text:
More Fun With Music
by DoolinDalton
by Brian Thornton
My last post was about tinnitus and how it inhibited me from (most of the time) listening to music while I was writing. I went on to mention that I do occasionally listen to certain types of music while writing certain scenes.
Today I'm going to delve into what music I actually listen to when writing.
I break it down into four general categories completely of my own invention: evocative; action; timely; and romantic.
Why, yes, this is what "cool" looks like.
The second short story I published with Alfred Hitchcock's Mystery Magazine was a tale about a mob "fixer" in 1962 Las Vegas. It was titled "Suicide Blonde."
The entire time I worked on this story I had Miles Davis' immortal "Kind of Blue" (1959) playing in the background. I know it's been mentioned so many times that it's pretty much a cliché, but 50s/60s club jazz is practically a soundtrack for the crime fiction of the era.
Songs such as "So What?", "Freddie Freeloader, and especially "All Blues" just paint a picture for me: a landscape populated by slick guys in sharp suits, driving long cars with fins, dating glamorous women...
Yep, Davis's stuff from the era definitely helped set the mood.
There's so much to make fun of here.
How about we start with the hair?
As I mentioned in my last post, I listen to a lot of soundtrack stuff when I'm writing action scenes. (How the West Was Won, I mentioned explicitly). But I don't just listen to soundtracks and western themes when writing action. I listen to anything with a driving, compelling beat. I once listened to Sammy Hagar's "I Can't Drive 55", the Scorpions' "Lovedrive" and Golden Earring's "Radar Love" over and over on a loop while writing a car chase scene (and did it for so long that I still haven't listened to any of them since!).
Similar to evocative above, but not necessarily the same thing. These are literally "period pieces," music written and performed during the era I'm writing about. For example, I write a lot of mid-19th century America stuff. And if you're gonna use mid-19th century American music, you've got two choices: Stephen Foster, and anything else.
Foster just depresses me.
And I think it's pretty clear WHY…
So I tend to go with the "anything else." I mostly listen to mid-19th century music from this gent:
Oh come on! The medals! That mustache!
This guy practically screams FUN!
He is, of course, Louis Moreau Gottschalk, a half Jewish/half Creole piano maestro and composer from Louisiana who studied in Paris (where he was duly snubbed for being American.) and toured the world giving concerts up until he dropped dead on a concert stage (from malaria) in Rio at the age of 40.
Gottschalk's stuff is both timely and evocative. I listen to it a goodly bit while writing in the period. I am partial to the interpretations of Laure Favre-Kahn, but your mileage may vary.
Which leaves us with …
And by this I mean "emotional" more than "lovestruck" (although the two are hardly mutually exclusive). Any good singer-songwriter stuff will work for these scenes: Fleetwood Mac, Neil Young, Sarah McLaughlin, Elton John. Stuff that makes you FEEL.
And yes, that includes stuff by THIS guy:
I defy you to listen to "The Pretender" and not have an emotional response!
I use this stuff to fuel my dialogue in these sorts of scenes, because music that sparks an emotional responses helps me get the right words flowing.
How about you? What music gets your right words flowing?
Posted by DoolinDalton at 02:05
David Dean 15 May, 2014 08:14
Enjoyed your choices, Brian. I've always loved Jackson Browne songs especially, and "The Pretender" is definitely a classic of its kind.
janice law 15 May, 2014 08:28
I cannot write to music, but I did have a character once who was a fantasy writer who liked Monteverdi
Eve Fisher 15 May, 2014 10:05
I write a lot to silence. But when I do play music, it's almost entirely to instrumental music, or foreign enough so that the words don't interfere with the words I'm writing: medieval and baroque classical music, Gregorian chant, world music (African or Indian when I want a beat, Celtic for a mood). Occasionally jazz. I love Kind of Blue and at this point I can play it in my own mind by heart.
I only listen to rock and roll in the car, when I'm doing some hard driving.
Herschel Cozine 15 May, 2014 13:44
I seldom listen to music while writing. Not that I don't care for it. Good music is essential. But my idea of "good" and today's noise are poles (or generations) apart.
Jeff Baker 15 May, 2014 19:43
Time was I wrote to the evening jazz show. I tend to get "deep in the plak-tow" and zone-out when I'm writing. One thing I can't listen to is country music---sometimes their stories are more compelling than mine and I stop to listen! And I love Gottschalk!
Leigh Lundin 15 May, 2014 22:24
I worked with a video editor who somehow related his work to Creedence Clearwater and played it endlessly, several lifetimes worth. I heard it so much, I realized nuances I never wanted to know, such as Proud Mary keeps on burning, isn't pronounced 'burning' at all, but 'boining'. Where did that come from?
Thinking about it, I need a palate cleanser, blues maybe. Yeah.
Dixon Hill 15 May, 2014 22:58
I listened to U-2's Joshua Tree album so many times, when writing a piece, that my oldest son still refuses to ever listen to them again. LOL
--Dixon
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A Greek God in Every Book
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Odds & Ends, Bits & Pieces
The Nothing
Christopher Columbus and Me
In the Heart of Dark Ghost Trains
A Visit with Darlene Poier and Laura Crowe
Literary Rags
A Saturday Morning Post
Crime Cruise-Ocho Rios
The Elements of Style
Random Thoughts On Writing
Twilight of the Temperature
Chimes at Midnight, Nothing...


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The 2007 ATS F3 cup was the fifth edition of the German F3 Cup. It commenced on 28 April 2007 and ended on 30 September after eighteen races. The title was won by Carlo van Dam in penultimate Sachsenring round.

Teams and drivers

Calendar
With the exception of two rounds at TT Circuit Assen, all rounds took place on German soil.

Results

Standings

ATS Formel 3 Cup

Points are awarded as follows:

ATS Formel 3 Trophy

Points are awarded as follows:

† — Drivers did not finish the race, but were classified as they completed over 90% of the race distance.

ATS Formel 3 Junior-Pokal (Rookie)
Points are awarded for both races as follows:

† — Drivers did not finish the race, but were classified as they completed over 90% of the race distance.

References

External links

German Formula Three Championship seasons
Formula Three season
German
German Formula 3 Championship

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Re: Can of Strongbow, I'm a mess; desperately clutching onto a leaflet on depression.
Anyone enjoying the music on this thread needs radio 6 in their life!
Saw them live at the Kings Cross Scala a couple of weeks ago. Agreed - excellent!


Last week, the Republicans gathered in Florida, and made their case for the election of Mitt Romney and a new direction for our government. This week, the Democrats are in North Carolina for their convention, making the argument that President Obama deserves another four years to continue building on the limited recovery to date. So, with everyone in a political mood, I thought it was time to devote our weekly poll to the upcoming election.
I'm asking more than whether you plan to vote for Obama or Romney. I also thought I'd use this week's poll to gauge the level of enthusiasm or support window and door industry professionals are showing for their favored candidate.
And, of course, we'd like to hear from you. We don't get into politics too often here, but let's hear your views. Who will be better for the country? Who will be better for business? Who will be better for the window and door industry. If you are supporting a particular candidate, post a comment and tell us why.
Are Bells and Whistles Coming Back?
We're now just a few days out from THE SHOW OF SHOWS, and in this week's post we give you some last minute tips and tricks to make your time on the floor and in Vegas more successful and efficient! Plus take a tour through the booth of Erdman Automation in our video spotlight. Check it out!
What's Up with the Housing Market?


You read my mind and it is all because I need to offer some type of free training program to my growing audience but am afraid no one will sign up. In my news letter I let my peeps know something special was coming this fall but fell short of committing to a date. I have not felt good all week unable to rest and everything. Thank you for permission to go deeper.
Hey Janice – I'm glad that this article helps you to go deeper. My advice would be to do it scared. No amount of worry or anxiety will alleviate the fear of uncertainty. Sometimes we have to move forward by taking risks and trying things out.
Step into your power and fully engage and get excited about your free training program – give it the energy of excitement and passion rather than the hesitant energy of fear.
Here's to going deeper – You have FULL permission!


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KCK women remember friend killed in Orlando nightclub shooting
Antonio Brown was close to finishing doctorate
Taisha Walker
Two women in Kansas City, Kansas, share memories of a good friend who they'd planned to visit soon -- until he was killed at the Pulse nightclub in Orlando on Sunday.
Two Kansas City, Kansas, women are remembering a friend who was killed in the Orlando nightclub massacre early Sunday.Chelsea Jones and Jaden Simons said Antonio Brown left quite an impression on them, ever since they first met him in college.Brown, a veteran, had recently been promoted to the rank of captain and was close to finishing his doctorate. His friends said they planned to visit him in Orlando, where he had been hired for a new job."He was, like, 'All right. I'm putting it in my calendar, telling them I'm off,'" said Jones.They never got to celebrate."I had booked the trip and then I had got off work at about 5 o'clock. I called him up and told him, 'Hey, I booked the flight. We'll be there next Friday at 2 o'clock.' He was, like, 'I'll be there. I'll pick y'all up,'" said Jones. "And that was the last time I talked to him."Jones said Brown lived his life to the fullest, something she said is helping comfort her through the pain."That happened in Orlando, but we're here in Kansas and it was one of our friends that got affected and he touched a lot of people," she said. "And of the other 49 people, imagine how many lives in the world they touched or could have touched that are not here."Friends said Brown was at the Pulse nightclub on Friday evening, the night before the shooting. He decided to return for Saturday's Latin Night event.
KANSAS CITY, Kan. —
Two Kansas City, Kansas, women are remembering a friend who was killed in the Orlando nightclub massacre early Sunday.
Chelsea Jones and Jaden Simons said Antonio Brown left quite an impression on them, ever since they first met him in college.
Brown, a veteran, had recently been promoted to the rank of captain and was close to finishing his doctorate. His friends said they planned to visit him in Orlando, where he had been hired for a new job.
"He was, like, 'All right. I'm putting it in my calendar, telling them I'm off,'" said Jones.
They never got to celebrate.
"I had booked the trip and then I had got off work at about 5 o'clock. I called him up and told him, 'Hey, I booked the flight. We'll be there next Friday at 2 o'clock.' He was, like, 'I'll be there. I'll pick y'all up,'" said Jones. "And that was the last time I talked to him."
Jones said Brown lived his life to the fullest, something she said is helping comfort her through the pain.
"That happened in Orlando, but we're here in Kansas and it was one of our friends that got affected and he touched a lot of people," she said. "And of the other 49 people, imagine how many lives in the world they touched or could have touched that are not here."
Friends said Brown was at the Pulse nightclub on Friday evening, the night before the shooting. He decided to return for Saturday's Latin Night event.


