text:
Baroeg (ook wel, abusievelijk: de Baroeg) is een poppodium in de Nederlandse stad Rotterdam.

Beschrijving

Baroeg noemt zich een 'subcultureel poppodium', waarmee verwezen wordt naar de diverse activiteiten die er gehouden worden voor liefhebbers van moderne alternatieve muziek.

Jaren tachtig
In 1981 begon Baroeg als open jongerencentrum en was een gewaardeerd onderdeel van de Rotterdamse wijk Lombardijen, aan de Spinozaweg in het Spinozapark. Eind 70-er, begin 80-er jaren was er veel onrust onder jongeren. Een economische crisis en massale jeugdwerkloosheid waren de oorzaken. Jongerenwerk Zuid richtte een intitiatiefgroep comité op. Dankzij hen werd een nota geschreven over jongerenwerk op Zuid. Dat is de basis geweest voor het ontstaan van Baroeg. Op 6 mei 1981 werd Stichting Open Jongerencentrum Baroeg opgericht met als doel het bevorderen en realiseren van ontspannings-, ontmoetings- en communicatiemogelijkheden voor jongeren in Rotterdam en Nieuw-Zuid en het geven van informatie alsmede hulpverlening en belangenbehartiging.

Een afgekeurd architectuur-ontwerp voor een ander jongerencentrum, Kaassee, werd gebruikt voor het Baroeggebouw. OJC Baroeg zit aan de Spinozaweg. Baruch de Spinoza was een Nederlandse filosoof en politiek denker in de 17e eeuw. Jongeren werkten zelf mee aan de inrichting van het pand. Het pand werd officieel geopend op 2 oktober 1982.

De naam is een verbastering van de voornaam van Baruch Spinoza, naar wie deze locaties zijn genoemd. Er werden veel jeugdactiviteiten georganiseerd, zoals de maandelijkse 'kids gabber party' voor jongeren onder de 16 in de jaren 90. Ook werden er sportavonden georganiseerd met kickboksen, aerobic, jazzballet en zelfverdediging. Elke middag werden activiteiten georganiseerd en kwam er een doka en een zeefdrukruimte.

De eerste paar jaar lag de nadruk op het programmeren van -vooral- Nederlandse pop.

Een reeks bekende Nederlandse bands stond op het podium in de periode 1983 -1988, zoals The Nits, Mark Foggo, De Div, Toontje Lager, Frank Boeijen Groep, Spasmodique, Kiem, Claw Boys Claw, Clan of Xymox, Roots Syndicate, I've Got The Bullets, Tröckener Kecks en De Dijk. Verder deden ook artiesten als Jules Deelder en Armand Baroeg aan.

Binnen zijn een bar en een zaal met podium. Op dat podium treden wekelijks bands op: voornamelijk metal, maar ook punk, hardcore en andere stijlen. Naast deze concerten worden in Baroeg dansavonden gehouden. Bekendst in Rotterdam en omgeving is de maandelijkse Downward Spiral (EBM, gothic en meer.) Andere dansavonden variëren van cybergothic tot wave tot drum&bass. In het verleden stonden bands als Tröckener Kecks, Claw Boys Claw, Cradle of Filth, Within Temptation op het podium hoewel die met een capaciteit van 400 bezoekers niet meer te betalen zijn.

In 1987 kwam René Veerkamp in dienst als jongerenwerker. Naast het opzetten van werkgelegenheidsprojecten kreeg hij de taak om de programmaraad van Baroeg te begeleiden. Veerkamp begon vanaf medio 1988 voorzichtig zijn stempel te drukken op de toenmalige popprogrammering door iets geheel anders te proberen: hardrock, punk en hardcore. Onder leiding van de programmeur Veerkamp hebben vele jonge Rotterdamse bandjes hier hun eerste optreden verzorgd en dankzij dezelfde Veerkamp het podium gedeeld met menig grote tourende band. Als er 2 of 3 grote namen stonden werden er ook 2 a 3 onbekende lokale bands bij gezet, als extra voor publiek en bands. Het Haagse Noisy Act Of Protest kwam spelen, evenals hardrock acts als Vulture en Vengeance. De eerste Nederlandse punkband was de Groningse formatie De Boegies in 1988.

Jaren negentig
Voorjaar 1991 werd de wijk Lombardijen toegevoegd aan de deelgemeente IJsselmonde, wat voor Baroeg betekende dat de subsidiëring niet meer plaatsvond vanuit het stadhuis, maar vanuit IJsselmonde.

In de overgang van welzijnswerk naar cultuur werd in 1993 een doorbraak geforceerd om Baroeg in één jaar uit te laten groeien naar een poppodium van formaat. De nadruk kwam te liggen op hardere muziekstijlen als death metal, black metal, punk en hardcore. Baroeg bereikte in 1994 haar doelstelling. Mede te danken aan het groeiende aantal gemotiveerde vrijwilligers dat zich in die tijd aanmeldde.

In 1989 en 1990 werd er in Baroeg aan hiphop gedaan, met succesvolle concerten van bands als Damn en 24K. Ook was er in 1990 de Acid en House-explosie. DJ's Ludi , DJ Paul, Ronald Molendijk en Lucien Foort kwamen draaien. Tijdelijk raakten de bandoptredens op de achtergrond. Wel kwam de eerste buitenlandse punkband spelen: GBH in 1991.

In 1994 kwam er financiële ruimte om een eigen P.A. aan te schaffen. Dat maakte het mogelijk om in de jaren daarna het live-aanbod nog verder uit te breiden.

De nadruk bleef liggen op death en black metal, maar ook gothic, electro, punk, hardcore en diverse melodische hardrockstijlen kregen een vaste plek in de programmering.

In 1998 treedt de symfonische metal band Within Temptation op in Baroeg, een band die later een van de succesvolste bands van Nederland wordt.

Jaren nul
In het begin van het nieuwe millennium waren de bezuinigingen voelbaar. Baroeg had al een paar keer op de rand van de financiële afgrond gestaan. Stug doorgaand vierde Baroeg in 2001 toch het 20-jarig bestaan.

Het voortbestaan van Baroeg werd in april 2001 opnieuw bedreigd door bezuinigingen van de gemeente. De vijftig medewerkers en hun verrassend grote achterban waren echter duidelijk: "Baroeg moet blijven." In een reeks benefietconcerten traden ruim 130 bands op voor het behoud van Baroeg. Daarnaast verschenen twee benefiet-cd's. In 2001 werd Baroeg door de Vereniging Nederlandse Poppodia en -Festivals (VNPF) onderscheiden met de titel 'Nederlands podium van het jaar' vanwege de doelgroepgerichte en consequente programmering.

Sommige optredens en feesten trekken fans uit heel Nederland en soms ook wel het buitenland aan. Door het alternatieve karakter van deze club en haar gasten en vrijwilligers is er in het verleden weleens sprake geweest van onbegrip en zelfs wantrouwen onder de bewoners. Toch namen in de zomer van 2002 veel plaatselijke middenstanders deel aan de actie "Baroeg moet blijven" door pamfletten op de winkelruiten te plakken. Bij de Rotterdamse marathon van dat jaar stonden voorstanders van de Baroeg met een spandoek langs de route, die over de Spinozaweg liep, en was op het wegdek de leus "Baroeg moet blijven" geschilderd.

In het verleden heeft Baroeg in financieel zwaar weer verkeerd maar heeft het ook met weinig subsidie het hoofd boven water kunnen houden.

In 2003 werd een van de eerste clubshows van Epica geboekt

In de periode 2009-2012 werd Baroeg voor het eerst opgenomen in het Cultuurplan van gemeente Rotterdam en dat gaf het podium de mogelijkheid om verder te professionaliseren.

Jaren tien
In 2012 kreeg Baroeg de ANBI-status, op 1 januari 2013 werd Baroeg een 'kernpodium C' bij Fonds Podiumkunsten (FPK). Dit gaf niet alleen landelijke erkenning, maar vanaf dat moment kon Baroeg ook verlies dekkende subsidies aanvragen bij het FPK bij producties met Nederlandse bands, solomuzikanten of dj's.

Begin 2016 ontstond op initiatief een voormalig bestuursvoorzitter Erik de Boer een heuse vriendenclub, de Vrienden van Baroeg (VvB). Met de VvB genereert Baroeg niet alleen extra inkomsten, maar doet het podium ook aan klantenbinding. Een ander hoogtepunt was het Baroeg 35 jaar-feest met headliners Enslaved en Trouble.

In 2020 werd half maart alles anders door de uitbraak van Covid-19. De capaciteit van Baroeg moest door de overheidsmaatregelen worden verlaagd van 350 staande bezoekers naar 25 mensen op een stoeltje. Internationale tours werden geannuleerd, veel concerten zijn meerdere keren verplaatst en BOA kon helaas niet doorgaan. Vervolgens lag de focus op live-streams van met name Baroeg-vrijwilligers en VvB-ambassadeurs, alsmede streams van bands die live optraden op het podium van Baroeg. Dat leverde een nominatie op voor een Rotterdam Music Award in de categorie Beste Corona Initiatief.

Tijdelijke sluiting in 2007
Vanwege een gewelddadig barkrukincident op 2 juni 2007 is die datum een zwarte bladzijde in de geschiedenis van Baroeg. Een 24-jarige Poolse man overleed een dag later aan zijn verwondingen. Op last van de burgemeester bleef Baroeg drie maanden gesloten. Op 4 juni meldde de politie dat twee verdachten, beide Rotterdammers, waren aangehouden. Voor politieonderzoek werd het poppodium twee weken gesloten. Kort daarna werd op last van burgemeester Opstelten besloten om de sluitingstermijn te verlengen tot drie maanden, ondanks protest van onder meer de SP en Leefbaar Rotterdam, vanwege aantasting van de openbare orde en veiligheid, nalatigheid en het afwijken van de exploitatievergunning. Op 27 februari 2008 werden de twee Rotterdammers veroordeeld tot gevangenisstraffen van zes en vijf jaar.

Baroeg Open Air

In het kader van 25 jaar Baroeg wilde de bestuursvoorzitter/coördinator Chris Spaanenburg een buitenfestival op poten te zetten. Hij slaagde daarin. De eerste editie van Baroeg Open Air (BOA) vond plaats op zaterdag 2 september 2006 in het Spinozapark. Dit werd daarna elke twee jaar georganiseerd. Ook in 2011, het dertigjarig bestaan, is het festival georganiseerd; in samenwerking met het SKVR is een educatief talentprogramma georganiseerd onder de naam "Rock Central". Sindsdien wordt BOA elke zomer herhaald. Sinds 2019 is het festival niet langer gratis.

