optimization process of a detector system is always the target science for which it will be built. In the OLIMPO case, moreover, it has to fit an already developed cryogenic and optical system. This implies that the first step is the choice of the material of the superconducting film and the dielectric substrate, the size of the detector arrays, the geometry and size of the absorbers, the geometry and size of the radiation couplers, the number of detectors per array, and the illumination configuration. These steps have been performed through optical simulations.
The second step concerns the optimization of the readout scheme: the geometry and size of the feedline; the geometry and size of the capacitors, on which the resonant frequencies of the resonators depend; and the coupling between the resonators and the feedline. This optimization has been done through electrical simulations.
The last step regards the optimization of the \emph{cold electronics}: the choice of the material and size of the coaxial cables; the magnitude of the power attenuators; the gain, noise, and operation temperature of the cryogenic amplifier.
\subsection{KID optimization, fabrication and results}
The detailed description of the optimization and fabrication of the OLIMPO detector systems and the measurement results can be found in \cite{Paiella2017,Paiella2018}.
All the four arrays are fabricated in a \SI{30}{nm} thick aluminum film deposited on silicon substrates of different thickness depending on the observed radiation frequency. The substrate acts also as a backshort, since the face opposite to the detectors has been coated with aluminum. The properties of different aluminum film thicknesses have been measured as described in \cite{Paiella2016}, and the results have been used for the optical simulations. A compromise between optical simulation results and critical temperature (on which the optimal working temperature and the minimum detectable radiation frequency depend) forced us to choose \SI{30}{nm} for the aluminum film thickness. For this film, we measured the critical temperature, $T_{c}=\SI{1.31}{K}$; the residual resistance ratio, ${\rm RRR}=3.1$; the sheet resistance, $R_{s}=\SI{1.21}{\Omega/\Box}$, and the surface inductance, $L_{s}=\SI{1.38}{pH/\Box}$.
The optimal absorber solution results to be a front--illuminated IV order Hilbert pattern, where the characteristic length scales with the observed radiation wavelength. The 150 and 250 GHz arrays are coupled to the radiation via a single--mode waveguide, while the 350 and 460 GHz are coupled via a single--mode flared waveguide. The number of detectors per array is 23, 39, 25 and 43 for the 150, 250, 350 and \SI{460}{GHz} array, respectively.
The capacitors of the KIDs have been designed so that the lumped element condition is satisfied for all the resonators and the resonant frequencies fall into the range $\left[100;600\right]$ MHz. This is done by means of large capacitors, which have also the advantage of reducing the TLS (two--level system) noise \cite{Noroozian2009}. Moreover, the resonant frequencies are such that the \SI{150}{GHz} and the \SI{460}{GHz} arrays can be fed and read out with the same line as well as the \SI{250}{GHz} and the \SI{350}{GHz} arrays. In this way, each readout electronics manages about 65 detectors. Each detector is coupled to a $\SI{50}{\Omega}$--matched microstrip feedline (the width of which is different array by array) by means of capacitors, designed to constraint the coupling quality factor to about $1.5\times10^{4}$ guaranteeing, thus, a quite large detector dynamics, and that the total quality factor results dominated by the coupling one.
The arrays have been fabricated at the IFN--CNR. The detectors have been realized by electron--beam litography, electron--gun evaporation and lift--off \cite{Colantoni2016} on high--quality, high--resistivity ($\rho>\SI{10}{k\Omega.cm}$) intrinsic Si(100) wafers, double--side polished. The sample holders of the detector arrays are made of ergal alloy (aluminum 7075) as well as the horn arrays, in order to guarantee good thermalization and low power losses through the horns.
The OLIMPO detectors have been fully characterized: the electrical properties, such as the quality factors and the resonant frequencies, have been measured in a dark laboratory cryostat and result in agreement with the simulations; the optical performance has been measured in the OLIMPO cryostat and results in a Rayleigh-Jeans noise equivalent temperature lower than $\SI{500}{\mu K/\sqrt{Hz}}$ under a blackbody load of about \SI{90}{mK}, for all the OLIMPO arrays, and a global optical efficiency of about 10\%, averaged over the four channels.