Bristol, UK September 28th, 2018. Emerging automotive interfaces could make driving safer by significantly reducing 'glance time', a study by technology firm Ultrahaptics and the University of Nottingham has found. The study compared a new automotive interface, for controlling environmental features such as music and air conditioning, to the current use of touchscreens. It was found to reduce errors, cut time spent with eyes off the road by up to 25%, and to be preferred by users. Nearly 40% of users were able to perform tasks without taking their eyes off the road at all.
Mid-air gestures were combined with mid-air touch feedback to simulate the tactile presence of buttons and sliders on the user's hand, without the user having to physically touch any controls. The study, Exploring the Use of Mid-Air Ultrasonic Feedback to Enhance Automotive User Interfaces, was awarded 'Best Paper' at the Automotive UI conference in Toronto on 24th September 2018.
The paper centers on comparisons between popular touchscreen technologies and emerging gesture recognition systems, which were first launched in cars on the market in 2016. Gesture recognition systems use 3D sensing technologies to enable drivers to control multimedia with the wave of a hand, or by performing a hand gesture. Ultrahaptics' mid-air touch technology was added to gesture recognition in the study to produce the feeling of touch (termed 'haptic feedback') by projecting ultrasound waves onto the user's palm and fingers, creating tactile points of pressure which the user could feel.
48 participants took part in the study, each completing four simulated drives in a specially adapted Audi TT chassis in front of a curved screen. Each drive featured different types of in-car interfaces: a touchscreen without haptic feedback, a touchscreen with mid-air haptic feedback, gesture control without haptic feedback, and gesture control with mid-air haptic feedback. The researchers tested two different types of interactions: a slider bar and button presses. User experience was measured across a whole spectrum, including eye-tracking ("eyes off the road" time), accuracy and efficiency, and participants' subjective assessment.
Results from the study suggest that adding haptics to gesture control reduced both the total and the mean glance duration times (or "eyes off the road" time) for both button and slider controls. The effect was most distinct in the slider task, with gesture control plus haptics resulting in an average 25% decrease in total glance time compared to touchscreens. The mean glance duration was under two seconds for mid-air haptics for both buttons presses and slider bars. The study concluded there was three times greater accuracy on the slider task when using gesture control with haptics compared to a touchscreen.
Speaking of the findings, Ultrahaptics' Director of Research, Dr Orestis Georgiou commented "These numbers are not just an incremental improvement, but potentially a massive shift in safety. Driver distraction and safety are central to in-car controls, and distraction costs lives. Half a second cut from a driver distraction interaction at 70mph means your response to an incident will come 15.6 meters sooner. By significantly reducing glance time these technologies pave the way for a revolution of next generation, safer, easier to use interfaces. This study was a great example of collaboration between industry and academia, and we were hugely excited to be recognised as 'best paper' by the Human-Machine Interface industry experts at the ACM Automotive UI Conference".


Romelu Lukaku is exerting influence on Manchester United dressing room already.
Romelu Lukaku has quickly set about marking his territory at Manchester United and has already become a key figure in the club's dressing room, according to reports.
The Red Devils lost Wayne Rooney over the summer, while Zlatan Ibrahimovic is still undergoing rehabilitation, leaving a leadership vacuum, and replacement skipper Michael Carrick has not been the only player to fill that void.
According to the Manchester Evening News, younger players have started to find their voice and Lukaku has made an instant impact at Old Trafford since making a £75 million move to the club from Everton.
Firstly he boldly stepped up to take on penalty duties from Rooney, the previous go-to spot-kick taker – though he did miss one against Leicester City – and has also made his presence felt in other ways. The Belgian is said to 'regularly berate' Daley Blind for his service, demanding the Dutch defender provide him with better quality passes and crosses.
But perhaps the biggest star of United's new-look dressing room hierarchy is Ander Herrera, who – despite finding himself on the bench this season – has been very vocal in getting his teammates to perform at their highest level.
According to MEN, he motivated his teammates for the Champions League tie against CSKA Moscow, has been giving Eric Bailly defensive tips and reminded players who to mark from the touchline against Crystal Palace.
Mourinho deliberately made a point of not appointing a vice-captain and will already feel like that decision has paid off. Lukaku, Herrera and Paul Pogba have all shown real leadership qualities on and off the pitch this season, and that has helped propel United up the Premier League table, level on points with rivals City.
I just hope he will last long..
What do you make of this photo of Obama drinking beer?
What Is Impetigo? How to Deal with It?


Could national crisis be the touchstones from which an individual rises up and renews herself body, mind, and spirit? Could an individual's revitalization, setbacks, and determination to overcome obstacles inspire others to embark on their own journey of renewal? What would give birth to this courageous new individual and national spirit?
I believe that individual acts of intuition will serve as the first sparks.
These sparks will deepen our understanding of our body, mind, and spirit at its best.
In March 2011, several days before the tsunami, earthquake and nuclear crisis in Japan, I felt elated about life. So elated, that I believed if I had to come back to this world again, I would be me again. I could not have chosen better parents, a more fitting "out of box" life path, nor the good fortune of having met a few beautiful and inspiring men who taught me how to love. One even became my husband.
Naturally while outside life events were sometimes challenging, it was only the limitations of my own mind, body and spirit which did not make me blissfull all the time. And just when I thought I would like to come back to this world as me again, a new thought arose. Why come back to experience more of the same? And as soon as that thought arose, I began to meet a series of teachers who were both humble and wise.
And so in 2011 started a journey where I began to push beyond previous barriers and realize how little I knew: about the body, about the spirit and even the mind.
I thought it would be useful to share the wisdom of the some of those I found along my path and the mistakes I made so that your path will be easier. Hence this site is for anyone who is curious about experimenting to go beyond a previous best and open enough to test things for himself or herself. It is for those who are not afraid to fail, not afraid to ask or question.
When we embark on this path all becomes new. All becomes quite an adventure far beyond anything one can imagine. One's life can never quite be the same.
Join me on this new adventure where I still have much much to learn. Each section will start with simple things we can do to test our experience. Many have nothing to do with what people consider "yoga" in that they are as simple and as elementary as an understanding of movement or exercise, water, food and sleep.
Know that most was new to me. I was the one who thought I knew everything about food, and the mind. As for the body, I was a bit behind others — a bit more modest and far less flexible. In general as my mind was strong, I would simply ask the body to follow. If I wanted to wake up at 5am since a child, it would just simply have to do so. Until, of course it rightfully rebelled.
Whether you wish to make a fundamental change in a nation, an organization, your family, a spouse, a child or simply yourself, the achievement is almost just as difficult.The benefit of changing yourself first is that regardless of the state of others around you, you may not only experience serenity and balance in any context but also the capacity to act in the world more lovingly, more effortlessly and far more effectively.
May your path be steady, may it be joyful and may you move far beyond the best in all of us.
All errors are mine and I ask indulgence. The website is the first step in an investigation to explore a possible philosophy or understanding body, mind and spirit and is by no means conclusive. It is meant for others to have a place to begin and is not meant to replace any health information or medical advice. Each one of us is different, what works for one, may not always work for another.
Each individual who is interviewed on this site is not responsible for the views of all others on this site nor does that individual embrace a common philosophy or message. Likewise, commentaries posted on this site are the sole opinion of the author of each article.
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EU NAVFOR can confirm that oil tanker, MT NAVIG8 Providence, came under attack by suspected armed pirates earlier today in the Gulf of Oman.
MT NAVIG8 Providence was at sea 100 nautical miles east of Muscat when she was approached by six armed men in a skiff. It is understood that as the skiff moved towards the tanker, there was an exchange of small arms fire between the suspected pirates and the maritime security team on board the tanker.
In an email to EU NAVFOR, the master of the MT NAVIG8 Providence stated that his ship's protection team saw a ladder in the skiff.
After carrying out defensive manoeuvres in accordance with the Shipping Industry recognised Best Management Practices (BMP4), together with the armed response from MT NAVIG8 Providence's protection team, the suspected pirates broke off their attack and the vessel and crew are now safe.
Counter-piracy naval forces are coordinating a response to search for the skiff.


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text:
\section{Introduction}
\label{sec:intro}

In many applications, one faces the crucial dilemma of choosing an appropriate distance $D(\cdot,\cdot)$ between data elements.
In some cases, those distances can be picked up {\em a priori} from well-grounded principles (e.g., Kullback-Leibler distance in statistical estimation~\cite{CT-2012}).
In other cases, one is rather left at testing several distances~\cite{Bhat-1982}, and choose {\em a posteriori} the  distance
that yielded the best performance.
For the latter cases, it is judicious to consider a family of parametric distances $D_\alpha(\cdot,\cdot)$, and learn~\cite{learningalpha-2010} the hyperparameter $\alpha$ according to the application at hand and potentially the dataset (distance selection).
Thus it is interesting to consider parametric generalizations of common distances~\cite{Dico-2009} to improve performance in applications.