Externe link
 Website Baroeg

Poppodium in Nederland
Muziek in Rotterdam
IJsselmonde (stadsdeel)


My name is Patrick Robichaud. I am a guitarist/songwritter from Bathurst NB. I play mainly acoustic guitar, and my style range from soulful acoustic singing to technical finger style arrangement. Ive been play for about 10 years. Last year im not sure exacally when, I discover a Guitarist by the name of Jon Gomm. Amazed by his unique way of playing guitar. I start particing thise new to me way to play. Today i am arm with a yamaha acoustic guitar amd a handfull of soulfull acoustic singing song and a few fingerstyle intrumental.


text:
KEiiNO wins Melodi Grand Prix 2019 and will represent Norway at Eurovision with "Spirit In The Sky"
Alexandra Nagy March 4, 2019, 6:42 am
Norway recently held the 57th national selection show "Melodi Grand Prix" for the Eurovision Song Contest 2019 in Oslo, and they've got a winner: KEiiNO will fly the Norwegian flag in Tel-Aviv this year with their song "Spirit In The Sky".
The Norwegian-Sami trio KEiiNO consists of Fred Buljo, Alexandra Rotan and Tom Hugo. Their collaboration began with Hugo and his husband Alex Olsson composing the outline of a song inspired by struggles for equal rights regardless of ethnicity, gender identity and sexuality.
Here, you can check out their entry:
Announced acts so far are Srbuk for Armenia, Tamta for Cyprus, Jonida Maliqi for Albania, Eliot for Belgium, Miki for Spain, Serhat for San Marino, Duncan Laurence for The Netherlands, Tamara Todevska for North Macedonia, Michela Pace for Malta, Bilal Hassani for France, Lake Malawi for the Czech Republic, PÆNDA for Austria, Darude feat. Sebastian Rejman for Finland. Michael Rice for the United Kingdom, Sergey Lazarev for Russia, Mahmood for Italy, Kate Miller-Heidke for Australia, D-Moll for Montenegro, Kobi Marimi for Israel, Joci Pápai for Hungary, Jurijus for Lithuania, Leonora for Denmark, S!sters for Germany, Ester Peony for Romania, Victor Crone for Estonia, Roko for Croatia, Carousel for Latvia, and Tulia for Poland. The other countries are expected to reveal their acts in the forthcoming months.
The 2019 Eurovision Song Contest will be hosted at the Expo Tel Aviv in Israel after Netta won last year with the song "Toy". The two Semi-Finals will take place on 14 May and 16 May with the Grand Final taking place on 18 May. A total of 42 countries will compete in the contest.
What do you think about Norway's entry this year? Don't forget to let us know on Twitter @CelebMix!
Written by Alexandra Nagy
I'm Alexandra from Hungary, now living in the UK, and writing is not just my hobby - it's my passion. I'm a writer/journalist addicted to music, travelling, football, movies & books, proudly supporting Derby County Football Club.
Any enquiries: abigofficial@gmail.com
CelebMix EXCLUSIVE Interview: Newton Faulkner
Niall Horan Gives Fans Preview of New Song 'Finally Free'
Have you gotten the NiallMoji app yet?
Four artists we would love to see Niall Horan tour with
Niall Horan's "Slow Hands" officially confirmed his Highest Charting Single
Niall Horan Is Coming To Las Vegas Next Month

redpajama_set_name: RedPajamaCommonCrawl


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About Holland & Barrett
Holland and Barrett is the UK's leading retailer of vitamins, minerals and herbal supplements.
Their stores are a familiar sight in almost every major city and town across the U.K, with new outlets opening up all the time.
Interest in natural food supplements has increased considerably over the last few years and Holland and Barrett has always had a commitment to its customers to provide high quality products at value for money prices.
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It's hard to believe that summer is coming to an end and kids are getting ready to go back-to-school. Whether you're helping your children get ready for school or going to college/university yourself, this year plan ahead and go back to school in eco-style!
Before you hit the stores, do an inventory of any school supplies from previous years. Decrease your shopping list and determine what you actually need for the upcoming school year. Most supplies, such as sturdy backpacks, lunch kits, pencils can last more than year, so you don't need to buy them every year.
If old school supplies can't be reused; donate them to a local charity so children in need can use them. Most local churches; schools and shelters will accept them.
There are lots of school supplies available which are environmentally friendly and affordable. Some of the greener products I have seen include paper and notebooks made of recycled paper and supplies such as binders and pens/pencils made from recycled materials.
When preparing lunches, think litter-less! Not only does it save money, since you won't always be purchasing brown bags, but it also reduces the amount of waste you're producing.
If you're moving away for college/university, ask your family or friends for unused furniture or household items. If you do have to buy, check out your local thrift store or on sites like Craig's list and Kijiji, it's cheaper than buying new and you'll be recycling!
Last but not least, encourage your kids to join the school's green club and if there isn't one, help to start one! In elementary school I learned a lot about environmental issues through my school's green club. Most colleges/universities also have environmental clubs. They're a great way to take part in environmental causes as well as to network and meet people in the environmental field! I found my first environmental job through my university's green club.
Start off the new school year right with the environment in mind! How will you go green this school year?
Prabh's environmental journey began in 1992 when she discovered a passion for green living after watching the cartoon movie, Ferngully: The Last Rainforest. Since then she has been an avid environmentalist for over 20 years, cultivating sustainability within her own personal and professional life. She went on to complete her Master in Resource and Environmental Management from Dalhousie University in Halifax, Nova Scotia and undergraduate degree in Environmental Studies from McMaster University, Hamilton, Ontario. During her Master's degree, Prabh worked on policy oriented research on sustainability reporting frameworks, community based social marketing, resource efficiency and waste management practices. Prabh is currently the Manager of Strategy Development & Corporate Sustainability at Toronto Pearson Airport. Prabh leads the development and delivery of the airport's sustainability strategy. Prabh enjoys reading and writing about the environment and loves to share her tips and passion for living sustainably.
Quebec's responsible consumption in 2014: Where do we stand?


text:
TV Clips: Sneak Peeks at Gossip Girl Season 3
Bringing You Up to Speed
Season 3 Main Teaser Promo
Mini Promos
"No Headbands in College"
WTF - Serena
WTF - Dan
WTF - Blair
WTF - Chuck
WTF - Nate
Brief Sneak Peeks
Posted by Jen Johans at 9:46 AM
Labels: 2000s, Blake Lively, CW, Ed Westwick, G, Gossip Girl, Leighton Meester, Made for TV, Season 3, Sneek Peek, TV, TV Clips, Video Clips
Video Clips: Fringe: Season One (2009-2009) -- Arriving on DVD & Blu-ray 9/8
Fans can now enter for a chance to win a trip to the set of Fringe at www.CompleteThePattern.com. The grand prize winner will win a trip to Vancouver, BC. The first prize winner will get a hi-def home entertainment system and five second prize winners will receive a copy of the Complete First Season on DVD.
"Teleportation. Mind control. Invisibility. Astral projection. Mutation. Reanimation. Phenomena that exist on the Fringe of science unleash their strange powers in this thrilling, critically-acclaimed series, as Warner Home Video releases Fringe: The Complete First Season on DVD and Blu-ray™ Hi Def on September 8, 2009.
"Featuring a collectible lenticular slipcase, and packed with nearly 6 hours of special features, including featurettes, production diaries, producer and writer commentaries, deleted scenes, gag reel, Blu-Ray exclusive content and much more in a release timed to the premiere of Season 2 on FOX."
"From J.J. Abrams (Lost), Alex Kurtzman and Roberto Orci (the team behind Star Trek, Mission: Impossible III and Alias) and executive producers Jeff Pinkner and Bryan Burk (both of Lost and Alias), Fringe revolves around three unlikely colleagues – a beautiful, young and determined FBI agent (Anna Torv), a brilliant but off-the-wall scientist (John Noble), and his sardonic, roguish son (Joshua Jackson) – who team up to investigate a series of peculiar deaths and disasters known as "The Pattern." The trio suspects that someone is using the world as a laboratory. And many of the clues lead them to Massive Dynamic, a shadowy global corporation that may be more powerful than any nation. Season 1 also starred Lance Reddick, Kirk Acevedo, Blair Brown, Jasika Nicole and Mark Valley. Fringe is from Bad Robot Productions in association with Warner Bros. Television."
DVD & Blu-ray Trailer
Video Clip: "The Arrival"
(Behind-the-Scenes)
Photo Slideshow
Video Clip: "Circadian Rhythms"
• The pilot episode of Fringe was watched by 9.13 million viewers, and as of March 2009 the show continues to draw an average of 9.9 million viewers a week.
• Fans and critics all love Fringe! Fringe won TV.com's reader poll for Best New Fall Show, and Entertainment Weekly picked Fringe as #7 on their 10 Best TV Shows of 2008.
• Executive producers include J.J. Abrams (Star Trek, Lost, Alias), Roberto Orci (Star Trek, Mission Impossible: III, Alias), and Alex Kurtzman (Star Trek, Mission Impossible: III, Alias), among others.
• The show was nominated for a 2009 Writers Guild Award for Best New Series.
• This release includes over 6 hours of brand new special features, plus an additional hour of exclusive content on the Blu-Ray release.
DVD Special Features:
(Over 6 hours of brand new special features, plus an additional hour of exclusive content on the Blu-Ray release)
• "Evolution: The Genesis of Fringe" featurette - The creators of the show discuss how the series unfolded and the qualities that make it so unique
• "Behind the Real Science of Fringe" featurette - From teleportation to re-animation, Fringe incorporates recent discoveries in science. Consulting experts and scientists who are the authorities in their field address the areas of science which are the inspiration for the show.
• "A Massive Undertaking: The Making of Fringe
(on select episodes) - An in-depth exploration of how select episodes came to be made: from the frozen far reaches of shooting the pilot in Toronto, to the weekly challenges of bringing episodes to air
• "The Casting of Fringe"- The story, as told by producers and cast, of how Anna Torv, Joshua Jackson, John Noble and others came to be cast in the series.
• "Fringe Visual Effects" featurette - Goes deep into the creation of the shared dream state with some of the biggest VFX shots of the show.
• Dissected Files: Unaired Scenes
• Unusual Side Effects: Gag Reel
• Deciphering the Scene
• Roberto Orci Production Diary
• Gene the Cow Montage
• Three Full-Length Commentaries from writers/producers, including J.J. Abrams, Roberto Orci, Alex Kurtman, J.R. Orci, David Goodman, Bryan Burk, Akiva Goldsman and Jeff Pinkner.
Posted by Jen Johans at 8:41 PM
Labels: 2000s, Anna Torv, F, Fringe, J.J. Abrams, John Noble, Joshua Jackson, Kirk Acevedo, Lance Reddick, Video Clips
Video Clip: Tinker Bell and The Lost Treasure (2009) -- Sneak Peek of the Opening 6 Minutes
On DVD & Blu-ray 10/27
Read Jen's Review of Tinker Bell and The Lost Treasure
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Mini Movie Synopsis:
"Take a Journey with Tinker Bell and her friends on her quest to save the most precious moonstone in all of Pixie Hollow. Tinker Bell and The Lost Treasure arrives on Disney DVD and Blu-ray October 27 2009."
Note: In case you're using a smaller screen or a hand-held device, here's another version of the video from Walt Disney Studios.
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Video Clips: Fringe: Season One (2009-2009) -- Arr...
Video Clip: Tinker Bell and The Lost Treasure (200...


text:
//
//  MainTableViewController.m
//  PLCAudioRecorderDemo
//
//  Created by PlutusCat on 2017/4/26.
//  Copyright © 2017年 PlutusCat. All rights reserved.
//

#import "MainTableViewController.h"
#import "MainTableCell.h"

@interface MainTableViewController ()