\subsection{Cold electronics optimization}
With \emph{cold electronics} we mean the components placed inside the cryostat, necessary to feed and read out the detectors. These components include coaxial cables, power attenuators, low noise amplifiers and dc--blocks. They have to be chosen in such a way that the noise equivalent power (NEP) of the active components of the \emph{cold electronics} is lower than the expected noise equivalent power of the detectors.
Theoretically, the noise of a KID is mainly due to the generation--recombination noise (the TLS noise can be neglected by design), thus its NEP can be evaluated as
\begin{equation}
{\rm NEP}_{g-r}=2\Delta\sqrt{\frac{N_{qp}}{\tau_{qp}}}\;,
\end{equation}
where $\Delta=1.764\;k_{B}T_{c}$ is half Cooper pair binding energy, with $k_{B}$ the Boltzmann constant, $N_{qp}$ is the quasiparticle number, and $\tau_{qp}$ is the quasiparticle lifetime (measured in \cite{Paiella2018}). For the OLIMPO detectors, the generation--recombination NEP is collected in table \ref{tab:NEP_gr}.
\begin{table}[h]
\caption{\small\label{tab:NEP_gr}Values of the generation--recombination NEP for the OLIMPO channels.}
\begin{center}
\begin{tabular}{cc}
\br
Channel&${\rm NEP}_{g-r}$\\
$\left[{\rm GHz}\right]$&$\left[{\rm W}/\sqrt{{\rm Hz}}\right]$\\
\mr
150&$3.1\times 10^{-17}$\\
250&$2.8\times 10^{-17}$\\
350&$2.1\times 10^{-17}$\\
460&$1.8\times 10^{-17}$\\
\br
\end{tabular}
\end{center}
\vspace{-0.5cm}
\end{table}
As we already said, a KID is a superconductive resonator, which is optimally sensitive when operated close to its resonant frequency. This means that, since the quality factors are very high, due to the superconductor properties, and thus the resonances are very deep, the readout power has to be amplified. This is done by means of a cryogenic low noise amplifier, able to amplify the signal output from the detectors, with very low intrinsic noise. For the OLIMPO experiment, the two LNAs, necessary for the two readout lines, have been provided by Arizona State University\footnote[1]{http://thz.asu.edu/products.html} (ASU) \cite{6881015}. These amplifiers dissipate about \SI{13}{mW} each ($V=\SI{1.6}{V}$ and $I=\SI{8}{mA}$ at \SI{10}{K}), and amplify \SI{33}{dB}, with a noise temperature of \SI{5}{K}, and a \SI{1}{dB} gain compression point, referred to the input, of \SI{-61}{dBm} at \SI{10}{K}, for a \SI{300}{MHz} signal. The noise equivalent power associated to the cryogenic amplifier is given by
\begin{equation}
{\rm NEP}_{amp}=\frac{N_{qp}\Delta}{\tau_{qp}}\sqrt{\frac{k_{B}T_{amp}}{P_{read}}}\;;
\label{eq:NEP_amp}
\end{equation}
where $T_{amp}$ is the noise tempertaure, and $P_{read}$ is the total readout power at the LNA input.
Since the OLIMPO cryostat does not feature a \SI{10}{K} stage, and since the coldest stage where they can be mounted is the vapor $^{4}$He shield, at a temperature of about \SI{30}{K}, we need to extrapolate the values of the LNA noise temperature at \SI{30}{K}, in order to compare the NEP associated to the LNA and the generation--recombination one.