Some distances can be designed from inequality gaps~\cite{Jensen-1982,Holder-2017}.
For example, the Jensen divergence $J_F(p,q)$ (also called the Burbea-Rao divergence~\cite{Jensen-1982,Jensen-2011}) is designed from the inequality gap of Jensen inequality
\begin{equation}
F\left(\frac{p+q}{2}\right) \leq \frac{F(p)+F(q)}{2},
\end{equation}
 that holds for a strictly real-valued convex function $F$:
\begin{equation}
J_F(p,q)=\frac{F(p)+F(q)}{2}-F\left(\frac{p+q}{2}\right).
\end{equation}
We can extend the Jensen divergence to a parametric family of skew Jensen divergences $J_F^\alpha$ (with $\alpha\in (0,1)$) built on the convex inequality gap:
\begin{equation}
F((1-\alpha)p+\alpha q) \leq (1-\alpha)F(p)+\alpha F(q).
\end{equation}
The skew Jensen divergences $J_F^\alpha$ are defined by:
\begin{equation}\label{eq:jf}
J_F^\alpha(p:q)=(1-\alpha)F(p)+\alpha F(q)-F((1-\alpha)p+\alpha q),
\end{equation}
satisfying $J_F^\alpha(q:p)=J_F^{1-\alpha}(p:q)$ and $J_F^{\frac{1}{2}}(p:q)=J_F(p,q)$.
Here the ':' notation emphasizes the fact that the distance is potentially asymmetric: $J_F^\alpha(p:q)\not =J_F^\alpha(q:p)$.
The term divergence is used in information geometry~\cite{IG-2016} to refer to the smoothness property of the distance function that yields an information-geometric structure of the space induced by the divergence.
Let $[p,q]=\{(pq)_\lambda:=(1-\lambda)p+\lambda q, \lambda\in[0,1]\}$ denote the line segment with endpoints $p$ and $q$.
For scalars $a$ and $b$, $[a,b]$ denotes the interval $[\min(a,b),\max(a,b)]$.
Then we can rewrite Eq.\ref{eq:jf}:
\begin{equation}
J_F^\alpha(p:q)=(F(p)F(q))_\alpha-F((pq)_\alpha).
\end{equation}
In applications, it is rather the relative comparisons of distances rather than their absolute values that is important.
Thus we may multiply a distance by any positive scaling factor and include it in the class of that distance.
When $F$ is strictly convex and differentiable, the class of Jensen divergences include in the limit cases the Bregman divergences~\cite{Jensen-2011,Zhang-2004,Bregman-2005}:
\begin{eqnarray}
\lim_{\alpha\rightarrow 0^+} \frac{J_F^\alpha(p:q)}{\alpha}&=&B_F(q:p),\\
\lim_{\alpha\rightarrow 1^-} \frac{ J_F^\alpha(p:q)}{1-\alpha}&=&B_F(p:q),
\end{eqnarray}
where
\begin{equation}
B_F(p:q)=F(p)-F(q)-(p-q)^\top\nabla F(q),
\end{equation}
is the Bregman divergence~\cite{JB-2013}.
Overall, one may define the smooth parametric family of scaled skew Jensen divergences:
\begin{equation}
\mathrm{sJ}_F^\alpha(p:q) =\frac{1}{\alpha(1-\alpha)}J_F(p:q),
\end{equation}
that encompasses the Bregman divergence $B_F(p:q)$ and the reverse Bregman divergence $B_F(q:p)$ in limit cases (with $\alpha\in\bbR$).

\begin{figure}
	\centering
	\includegraphics[width=\textwidth]{BhatKL-JensenBregman.pdf}

	\caption{Links between the statistical skew Bhattacharyya distances and parametric skew Jensen divergences when distributions belong to the same exponential family.
	\label{fig:link}}
\end{figure}

There is a nice relationship between the  Jensen divergences operating on parameters (e.g., vectors, matrices) and a class of statistical distances between probability distributions (see Figure~\ref{fig:link}):
Let $\{p(x;\theta)\}_\theta$ be an exponential family~\cite{Bregman-2005} (includes the Gaussian family and the finite discrete ``multinoulli'' family) with convex cumulant function $F(\theta)$.
Then the skew Bhattacharryya distance~\cite{Bhat-1946}:
\begin{eqnarray}
\mathrm{Bhat}_\alpha(p:q)=-\log \int p(x)^{1-\alpha}q(x)^\alpha\mathrm{d}x,\\
\mathrm{Bhat}_\alpha(p:q)=-\log \int p(x)\left(\frac{q(x)}{p(x)}\right)^{\alpha}\mathrm{d}x,
\end{eqnarray}
between two distributions  belonging to the same exponential family amounts to a skew Jensen divergence~\cite{Jensen-2011}:
\begin{equation}\label{eq:bhat2jensen}
\mathrm{Bhat}(p(x;\theta_1):p(x;\theta_2))= J_F^\alpha(\theta_1:\theta_2).\\
\end{equation}
We further check that:
\begin{eqnarray}
\lim_{\alpha\rightarrow 0^+} \frac{1}{\alpha}\mathrm{Bhat}_\alpha(p:q)&=&\mathrm{KL}(p:q),\\
\lim_{\alpha\rightarrow 1^-} \frac{1}{1-\alpha}\mathrm{Bhat}_\alpha(p:q)&=&\mathrm{KL}(q:p),
\end{eqnarray}
where
\begin{equation}
\mathrm{KL}(p:q)=\int p(x)\log\frac{p(x)}{q(x)}\mathrm{d}x,
\end{equation}
is the Kullback-Leibler divergence~\cite{CT-2012}.

The proof of the skewed Bhattacharrya distance converging to the Kullback-Leibler divergence~\cite{CT-2012} proceeds as follows:
We have:
\begin{equation}
\left(\frac{q(x)}{p(x)}\right)^\alpha=\exp\left(\alpha\log \frac{q(x)}{p(x)}\right)\simeq_{\alpha\rightarrow 0} 1+\alpha\log \frac{q(x)}{p(x)}.
\end{equation}
Thus we get:
\begin{equation}
\log p(x)^{1-\alpha}q(x)^{\alpha}  \simeq_{\alpha\rightarrow 0} \log \int \left(p(x)+\alpha\log \frac{q(x)}{p(x)}\right)\mathrm{d}x=\log (1-\alpha\mathrm{KL}(p:q)),
\end{equation}
 and therefore
\begin{equation}
\lim_{\alpha\rightarrow 0^+} \frac{1}{\alpha}\mathrm{Bhat}_\alpha(p:q)=\mathrm{KL}(p:q),
\end{equation}
since $\log(1+x)\simeq x$ when $x\rightarrow 0$.

In statistical signal processing, information fusion and machine learning, one often considers the skew  Bhattacharryya distance~\cite{BhatApp-1996,BhatApp-2016,BhatApp-2017} or the Chernoff distance~\cite{Chernoff-2013,ChernoffIG-2017,Chernoff-2017} for exponential families (e.g., Gaussian/multinoulli): This highlights the  important role in disguise of the equivalent skew Jensen divergences (see Eq.~\ref{eq:bhat2jensen}).

The paper is organized as follows:
Section~\ref{sec:chorddiv} introduces the novel triparametric family of chord gap divergences that generalizes the skew Jensen divergences (\S\ref{sec:chorddiv-def}), describes several properties (\S\ref{sec:chorddiv-prop}), and deduces a generalization of the statistical Bhattacharyya distance (\S~\ref{sec:gen}).
Section~\ref{sec:clustering} considers the calculation of the centroid (\S\ref{sec:centroid}) for the chord gap divergences, and report probabilistic guarantee of
 the $k$-means++ seeding (\S\ref{sec:kmpp}) by highlighting the Taylor-Lagrange remainder forms of those divergences.

\section{The chord gap divergence}\label{sec:chorddiv}

\subsection{Definition}\label{sec:chorddiv-def}

\begin{figure}
\centering
\includegraphics[width=0.7\textwidth]{trigapdivergence.pdf}
\caption{The triparametric chord gap divergence: The vertical distance beetween the upper chord $U$ and the lower chord $L$ is non-negative and zero iff. $p=q$.\label{fig:chorddiv}}
\end{figure}

Let $F:\calX\rightarrow \bbR$ be a {\em strictly convex} function.
For $\alpha,\beta\in (0,1)$ with $\alpha\not=\beta$ and $\alpha\beta<1$,
the chord
\begin{equation}
L=[((pq)_\alpha,F((pq)_\alpha))((pq)_\beta,F((pq)_\beta))],
\end{equation}
is  below the distinct chord
\begin{equation}
U=[(p,F(p))(q,F(q))].
\end{equation}
Thus we can define a divergence as the {\em vertical gap} between these two U/L chords for a given coordinate
$x\in [(pq)_\alpha,(pq)_\beta]$:
\begin{equation}
\boxed{J_F^{\alpha,\beta,\gamma}(p:q)=(F(p)F(q))_\gamma -(F((pq)_\alpha)F((pq)_\beta))_\lambda}
\end{equation}
 such that $((pq)_\alpha(pq)_\beta)_\lambda=(pq)_\gamma$ with $\gamma\in (\alpha,\beta)$ (see Figure~\ref{fig:chorddiv}).
 A calculation shows that:
\begin{equation}
\lambda=\lambda(\alpha,\beta,\gamma)=\frac{\gamma-\alpha}{\beta-\alpha},
\end{equation}
or that
\begin{equation}
\gamma=\lambda(\beta-\alpha)+\alpha,
\end{equation}
for $\lambda\in [0,1]$ ($\gamma\in [\alpha,\beta]$)
when $\alpha\not=\beta$, so that we get :
\begin{eqnarray}
J_F^{\alpha,\beta,\gamma}(p:q) &=& (F(p)F(q))_\gamma -(F((pq)_\alpha)F((pq)_\beta))_{\frac{\gamma-\alpha}{\beta-\alpha}},\quad \gamma\in [\alpha,\beta]\\
&=& (F(p)F(q))_{\lambda(\beta-\alpha)+\alpha} - (F((pq)_\alpha)F((pq)_\beta))_{\lambda},\quad \lambda\in [0,1].
\end{eqnarray}