@end

@implementation MainTableViewController

- (void)viewDidLoad {
    [super viewDidLoad];

    UIRefreshControl *refreshControl = [[UIRefreshControl alloc] init];
    [refreshControl addTarget:self action:@selector(refresh:) forControlEvents:UIControlEventValueChanged];
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}

- (void)refresh:(UIRefreshControl *)refreshControl {

    dispatch_time_t delayTime = dispatch_time(DISPATCH_TIME_NOW, (int64_t)(3.0/*延迟执行时间*/ * NSEC_PER_SEC));

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}

#pragma mark - Table view data source

- (NSInteger)numberOfSectionsInTableView:(UITableView *)tableView {

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/* */
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}

/* */
// Override to support conditional editing of the table view.
- (BOOL)tableView:(UITableView *)tableView canEditRowAtIndexPath:(NSIndexPath *)indexPath {
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}

/* */
// Override to support editing the table view.
- (void)tableView:(UITableView *)tableView commitEditingStyle:(UITableViewCellEditingStyle)editingStyle forRowAtIndexPath:(NSIndexPath *)indexPath {
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        // Create a new instance of the appropriate class, insert it into the array, and add a new row to the table view
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}

/* */
// Override to support rearranging the table view.
- (void)tableView:(UITableView *)tableView moveRowAtIndexPath:(NSIndexPath *)fromIndexPath toIndexPath:(NSIndexPath *)toIndexPath {

}

/* */
// Override to support conditional rearranging of the table view.
- (BOOL)tableView:(UITableView *)tableView canMoveRowAtIndexPath:(NSIndexPath *)indexPath {
    // Return NO if you do not want the item to be re-orderable.
    return YES;
}

- (CGFloat)tableView:(UITableView *)tableView heightForFooterInSection:(NSInteger)section {
    return K_AUTOSIZE_HEIGHT(20);
}

/* */
#pragma mark - Navigation

// In a storyboard-based application, you will often want to do a little preparation before navigation
- (void)prepareForSegue:(UIStoryboardSegue *)segue sender:(id)sender {
    // Get the new view controller using [segue destinationViewController].
    // Pass the selected object to the new view controller.
}

- (void)didReceiveMemoryWarning {
    [super didReceiveMemoryWarning];
    // Dispose of any resources that can be recreated.
}

@end

redpajama_set_name: RedPajamaGithub


text:
\section{Introduction}

A variety of techniques have emerged recently with the aim of
turning transfer operators into an efficient numerical tool for
practical applications. Domain based transfer operator approaches,
for example, start by subdividing the phase-space into distinct
cells and considering transition rates between these phase-space
regions. One of the simplest and most common approaches of this type
is Ulam's method (see e.g.\ \cite{JD96}). Other methods include
wavelet and spectral methods for the infinitesimal FP-operator
\cite{JK09, FJK11}, eigenfunction expansion methods \cite{BMM12} and
periodic orbit expansion techniques \cite{Cvi12, PC10}. Also the
modelling of many-particle dynamics, such as protein folding, has
been approached using short trajectories of the full,
high-dimensional molecular dynamics simulation to construct reduced
Markov models \cite{Noe09}. For a discussion of convergence
properties of the Ulam method in one and several dimensions, see
\cite{BM01} and \cite{BKL02}, respectively. However, such methods
have only found a fairly limited range of applicability, with
difficulties arising due to the high-dimensionality of the
phase-space.

In the following we will focus on integral equation formulations for
propagating phase space densities along ray trajectories using
transfer operators. One such formulation is given by the rendering
equation \cite{JK86} which has its origins in computer graphics, but
has been applied more widely since \cite{AL06, GT09}. The rendering
equation can again be formulated in terms of transfer operators
\cite{GT09, SAE14}. A boundary integral FP-operator approach called
{\em dynamical energy analysis} (DEA) has been introduced in
\cite{GT09} and further developed in \cite{CGT11}. In a sequence of
papers \cite{CTG12, CT13} the method has evolved into an mesh-based
tool called {\em discrete flow mapping} (DFM) described in
\cite{PRSL13, Wamot14}. This has proven to be an efficient numerical
tool making it possible to handle trajectory flow problems on
complex surfaces (consisting of circa $10^5$ to $10^6$ mesh cells)
on the time-scale of a few hours on standard desktop computers
\cite{Wamot14}.

Here we will extend the DEA approach towards dynamical systems with
uncertainties and stochastic dynamics. The reasons for doing so are
twofold: firstly, in many physically relevant situations, the system
dynamics are inherently stochastic or system parameters are not
known exactly and a probabilistic approach will be necessary.
Secondly, including stochasticity in a transfer operator changes the
properties of the operator fundamentally in a way that opens the
door for a wider range of numerical solution techniques. Techniques
for constructing stochastic ray-tracing operators have been
presented in \cite{PC98, PC99a, PC99b, GP01} in the context of the
FP operator, and in acoustics in terms of the radiosity equation
\cite{AL98}.

In this paper we construct a stochastic ray-tracing
operator that leads to a boundary integral formulation for
stochastic dynamics in billiards.
That is, the underlying dynamical system is that of a particle or point mass
moving on a billiard table with constant velocity (without friction) inside a compact domain
$\Omega$ with piecewise smooth boundary $\Gamma$ as described by
Sinai \cite{YS04}, see also \cite{Cvi12}, Ch. I, Sec. 8. The particle
is assumed to undergo specular
reflections upon collision with the smooth sections of $\Gamma$. As
the overall energy of the system is constant, the billiard dynamics
(integrable, mixed or chaotic) is completely controlled by the
geometry of $\Gamma$. However, for the stochastic evolution
considered here, both the position of the transported particle and
the nature of its reflection at the boundary will be considered as
uncertain. Typically, the mean transported position and reflected
direction will be those of the standard (deterministic) billiard
map. The effect is that total energy remains constant, but the
stochasticity will clearly influence the billiard dynamics as will
be explored in Section \ref{Sec:dynsys}.
The resulting stochastic evolution operator will be of Fokker-Planck type
as discussed in \cite{PC10, PC98}.

We note that statistical methods related to the stochastic approach
proposed here have been used in a variety of engineering
applications. In particular, the so-called statistical energy
analysis (SEA) (see for example \cite{RL69} and \cite{RL95}) for
modelling vibro-acoustic energy distributions and the random
coupling model (RCM) \cite{RCM} for modelling electromagnetic
fields, see also \cite{Gradoni14}. In SEA and RCM the structure is
subdivided into a set of subsystems and ergodicity of the underlying
ray dynamics as well as quasi-equilibrium conditions are postulated.
The result is that the density in each subsystem is taken to be
approximately constant leading to greatly simplified equations based
only on coupling constants between subsystems. The disadvantage of
these methods is that the underlying assumptions are often hard to
verify {\em a priori} or are only justified when an additional
averaging over `equivalent' subsystems is considered. The
shortcomings of SEA have been addressed by Langley \cite{RL92, RL94}
and more recently in a series of papers by Le Bot \cite{AL06, AL98,
AL02}.

In this work we focus on stochastic ray-tracing approximations for
linear wave problems in two-dimensions, or equivalently on
stochastic billiard dynamics; the models developed can easily be
generalized to higher dimensions. We propose a new boundary integral
approach based on the use of stochastic evolution operators to
incorporate uncertain ray dynamics into our model in a quantifiable
manner. Propagating densities with uniformly distributed probability
of location and direction leads to the quasi-equilibrium approaches
mentioned above (SEA and RCM). We will show that choosing a scaled
and truncated Gaussian probability distribution instead leads to a
model that interpolates between SEA and deterministic ray tracing.
This interpolation takes place at the level of the governing model,
in contrast to DEA which provides a similar interpolation due to the
precision of the chosen numerical approximation method \cite{GT09}.
Once an estimate of the level of uncertainty in the model has been
prescribed, an appropriate numerical solution approach can be
applied.

The paper is structured as follows: in Sec.\ \ref{sec:int-eq} a
boundary integral description of deterministic ray tracing in
billiards will be presented. The addition of noise into the model
will then be outlined and an approach that interpolates between a
deterministic and a random trajectory flow will be described. In
Sec.\ \ref{sec:impl}, the numerical implementation of the model will
be outlined and illustrated via the example of stochastic ray
tracing in a rectangular billiard. The decay of correlations and the
asymptotic escape rate will be studied to diagnose the behaviour of
the rectangular billiard model as it makes the transition from
regular and deterministic to probabilistic dynamics.

\section{Boundary Integral Equation Formulation}
\label{sec:int-eq}

\subsection{A boundary integral description of deterministic ray tracing via transfer operators}\label{sec:detop}
Consider the trajectory flow described by a Hamiltonian
$\hat{H}=c|\mathbf{p}|$ in a finite two-dimensional domain $\Omega$
as depicted in Fig.\ \ref{boundary-map}, where $c$ is the speed of
propagation and $\mathbf{p}$ is the inward momentum (or slowness)
vector. Denote the phase-space on the boundary of $\Omega$ with
fixed total energy $\hat{H}=1$ as $Q =
\Gamma\times(-c^{-1},c^{-1})$, where $\Gamma$ is the boundary of
$\Omega$. The associated coordinates are $X=[s,\:p] \in Q$ with
$s\in[0,L)$ (arc-length) parameterising $\Gamma$ and  $p \in
(-c^{-1},c^{-1})$ parameterising the component $\mathbf{p}$
tangential to $\Gamma$. Explicitly, the momentum coordinate $p$ is
defined in terms of the angle $\theta$ between $\mathbf{p}$ and the
normal to $\Gamma$ at $s$ (see Fig.\ \ref{boundary-map}) as
$p=c^{-1}\sin(\theta)$. We adopt the convention that $\theta
\in(-\pi/2,\pi/2)$ and is positive for counter-clockwise
propagation. The deterministic boundary flow map is denoted
$\varphi:Q\rightarrow Q$, and maps a vector in $Q$ via the
Hamiltonian flow to another vector in a subset of $Q$. This map
defines a deterministic evolution of the form $\varphi(X')=X_{}$,
where $X'_{}=[s',\:p']$, $X=[s,p]$ . Fig.\ \ref{boundary-map} shows
that geometrically $\varphi$ corresponds to the composition of a
translation (from $s'$ to $s_{}$) and a rotation to the direction
corresponding to a specular reflection.

\begin{figure}
\begin{center}
\includegraphics[width=0.8\textwidth]{BMAP.eps}
\end{center}
\caption{Propagation of ray trajectories using a deterministic
boundary map.} \label{boundary-map}
\end{figure}

The propagation of a phase-space density $\rho$ by the boundary map
$\varphi$ through a single reflection is given by the
Frobenius-Perron operator acting on this map
\begin{equation}\label{FPO}
\mathcal{L}\rho(X)=\int_{Q}\delta(X-\varphi(X'))\rho(X')dX'.
\end{equation}
For an initial boundary distribution $\rho_{0}$ on $Q$, the final
density after adding contributions from all refections may be
computed using the following boundary integral equation (see
\cite{GT09}, \cite{CTG12} and \cite {CT13}),
\begin{equation}\label{DetIE}
(I-\mathcal{L})\rho=\rho_{0}.
\end{equation}
Note that for the sum over all reflections to converge, energy
losses must be introduced into the system, which could take place at
the boundaries themselves, or along the trajectories. In general, a
weight factor $w$ will be added inside the integral in the
definition of $\mathcal{L}$ which contains a dissipative term, and
for the extension to multiple domains connected at interfaces $w$
will also contain reflection/transmission probabilities at these
interfaces. For non-convex polygons, $w$ will additionally include a
visibility function.

