text:
Calendar of State Papers, Spain
Calendar of State Papers, Spain, Volume 10, 1550-1552
Index: H, I
Calendar of State Papers, Spain, Volume 10, 1550-1552. Originally published by His Majesty's Stationery Office, London, 1914.
This free content was digitised by double rekeying and sponsored by the Arts and Humanities Research Council. All rights reserved.
H I
Hainault, 31, 32, 49, 293, 449, 557.
Haller, Christopher, letter from, to St. Mauris, 193.
Hamburg, Roland van, 305306.
Hamburg, 215, 229, 345, 370, 381, 425, 468, 493.
Hamilton, James. See Arran, Earl of.
-, John. See St. Andrews, Archbishop of.
Hamilton Castle, 507.
Hampton Court, 332, 342, 546, 548.
Hanseatic Towns, the, 2, 215, 377, 425, 468, 494, 526, 528, 552, 591, 602.
Harris, Richard, an English merchant, 290,
Harwich, letter dated from, 122.
-, 113, 114, 119, 120, 121, 122, 124, 125, 127, 136, 141, 142, 149.
Hastings, Francis, second Earl of Huntingdon, 553.
Hausschein (colampadius), 152 note.
Haverton, John, Scottish sea-capttain, 114.
Le Havre, 177, 217, 264, 308, 345, 494, 516, 522.
Hebrides, the, 147.
Henry VI. King of England, 163.
Henry VII, King of England, 319, 323.
Henry VIII, King of England, 46, 52, 57, 58, 59, 81, 85, 118 note, 176, 205, 207 note, 230, 240, 259, 312, 383, 437, 582 and note.
Henry II, King of France, his relations with the Emperor. See the Emperor.
-, -, his relations with England. See England.
-, -, his policy in Germany, 2, 2427, 37, 50, 51, 215, 219220, 244, 273, 293, 301, 307, 334, 356, 369, 377, 378, 381, 382, 392, 400, 475, 493 and note, 494 note, 537, 538542, 544, 602.
-, -, encourages rebellion in Ireland, 176, 197, 227, 244, 273, 286, 328, 445, 587 note.
-, -, his policy in Italy, 13, 11, 14, 15, 2125, 29, 33, 51, 60, 75, 77, 89, 93, 197, 264, 275277, 281, 283, 289290, 294295, 301, 309, 318, 325, 333334, 343345, 369, 408, 427. 455, 457463, 475, 518520, 530, 543545, 583585, 616.
-, -, his relations with the Turk, 5, 46, 77, 93, 244, 264, 301, 309, 466, 475, 543, 544, 605.
-, -, further mentioned, 36, 37, 50, 64, 77, 87, 88, 89, 92, 144, 145, 167, 181182, 217, 249, 250251, 292, 327, 346 note. 370, 426, 449, 454, 467, 469, 471, 493, 507, 508, 548, 557, 564 note, 585588 note, 590593, 596600, 605, 608609, 615, 616.
Henry, Jehan Duboys' courier, 124, 125, 130, 134, 135.
Herbert, Sir William, Earl of Pembroke (in 1551), 18, 19, 39, 216, 347. 381, 386, 392, 425, 493, 514, 526, 548, 549, 553, 562, 565566, 579, 592.
Herbertstein, Count, 467.
Hercules Gallicus, 182.
Hertford, Earl of. See Seymour, Edward.
Hesdin, 92, 593, 605.
Hesse, Philip, Landgrave of, 377, 568.
-, William of, eldest son of Landgrave Philip, 378.
Hildesheim, 402.
Hoby, Sir Philip, English ambassador to the Emperor (1550), 11, 17, 57, 58, 105, 153, 176, 188192, 238.
His recall, 167, 171, 173174, 187.
His mission to France (May-July, 1551), 292, 299, 328330, 346 note.
-, -, his mission to Brussels (Feb., 1552), 451 and note, 455, 464, 473475, 476482, 493, 504, 514, 517, 531534.
-, -, further mentioned, 234, 350, 363, 393, 526527, 553, 557560, 576.
Holbein, 156 note.
Holland, 146, 147, 217, 265, 281, 331, 375, 409, 495, 509, 551, 555.
Holstein, Adolphus, Duke of, 118, 137, 379, 402, 499.
-, 293.
Holy Isle, 78.
Hooper, John, Bishop of Gloucester and Worcester, 140, 254, 261, 591, 593.
Horoscopes and fortune-telling, 121, 130, 594.
Horn, Count of, in England, 594.
Hourdel, banks of, 24.
Household, Great Master of the. See Paulet, William, Lord St. John.
Howard, Thomas, third Duke of Norfolk, 14, 370, 454.
-, Lord Thomas, 386.
-, Lord William, 582.
Hull, 263.
Humbercourt, M. de, in England, 594.
Hume Castle, 339.
Hunaudaye, M. de la, son of Admiral d'Annebault, 53, 62 note.
Hungary, Maria, Queen Dowager of, Regent of the Low Countries, letter from, to the Officers of the Flemish Admiralty, 581.
-, -, -, to the Margrave of Antwerp, 335.
-, -, -, to the master of the Customs of Antwerp, 550.
-, -, -, to the Echevins of Antwerp, 472.
-, -, -, to the Bishop of Arras, 183, 376.