\subsection{Properties of the chord gap divergence and subfamilies}\label{sec:chorddiv-prop}

We have:
\begin{eqnarray}
J_F^{\alpha,\alpha,\alpha}(p:q)&=&J_F^{\alpha}(p:q),\\
 J_F^{0,1,\gamma}(p:q)&=&J^\gamma(p:q),\\
J_F^{\alpha,\beta,\gamma}(q:p)&=& J_F^{1-\alpha, 1-\beta,1-\gamma}(p:q),
\end{eqnarray}
since $\lambda(1-\alpha,1-\beta,1-\gamma)=\frac{\gamma-\alpha}{\beta-\alpha}=\lambda(\alpha,\beta,\gamma)$ using the fact that $(ab)_{1-\delta}=(ba)_\delta$ for $\delta\in [0,1]$. Thus we also have:
\begin{equation}
J_F^{1-\alpha,1-\alpha,1-\alpha}(p:q)=J_F^\alpha(q:p).
\end{equation}

More importantly, we can express the chord gap divergence as the difference of two skew Jensen divergences (Figure~\ref{fig:chorddiv}):
\begin{equation}\label{eq:Jdiff}
J_F^{\alpha,\beta,\gamma}(p:q)=J_F^\gamma(p:q)-J_F^\lambda((pq)_\alpha:(pq)_\beta),
\end{equation}
with $\lambda=\frac{\gamma-\alpha}{\beta-\alpha}$ or $\gamma=\lambda(\beta-\alpha)+\alpha$ for $\lambda\in [0,1]$ and $\gamma\in [\alpha,\beta]$.
Thus the chord gap divergence can be interpreted as a {\em truncated} skew Jensen divergence: The truncation of the vertical gap measured by
$J_F^\gamma(p:q)$ from which we remove the vertical gap measured by $J_F^\lambda((pq)_\alpha:(pq)_\beta)$.

A biparametric subfamily $J_F^{\beta,\gamma}$  of $J_F^{\alpha,\beta,\gamma}$ is obtained by setting $\alpha=0$ so that $(pq)_\alpha=p$, so that the two upper/lower chords $L$ and $U$ coincide at extremity $p$:

\begin{eqnarray}
J_F^{\beta,\gamma}(p:q)&=&(F(p)F(q))_{\gamma}-(F(p)F((pq)_\beta))_{\frac{\gamma}{\beta}},\\
&=& \left(\frac{\gamma}{\beta} -\gamma \right) F(p)+\gamma F(q)-\frac{\gamma}{\beta} F((pq)_\beta),\\
&=&  \gamma \left( \left(\frac{1}{\beta} -1 \right) F(p)+ F(q)-\frac{1}{\beta} F((pq)_\beta)\right).
\end{eqnarray}

When $\beta=\frac{1}{2}$, we find that $J_F^{\frac{1}{2},\gamma}(p:q)=2\gamma J_F(p:q)$:
\begin{eqnarray}
J_F^{\gamma}(p:q)&=&2\gamma \left(\frac{F(p)+F(q)}{2} -F\left(\frac{p+q}{2}\right) \right)\\
\end{eqnarray}
is the ordinary ($\gamma$-scaled) Jensen divergence.
When $\beta\rightarrow 0$, we have $\lim_{\beta\rightarrow 0} \frac{1}{\gamma} J_F^{\beta,\gamma}(p:q)=B_F(q:p)$ (with $\gamma\in(0,\beta)$)
since $-\frac{1}{\beta} F((pq)_\beta)\simeq -\frac{1}{\beta}-(q-p)^\top \nabla F(p)$ using a first-order Taylor expansion.

We may also consider $\beta=1-\alpha$, and define the biparametric subfamily:
\begin{eqnarray}
{J'}_F^{\alpha,\gamma}(p:q) &=& (F(p)F(q))_\gamma -(F((pq)_\alpha)F((pq)_{1-\alpha}))_{\frac{\gamma-\alpha}{1-2\alpha}},\quad \gamma\in [\alpha,1-\alpha],\\
&=& (F(p)F(q))_{\lambda(1-2\alpha)+\alpha} - (F((pq)_\alpha)F((qp)_\alpha))_{\lambda},\quad \lambda\in [0,1].
\end{eqnarray}

Chord gap divergences operating on matrix arguments can be obtained by taking  strictly convex matrix generators~\cite{JB-2013} (e.g., $F(X)=-\log\det |X|$ where $|X|$ denotes the determinant of $X$) for symmetric positive definite matrices $X\in \bbP_{++}$, $\bbP_{++}=\{X\ : \ X\succ0 \}$ denote the space of positive definite matrices,   a convex cone. This may be useful in applications based on covariance matrices~\cite{JB-2013} (or correlation matrices).

\subsection{Generalized Bhattacharrya distances}\label{sec:gen}
The  interpretation given in Eq.~\ref{eq:Jdiff} yields a triparametric family of Bhattacharryya statistical distances~\cite{Bhat-1946} between members $p(x)=p(x;\theta_p)$ and  $q(x)=p(x;\theta_q)$ of the {\it same} exponential family (with a slight abuse of notation
 that $\mathrm{Bhat}_\alpha(\theta_p:\theta_q)=\mathrm{Bhat}_\alpha(p(x;\theta_p):p(x;\theta_q))$):

\begin{equation}
\mathrm{Bhat}_{\alpha,\beta,\gamma}(\theta_p:\theta_q)= \mathrm{Bhat}_\gamma(\theta_p:\theta_q)-\mathrm{Bhat}_\lambda((\theta_p\theta_q)_\alpha:(\theta_p\theta_q)_\beta).
\end{equation}
It follows that:
\begin{eqnarray}\label{eq:gbhatef}
\lefteqn{\mathrm{Bhat}_{\alpha,\beta,\gamma}(\theta_p:\theta_q) =}\\ \nonumber
&& -\log
\frac{\int p(x;\theta_p)^{1-\gamma} p(x;\theta_q)^{\gamma} \mathrm{d}x}{
\int p(x;(\theta_p\theta_q)_\alpha)^{1-\lambda} p(x;(\theta_p\theta_q)_\beta)^{\lambda} \mathrm{d}x}.
\end{eqnarray}
Note that when $\alpha=\beta$, we have:
\begin{equation}
p(x;(\theta_p\theta_q)_\alpha)^{1-\lambda} p(x;(\theta_p\theta_q)_\beta)^{\lambda}=p(x;(\theta_p\theta_q)_\alpha),
\end{equation}
and therefore the denominator becomes $\int p(x;(\theta_p\theta_q)_\alpha)\mathrm{d}x=1$, and we recover the skew Bhattacharryya distance, as expected.

We shall extend the generalized Bhattacharrya divergence of Eq.~\ref{eq:gbhatef} to arbitrary distributions by
generalizing the notion of {\em interpolated distribution}:
\begin{equation}
p(x;(\theta_p\theta_q)_\delta)=\Gamma_\delta(p(x;\theta_p),p(x;\theta_q)).
\end{equation}
When $\delta$ ranges from $0$ to $1$, we obtain a {\em Bhattacharyya arc} linking distribution $p(x;\theta_p)$
to distribution $p(x;\theta_q)$ (the arc is called an exponential or $e$-geodesic in information geometry~\cite{IG-2016}).
We define:
\begin{equation}
\Gamma_\delta(p(x),q(x)) =\frac{p(x)^{1-\delta}q(x)^{\delta}}{Z_\delta(p(x):q(x))},
\end{equation}
with
\begin{equation}
Z_\delta(p(x):q(x))=\int p(x)^{1-\delta}q(x)^{\delta}\mathrm{d}\nu(x).
 \end{equation}
Note that we need the integral to converge properly in order to define $\Gamma_\delta(p(x),q(x))$.
This always holds  for distributions belonging to the same exponential families
since  $(\theta_p\theta_q)_\delta$ is guaranteed to belong to the natural parameter space, and
\begin{equation}
Z_\delta(p(x;\theta_p):p(x;\theta_q))=\exp(-J_F^\delta(\theta_p:\theta_q)).
\end{equation}

By extension, the triparametric Bhattacharryya distance can be defined by:
\begin{eqnarray}
\lefteqn{\mathrm{Bhat}^{\alpha,\beta,\gamma}(p(x):q(x)) =}\nonumber\\
&& -\log \left( \frac{\int p(x)^{1-\gamma} q(x)^{\gamma} \mathrm{d}\nu(x)}{
\Gamma_\alpha(p(x),q(x))^{1-\gamma} \Gamma_\beta(p(x),q(x))^{\gamma}} \right).
\end{eqnarray}
Thus we explicitly define the generalized Bhattacharrya distance by:
{
\begin{eqnarray*}
\lefteqn{\mathrm{Bhat}^{\alpha,\beta,\gamma}(p(x):q(x))=}\nonumber\\
&& -\log \left(
\frac{\int p(x)^{1-\gamma} q(x)^{\gamma} \mathrm{d}\nu(x)}{
\int \left(\frac{p(x)^{1-\alpha}q(x)^{\alpha}\mathrm{d}\nu(x)}{\int p(x)^{1-\alpha}q(x)^{\alpha}\mathrm{d}\nu(x)}\right)^{1-\lambda}
\left(\frac{p(x)^{1-\beta}q(x)^{\beta}\mathrm{d}\nu(x)}{\int p(x)^{1-\beta}q(x)^{\beta}\mathrm{d}\nu (x)} \right)^{\lambda} \mathrm{d}\nu(x)
}\right).
\end{eqnarray*}
}

Notice that when $\alpha=\beta$, for any $\lambda\in [0,1]$, the denominator collapses to one, and we find
 that $\mathrm{Bhat}_{\alpha,\beta,\gamma}(p(x):q(x)) = \mathrm{Bhat}_{\alpha}(p(x):q(x))$, as expected.