This has been done by combining the measurements provided by ASU at 10, 20 and \SI{300}{K}, with the measurements performed by us in a laboratory cryostat at 4 and \SI{44}{K}. Since \SI{44}{K} is the temperature closest to \SI{30}{K} at which we were able to cool the amplifier quickly, the measurements at this temperature have been performed at different supply voltages. All these data are collected in table \ref{tab:LNA}. The noise measurements have been done through an \emph{Anritsu MS2717B} spectrum analyzer, set to a resolution bandwith ${\rm RBW}=\SI{1}{Hz}$, at the LNA output, and have been scaled to the LNA input thanks to the gain measured with an \emph{Anritsu M52034B} vector network analyzer (VNA). All these measurements refer to \SI{300}{MHz}. The conversion between noise power and noise temperature is given by
\begin{equation}
{\rm Noise\;Temperature}=\frac{{\rm Noise\;Power}}{k_{B}\:{\rm RBW}}\;.
\end{equation}
\begin{table}[h]
\caption{\small\label{tab:LNA}Value of the supply voltage, gain, noise power and temperature at the input of the LNA provided by ASU, at different operation temperatures, at \SI{300}{MHz}.}
\begin{center}
\begin{tabular}{cccccc}
\br
\multicolumn{1}{c}{\multirow{2}{*}{T}}&
\multicolumn{1}{c}{\multirow{1}{*}{LNA}}&
\multicolumn{1}{c}{\multirow{2}{*}{Gain}}&
\multicolumn{1}{c}{\multirow{1}{*}{Noise Power}}&
\multicolumn{1}{c}{\multirow{1}{*}{Noise Temperature}}&
\multicolumn{1}{c}{\multirow{3}{*}{Notes}}\\
\multicolumn{1}{c}{\multirow{1}{*}{}}&
\multicolumn{1}{c}{\multirow{1}{*}{Voltage}}&
\multicolumn{1}{c}{\multirow{1}{*}{}}&
\multicolumn{1}{c}{\multirow{1}{*}{@ LNA input}}&
\multicolumn{1}{c}{\multirow{1}{*}{$T_{amp}$}}&
\multicolumn{1}{c}{\multirow{1}{*}{}}\\
\multicolumn{1}{c}{\multirow{1}{*}{$\left[{\rm K}\right]$}}&
\multicolumn{1}{c}{\multirow{1}{*}{ $\left[{\rm V}\right]$}}&
\multicolumn{1}{c}{\multirow{1}{*}{$\left[{\rm dB}\right]$}}&
\multicolumn{1}{c}{\multirow{1}{*}{$\left[{\rm dBm}\right]$}}&
\multicolumn{1}{c}{\multirow{1}{*}{$\left[{\rm K}\right]$}}&
\multicolumn{1}{c}{}\\
\mr
4 & 1.6 & 33 & $-$192.0$\pm$0.2 &4.57$\pm$0.21&\\
44 & 1.5 & 32.1 & $-$189.1$\pm$0.2 &8.91$\pm$0.41&\\
44 & 1.6 & 32.4 & $-$189.4$\pm$0.2&8.31$\pm$0.38&\\
44 & 1.7 & 32.7 & $-$189.7$\pm$0.2&7.76$\pm$0.36&Measurements performed \\
44 & 1.8 & 32.9 & $-$189.9$\pm$0.2&7.41$\pm$0.34&by us in a laboratory cryostat\\
44 & 1.9 & 33.0& $-$190.0$\pm$0.2&7.24$\pm$0.33&\\
44 & 2.0 & 33.1 & $-$190.1$\pm$0.2&7.08$\pm$0.33&\\
44 & 2.1 & 33.2 & $-$190.2$\pm$0.2&6.92$\pm$0.32&\\
\mr
10 & 1.6 & 33 & & 5&\\
20 & 1.6 & & & 6&provided by ASU\\
300 & 2.1 &30& & 45&\\
\br
\end{tabular}
\end{center}
\end{table}
The value of the noise temperature of the LNA at \SI{30}{K} has been extrapolated by fitting the data with the function $aT^{2}+bT+c$, see the \emph{left panel} of figure \ref{fig:LNA}. We obtained $a=\SI{1.67e-4}{K^{-1}}$, $b=8.59\times10^{-2}$, and $c=\SI{4.20}{K}$, and therefore
\begin{equation}
T_{amp}\left(\SI{30}{K}\right)=\SI{6.93}{K}\;.