\subsection{Stochastic trajectory tracking in billiards}\label{sec:theory}
\subsubsection{The stochastic propagation operator}
Building upon the deterministic propagation models described in the
previous section, we propose a family of phase space density
propagation models with transfer operators of the form
\begin{equation}\label{StochasticTO}
\mathcal{L}_{\boldsymbol{\sigma}}\rho(X)=\int_Q
f_{\boldsymbol{\sigma}}(X-\varphi(X'))\rho(X')dX'.
\end{equation}
This operator bears a strong similarity to (\ref{FPO}), but the
$\delta$ distribution term has been replaced with a probability
density function (PDF) $f_{\boldsymbol{\sigma}}$ such that
\begin{equation}\label{StochasticPDF}
\int_Q f_{\boldsymbol{\sigma}}(X)dX=1.
\end{equation}
Here, $f_{\boldsymbol{\sigma}}$ is the probability distribution and
$\boldsymbol{\sigma}$ is the parameter set controlling its shape.
With reference to applications, such a probabilistic behaviour could
be attributed to, for example, fluctuations in the wave speed $c$,
roughness of the reflecting surface or uncertainty in the exact
position of the boundary. In the following, we will always assume
that the total energy $\hat{H}=c|\mathbf{p}| = 1$ remains fixed and
that the total probability is conserved, that is, condition
(\ref{StochasticPDF}) holds throughout. Note that in contrast to the
models considered in \cite{PC10, PC98}, the range of integration in
the billiard models considered here is in general bounded, which has
implications for the choice of suitable PDFs
$f_{\boldsymbol{\sigma}}$.

The simplest case is to take $f_{\boldsymbol{\sigma}} = const$, upon
which one arrives at a model describing propagation to all
admissible positions and directions with equal probability. The
systems is thus by definition ergodic and independent of the
underlying classical dynamics. Note that ergodicity is a key
assumption for an SEA or RCM treatment to be valid.

\begin{figure}
\begin{center}
\includegraphics[width=\textwidth]{TruncRanges.eps}
\end{center}
\caption{Tracking ray trajectories via a noisy boundary map and
truncation limits $s^\pm$ for the random variable $s_\varepsilon$.}
\label{TruncRange}
\end{figure}

In general, we would like to arrive at a stochastic operator which
includes both the deterministic operator in Eq.\  (\ref{FPO}) and
the random propagation model described above as limiting cases. In
addition, the PDF $f_{\boldsymbol{\sigma}}$ needs to obey conditions
on the sampling ranges due to the limited range of the boundary map
$\varphi$. For simplicity we will restrict to convex domains
$\Omega$ to avoid additional complications due to incorporating
visibility functions.

\subsubsection{The probability density function - normalisation}
We may interpret the evolution
given by the operator in Eq.\ (\ref{StochasticTO}) as originating from a
stochastic boundary map $\varphi_{\boldsymbol{\sigma}}$ with added noise,
that is,
\begin{align}\label{Gaussian}
\begin{split}
\varphi_{\boldsymbol{\sigma}}(X') &= {X},\\
&=\varphi(X')+X_\varepsilon,
\end{split}
\end{align}
where $X_\varepsilon = [s_\varepsilon, p_\varepsilon]$ are random
variables drawn from the  PDF $f_{\boldsymbol{\sigma}}$. Note that
$s_\varepsilon$ is understood as a shift in counter-clockwise
direction. For $ X \in Q$ given, we have to ensure that
$\varphi(X')= X - X_\varepsilon$ is still in the range of the
deterministic map $\varphi$; this yields restrictions on the
possible values of $X_\varepsilon$ and thus on the domain of
$f_{\boldsymbol{\sigma}}$.

We define $\varphi=[\varphi_s,\:\varphi_p]$ in terms of its position
and momentum components and write the initial coordinate as $X' =
[s',p']$. The range of admissible values for $\varphi_s(X')$ is
$[0,L)\setminus E(s')$, where $E(s')$ is the (closed) set of all
points on the same straight edge as $s'$, see Fig.\
\ref{TruncRange}. Note that for curved edges we set $E(s')=s'$ as
shown on the RHS of Fig.\ \ref{TruncRange}. Furthermore, we have
that $\varphi_p(X')\in(-c^{-1},c^{-1})$. It is therefore necessary
to truncate the ranges from which $X_\varepsilon$ are sampled to the
ranges where for fixed $X$, $\varphi(X')\in([0,L)\setminus
E(s'))\times(-c^{-1},c^{-1})$ in Eq.\ (\ref{Gaussian}). Denoting
these truncated ranges by $(X^-,X^+)$ where
$X^{\pm}=[s^\pm,\:p^\pm]$, the PDF $f_{\boldsymbol{ \sigma}}$ will
have support on $X_\varepsilon\in(X^-,X^+)$ only. The truncated
sampling ranges are given as $s^+(s',s)=\min\{x>0: s+x\in
{E}(s')\:\:(\mathrm{mod}\:L)\}$ and correspondingly
$s^-(s',s)=\max\{x<0:s+x\in {E}(s')\:\:(\mathrm{mod}\:L)\}$ (see
Fig.\ \ref{TruncRange}). Likewise in the momentum coordinate,
$p^+(p)=c^{-1}-p$ and $p^-(p)=-c^{-1}-p$. Using Heaviside functions
we define a cut-off function for restricting the support of
$f_{\boldsymbol{\sigma}}$ to $(X^-,X^+)$ as follows
\begin{align}
\begin{split}
&\chi(X_\varepsilon;X^-,X^+)\\
&=(H(s^+-s_\varepsilon)-H(s^- -s_\varepsilon))(H(p^+-p_\varepsilon)-H(p^--p_\varepsilon)).\\
\end{split}
\end{align}
Note that we have omitted the dependence of $s^\pm$ and $p^\pm$ on
$X'$ and $X$ for brevity.

Having obtained the domain of the PDF, we can now construct
$f_{\boldsymbol{\sigma}}$ explicitly; we will derive the PDF from an
uncorrelated bivariate Gaussian distribution with mean
$\mathbf{0}=[0,0]$ and standard deviation $\boldsymbol{\sigma}=
[\sigma_1,\sigma_2]$. A normalized PDF is then obtained by setting
\begin{align}\label{ScaledPDF}
f_{\boldsymbol{\sigma}}(X_\varepsilon;X^-,X^+)=\frac{\chi(X_\varepsilon;X^-,X^+)\exp{\left(\displaystyle-\frac{s_\varepsilon^2}{2\sigma_1^2}\right)}\exp{\left(\displaystyle-\frac{p_\varepsilon^2}{2\sigma_2^2}\right)}}{2\pi\sigma_1\sigma_2\psi_{\sigma_1}(s^-,s^+)\psi_{\sigma_2}(p^-,p^+)},
\end{align}
where the normalization defined through $\psi_{\sigma_1}$ and $
\psi_{\sigma_2}$ is given as
\begin{align}
\psi_{\sigma_1}(s^-,s^+)=\frac{1}{2}\left(\mathrm{erf}\left(\frac{s^+}{\sqrt{2}\sigma_1}\right)-\mathrm{erf}\left(\frac{s^-}{\sqrt{2}\sigma_1}\right)\right),
\end{align}
and $\psi_{\sigma_2}$ is defined analogously. The normalisation
ensures that the PDF satisfies condition (\ref{StochasticPDF}) for
the truncated sampling ranges specified through $\chi$. Note that
the mean and variance of $f_{\boldsymbol{\sigma}}$ differs in
general from that of the underlying Gaussian distribution.

The two limiting PDFs are obtained by considering the limiting
values of ${\boldsymbol{\sigma}}$. Taking the limit of
(\ref{ScaledPDF}) as $\boldsymbol{\sigma}\rightarrow\mathbf{0}$ then
\begin{equation}\label{PDF0}
f_{\boldsymbol{\sigma}}(X_\varepsilon;X^-,X^+)\rightarrow\lim_{\boldsymbol{\sigma}\rightarrow\mathbf{0}}\frac{\chi(X_\varepsilon;X^-,X^+)}{2\pi\sigma_1\sigma_2}\exp{\left(\displaystyle-\frac{s_\varepsilon^2}{2\sigma_1^2}\right)}\exp{\left(\displaystyle-\frac{p_\varepsilon^2}{2\sigma_2^2}\right)}.
\end{equation}
The distribution becomes increasingly sharp and the bivariate
Gaussian tends to a two-dimensional delta distribution localised
around $X_\varepsilon = X- \varphi(X') = 0$, which describes the
deterministic flow discussed in the Section \ref{sec:detop}. Taking
the limit as $\sigma_1$, and $\sigma_2$ go to $\infty$ and using the
leading order asymptotic expansion of the error function about 0
returns
\begin{equation}\label{PDFinf}
f_{\boldsymbol{\sigma}}(X_\varepsilon;X^-,X^+)\rightarrow\frac{c}{2(s^+-s^-)}\chi(X_\varepsilon;X^-,X^+).
\end{equation}
Note that this is just the uniform distribution for
$s_\varepsilon\in(s^-,s^+)$ and $p_\varepsilon\in(p^-,p^+)$ (since
$p^+-p^-=2c^{-1}$) leading to the fully probabilistic regime
described above. The mean and variance of the normalized
distribution may be calculated from the PDF (\ref{ScaledPDF}) using
the standard formulae. The variance of the bivariate distribution
will tend to $\boldsymbol{\sigma}$ as
$\boldsymbol{\sigma}\rightarrow\mathbf{0}$. For large $\sigma_j$,
$j=1,2$ we have the variance of the uniform distribution. That is,
as $\sigma_1\rightarrow\infty$,
$\mathrm{Var}(s_{\varepsilon})=(s^+-s^-)^2/12$, and as
$\sigma_2\rightarrow\infty$, then
$\mathrm{Var}(p_{\varepsilon})=1/(3c^2)$. Clearly such data are
vital for applications in uncertainty quantification, for example,
for modelling uncertain high frequency vibro-acoustic or
electromagnetic wave propagation through a manufactured structure or
device.

We turn our attention to propagating a density along stochastic ray
paths according to the PDF (\ref{ScaledPDF}) via the transfer operator (\ref{StochasticTO}). We
proceed by considering the numerical evaluation of
$\mathcal{L}_{\boldsymbol{\sigma}}$; we will in particular consider some important
dynamical quantities, namely the rate of escape and the
decay of correlations. These will be studied to help diagnose the
behaviour of the model for different ranges of $\boldsymbol{\sigma}$.