For multivariate gaussians/normals belonging to the family $\{\calN(\mu,\Sigma)\ :\ \mu\in\bbR^d,\Sigma\in\bbP^d_{++}\}$, we have
the natural parameter~\cite{SMEF-2011}
\begin{equation}
\theta=(v,M)=(\Sigma^{-1}\mu,-\frac{1}{2}\Sigma^{-1}),
\end{equation}
and the
cumulant function:
\begin{equation}
F(v,M)=\frac{d}{2}\log 2\pi-\frac{1}{2}\log |-2M|-\frac{1}{4}v^\top M^{-1}v,
\end{equation}
that can also be expressed in the usual parameters:
\begin{equation}
F(\mu,\Sigma)=\frac{1}{2}\log (2\pi)^d|\Sigma|+\frac{1}{2}\mu^\top\Sigma^{-1}\mu.
\end{equation}
We have:
\begin{equation}
(\theta_p\theta_q)_\delta=((1-\delta)\Sigma_p^{-1}\mu_p+\delta\Sigma_q^{-1}\mu_q,-\frac{1-\delta}{2}\Sigma_p^{-1}-\frac{\delta}{2}\Sigma_q^{-1}),
\end{equation}
so that we get~\cite{hero-2001}:
\begin{equation}
J_F^\alpha(p(x;\mu_p,\Sigma_p):p(x;\mu_q,\Sigma_q))=\frac{\alpha(1-\alpha)}{2}\Delta\mu^\top((1-\alpha)\Sigma_p+\alpha\Sigma_q)^{-1}\Delta\mu
+
\frac{1}{2}\log\frac{|(1-\alpha)\Sigma_p+\alpha\Sigma_q|}{|\Sigma_p|^{1-\alpha}|\Sigma_q^\alpha|},
\end{equation}
where $|.|$ denotes the matrix determinant and $\Delta\mu=\mu_q-\mu_p$.
This gives a closed-form formula for $\mathrm{Bhat}^{\alpha,\beta,\gamma}$ for multivariate Gaussians.
See~\cite{clusteringmvn-2009} for applications clustering multivariate normals.

\section{Centroid-based clustering}\label{sec:clustering}
Bhattacharrya clustering is often used in statistical signal processing, information fusion, and machine learning (see~\cite{BhatApp-1996,BhatApp-1979,BhatApp-2006,BhatKernel-2009,BhatC-2014,BhatC-2015} for some illustrative examples).
Popular clustering algorithms are {\em center-based clustering}, where each cluster stores a prototype (a representative element of the cluster), and each datum is assigned to the cluster with the closest prototype with respect to a distance function. The cluster prototypes are then updated, and the algorithm iterates until (local) convergence.
This scheme includes the $k$-means and the $k$-medians~\cite{kmeanscoresets-2004}.
Lloyd $k$-means heuristic updates the prototype $c$ of a cluster $X$ by choosing its center of mass $c=\frac{1}{|X|}\sum_{x\in X} x$ that minimizes the cluster variance: $\min_c \sum_{x\in X} \|x-c\|^2$ (this holds for any Bregman divergence too~\cite{Bregman-2005}).

\subsection{Chord gap divergence centroid}\label{sec:centroid}

We extend $k$-means for a weighted point set:
\begin{equation}
\calP=\{(w_1,p_2), \ldots, (w_n,p_n)\},
\end{equation}
with $w_i>0$ and $\sum_i w_i=1$, using the chord gap divergence by solving the following minimization problem:
\begin{equation}
\min_x E(x)=\sum_{i=1}^n  w_i J_F^{\alpha,\beta,\gamma}(p_i:x).
\end{equation}

By expanding the chord gap divergence formula and removing all terms independent of $x$, we obtain an equivalent minimization problem as a difference  of convex function programming~\cite{DC-2005}:
\begin{equation}
\min_x E(x)=\min_x A(x)-B(x),
\end{equation}
with
\begin{eqnarray}
A(x)&=&\sum_{i=1}^n (F(p_i)F(x))_\gamma, \\
B(x)&=&\sum_{i=1}^n (F((p_ix)_\alpha)F((p_ix)_\beta))_\lambda,
\end{eqnarray}
 both strictly convex functions.
It follows a concave-convex procedure~\cite{CCCP-2002} (CCCP) solving locally $\min_x A(x)-B(x)$:
initialize $x_0=p_1$ and then iteratively update as follows:
\begin{equation}
\nabla A(x_{t+1})=\nabla B(x_{t}).
\end{equation}
When the reciprocal gradient $\nabla A^{-1}$ (such that $\nabla A^{-1}(\nabla A(x))=x$) is available in closed form, we end up with the following update:
\begin{equation}
x_{t+1}=\nabla A^{-1}(\nabla B(x_{t})).
\end{equation}
Since we have
\begin{eqnarray}
\nabla A(x)&=&n\gamma \nabla F(x),\\
\nabla B(x)&=&\sum_i (1-\lambda)\alpha\nabla F(F((p_ix)_\alpha) +\lambda\beta \nabla F((p_ix)_\beta),
\end{eqnarray}
the update rule is
{%
\begin{eqnarray*}
\lefteqn{x_{t+1}=}\nonumber\\
&&\nabla F^{-1}\left(
\frac{1}{\gamma} \sum_i w_i\left( (1-\lambda)\alpha\nabla F((p_ix_t)_\alpha) +\lambda\beta \nabla F\left((p_ix_t)_\beta\right)\right)
\right).
\end{eqnarray*}
}

When $\alpha=\beta=\gamma$, we find the simplified update rule:
\begin{equation}
x_{t+1}=\nabla F^{-1}\left(\sum_i w_i \nabla F((p_ix_t)_\alpha\right),
\end{equation}
corresponding to the skew Jensen divergences~\cite{Jensen-2011}.
Note that it is enough to improve iteratively the prototypes to get a variational Lloyd's $k$-means~\cite{tJ-2015} that guarantees monotone convergence to a (local) optimum.

\subsection{Performance analysis of $k$-means++}\label{sec:kmpp}

For high-performance clustering, one may use $k$-means++~\cite{kmpp-2007} that is a guaranteed probabilistic initialization of the cluster prototypes.
For an arbitrary dissimilarity function $D(\cdot:\cdot)$, the cost function of $k$-means (also called potential function or energy function) for a weighted point set $\calP$ with cluster center set $\mathcal{C}$ is defined by
$$
\Phi(\mathcal{C})=\sum_{i=1}^n w_i \min_{c\in\mathcal{C}} D(p_i:c).
$$
Let $\Phi^*=\min_{\mathcal{C}\ :\ |C|=k} \Phi(\mathcal{C})$ denote the optimal cost function.
A heuristic $H$  delivering a cluster center set $\mathcal{C}_H$ is said $\kappa$-competitive when $\frac{\Phi(\mathcal{C}_H)}{\Phi^*}=\kappa$.
$\kappa$ is termed the competitive ratio~\cite{kmpp-2007}.
To get an expected competitive ratio of $2U^2(1+V)(2+\log k)$~\cite{tJ-2015}, we need to upper bound:
\begin{itemize}
\item $U$ such that the  divergence $D=J_F^{\alpha,\beta\gamma}$ satisfies the $U$-triangular inequality $D(x:z)\leq U(D(x:y)+D(y:z))$, and
\item $V$ such that the divergence satisfies the symmetric inequality $D(y:x)\leq V D(x:y)$.
\end{itemize}

The proof  follows the proof reported in~\cite{tJ-2015} for total Jensen divergences once we can express the divergences in their
Taylor-Lagrange remainder forms:
\begin{equation}
D(p:q)=(p-q)^\top H_D(p:q) (p-q),
\end{equation}
where $H_D(p:q)\succ 0$.
For example, the Taylor-Lagrange remainder form of the Bregman divergence~\cite{Mixed-2008} is obtained from a first-order Taylor expansion with the exact Lagrange remainder:
\begin{equation}\label{eq:tlbreg}
B_F(p:q)=\frac{1}{2} (p-q)^\top \nabla^2F(\xi) (p-q),
\end{equation}
for some $\xi\in [p,q]$. This expression can be interpreted as a squared Mahalanobis distance:
\begin{equation}
M_Q(p,q)=(p-q)^\top Q (p-q),
\end{equation}
with precision matrix $Q=\frac{1}{2}\nabla^2F(\xi)\succ 0$ depending on $p$ and $q$.
Any squared Mahalanobis distance satisfies $U=2$ (see~\cite{Ackermann-2010}) and $V=1$, and can be interpreted as a squared norm-induced distance:
\begin{equation}
M_Q(p,q)=\|Q^{\frac{1}{2}}(p-q)\|_2^2.
\end{equation}

We report the Taylor-Lagrange remainder form of the skew Jensen divergences:
There exists $\xi_1,\xi_2\in [p,q]$, such that the skew Jensen divergence can be expressed as
$J_F^\alpha(p:q)=(p-q)^\top H_F^\alpha(p:q) (p-q)$,
with
\begin{equation}
H_F^\alpha(p:q)=\frac{1}{2}\alpha(1-\alpha)(\alpha\nabla^2 F(\xi_1)+(1-\alpha)\nabla^2 F(\xi_2)).
\end{equation}

The proof relies on introducing the skew Jensen-Bregman (JB) divergence~\cite{Jensen-2011} defined by
\begin{equation}
\mathrm{JB}_F^\alpha(p:q) =(1-\alpha)B_F(p:(pq)_\alpha)+\alpha B_F(q:(pq)_\alpha),\\
\end{equation}
and observing the $\mathrm{JB}_F^\alpha(p:q) =J_F^\alpha(p:q)$
since $p-(pq)_\alpha=\alpha(p-q)$ and $q-(pq)_\alpha=(1-\alpha)(q-p)$ (and therefore the   $\nabla F((pq)_\alpha)$-terms cancel out).
Then we apply the Taylor-Lagrange remainder form of Bregman divergences of Eq.~\ref{eq:tlbreg} to get the result.
Notice that when $\alpha\rightarrow 0$ or $\alpha\rightarrow 1$, the scaled skew Jensen difference tend to Bregman divergences, and we have
$\lim_{\alpha\rightarrow 1} \frac{J_F^{(\alpha)}(p:q) }{\alpha(1-\alpha)} =  \frac{1}{2}(p-q)^\top \nabla^2 F(\xi_1) (p-q)=B_F(p:q)$
for $\xi_1\in [p,q]$, and $\lim_{\alpha\rightarrow 0} \frac{J_F^{(\alpha)}(p:q)}{\alpha(1-\alpha)}=   \frac{1}{2}(p-q)^\top \nabla^2 F(\xi_2) (p-q)= B_F(q:p)$
for $\xi_2\in [p,q]$
, as expected.