\end{equation}
The only information which is missing to calculate the LNA NEP via equation \ref{eq:NEP_amp} is $P_{read}$. The total readout power at the LNA input is the sum of all the bias powers of the tones, each attenuated by the corresponding resonator, on the same readout line. Moreover, in order to work in the linear regime of all the amplifier circuits of the \emph{cold} and \emph{room--temperature electronics}, the powers at the input of such amplifiers have to be lower than the 1 dB gain compression point of the amplifiers themselves. As we are going to see in section \ref{sec:room-temperature}, the amplifier room--temperature components have been chosen and ordered along the readout chain in such a way that the 1 dB gain compression points are matched, and therefore the only constraint on $P_{read}$ is given by the first amplifier: the LNA.
OLIMPO KIDs have been designed to be fed with a bias power of about \SI{-80}{dBm} each, and with a resonance deep of about \SI{10}{dB}. This means that, considering an average of 65 detectors per readout line, the total readout power at the LNA input is $P_{read}=\SI{-72}{dBm}$, below the \SI{1}{dB} gain compression point of \SI{-61}{dBm}. Therefore, using equation \ref{eq:NEP_amp}, we evaluated the LNA NEPs, collected in table \ref{tab:NEP_amp}, which result lower than the generation--recombination ones of table \ref{tab:NEP_gr}. The two LNAs have thus been safely mounted on the \SI{30}{K} shield of the OLIMPO cryostat.
\begin{table}[h]
\caption{\small\label{tab:NEP_amp}Values of the LNA NEP for the OLIMPO channels.}
\begin{center}
\begin{tabular}{cc}
\br
Channel&${\rm NEP}_{amp}$\\
$\left[{\rm GHz}\right]$&$\left[{\rm W}/\sqrt{{\rm Hz}}\right]$\\
\mr
150&$9.3\times 10^{-18}$\\
250&$7.6\times 10^{-18}$\\
350&$4.1\times 10^{-18}$\\
460&$3.0\times 10^{-18}$\\
\br
\end{tabular}
\end{center}
\vspace{-0.5cm}
\end{table}
The cryogenic coaxial cables complete the \emph{cold electronics}. We equipped the OLIMPO cryostat with coaxial cables made of three different materials, for the different thermal jumps: stainless steel from \SI{300}{K} to \SI{30}{K} and \emph{viceversa}, Cu--Ni from \SI{30}{K} to \SI{1.8}{K} and \emph{viceversa}, and Nb--Ti from \SI{1.8}{K} to \SI{0.3}{K} and \emph{viceversa}. In particular, the bias line from \SI{300}{K} to \SI{0.3}{K} is composed of a \SI{2}{m} long stainless steel cable, a \SI{350}{mm} long Cu--Ni cable, and a \SI{400}{mm} long Nb--Ti cable; the readout line from \SI{0.3}{K} to \SI{300}{K} is composed of a \SI{350}{mm} long Nb--Ti cable, a \SI{350}{mm} long Cu--Ni cable, and a \SI{2}{m} long stainless steel cable. The power losses, in terms of $S_{21}$ parameter, have been measured with the VNA at room--temperature and are shown in the \emph{right panel} of figure \ref{fig:LNA}. The maximum power loss of the bias line, in the frequency range of interest, at room--temperature is about 8 dB, which surely decreases at cryogenic temperature.