\section{Implementation and Results}\label{sec:impl}
\subsection{Discretisation}
A number of efficient methods for evaluating $\mathcal{L}$
numerically in domains including complex multi-component systems
have recently been developed \cite{PRSL13, Wamot14}. One advantage
of instead working with $\mathcal{L_{\boldsymbol\sigma}}$ is that it
is a compact integral operator and hence may be evaluated more
simply via direct discretisation methods rather than the variational
approaches described in \cite{PRSL13, Wamot14} and references
therein.
\begin{figure}
\begin{center}
\includegraphics[width=0.75\textwidth]{Rect.eps}
\end{center}
\caption{A rectangular billiard with prescribed boundary condition
$\rho_0$.} \label{Rect}
\end{figure}

Here we approximate $\mathcal{L}_{\boldsymbol\sigma}$ on a
rectangular billiard as shown in Fig. \ref{Rect}. The reason for
choosing this simple domain is that its integrable dynamics make it
ideal for identifying the effect of varying $\boldsymbol\sigma$ in
isolation of other sources of ray chaotic behaviour. In particular,
we make use of our experience in dealing with domains with corners
in \cite{PRSL13, Wamot14} and employ a piecewise constant
collocation method with $n$ elements in the position variable,
collocating at element centers. That is, we separate out and
approximate the spatial dependence of $\rho$ in the form
\begin{equation}
\rho(s,p)\approx\tilde{\rho}(p)\sum_{j=1}^{n}a_jb_j(s),
\end{equation}
where $b_j(s)=1$ if $s$ lies on the $j$th element and zero
elsewhere. The coefficients $a_j$ are the unknowns to be determined.
The semi-discrete operator $\mathcal{L}_\sigma$ is then evaluated at
the collocation points $s=s_i$ for $i=1,\ldots,n$ using equation
(\ref{StochasticTO}) as
\begin{equation}\label{StochasticTOdisc1}
\mathcal{L}_{\boldsymbol{\sigma}}\rho(s_i,p)=\sum_{j=1}^na_j\int_{-c^{-1}}^{c^{-1}}\tilde{\rho}(p')\int_{e_j}
f_{\boldsymbol{\sigma}}(X_i-\varphi(X'))ds'dp',
\end{equation}
where $X_i=[s_i,\: p]$ and the range of integration with respect to
$s'$ is on the $j$th element $e_j$. The phase space coordinate
$X'=[s',\:p']$ provides the variables integration $s'\in e_j$ and
$p'\in(-c^{-1},c^{-1})$. Note that the integral with respect to $s'$
may be calculated analytically in terms of the error function for
discretisation by flat (straight line) elements and using the
normalised PDFs described in the last section. This step is
important for \emph{efficient} computations of the discretised
transfer operator.

A full discretisation is then achieved by applying the Nystr\"{o}m
method in momentum space with $N$-point trapezoidal integration and
a step size $h$. Note that in order to evenly discretize with
respect to the direction of ray propagation, the integration
variable is changed from $p'$ to $\theta'$ using the relation
$cp'=\sin(\theta')$. This reduces the calculation in
(\ref{StochasticTOdisc1}) to a matrix-vector multiplication, with
matrix entries of the form
\begin{equation}\label{StochasticTOdisc2}
L_{I,J}=\frac{h\cos(\theta')}{c}\int_{e_j}
f_{\boldsymbol{\sigma}}(X_I-\varphi(X_J'))ds'.
\end{equation}
Here $X_I=[s_i,\: p_{\iota}]$ and so $I$ is the multi-index
$(i,\:\iota)$, with $p_\iota$, $\iota=1,\ldots,N$ giving the values
of the momenta corresponding to the trapezoidal rule grid points.
Likewise, $X_J'=[s',\: p_{k}]$ and $J$ is the multi-index $(j,\:k)$,
where $s'\in e_j$ is the integration point and $p_k$, $k=1,\ldots,N$
runs over the trapezoidal rule grid points as before. The density
$\rho$ can (by extension) be considered as periodic in the momentum
variable since $\rho(s,c^{-1})=\rho(s,-c^{-1})=0$, and so the
semi-discretisation in momentum space should converge
super-algebraically for smooth initial data. The convergence
properties of the method overall are demonstrated in the next
section. A further major advantage of this combination of methods is
that the need for numerical integration methods is completely
avoided.

\subsection{Convergence}

To test the convergence of the approximation of
$\mathcal{L}_{\boldsymbol\sigma}$ we propagate a stochastic boundary
(line) source through a single reflection. The dimensions of the
rectangle are taken to be $0.75$ by $0.25$ and we let $c=1$ meaning
that both the position and momentum variables have the same total
range. We also take $\sigma_1=\sigma_2=\sigma$ for simplicity,
although the extension to distinct $\sigma_1$ and $\sigma_2$ is
clearly straightforward. We number the edges as shown in Fig.
\ref{Rect} so that edges $1$ and $3$ have length $0.75$ and take
\begin{equation}
\rho_0(s,p)=\frac{I_{4}(s)\exp\left(\displaystyle\frac{-p^2}{2\sigma^2}\right)}
{\sqrt{2\pi\sigma^2}\mathrm{erf}\left(\frac{1}{\sqrt{2}\sigma}\right)},
\end{equation}
where $I_4$ is an indicator function for edge number 4. That is, the
source is applied along edge 4 as shown in Fig. \ref{Rect} and its
directivity depends on the parameter $\sigma$. Figure
\ref{ConvSigma} shows the result of approximating
$\mathcal{L}_\sigma\rho_0$ on sides 1 to 3 of the rectangle. The
plot shows the mean ray density along each of the 3 edges plotted
against the outgoing angle. The horizontal axis is a shifted value
of this outgoing angle which is unshifted on side 1, shifted by
$\pi$ on side 2 and by $2\pi$ on side 3. This is simply to show the
results for each edge side-by-side.
\begin{figure}
\begin{center}
\includegraphics[width=\textwidth]{ConvSig4n.eps}
\end{center}
\caption{Convergence of the ray density after one reflection and the
effect of changing $\sigma$ on the dynamics. For all plots except
$\sigma=0.01$: $\cdots$: $N=16$, $--$: $N=32$, ---: $N=64$,
$\cdot$-$\cdot$: $N=128$. For the $\sigma=0.01$, the
previous $N$ values should all be multiplied by 4. The horizontal
axis shows the outgoing angle in the range $-\pi/2$ to $\pi/2$ on
edge 1, on edge 2 it is shifted by $\pi$ and on edge 3 it is shifted
by $2\pi$. Edge numbers are indicated on the plot.}
\label{ConvSigma}
\end{figure}

Figure \ref{ConvSigma} shows the transition from probabilistic to
deterministic dynamics as $\sigma$ is decreased, and therefore
illustrates the theory outlined in the Section \ref{sec:theory}. In
particular, for $\sigma=10$ we see a uniformly distributed ray
density across all edges and all outgoing directions. For
$\sigma=0.01$ one sees that the ray density localises on edge 2 with
outgoing angle 0, i.e. perpendicular to the boundary. This is a
close approximation to the expected deterministic evolution. The
intermediate cases ($\sigma=1$ and $\sigma=0.1$) show the transition
between these two limiting cases. This transition will be considered
in more depth in the next section.
\begin{figure}
\begin{center}
\includegraphics[width=0.8\textwidth]{ConvRateNew.eps}\end{center}
\caption{Convergence rate in computing the total ray density
(\ref{TRD}) for different values of $\sigma$.}
\label{ConvR}\end{figure}

In order to test the convergence of the results shown in Figure
\ref{ConvSigma}, we integrate the boundary phase-space density over
$Q$ to estimate the total density
\begin{equation}\label{TRD}
\rho_{\mathrm{tot}}=\int_Q\mathcal{L}_{\boldsymbol \sigma}\rho_0 dX.
\end{equation}
For the basic discretisation approaches employed here and taking
$n=N$ one typically sees convergence in computing
$\rho_{\mathrm{tot}}$ to the first few significant figures with
absolute errors of estimated order between $\mathcal{O}(N^{-1})$ and
$\mathcal{O}(N^{-2})$ as shown in Figure \ref{ConvR}. Note that
these rates appear to be superior to the sub-linear rates expected
from a standard Ulam approach \cite{BM01}. Convergence rates are
generally higher for smaller values of $\sigma$, and usually
increase slightly when the number of discretisation points $n=N$ in
both the position and momentum variables is increased. Note that for
$\sigma=0.01$, the method has only converged sufficiently to produce
meaningful results when $N\geqslant 128$ and as such this case has
been omitted from the figure. This suggests that the singularly
perturbed problem for small $\sigma$ should be tackled using an
adaptive meshing procedure to resolve the peak(s) more efficiently,
rather than the uniform grid employed here. The development and
analysis of such approaches will be considered as part of future
work.

\subsection{Rate of escape and decay of
correlations}\label{Sec:dynsys}
The rates of escape and decay of correlation provide useful
information about the dynamics of the billiard system being studied
in terms of their description and classification (chaotic, mixed or
integrable).
The escape rate $\gamma$ measures  the decay
of the total phase space density, that is, the survival probability,
in case of an open or absorbing billiard.  This decay is exponential
for chaotic dynamics, that is,
\[ \int_Q \left[{\cal L}^n_{\sigma} \rho_0\right](X) \;dX \sim e^{-\gamma n};\]
similarly, for closed, chaotic systems, the decay of correlation scales
exponentially with a decay rate $\nu$ according to
\[\int_Q \rho_0 (X)  \left[{\cal L}^n_{\sigma}\rho_0\right](X)\; dX -
\left[\int_Q \rho_0 (X)  \overline{\rho}(X)\; dX\right]^2
\sim e^{-\nu n},\]
where  $\overline{\rho} = \lim_{n\to\infty} {\cal L}_{\sigma}^n \rho_0$ is the
natural density (if the limit exists).
Both, $\gamma$ and $\nu$ are closely linked to the spectrum of
${\cal L_{\sigma}}$ with $\exp(-\gamma)$ and $\exp(-\nu)$ being the
magnitude of the leading and next-leading eigenvalue of ${\cal L_{\sigma}}$ for
ergodic dynamics \cite{Cvi12}.

The rates $\gamma, \nu$ are also important when considering wave energy
propagation through a built up structure \cite{CT11}. In particular,
the suitability of the random wave superposition hypothesise of an
SEA-type approach can be analysed in this framework, since a fast
decay of correlations compared to the escape rate provide the ideal
setting for a diffuse random wave field to be created \cite{GT09}.
On the other hand, slow or non-decaying correlations in the dynamics
indicate regularity in the wave field and will
introduce non-random fluctuations and potentially long range
correlations between multiple sub-domains.