Using expression of Eq.~\ref{eq:Jdiff} for the chord gap divergence, and
 the fact that $(pq)_\alpha-(pq)_\beta=(\alpha-\beta)(q-p)$, we get the Taylor-Lagrange form
 of the chord gap divergence $J_F^{\alpha,\beta,\gamma}=(p-q)^\top H_F^{\alpha,\beta,\gamma}(p:q) (p-q)$
with

\begin{eqnarray}
H_F^{\alpha,\beta,\gamma}(p:q)&=& \frac{1}{2}\gamma(1-\gamma)\nabla^2 F(\xi')-\frac{1}{2}\lambda(1-\lambda)(\alpha-\beta)^2\nabla^2 F(\xi''),\\
&=& \frac{1}{2}\left(\gamma(1-\gamma)\nabla^2 F(\xi')-(\gamma-\alpha)(\gamma-\beta)\nabla^2 F(\xi'')\right),
\end{eqnarray}
}
for $\xi',\xi''\in\calX$.

An alternative proof considers the Taylor first-order expansion of  $F$ with exact Lagrange remainder:
\begin{equation}
F(x)=F(a)+(x-a)^\top \nabla F(a)+\frac{1}{2} (x-a)^\top \nabla^2 F(\xi) (x-a),\quad \xi\in [a,x].
\end{equation}
Therefore  we get the following Taylor   expansions with exact Lagrange remainders:

\begin{eqnarray}
F(p) &=& F((pq)_\alpha) + \alpha(p-q)^\top \nabla F((pq)_\alpha)+  \frac{1}{2}\alpha^2(p-q)^\top \nabla^2 F(\xi_1) (p-q), \quad \xi_1\in (p,(pq)_\alpha),\\
F(q) &=& F((pq)_\alpha) + (1-\alpha)(q-p)^\top \nabla F((pq)_\alpha)+  \frac{1}{2}(1-\alpha)^2(q-p)^\top \nabla^2 F(\xi_2) (q-p),
  \xi_2\in (q, (pq)_\alpha).
\end{eqnarray}

Multiplying the first equation by $1-\alpha$ and the second equation by $\alpha$ and summing up, we obtain:

\begin{equation}
(1-\alpha)F(p)+\alpha F(q)= F((pq)_\alpha)+ \frac{1}{2}\alpha^2(1-\alpha)(p-q)^\top  \nabla^2 F(\xi_1)(p-q)+  \frac{1}{2}(1-\alpha)^2\alpha \nabla^2 F(\xi_2)(p-q),
\end{equation}
since the gradient terms cancel out, and we get:
\begin{eqnarray}
J_F^{(\alpha)}(p:q)&=&(1-\alpha)F(p)+\alpha F(q)-F((pq)_\alpha),\\
&=& \frac{1}{2}\alpha(1-\alpha)(p-q)^\top \left(\alpha \nabla^2 F(\xi_1)+ (1-\alpha) \nabla^2 F(\xi_2)\right) (p-q).
\end{eqnarray}

Thus it follows the Taylor-Lagrange remainder form of skew Jensen divergences:

\begin{equation}
\boxed{J_F^{(\alpha)}(p:q) =  \frac{\alpha(1-\alpha)}{2}(p-q)^\top (\alpha \nabla^2 F(\xi_1)+(1-\alpha) \nabla^2 F(\xi_2)) (p-q).}
\end{equation}

When dealing with a finite (weighted) point set $\calP$, let
\begin{equation}
\rho=\frac{\sup_{\xi',\xi'',p,q\in\mathrm{co}(\calP)} \|(\nabla^2 F(\xi'))^{\frac{1}{2}}(p-q)\|}{\inf_{\xi',\xi'',p,q\in\mathrm{co}(\calP)} \|(\nabla^2 F(\xi''))^{\frac{1}{2}}(p-q)\|}<\infty,
\end{equation}
where $\mathrm{co}(\calP)$ denotes the convex closure of $\calP$.
Then it comes that $U=O_\rho(1)$ and $V=O_\rho(1)$ so that $k$-means++ probabilistic seeding is $\bar{O}_\rho(\log k)$ competitive for the chord gap divergence.

\section{Concluding remarks}\label{sec:concl}
We introduced the chord gap divergence as a generalization of the skew Jensen divergences~\cite{Jensen-2011,JB-2013}, studied its properties
and obtained a generalization of the skew Bhattacharrya divergences.
We showed that the chord gap divergence  centroid can be obtained using a convex-concave iterative procedure~\cite{Jensen-2011}, and analyzed the $k$-means++~\cite{kmpp-2007} performance by giving the Taylor-Lagrange forms of the skew Jensen and chord gap divergences.
We expect our contributions to be useful for the signal processing, information fusion and machine learning communities where the Bhattacharrya~\cite{BhatG-2008,BhatG-Clustering-2016} or Chernoff information~\cite{Bhat-1982,Chernoff-2013} is often used.
In practice, the triparametric chord gap divergence shall be tuned according to the application at hand (and the dataset for supervised tasks using cross-validation for example).

Public Java\texttrademark{} source code is available for reproducible research:\\
 \centerline{\url{http://www.lix.polytechnique.fr/~nielsen/CGD/}}

redpajama_set_name: RedPajamaArXiv


text:
College football College sports Sports Football Exree Loe Jared Bartlett Jaylen Warren Spencer Sanders Jackie Matthews Jarret Doege Lance Dixon Alonzo Addae Sean Mahone Tanner Brown Korie Black Demarco Jones Jason Taylor Winston Wright Tanner McCalister Yaddiya Tyren Irby Justin Johnson Mike Gundy Christian Holmes Reese Smith Daryl Porter Garrett Greene Casey Legg Matt Polk Kamryn Farrar Lamont Bishop Brennan Presley
Oklahoma State Big 12 West Virginia
Oklahoma State at West Virginia 11/6/2021
West Viginia's Major Harris has his jersey retired during the first half of an NCAA college football game against Oklahoma State in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Oklahoma State running back Jaylen Warren (7) is dtackled by West Virginia linebackers Exree Loe (6) and Jared Bartlett (10) during the first half of an NCAA college football game in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Oklahoma State quarterback Spencer Sanders (3) throws against West Virginia during the first half of an NCAA college football game in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Oklahoma State wide receiver Tay Martin (1) scores while defended by West Virginia cornerback Jackie Matthews (3) during the first half of an NCAA college football game in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
West Virginia quarterback Jarret Doege (2) throws against Oklahoma State during the first half of an NCAA college football game in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Oklahoma State quarterback Spencer Sanders (3) runs while defended by West Virginia linebacker Lance Dixon (5) and safety Alonzo Addae (4) during the first half of an NCAA college football game in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Oklahoma State running back Jaylen Warren (7) is defended by West Virginia safety Sean Mahone (29) during the second half of an NCAA college football game in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Oklahoma State placekicker Tanner Brown (49) boots an extra point during the second half of an NCAA college football game against West Virginia in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Oklahoma State cornerbacks Korie Black (4) and Demarco Jones (22) celebrate after a fumble recovery during the first half of an NCAA college football game against West Virginia in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
West Virginia wide receiver Winston Wright Jr. (1) is defended by Oklahoma State safeties Jason Taylor II (25) and Tanner McCalister (2) during the second half of an NCAA college football game against West Virginia in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
West Virginia running back Justin Johnson Jr. (26) is defended by Oklahoma State defensive end Tyren Irby (91) during the second half of an NCAA college football game in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Oklahoma State fans celebrate during the team's NCAA college football game against West Virginia in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Oklahoma State coach Mike Gundy, center, reacts during the second half of an NCAA college football game against West Virginia in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Oklahoma State cornerback Christian Holmes (0) is defended by West Virginia quarterback Jarret Doege (2) after intercepting the ball during the second half of an NCAA college football game in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
West Virginia wide receiver Reese Smith (15) is defended by Oklahoma State safety Tanner McCalister (2) during the second half of an NCAA college football game in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Oklahoma State wide receiver Tay Martin (1) tries to get away from West Virginia cornerback Daryl Porter Jr. (2) during the second half of an NCAA college football game in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
West Virginia quarterback Garrett Greene (6) runs against Oklahoma State during the first half of an NCAA college football game in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Oklahoma State quarterback Spencer Sanders looks for a receiver during the first half of the team's NCAA college football game against West Virginia in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Oklahoma State quarterback Spencer Sanders (3) hands off to running back Jaylen Warren (7) during the first half of the team's NCAA college football game against West Virginia in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
West Virginia's Casey Legg (48) kicks a field goal during the first half of the team's NCAA college football game against Oklahoma State in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Former West Virginia quarterback Major Harris has his jersey number retired, during the team's NCAA college football game against Oklahoma State in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Oklahoma State wide receiver Matt Polk (9) linebackers Lamont Bishop (11) and Kamryn Farrar (44) celebrate after a sack against West Virginia during the second half of an NCAA college football game in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
West Virginia coach Neil Brown reacts after a West Virginia turnover during the second half of an NCAA college football game against Oklahoma State in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Oklahoma State wide receiver Brennan Presley (80) tries to get away from West Virginia linebacker Lance Dixon (5) during the first half of an NCAA college football game in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)
Oklahoma State's Korie Black, on ground, mostly obscured, recovers the ball on an Oklahoma State punt after the ball touched a West Virginia player during the second half an NCAA college football game in Morgantown, W.Va., Saturday, Nov. 6, 2021. (AP Photo/Kathleen Batten)