\begin{figure}[h]
\begin{center}
\includegraphics[scale=0.40]{amplificatore.pdf}
\includegraphics[scale=0.40]{1.pdf}
\end{center}
\caption{\small\label{fig:LNA} \emph{Left panel}: Measured data (\emph{black} and \emph{blue} dots) and fit (\emph{red solid line}) of the noise temperature at the LNA input as function of the operation temperature. \emph{Right panel}: $S_{21}$ parameter measured for the coaxial cables at room--temperature. \emph{Dotted lines} are for stainless steel cables, \emph{dot--dash lines} are for Cu--Ni cables, \emph{dashed lines} are for Nb--Ti cables, and \emph{solid lines} represent the whole lines. Different colors indicate the different lines where the cables are.}
\end{figure}
Along the bias line, we have inserted three cryogenic power attenuators of magnitude \SI{10}{dB} each, thermalized at \SI{1.8}{K} so that their contribution to the total noise results negligible. This is necessary to guarantee a large dynamics for the bias power sweeps on the resonators, essential to find the optimal working point; remaining in the linear regime of the LNA. Precisely, remembering that the LNA \SI{1}{dB} gain compression point is \SI{-61}{dBm}, which means \SI{-69}{dBm} per tone at the detector array input, and since our \emph{room--temperature readout electronics} can send a maximum total power of \SI{-3}{dBm}, which means \SI{-21}{dBm} per tone, we need to attenuate \SI{48}{dB}. In first approximation, we have seen that the bias line attenuates at most \SI{8}{dB}, and the bias room--temperature coaxial cable (between the \emph{room--temperature readout electronics} and the cryostat) attenuates 8 dB, therefore we have to attenuate at least \SI{32}{dB}.
\section{\label{sec:room-temperature}\emph{Room--temperature readout electronics}}
The detection system is completed by the \emph{room--temperature electronics}. Our FPGA consists of a ROACH--2 board\footnote{https://casper.berkeley.edu/wiki/ROACH2}, coupled to a MUSIC DAC/ADC board\footnote{https://casper.berkeley.edu/wiki/MUSIC\_Readout}, the firmware of which has been developed by ASU, and is able to generate up to 1000 tones over a \SI{512}{MHz} bandwidth, with a demodulated output sampling rate up to about \SI{1}{kHz} \cite{Gordon2016}. Since the resonant frequencies of the OLIMPO resonators include values higher than \SI{256}{MHz}, the electronics has to be equipped with up--conversion and down--conversion microwave components. The block diagram of such electronics is shown in the \emph{left panel} of figure \ref{fig:roach}.
The microwave components have been chosen in such a way to optimize the bias--readout electronics in terms of noise, bias and readout power, and to work in the linear regime of the amplifier components (amplifiers and demodulator). The IQ mixer modulator requires as input the $I$ and $Q$ signals and their $\pi$--phase shifts, offset positive through four bias tees. The maximum total power delivered at the IQ modulator output is \SI{-3}{dBm}, and the noise floor is \SI{-159}{dBm/Hz}. The room--temperature amplifiers have been selected and located along the readout line in such a way that the power budget allow them and the IQ demodulator to work in the linear regime (the power at the input of such components is lower than the 1 dB gain compression point at the input) and that the total noise figure at the demodulator output was as low as possible. Table \ref{tab:warm_amp} shows the specifications of the two room--temperature amplifiers and the IQ demodulator, which result in a total gain ${\rm G}=\SI{46.9}{dB}$ and a total noise figure ${\rm NF}=\SI{0.44}{dB}$, both estimated at the demodulator output. The NF has been calculated as
\begin{equation}
{\rm NF}=10\log_{10}\left(n_{1}+\sum_{i=2}^{3}\frac{n_{i}-1}{\prod_{j=1}^{i-1}g_{j}}\right)\;,
\end{equation}
where $n_{i}=10^{{\rm NF}_{i}/10}$, $g_{j}=10^{{\rm G}_{j}/10}$, $i,j=1$ is Amp. 1, $i,j=2$ is Amp. 2, and $i,j=3$ is the IQ demodulator.