In this section we study the decay of correlations in the
rectangular billiard described earlier for different choices of the
parameter $\sigma$. In addition, we consider the rate of escape when
a small opening is introduced on the boundary and consider the
effect of changing both $\sigma$ and the size of the opening.

\begin{figure}
\begin{center}
\includegraphics[width=\textwidth]{CombSigma2.eps}
\end{center}
\caption{(a) The dependence of the asymptotic escape rate on
$\sigma^2$ in a rectangular billiard for two different hole sizes.
(b) The dependence of the decay of correlations on $\sigma^2$ in a
closed rectangular billiard. In each case the dotted lines show the
same quantities as the solid lines, but computed using half number
of discretisation points for both $n$ and $N$.}
\label{EscRate}\end{figure}

Figure \ref{EscRate} (a)  shows a plot of the asymptotic escape rate
$\gamma$ against $\sigma^2$, where the escape rate is given by minus
the logarithm of the spectral radius of the (numerical approximation
to the) operator $\mathcal{L}_{\sigma}$. In each case the opening is
on edge 2, and the two plots shown are for openings of size $0.05$
(from $y=0.1$ to $0.15$) and $0.1$ (from $y=0.15$ to $0.25$). For
large $\sigma$ values we see $\gamma$ settling down to a constant,
the size of which is approximately proportional to the opening size.
This would be expected, since for chaotic maps the asymptotic escape
rate due to a small opening is an exponential decay which to leading
order is proportional to the hole size (see for example \cite{OG12},
\cite{EA13}). For small sigma values we see that the escape rate
decreases towards zero. Again, this reflects the supporting theory
since as the map approaches a deterministic billiard map in a
rectangle, the integrable dynamics and ``sticky" trajectories (small
perturbations of the bouncing ball modes) slow the decay to an
algebraic rate \cite{GZ02}. Such a decay would be reflected by
$\mathcal{L}_{\sigma}$ having a spectral radius of $1$, and hence
$\gamma\rightarrow0$.

Figure \ref{EscRate} (b) shows a plot of the correlation decay rate
$\nu$ against $\sigma^2$, which may also be estimated from the
spectrum of the operator $\mathcal{L}_{\sigma}$. In this case we
look at the size of the second largest eigenvalue $\lambda^*$ of the
closed billiard (the largest eigenvalue is always one for a closed
system). The plot shows
$\nu=-\log(|\lambda^*|)$ increasing with $\sigma^2$. For very small
$\sigma^2$ the plot shows an almost zero decay rate as would be
expected for a system with deterministic and regular dynamics. For
large $\sigma^2$ we see convergence to a value of just over $0.5$,
which clearly indicates the stochastic behaviour introduced from the
noise in the billiard flow. In fact, the dependence of the decay
rate on $\sigma$ appears to follow two distinct behaviours. For
$\sigma^2<0.1$ one sees a rapid increase of $\nu$ with $\sigma$, and
for $\sigma^2>0.1$ the rate of increase is far slower. This can
perhaps be attributed to the PDF governing the noise in the billiard
flow. For $\sigma^2<0.1$, the noise added to the flow is closer to a
non-correlated Gaussian distribution and for $\sigma^2>0.1$, the
scaling and shifting become increasingly significant and the model
approaches a uniform distribution.

Considering Figures \ref{EscRate} (a) and (b) together, a change of
behaviour in the escape rate is also evident close to
$\sigma^2=0.1$. Here the escape rate begins to increase more quickly
before peaking just below $\sigma=1$, and then decreasing to a
constant rate for $\sigma^2>10$. The behaviour for $0.1<\sigma^2<10$
indicates a transition region where the trajectory flow is not yet effectively
random (uniformly distributed), but is also not behaving as a flow
with uncorrelated Gaussian noise. The dotted lines in each case show
a lower precision computation with $n$ and $N$ both halved. The
similarities between the plots suggest a good level of convergence in
the computations. This serves to highlight a further advantage of working
with $\mathcal{L}_{\boldsymbol{\sigma}}$ rather than the FP operator,
where such computations typically show little evidence of convergence \cite{CT11}.

\section{Discussion and conclusions}

A new boundary integral model to propagate ray densities via an
uncertain trajectory flow has been presented. The resulting
phase-space boundary integral representation reduces the
dimensionality of the model, and was shown to directly interpolate
between a deterministic and a random trajectory flow. The model was
implemented numerically via a simple discretisation approach using
piecewise constant collocation in space and a Nystr\"{o}m method in
the momentum variable. Discrete flow mapping type methods were
applied to give a highly efficient computational procedure. An
application to uncertain billiard dynamics in an integrable
rectangular domain was presented; the numerical results demonstrated
the transition between a deterministic and a random flow. Using the
rate of escape and the decay of correlations to further diagnose the
behaviour of the model gave parameter ranges where the model was
effectively behaving as a deterministic trajectory flow with a small
amount of uncorrelated Gaussian noise, a random (uniformly
distributed) flow and a transition phase in between.

In the future, the framework will be extended to three dimensional billiards
by introducing the analog of the PDF (\ref{ScaledPDF}) on
the boundary surface and its corresponding hemispherical momentum
space (see \cite{CTG12}). Practically one would have to also define
an efficient discretisation scheme, but in principle similar methods
to those here can be employed provided the closed boundary surface
consists of (or can be well approximated by) a union of flat
surfaces joined together at their edges. Such an extension would be
important for applications in room acoustics.

A further natural extension arises since one could allow the
parameters $\boldsymbol{\sigma}$ to depend on the phase space
coordinate. In fact, since the PDF (\ref{ScaledPDF}) already depends
on the phase space point indirectly through dependence on $X^{\pm}$,
this extension could be implemented directly in the model here
without extra modification. On a practical note, the dependence of
$\sigma_1$ on the spatial coordinate should to be assumed to be
piecewise constant to match the collocation scheme and maintain the
tractability of the integrals appearing in
(\ref{StochasticTOdisc2}). This extension would be important for
applications in computer graphics, where reflections may take place
from surfaces with different properties. A further consideration
here is that the methods also extend directly to built-up
multi-component structures in the same way as DEA \cite{CGT11}. This
opens up the formulation to applications to built-up vibro-acoustic
structures and complex electromagnetic environments.

\section*{Acknowledgement}
Support from the EU (FP7 IAPP grant MHiVec) is gratefully
acknowledged. We also wish to thank Dr Alex Bespalov and Dr Gabriele Gradoni for
stimulating discussions.

redpajama_set_name: RedPajamaArXiv


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Home > VALORANT > 100 Thieves splits with dicey and b0i
100 Thieves splits with dicey and b0i
100 Thieves has decided to separate from dicey and b0i, as stated in the announcement on their Twitter account.
dicey q joined the team in October 2020 with Asuna. The season started badly for the 100 Thieves, who did not qualify for the first stage of the VCT and made a top 6 in the Challengers 2 Phase 1. Very quickly, changes were made. The team recruited Ethan and benched dicey at the end of February. After that, he was only seen again in July, at the Challengers 1 Stage 3, replacing Ethan on a single map. He has been totally inactive since then.
b0i started playing on 100 Thievs in July, after leaving Andbox. First as a subsitute, then as a first-team player two months later, taking over the place of steel. The aim was to strengthen the team before the start of the Last Chance Qualifier, in order to qualify for the Valorant Champions. 100 Thieves was one of the favourites for this competition. But despite a good performance, the team was defeated by Rise in the Upper Bracket final and by Cloud 9 in the Lower Bracket final. The team finished in third place and saw its hopes of qualifying for the Valorant Champions evaporate.
Like many teams, 100 Thieves made the decision to reorganise with the aim of having a good VCT 2022 season and securing a place at the final event. Having not played for months, it's only natural that dicey has been released. As for b0i, his performance at the LCQ was mixed and not enough to convince. It's now time for them toexplore new horizons..
The two players have not communicated about their future on the game, although b0i expressed his gratitude and appreciation to the org in a Twitlonger. He concluded his message by saying that he would be back soon. So we should definitely see him back for next season.


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Posts Tagged 'Pentecostals'
Billie Livingston on Religion, Writing Fiction, Crooked Hearts, and Mercy
Tags: alcoholism, Catholicism, eleos, empathy, evangelicalism, feminism, fiction, Going Down Swinging, Graham Greene, mercy, Pentecostals, poetry, Raelism, religious fiction, St. Francis of Assisi, suicide, sympathy, The Chick at the Back of the Church, The Crooked Heart of Mercy, W.H. Auden
Billie Livingston, an independent novelist and poet, discusses the role of faith in her life and fictional writing. Our conversation meanders broadly through a number of different topics including the publishing industry, where works of literature are inspired from, and how the role of mercy and guilt play into Billie's own writings. We discuss her most recent novel "The Crooked Heart of Mercy" and learn how she views her spiritual journey in light of her many life experiences.
Join us on Facebook or Twitter for regular updates on guests!
Joseph Daniels on Religion and Trust
Tags: bonding trust, Bowling Alone, bridging trust, Catholics, Does, evangelicals, free trade, fundamentalists, immigration, liberal Protestants, Pentecostals, Robert Putnam, social capital, social trust
Prof. Joseph Daniels of Marquette University discusses why the two different kinds of social trust — "bridging" and "bonding" — are important for society and how religion matters in generating and maintaining this trust. It is noted that religious attendance significantly enhances social trust, although there are some denominational effects that temper this increase. We also discuss how different denominations view free trade and immigration.
Roger Finke on Religious Persecution
Tags: Abdul Rahman, Aum Shinrikyo, Baha'i faith, Catholics, China, clash of civilizations, Falun Gong, France, Iran, Japan, Jehovah's Witnesses, Nigeria, Pentecostals, religious freedom, religious liberty, religious persecution, religious pluralism, Russia, Salvation Army, Samuel Huntington, Shari'a Law, Smith v Oregon, United States
Roger Finke of Penn State University talks with Tony about the prevalence and reasons for religious persecution around the globe. We explore the connectcions between seemingly small violations of religious liberty and religious persecution. Prof. Finke further argues that even small violations of religious liberty can presage greater threats to a wider set of civil liberties. Our discussion covers all regions of the globe, with a focus on Japan, Nigeria, Iran, Russia, France and the United States.
Listerners are encouraged to email the host and let him know you are listening and to provide feedback (good or bad). The host's email is: tgill (at) uw (dot) edu
Gordon Melton on Mega-Trends in American Religion
Tags: Baptists, community churches, conservative churches, denominationalism, immigration, liberal churches, megachurches, Methodists, non-affiliation, Pentecostals, Protestantism, race, religious liberty, televangelism
J. Gordon Melton, director of the Institute for the Study of American Religion, discusses trends in American religion over the past two centuries with a focus on the future of denominationalism. Other topics discussed include the non-affiliated, new religious groups, and race in American religion. (To download, right click on the button to the right and choose "save target as….")