text:
Let them entertain you
By John Orr | Bay Area News Group
Broadway By the Bay has staged a completely satisfying and triumphant "Gypsy" at the Fox Theatre in Redwood City.
At the end of the Sunday matinee I saw, the mostly white-haired audience was standing up and cheering the excellent production of what some people consider the greatest "book musical" ever written.
It's certainly a cultural-literacy touchstone. Anybody considered culturally literate will have read and seen "Hamlet," will have seen "Star Wars" and the 1939 "Wizard of Oz" and will have seen "Gypsy."
Ethel Merman helped develop the show, "Gypsy: A Musical Fable," with a lot of help from Jule Styne, Stephen Sondheim and Arthur Laurents. It is based on burlesque star Gypsy Rose Lee's memoir, and is really about Gypsy's mother, Mama Rose. The songs are great, and chances are that we all have heard some of them: "Let Me Entertain You," "Small World" and "Everything's Coming Up Roses," at least.
It's a powerful story, of what many people consider the ultimate stage mother, pushing her children Baby June and Louise, to become stars on the vaudeville circuit, at the time vaudeville itself was dying. Mama Rose is a powerful character, pushing, pushing, pushing to get what she wants, at one point telling the girls, "Children, go play in the alley" while she is negotiating a theater deal. Frank Rich of the New York Times called it the "American musical theater's answer to 'King Lear.'"
Eventually, Baby June runs away. In real life, Mama Rose actually tried to shoot the man June ran away with, but that isn't mentioned in the musical. June grew up to be the actress June Havoc, who had a successful career in movies and on television.
That left Mama Rose with Louise, thought to have much less talent than June. Rose continues to push the same, crummy old act, with a starving cast, playing in seedier theaters. Eventually, the big break: A strip club. Turns our Louise has some talent after all. In real life, she became Gypsy Rose Lee and was very famous.
Her memoir, turned into the successful musical, supported her after she stopped stripping.
This excellent production, on stage through Oct. 9, has Heather Orth as Mama Rose, and while she doesn't have Ethel Merman's unique voice, she's still terrific in the role. It is a complex character, one that has been hated, and yet found understandable. Her own ambitions are so strong that they drive her to monstrous lengths, like the royalty in Shakespeare's histories and tragedies.
Orth has a strong stage presence — she ought to, she has Amazonian height — and very good vocal chops, which are needed to handle Styne's excellent melodies.
The sturdy Walter M. Mayes is on board as Rose's beau and the girls' agent, Herbie. Mayes is always fun to watch on stage, and here he brings not only a solid acting performance and a good singing voice, he brings height. He may be the only musical actor in the Bay Area taller than Orth.
Mary Kalita is beautiful and appealing as June. She has to go from being a little girl to a young woman, all the while developing a more and more complex relationship with Mama Rose, before taking off. Mama Rose keeps wanting to sell the girls as 9-year-olds, even after their bosoms develop. In real life, Rose kept three separate birth certificates for June. Havoc died without ever knowing how old she really was.
While Louise was supposed to be the less talented one, Samantha Bruce actually has the most beautiful voice in this production. She's also very pretty and a fine actress, taking Louise from being the sweet little seamstress who is nice to everybody, to the rather hard-case stripper who doesn't want Mama Rose's help anymore. Bruce is fabulous.
Director Amanda Folena — who is soon to take over as artistic director of Broadway By the Bay, following the imminent retirement of Brooke Knight, does a fine job. There is a full pit orchestra, directed by Rick Reynolds, and the music is fabulous. It's very difficult, apparently, to find good trumpet players for show orchestras, but Reynolds found at least one for this show, which is amazing.
The Fox Theatre itself was good for this show. The lighting and sound were excellent and the stage is large and sufficiently adaptable to big shows. The auditorium is still kind of seedy, with old loge chairs in back and folding chairs down front. Nice folding chairs, with padding, but still … folding chairs.
The nice thing is, management doesn't care if the audience carries beer and wine into the auditorium. If somebody spills on the upholstery, what does it matter? It will all have to be replaced before too long anyway.
Broadway By the Bay is to be applauded for this show. It's well worth seeing.
Email John Orr at jorr@dailynewsgroup.com.
What: "Gypsy"
Book by Arthur Laurents, music by Jule Styne, lyrics by Stephen Sondheim
Presented by: Broadway By The Bay
When: Through Oct. 9
Where: Fox Theatre, 2215 Broadway, Redwood City
Tickets: $22-$48; Broadway By The Bay box office, 851 Burlway Road, Suite 300, Burlingame; 650-579-5565; www.broadwaybythebay.org
John Orr
John Orr is a freelance writer, and a member of the American Theatre Critics Association. Email him at johnorr@regardingarts.com. He was formerly a staff writer and editor for the Bay Area News Group.
Study finds single-payer health care plan saves money
According to a new study, published last week by University of California scientists in the journal PLOS Medicine, universal coverage plans would actually save money on health care.
A dentist was filmed extracting a tooth while on a hoverboard. He was found guilty on 46 counts
A dentist in Anchorage, Alaska, has been convicted on dozens of charges after he was filmed extracting a patient's tooth as he stood on a hoverboard, according to the Alaska Department of Law.
Why would the Club prevent car break-ins?
And: 'When we go to San Francisco, I don't leave my car.'
Livermore downtown plan debate: Council calls out groups as 'hot air'
The city asked for proposals for potential hotel developers a citizen committee said they talked to for a west side downtown hotel, but none were brought forward.


text:
The Vlasov Archives
Russian Nationalism: Imaginaries, Doctrines and Political Battlefields
By HISTFRSeptember 26, 2020October 23rd, 2020No Comments
Laruelle, Marlene. Russian nationalism: Imaginaries, doctrines, and political battlefields. Routledge, 2018.
This book, by one of the foremost authorities on the subject, explores the complex nature of Russian nationalism. It examines nationalism as a multilayered and multifaceted repertoire displayed by a myriad of actors. It considers nationalism as various concepts and ideas emphasizing Russia's distinctive national character, based on the country's geography, history, Orthodoxy, and Soviet technological advances. It analyzes the ideologies of Russia's ultra-nationalist and far-right groups, explores the use of nationalism in the conflict with Ukraine and the annexation of Crimea, and discusses how Putin's political opponents, including Alexei Navalny, make use of nationalism. Overall the book provides a rich analysis of a key force which is profoundly affecting political and societal developments both inside Russia and beyond.
Part I: Nationalism as Imperial Imaginary: Cosmos, Geography, and Ancient Past
Chapter 1. Cosmism: Russian Messianism at a Time of Technological Modernity
Chapter 2. Larger, Higher, Farther North… Russia's Geographical Metanarratives
Chapter 3. Alternate History and New Chronology: Rewriting Russia's Past
Part II: Nationalism as Doctrine: Experimenting new Repertoires
Chapter 4. Beyond Slavophilism: The Rise of Aryanism and Neo-Paganism
Chapter 5. A Textbook Case of Doctrinal Entrepreneurship: Aleksandr Dugin
Chapter 6. Pamiat 2.0? The Izborskii Club, or the New Conservative Avant-Garde
Part III: Nationalism as Political Battlefield: In the Streets, for or against the Kremlin
Chapter 7. Black Shirts and White Power: The Changing Faces of the Far Right
Chapter 8. Aleksei Navalny and the Natsdem: A pro-Western Nationalism?
Chapter 9. The Three Colors of Novorossiya, or the Mythmaking of the Ukrainian War
Link to book (Open Access)
About HISTFR
Heidegger, Black Notebooks, and Russia
HISTFRSeptember 26, 2020
Entangled Far Rights: A Russian-European Intellectual Romance in the 20th Century
Eurasianism and the European Far Right: Reshaping the Europe–Russia Relationship
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There's this boring, dirty, problem most organisations have and it has to do with legacy apps. Apps that were created over 10 years ago to solve a specific – at point of inception - business problem. You know the ones: those that were developed, tweaked and adapted over time and continue delivering results that address a specific issue.
But the world of app delivery has moved on. Enterprises are adopting SaaS solutions, or are developing cloud native apps and are, generally, innovating on new platforms. And yet, we can't lose sight of those essential legacy apps that we are tied to. The one that is checking you in at the airport or signing you up to your new mobile contract. These apps are still doing their job well and there is no compelling business case to change them but despite all their years of hard work and service, and through no fault of their own, they are struggling to adapt to the latest operating environments.
Most of these organisations/apps/developers fall into a small number of different categories. In my experience, of the majority of apps on the market, half of organisations have solved this legacy app issue. But the other half adopts a "if it's not broke, don't touch it" approach, mainly because every time they try to make changes a problem appears. And the more a highly integrated and established app is touched, the bigger the problem gets.
As employees and consumers demand mobility, these legacy apps are struggling to cope. They cannot work on the new shiny devices of our time – the latest Surface, iPad or android device – that are easily portable. So as users want to work, wherever they are and, on whatever device they want - they are tied to an office or a device that just doesn't meet user demands.
The job of IT cannot be to say: 'sorry we can't do this'. IT needs to find a way to combine the wide and varied range of software, platforms and devices available on the market and satisfy increasing user demands. As user expectations increase, it simply isn't good enough to suggest that a user is restricted and unable to do X, Y or Z.
Cloudhouse makes legacy apps work anywhere. Its mission is to help customers held back by the barriers of moving complex legacy applications to Microsoft Azure and Windows 10.
Have a legacy app that you're struggling to deliver and deploy to the cloud? Get a demo of Cloudhouse today. Not ready for a demo? Join our upcoming 'Cloudhouse in Action' webinar.