\begin{table}[h]
\caption{\small\label{tab:warm_amp}Specifications of the amplifiers components.}
\begin{center}
\begin{tabular}{ccccc}
\br
\multirow{2}{*}{Component}&Gain (G)&\multicolumn{2}{c}{\SI{1}{dB} gain compression point}&Noise Figure (NF)\\
&$\left[{\rm dB}\right]$&@ input $\left[{\rm dBm}\right]$& @ output $\left[{\rm dBm}\right]$&$\left[{\rm dB}\right]$\\
\mr
Amp. 1&20&2&22&0.4\\
Amp. 2&22.5&$-$9.5&13&2.7\\
IQ demodulator&4.4&13&17.4&13.2\\
\br
\end{tabular}
\end{center}
\vspace{-0.5cm}
\end{table}
For this electronics, we measured the loopback noise by closing it on a power attenuator of \SI{36}{dB}, in such a way to have \SI{-56}{dBm} at the Amp. 1 input (total power of \SI{-20}{dBm} at the output of the IQ modulator), similar to that we expect at the output of the LNA (\SI{-40}{dBm}), attenuated by the cryogenic and room--temperature readout line (\SI{-16}{dB}). In this way, the noise floor of the IQ modulator is reduced to the room--temperature thermal noise: \SI{-174}{dBm/Hz}. The measured loopback noise, shown in the \emph{right panel} of figure \ref{fig:roach} compared to the OLIMPO detector array noises, results $\left(-117\pm1\right)\SI{}{dBc/Hz}$, which means $\left(-126.1\pm1.0\right)\SI{}{dBm/Hz}$, for both the $I$ and the $Q$ channels. The expected noise can be estimated as
\begin{equation}
{\rm Noise}=\SI{-174}{dBm/Hz}+{\rm G}+{\rm NF}=\SI{-126.6}{dBm/Hz}\;,
\end{equation}
which is compatible with the measured one. Therefore the microwave components have been correctly optimized, and the \emph{readout electronics} noise is indeed lower than that measured on the four OLIMPO detector arrays, as shown in the \emph{right panel} of figure \ref{fig:roach}.
\begin{figure}[h]
\begin{center}
\includegraphics[scale=0.60]{block_ROACH.pdf}
\includegraphics[scale=0.41]{noises.pdf}
\end{center}
\caption{\small\label{fig:roach} \emph{Left panel}: Block diagram of the \emph{room--temperature electronics}. The ROACH--2 and MUSIC DAC/ADC boards are completed by a set of microwave components to form the bias--readout electronics. \emph{Right panel}: Measured noises of the \emph{room--temperature electronics} (\emph{black lines}) closed on a \SI{36}{dB} attenuator (loopback mode) and of the OLIMPO detector arrays (\emph{color lines}), for both the $I$ (\emph{solid lines}) and $Q$ (\emph{dashed lines}) channels.}
\end{figure}
\section{Conclusion}
We have designed, optimized, fabricated and characterized four arrays of horn--coupled LEKIDs, able to work in the OLIMPO experiment. In this paper we have focused the attention on the optimization process of the \emph{cold} and \emph{room--temperature electronics}.
The \emph{cold electronics} has been optimized in terms of gain, noise, and operation temperature of the LNA; power attenuation and temperature thermalization of the coaxial wiring; and magnitude of the power attenuators. The \emph{room--temperature electronics} has been optimized in such a way that the generated tones were at the resonant frequencies of the KIDs; the signal powers were in the dynamics of each microwave components; and the loopback noise was lower than the one measured for the detector arrays.
All the work has been done by extrapolating the LNA noise at 30 K from measurements at different temperatures; and by measuring the $S_{21}$ parameter of the coaxial cables, the loopback noise of the \emph{room--temperature electronics}, and the noise of the KID arrays.
We obtained that the LNA noise is lower than the expected KID noise as well as the loopback noise of the \emph{room--temperature electronics} is lower than the measured KID noise.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 6,009
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