Small CUs in sheer numbers are big business.
Landmark's motto, "You're worth more here," seems especially appropriate for the times.
Rudy Hanley's formative years appear similar to those of many young Americans. But that's just part of the story.
Maurice Smith, president/CEO of Local Government Federal Credit Union, Raleigh, N.C., has been voted Credit Union Magazine's CU Hero of the Year.


text:
Home US & World News Bloomberg Brainstorm: Shut Down Park Avenue
Bloomberg Brainstorm: Shut Down Park Avenue
Today's NY Sun reports that Mayor Bloomberg is expected to announce his next brain storm for NYC at an event on Monday afternoon.
The Sun says that Bloomberg will propose closing a five-mile stretch of road to automobiles – running from Lower Manhattan to Central Park. The closure will last three days in August, as part of a city Department of transportation program that, if successful, could lead to regular street closings.
The proposal is intended to provide New Yorkers and visitors with a safe place to jog, stroll, and ride without the congestion normally associated with the city's streets. The car-free zone will run from the start of Centre Street in Lower Manhattan to 72nd Street on the Upper East Side by way of Lafayette Street, Fourth Avenue, and Park Avenue, and it will be closed between 7 a.m. and 1 p.m. on three consecutive Saturdays: August 9, August 16, and August 23.
But while the plan is intended to accommodate residents, some fear that, even on a weekend, the toll on businesses will be higher than the value gained.
A source familiar with the project said the concept is loosely based on a common practice in some European cities, where main thoroughfares are closed periodically for pedestrian and bicycle access.
Certain interactive activities, including yoga, could be permitted in the public space in New York, the source said, but planners want to avoid a "funnel cake" carnival atmosphere that is common in many of the city's street fairs. Vendors must be licensed and would be restricted to selling on the sidewalks along the route.
Orthodox Jews do not drive on Saturdays, so they would be unaffected. And many Manhattanites with country homes leave on Friday afternoons and do not return until Sunday night or Monday morning, so they may not even notice the Saturday street closures.
While at first there was some concern that the police department would not approve the event, Commissioner Raymond Kelly is said to approve of the proposal, according to a source familiar with the plan. Closing the 5-mile stretch of roads requires a lot of manpower to cordon off hundreds of side streets and direct traffic on crosstown thoroughfares.
(Source: NY Sun)
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JOLI June 16, 2008 9:54 am at 9:54 am
I have a better idea. Close down all the roads highways etc we will be solving all the worlds problems. No pollution, global warming, low oil etc……..
Y.W. Editor June 16, 2008 9:56 am at 9:56 am
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What is wch oasis columbia mo?
The credit card charge WCH OASIS COLUMBIA MO was first recorded on March 14, 2014. It has not been reported by any users.
This is from MU Women's and Children's Hospital - Oasis Cafe.


text:
Books.ch
Buch.ch
Otaku: Japan's Database Animals
Hiroki Azuma
University of Minnesota Press, 2009 - 144 Seiten
In Japan, obsessive adult fans and collectors of manga and anime are known as otaku. When the underground otaku subculture first emerged in the 1970s, participants were looked down on by mainstream Japanese society as strange, antisocial loners. Today otaku have had a huge impact on popular culture not only in Japan but also throughout Asia, Europe, and the United States. Hiroki Azuma's Otaku offers a critical, philosophical, and historical inquiry into thecharacteristics and consequences of this consumer subculture.
Eingeschränkte Leseprobe - 2009
Hiroki Azuma is codirector of the Academy of Humanities in the Center for the Study of World Civilizations at the Tokyo Institute of Technology. A leading cultural critic in Japan, he is the author of seven books, including Ontological, Postal, which won the 2000 Suntory Literary Prize.
Titel Otaku: Japan's Database Animals
Autor Hiroki Azuma
Übersetzt von Jonathan E. Abel, Shion Kono
Verlag University of Minnesota Press, 2009


Newcomer Family Obituaries - Lana Wyatt 1950 - 2019 - Newcomer Cremations, Funerals & Receptions.
Lana Wyatt, 68, of Dayton, passed away on Jan. 19, 2019 peacefully at home.
She was born on May 8, 1950 to the late George and Maja (Krupgewert) Griffith in Superior, WI.
In 2000, she married James Wyatt where they made Dayton their home.
She was a long time member of Parkview United Methodist Church in Miamisburg.
Lana is survived by her loving Husband of 18 years, James; siblings, George, Thomas, Robert, Marta Albitar Naji, and Sandy; and many other loving family and friends.
Visitation is Sat., Jan. 26, 2019, 10:00 am at Parkview United Methodist Church in Miamisburg. A Memorial Service will follow at 11:00 am.
To share a memory of Lana with her family, please click the Share Memories button above.
Add your memories to the guest book of Lana Wyatt.
Lana was a true blessing and friend to everyone. The earth lost a precious soul, but heaven gained an angel.


Toxins, Pollution, and Water Quality including information on using caged mussels to test for toxins such as PCBs and dioxin in the Bay & tributaries, sources of Bay pollution, water quality testing in the Bay, & other topics.
Mind Disrupted Biomonitoring Report From Alaska Community Action on Toxics, Commonweal & Learning Developmental Disabilities Initiative.
A new report by ACAT, Commonweal, and the Learning and Developmental Disabilities Initiative details the first-ever biomonitoring project identifying toxic chemical pollution in people from the learning and developmental disability community. Mind, Disrupted examines 61 toxic chemicals present in the bodies of study participants in the context of rising rates of autism, attention-deficit hyperactivity disorder, and other learning and developmental disabilities.
Maine's Surface Water Ambient Toxics (SWAT) monitoring program was established in 1993 (38 MRSA §420-B) to determine the nature, scope and severity of toxic contamination in the surface waters and fisheries of the State.
Appendix C:Standard Operating Procedures (SOPs).
Appendix A: Data Quality Objectives (VRMP QAPP-Table 3a).
Appendix B: Frequency of Precision Measurements (VRMP QAPP-Table 3c).
Appendix D (coversheet): Field data sheets and IDEXX bacteria lab sheets.
Appendix E: Sample Holding Times and Preservation (VRMP QAPP-Table 3d).
Appendix H: Sampling Position Requirements (VRMP QAPP-Table 4a).
Appendix I: Maintenance, Testing and Inspection Procedures (VRMP QAPP-Table 5a).
Appendix J: Data Management Overview (VRMP QAPP-Section 5.10).
Appendix K: Criteria used to Review/Validate Data (VRMP QAPP-Table 6).
Appendix L: IDEXX Lab QA-QC Steps (from VRMP QAPP Appendix 11).


Havel's blades. After dozens of quilt projects, once you have finally dulled the blade of your Havel 60mm Rotary Cutter, you will need a replacement. Just unscrew the back of the device and slide the dull blade off. Replace it with a 60mm replacement blade and screw it into place. Then get back to what matters: precision cutting for beautiful quilts. One blade per pack.


Need help creating a massage business plan for your chair massage business?
With many massage schools, you finish the program and then wonder how to start your massage business. You find yourself stuck without a massage business plan to get your massage business up and going.
At Relax to the Max we understand how important it is to have a plan for your chair massage business before you finish your chair massage training. You want to be able to hit the ground running, so to speak, and get your chair massage business started and making you money right away. So we've arranged to provide you, at no cost, a massage business plan in the form of the Marketing Chair Massage 101 e-course.
This comprehensive course is delivered daily to your inbox for about five months and will provide you with a business plan massage-specific for your chair massage practice. There's no need to create a massage business plan from scratch. The work has already been done for you.
The course leads you step-by-step through the process of starting and building your chair massage practice. Just take a look at the table of contents and you'll see that it really is like a massage business plan for your massage business.
And we don't make you wait until you've finished our chair massage training before giving you this vital information. As soon as you register, we'll send you a special link so you can get signed up for free and get started planning your business and your future right away. Even if you decide to drop out of the program or take advantage of our money back guarantee, the e-course is yours to keep.
This Marketing Chair Massage 101 e-course is worth about US$100 at www.bodyworkbiz.com, but is provided to all Relax to the Max students free of charge. It's just one of the many ways that Relax to the Max helps graduates plan their massage business and build a career that is truly soul-satisfying.
Be sure to check out the links on the left hand side of the page to find out about other ways that you can benefit from chair massage training at Relax to the Max.


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Ammon Bundy to appeal to another judge to be released pending trial, court records show
Updated Jan 09, 2019; Posted Feb 01, 2016
Detention hearing for Ammon Bundy and other Oregon standoff leaders
Gallery: Detention hearing for Ammon Bundy and other Oregon standoff leaders
By Maxine Bernstein | The Oregonian/OregonLive
Lawyers for Ammon Bundy this week will challenge U.S. Magistrate Judge Stacie F. Beckerman's order to keep Bundy in custody pending trial.
Beckerman on Friday denied release for Bundy, citing his repeated disregard of federal orders to leave the Malheur National Wildlife Refuge, where he's accused of leading a month-long armed takeover of the federal property that began Jan. 2.
The judge also determined Bundy, the leader of the armed occupation, would be a danger to the community, noting his and other siege leaders' threatening statements on social media, obvious firepower and the loss of one man's life, referring to the shooting death by state police of occupier Robert "LaVoy'' Finicum last Tuesday.
In a court filing Sunday, Bundy's lawyers argue that Bundy can be released, with GPS monitoring and orders that he not return to Oregon from his home in Idaho, except for his court appearances.
Ammon Bundy and his family moved to Idaho seven months before the refuge takeover occurred so his kids could have a better life, his lawyer Lissa Casey told the court on Friday. His wife's parents live in Idaho, and Ammon Bundy had been and could continue to run his Arizona fleet repair business "remotely'' from Idaho, using his computer and phone, Casey said.
"He has no desire to go anywhere but home to provide for his family,'' Casey told the court. "He's done in Harney County.''
Casey and co-counsel Mike Arnold said the government failed to prove with clear and convincing evidence that no conditions of his release will assure the safety of the community.
They will ask U.S. District Court Chief Judge Michael W. Mosman on Tuesday to revoke Beckerman's order.
Mosman will hear their appeal because he's the duty district judge assigned this month to consider such reviews.
Bundy, 40, and 10 others face a felony conspiracy charge, accused of using intimidation, threats and force to impede federal officers from doing their jobs at the federal wildlife sanctuary in Harney County. FBI agents and state police arrested Ammon Bundy last Tuesday as he and other occupation leaders were driving along U.S. 395 to a community meeting in John Day. Occupation spokesman Robert "LaVoy" Finicum, 55, was shot and killed by state police after he attempted to elude the felony police stop.
Bundy's request for a review of Beckerman's findings is expected to be heard by Mosman at 10 a.m. Tuesday.
At 10:30 a.m., federal prosecutors plan to challenge Beckerman's release order for another defendant, Joseph O'Shaunghessy.
O'Shaughnessy's lawyer Amy Baggio Friday successfully argued that her client wasn't among the key players in the alleged conspiracy and did not spend one night at the refuge, providing receipts from the Silver Spur Motel where she said O'Shaughnessy stayed the first week in January. She also argued that O'Shaughnessy only went to the refuge to try to "bear witness' to any federal law enforcement actions taken against the occupiers.
Co-defendant Pete Santilli, who remains in custody, also is scheduled to go before Judge Mosman Tuesday at 10:30 a.m., according to the court's docket.
It's possible other co-defendants may appeal Beckerman's detention orders as well.
-- Maxine Bernstein
mbernstein@oregonian.com
@maxoregonian