text:
If the woke actors of Rada want to cancel George Bernard Shaw, they should return his money
The students are not just going in for cultural revisionism; they are thankless with it
Melanie McDonagh 13 September 2020 • 7:00pm
My Fair Lady - based on Shaw's Pygmalion Credit: dvdbash.wordpress.com
What's the first thing you think of when you hear the name George Bernard Shaw? Fabianism? My Fair Lady? – a film which came from his play, Pygmalion. Feminist? One of the most prolific playwrights of his day? Or as you might otherwise say, the author of taxingly long, verbose plays? Early vegetarian? Nope. If you're the student body of the Royal Academy of Dramatic Art, Rada, you don't think of any of these things.
The students at this elite institution have been drawing up an "anti-racism action plan" and one proposal is to change the name of its George Bernard Shaw Theatre because "this man spoke in favour of eugenics and fascism".
Eh? Well, he did support eugenics. But then, an awful lot of progressives did the same. As for fascism, Bernard Shaw's worse error was backing Soviet Russia under Stalin. There was his enthusiastic contribution to a pamphlet by Sidney and Beatrice Webb called Soviet Communism – A New Civilisation?, which doesn't bear reading.
He was still a great Irishman, a free thinker, a genuine radical, a playwright who made audiences think and argue … and a philanthropist whose bequests have benefited, among other bodies, Rada. So the Rada students are not just going in for cultural revisionism; they are thankless with it.
It's not their only exciting proposal. They are against performing Restoration comedies because most characters are "figureheads of the Empire". (No, they're not. Filthy minded, yes). They have an animus against Received Pronunciation. From my pre-Covid role as a theatre critic, can I just say that an obsession with pronunciation of any kind would be nice from young actors, given the number who don't know how to enunciate their words.
But, it seems, the important thing is that students' experience at Rada is "filtered through imperialism, colonialism, white supremacy and a Westernised history".
That's more or less what you expect from student bodies right now. What is far more worrying is that the Rada bosses, instead of telling them to go away and practise voice projection, are promising "to decolonise the curriculum". If they are that keen on eradicating the past, what they should do is return the money they have received over the past 70 years from that tainted source, the Shaw estate – £78,000 last year alone. I'll tell you when it happens.
A costly new normal
Race and social exclusion is the stuff of the best film of the year, Ladj Ly's Les Misérables, now on release here, a relentlessly grim depiction of life for immigrants in the banlieues of eastern Paris. Emmanuel Macron was shaken when he saw it. So was I. It's one of those films where you end up having a row with the friend you go to see it with. She was sorry for the marginalised young. I was channelling my inner Charles de Gaulle.
At the matinee performance we made up half the audience. The tickets were £17.50. Pre-Covid, I could have seen live opera for that price. This is no way to get back to normal, even the new normal. At half the price they could have doubled the audience.
Grace of the bean bag
RIP, Sir Terence Conran, the man who revolutionised everyday design in Britain. But on the debit side, there is … the bean bag, the most hopeless item of furniture ever invented. Have you ever tried to sit gracefully in a bean bag? Or get out of one? I rest my case.


Sicily, panna cotta and a confession.
Keeping a blog is a bit like a confessional. Not that I've ever been in a confessional, but I do feel like an apology "Forgive me Father, it's been 6 weeks since my last confession" is in order. So, sorry.
Last time I was moaning about the place I grew up. This time I will have a little moan about a place where other people have grown up and update on where we are with the treatment and the maintenance.
The end of September maintenance came and went without any incident. It's all becoming routine now. Soon, after Christmas, I will have been going Ward 60 for two years either three weekly, or bi-monthly. They have been very good indeed and have definitely helped through this period. The nurse that gives her time for me the have the maintenance after hours is getting married in the Spring, so I need to sort a gift out for her. I couldn't have the maintenance at all, if people weren't prepared to give up their spare time for me, so I am very grateful. My haematologist and I discussed a suitable gift when I was there at the end of September, so we will have to see if we can organise that. We chatted about a "joint gift". She gets married on the day we fly to New York, which is a bit of a shame, as I would have popped along and sat at the back of the church and maybe taken some photos.
Yet another Leica Forum One Challenge has been and gone. This was the eighth one this year – Palermo in Sicily. Despite many of the attendees liking the city, I found that it was a place without any charm whatsoever. It was dirty, unkempt, still suffering considerably from wartime bomb-damage and with a population who were discourteous and unfriendly. We were fortunate that we had an excellent hotel, The Porte Felice, which we would highly recommend. A really nice room, comfortable, decent breakfast if you want one and about 20 minutes walk from the city centre. Further, there is an excellent restaurant about 5 minutes walk in the other direction, Ristorante Gadir, where we easily had the best meal of the week. It is along a dark, unlit street, with open skips, feral cats, high rise flats in the poorest part of town and is incongruous to say the least. You could uplift the place and drop it into the west end, or Paris and it would fit right in. The situation is very odd and they are unlikely to get any tourist custom, given its location. Maybe that's what they want. Certainly we were the only tourists in there that Thursday, but our friends Jono and Emma did venture there on the Friday on our recommendation and also had an excellent meal.
The best bit about the break was the drive down to Segesta, to see the 2,500 year old Greek temple and amphitheatre. A beautiful setting on a beautiful day.
One slight worry while we were in Sicily was that I started to get pins and needles in my fingers and right hand. Fortunately, they have gone now, but they are a potential side-affect of the Rituximab, so I will need to keep an eye on that.
We also spent some time at the beginning of the week in Kent, a county that one tends to pass through as quickly as possible to get to somewhere else, which is a shame as it's a nice place to spend some time. We found the church where Ann's new-found family were lords of the manor and a lot else besides, back in the 14C, together with a very nice pub with rooms, The Five Bells at East Brabourne, which will deserve a proper visit one day. Canterbury Cathedral is lovely when you get there as the first visitors of the day, before the crowds.
So, it's downhill to Christmas and another New Year now. Ought to get some shopping done really.
That'll be three Hail Mary's then, will it?
PS. There is some news following on from the ridiculous train delay I had at the end of August (see post below). Those very nice people at Virgin West Coast, sent me a cheque for £50 AND a free Standard Return ticket, anywhere in the country, in the next 12 months. So that's not so bad.


text:
Charismatic and with a voice of gold, Brittany Howard of Alabama Shakes will present premiere her first solo album "Jaime" on 20 released September this year.
To coincide with the album news, a unique Parisian date at l'Alhambra has also been announced for 4 September 2019.
Brittany Howard recorded this album after crossing the United States from Nashville to Topanga, a small California town wedged between the mountains and the beach. "Jaime" album bears the name of her sister, who taught her to play the piano and write poetry, and who died of cancer when she was a teenager.
"The album is her memory, she really shaped as a human being. But the record does not talk about it but me."
Tickets on sale Friday 5 July at 11am local time.
TagsAlabama Shakes • Brittany Howard • l'Alhambra Paris • music • new album • tour


At certain stages in life, one stops and looks at the purpose of existence or his/her "mission." Organizations do likewise: always attending to their mission and purpose of existence in order to rise up to it.
As part of a bigger academic institution, ICP's mission has always been that of "human capital development." Having defined that ultimate goal, ICP has devoted its continuous effort in recent years to determine the best path to arrive at that goal. In order to build on its long history of existence, the best path was to expand into larger and more sustainable programs that respond to the needs of the Palestinian community.
Centers of excellence are being created to ensure projects are mainstreamed into permanent programs with clear goals and objectives. Even if those centers are still being shaped up and built upon, we believe they are the start for guaranteeing further projects that contribute to their growth.
To begin, ICP managed to increase its longer-term projects (more than one year) from less than one to over seven projects currently being implemented. We provided the needed human resources, as well as the required facilities and logistics to ensure efficient implementation of these projects. We currently have 15 full-time staff. We have also renovated, through the support of our donors, the Mar Andrea building, which is being utilized for offices, training halls, as well as incubation facilities for some projects.
Evaluation of quality of our services is continuous: internally, externally, and through our beneficiaries. Numerous projects succeeded in design and implementation, and in many of them were labeled as "first time successes" in Palestine. Examples included the first professional diplomas using blending learning and the internet technology, first "E-Business Diploma," first "Small Enterprises Diploma," first "Project Management Diploma," first "Public Administration Diploma," first "Cooperative Diploma," and first "Prevention and Intervention of Drug Abusers." Several projects excelled and received positive feedback from partners locally and internationally, resulting in renewed projects and additional grants. We acknowledge, however, that self-assessment and continuous revision of programs is a necessity in order to succeed with the responsibilities we have assumed.
We believe in promoting solid technical, entrepreneurial, and managerial education, and providing access to such education to as many individuals and organizations as possible, while always recognizing and emphasizing the need to develop a common strategic vision and definition for development in Palestine.
ICP prides itself in offering a unique blend of components in order to provide high-quality training activities, organizational development, and consulting services. Community planning is conducted on a continuous basis to promote cooperative working between organizations in order to develop a shared strategic vision for local community, sector, or geographical area; providing greater opportunities for community participation; and encouraging more integrated service delivery across organizational boundaries.
Finally, a warm "thank you" to all our friends, supporters, and our team at ICP and Bethlehem University, all of whom have been the fuel for our work. But most importantly, we thank our beneficiaries, whom we do not consider as recipients of services, but as equal partners in designing and implementing programs that contribute to the overall development of our country.