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Kohelet Channel
UNIFIL – A Last Chance to Reform Ineffective UN Missions While Protecting Israel
17 Av 5780 | 7 August 2020
UNIFIL-Kohelet-Download and view as PDF
Overview: From the start of the Trump Administration, the U.S. has sought to reform the bloated United Nations. Peace-keeping missions were to be a central part of this reform, as they are the most expensive aspect of the UN's operations, but commonly fail to deliver tangible results while being plagued with scandal, corruption, and criminality.
To date, the U.S. has not succeeded in reigning in any peacekeeping missions. Aug. 31st offers a final opportunity to do so, while strengthening Israel's security at a time when it faces imminent threats on the northern border from the Iranian-backed Hezbollah.
UNIFIL, the temporary U.N. presence in Lebanon, is not fulfilling its mandate to disarm Hezbollah. Instead, it serves as Hezbollah's de facto human shield, limiting the IDF's freedom to maneuver in a potential conflict. The organization is expensive and bloated compared to other peacekeeping missions around the world, has had significant mission creep, and like other U.N. entities, it is biased against Israel. This month, there will be a golden opportunity to fix UNIFIL's structural problems, from an Israeli standpoint. This special opportunity might not return for a long time.
For the sake of Israeli and American strategic interests, it would be best if the United States demanded that the Security Council let UNIFIL's mandate expire, without a further extension, or alternatively scale it back significantly.
Background: UNIFIL, the temporary U.N. force in Lebanon, was established in 1978 after Operation Litani, under U.N. Security Councils Res. 425 and 426. Its mandate was limited as confirming the withdrawal of Israeli forces from southern Lebanon, restoring international peace and security, and assisting the Government of Lebanon in ensuring the return of its effective authority in the area. Following the Second Lebanon War in 2006, UNIFIL's mandate was expanded to include the following objectives: coordinating its activities with Israeli and Lebanese authorities; extending humanitarian and civilian assistance in Lebanon; and monitoring the cessation of hostilities along the Blue Line. As with other U.N. peacekeeping missions, UNIFIL's mandate must be affirmatively renewed on a yearly basis by the U.N. Security Council; the current mandate is valid till the end of August.
Size and budget by international metrics: UNIFIL's annual budget currently stands at $512 million. For comparison's sake, the total budget for global peacekeeping missions stands at $6.5 billion, meaning that UNIFIL's budget amounts for 7.8% of the total global peacekeeping budget. The force initially included some 2,000 personnel but expanded dramatically after the Second Lebanon War to 10,900 today (with plans for up to 15,000), recruited from 45 countries around the world. That is, UNIFIL's manpower has grown by 545% and its capacity has grown by 750%. Compared to other peacekeeping missions, UNIFIL's budget and manpower allocation are exceptionally large. The peacekeeping force in Darfur—the scene of a genocide, with ongoing violence that continues to claim lives—has a budget of $260 million and just 6,511 personnel. The peacekeeping force on the Golan Heights includes 1,007 personnel; the force in Abyei in Sudan has 4,044 personnel and a budget of $257 million. The most dangerous peacekeeping operation in the world, in Mali, has a deployment of some 15,200 personnel with a budget of $1.2 billion.
The United States contributes 27.89% of the total U.N. peacekeeping budget (roughly $1.81 billion). UNIFIL's share of the U.S. contribution is therefore equivalent to $142.7 million.
Problems for Israel in UNIFIL's operations: Over the years, UNIFIL has proven itself to lack the motivation and ability to prevent violations of U.N. Security Council resolutions concerning Hezbollah and the Lebanese Armed Forces (LAF). For example:
Over the past decade, Hezbollah has dug a series of attack tunnels into Israel territory right under UNIFIL peacekeepers' noses, with the intention of sending thousands of Hezbollah militants to seize control of Israeli villages adjacent to the fence and to perpetrate spectacular atrocities (Israel destroyed these tunnels in Operation Northern Shield in 2018-2019).
When Israeli soldiers were kidnapped from Mount Dov in 2000, UNIFIL soldiers observed and recorded the event without intervening or alerting Israel.
In an incident near Misgav Am in 2010, when Lebanese soldiers shot at IDF troops without provocation and killed Lt. Col. Dov Harari, the UNIFIL force was unable to prevent the clash or retaliate against the LAF.
In late 2018, during work to demarcate the Blue Line, LAF forces violently blocked UNIFIL peacekeepers for an hour and a half, without provoking a response.
In June 2020, Lebanese soldiers were seen aiming an RPG launcher at IDF tanks during routine activity, as UNIFIL troops stood by helplessly between the forces.
UNIFIL can be dismantled or reformed: As its name suggests, UNIFIL was always intended to be temporary, but like many U.N. institutions, it has enjoyed a bureaucratic persistence not justified in any way by its effectiveness, mission success, or efficiency.
If UNIFIL's mandate is not extended at the end of the month by the Security Council, its mission will end immediately. However, unlike most U.N. agencies, UNIFIL could also be reorganized. The mandate renewal – which cannot happen over a U.S. veto – gives the United States leverage considerable leverage to push for sustainable reforms of the organization. This would be consistent with the Trump administration's ambitions to shrink and streamline bloated and ineffective peacekeeping missions.
Neither the U.S. nor Israel has yet take advantage of the potential of dismantling or scaling back UNIFIL's presence. Israel has misguidedly has urged the United Nations to beef UNIFIL's authority and manpower in order to make it more effective—not understanding that the organization has neither the motivation nor the ability to clash with Hezbollah forces. Such reforms are doomed to failure and are impossible to implement and enforce in the long run. The only reform (short of not reauthorizing the mission) that is self-enforcing and can withstand a potential loss of critical scrutiny of UNIFIL by future U.S administrations is a simple reduction of UNIFIL personnel. This will restore the organization to its historic levels, save U.S. taxpayer dollars, while boosting the IDF's freedom of maneuver, defensive capabilities, and reconnaissance abilities in southern Lebanon.
Prof. Eugene Kontorovich
Reducing UNIFIL could be a significant step in fixing the UN
UNIFIL
A new book by Prof. Moshe Koppel explores the central differences between traditional societies – including traditional Judaism – and contemporary cosmopolitan ones.
korenpub.com/products/judaism-straight-up
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Facilities plan for closure, and sometimes, post-closure. The funding mechanism for these plans is termed Financial Assurance Instrument (FAI). An FAI resembles an insurance policy, which is available to allow the state to take over closure or post-closure maintenance and monitoring functions should an owner or operator be unable or unwilling to fulfill these duties. FAIs are a constant reminder that the last day of business is not the last day of environmental responsibility.
This IPD may be used through Dec. 21, 2018, by permitted facilities when calculating the annual inflationary update to their financial assurance instruments.
These numbers can be divided (current year/previous year) for yearly updates or (current year/2004) for cost estimate updates.
The source of the IPD is the U.S. Department of Commerce, Bureau of Economic Analysis' Table 1.1.9. IPD for Gross Domestic Product was last revised on Nov. 28, 2018.The U.S. Department of Commerce will next update the IPD on Dec. 21, 2018. This webpage will be updated following release.
ADS Maple Hill Landfill, Inc.
MS Inc formerly Modern Sanitation Inc.
T & C Disposal, Inc.


Just got back from a 2 week trip to New Zealand - it's been my #1 "bucket list" place for a long time. I was especially excited to see trees that are San Francisco street trees (New Zealand Christmas trees, giant dracaena, tea trees, etc.) in their native habitat.
One thing I noticed was LOTS of Monterey cypress (Cupressus macrocarpa) and Monterey pine (Pinus radiata, which the New Zealanders call "Radiata pine") in the countryside, used as windbreaks, shade for sheep and other livestock, accent trees, etc. Which made big parts of the countryside look a lot like California! There were also many stands of Monterey pine used used as lumber trees - without any evidence of pine canker that i could see.
Northern hemisphere conifers (Douglas fir is a prominent example) have become naturalized in big parts of New Zealand, and have become invasive pests, taking over entire landscapes. Interestingly, our Monterey pine and Monterey cypress are not invasive, because the cones of the tree typically only open and disburse their seeds where there is fire or extremely hot weather.
I spent three days hiking through native beech forest on the Routeburn Track on the South Island. It was very cool to see forests composed almost entirely of different species of Nothofagus (a cousin of our northern hemisphere beeches) because they were so new to me (the only Nothofagus I can remember seeing here in CA was a giant specimen at Filoli, south of San Francisco). One cool tree I encountered along the way: the tree fuchsia - Fuchsia excorticata, the world's largest fuchsia, with distinctive papery bark (and recognizable fuchsia flowers).
Of course, I made a point to find New Zealand Christmas trees (Metrosideros excelsa) on the North Island, although sadly by the time we got there on January 2, they were almost all out of bloom (these native trees seemed to be strict about blooming at Christmas time). They're called by the Mauri name "Pohutukawa" in New Zealand, and the New Zealanders were very surprised to find that they were popular street trees in San Francisco.
Sadly we didn't get to see any Nikau palms (New Zealand's only native palm, and one of my favorites of the palms) in their glory - saw a few of them planted as street trees (!) in Whangarei in the north island, and every once in a while saw one in the kauri forest on the west side of the north island. I was surprised to find that the best places to see them in New Zealand were on the west side of the cooler south island.
It was a great trip - New Zealand is a great place to visit for many reasons, and interesting trees is definitely one of them!
A Ceiba speciosa 'Majestic beauty' (floss silk tree) in bloom at the edge of the new park (used to be a parking lot) at Shotwell/17th/Folsom in the Mission. The tree and others nearby were planted in 1997. The species normally doesn't do very well in San Francisco - it is much happier (and more common) in Southern California.
Great SF Magazine article by Lynn Rapoport, a tree wonk who's also a great freelance journalist. She does a great job explaining why it's fun and satisfying to learn about our urban forest!
Ceanothus seems to be in bloom all over the city as I write (early April 2017). There are 50 or so speciesof Ceanothus, but very few that can be trained as a tree. Ceanothus 'Ray Hartman" is one - it's a hybrid (cross) between two parent species: Ceanothus arboreus from Catalina Island in southern California, and the northern California Ceanothus griseus. It's the only Ceanothus planted as a street tree in San Francisco, and one of the very few California natives that you'll see planted in sidewalk cuts on the street (along with Catalina ironwood).
These trees in Cole Valley at the corner of Waller and Cole are some of the best in San Francisco.
(And I wish I knew who this "Ray Hartman" was/is - doesn't seem to be any info on the web about him. Let me know if you know!
Just got back from a week in the Azores - Sao Miguel and Terceira islands. The Azores are Portuguese islands in the middle of the Atlantic Ocean - 800 miles west of Portugal, and about 2000 miles east of Boston - volcanic islands, with a mild, San Francisco-like climate (coastal, rarely above 80 degrees fahrenheit, and rarely below 45 degrees).
It was interesting to see so many introduced trees in the Azores that are popular as ornamentals here in San Francisco. Metrosideros excelsa (New Zealand Christmas tree) is often used as an ornamental, but also naturalized in the forests of hte islands (which I have never seen here in California). The New Zealand Christmas tree in the photo above was a huge specimen in Ponta Delgada, the capital city of the Azores - so big that it had supports to hold up its limbs - if you look carefully you'll see the many vertical steel supports. Araucarias are everywhere as specimen trees -- especially Norfolk Island Pine trees. (The Norfolk Island Pine in the photo below was a young specimen just outside our hotel window in Angra de Heroismo, the largest city on Terceira Island- the hotel was in an early 1600s stone fort built by the Spanish during a 40 year period when they controlled the islands). And Pittosporum undulatum (Victorian box) is everywhere as a naturalized tree - to the point where there were forests of the tree - it has become an ecological problem on the islands.
There are trees that are native to the Azores - in fact endemic to them (found in nature only there). It was interesting to see native species that were closely related to trees I recognized, but which had developed into separate species as a result of the physical isolation of the islands. Laurus azorica, for example, was obviously a close relative of the Grecian bay (Laurus nobilis) that is found on our streets.
And London planes (Platanus X acerifolia) lining the roads everywhere. The trees below were in a back road on Terceira island.