-, -, -, to the Customs Officers of Brabant, Zeeland and Dunkirk, 513.
-, -, -, to M. de la Capelle, 508, 525.
-, -, -, to the Duke of Chastelherault, 595.
-, -, -, to M. de Courrires, 472, 511.
-, -, -, to Thomas Dansell, 666.
-, -, -, to Edward VI, 464, 497, 538.
-, -, -, to d'Eecke, 107, 352, 525.
-, -, -, to the Emperor, 157, 295, 387, 469, 496, 511, 535, 537, 563, 573, 574, 585, 589, 596, 605, 616.
-, -, -, to the Emperor's Council of State, 197.
-, -, -, to the captain of L'Escluse, 450.
-, -, -, to Prince Philip, 449.
-, -, -, to Simon Renard, 31, 48, 72, 241.
-, -, -, to Count de Rulx, 308.
-, -, -, to Jehan Scheyfve, 106, 110, 122, 148, 153, 195, 343, 356, 371, 383, 398, 416, 464, 475, 511, 539, 540.
-, -, -, to the Queen Dowager of Scotland, 608.
-, -, -, to Count Van Buren, 193, 194, 352, 496, 525.
-, -, -, to M. de Vaudeville, 446, 498.
-, -, -, to the Master of the Customs in Zeeland, 450, 513.
-, -, safe-conduct issued by, for the Queen Dowager of Scotland, 148.
-, -, letters to, from the Bishop of Arras, 156, 283, 467.
-, -, -, from M. de Courrires, 504, 514, 526, 629.
-, -, -, from Jehan Duboys, 220, 345.
-, -, -, from Edward VI, 472.
-, -, -, from d' Eecke, 121, 123, 135, 146, 308, 331, 356, 364, 494, 551, 560, 589, 594.
-, -, -, from the Emperor, 105, 111, 117, 137, 146, 370, 447, 455, 498.
-, -, -, from the Emperor's Council of State, 173, 175, 271.
-, -, -, from Hendrik Jacobsen, 78.
-, -, -, from the Lady Mary, 224.
-, -, -, from Guillaume de Poitiers, 382, 398, 450, 470, 471.
-, -, -, from Simon Renard, 331.
-, -, -, from Count de Rulx, 4, 16, 94, 105, 391.
-, -, -, from St. Mauris, 137.
-, -, -, from Jehan Scheyfve, 91, 100, 110, 111, 118, 140, 161, 172, 183, 184, 185, 204, 230, 318, 325, 346, 371, 375, 395, 403, 409, 410, 438, 445, 451, 466, 483, 485, 504, 614, 526, 529, 546, 552, 557, 561, 564, 566, 576, 581, 589, 604, 610, 618.
-, -, -, from Matthew Strick, 507.
-, -, -, from Count Van Buren, 194.
-, -, -, from M. de Vandeville, 454.
-, -, 39, 48, 130, 131, 132135, 167, 170, 192, 198, 204, 252. 256, 273, 276 note, 290, 360, 499, 549, 550, 551, 564557.
Hungary, 63, 395, 498.
Huntingdon, Earl of. See Hastings, Francis.
Huntley, Earl of (Gordon), 168, 586 note.
Iceland, 187 note.
Imola, Bishop of. See Dandino.
Indies, the, 27, 115, 217, 296, 352, 367, 449, 497, 551.
Inglefield, Francis, of the Lady Mary's household, 356 note, 364.
Innsbruck, letters dated from, 415, 435, 448, 457, 464, 467, 491, 499, 521, 585.
-, 387, 436, 455, 470, 492, 530, 534.
Inquisition, the (in the Low Countries), 138, 139, 153, 167, 170, 171.
-, in Italy, 286, 607608.
Insurance, marine, reports on, 352355, 364368.
Interim, the, 37, 215, 329, 425.
Ipswich, 114, 122, 136, 141, 146.
Ireland, 44, 87, 97, 108, 110, 113, 115, 119, 166, 169, 176, 186, 187, 191, 197, 216, 223, 227, 244, 263, 286, 291, 293, 301, 323, 328, 445, 468, 490492, 512, 513, 515, 534, 535, 560, 562, 582 and note, 587588 note, 591, 598.
Irish pirates, 146, 147.
Isabella, the Empress, 11 note.
Italy, 13, 11, 14, 15, 2125, 29, 3336, 38, 5154, 60, 7377, 89, 93, 197, 264, 273278, 280, 283, 286, 288290, 294295, 296298, 301, 325, 327, 333334, 336, 343345, 375, 376, 378, 400, 447449, 451, 455464, 475, 498, 503, 518521, 527, 530, 542546, 583585, 600, 607608, 616.


top of the list for favorite things.
its everything i've ever wanted for christmas.
so it was such a sweet surprise.
like yelling chaos, but that just adds to the charm.
i'm already so excited for next year's performance.
just for the christmas program.
it really doesn't get any better.
she wouldn't be outshone by her sister.
how freaking adorable is this???
mimi introduced her to hand lotion.


Didn't we have this discussion before? didn't we agree you shouldn't touch any thing that deals with DC power? Me and Nigel can come up and take a look for you and fix your truck.
When are you going to be out of town again?


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Q: Audio - format and bitrate effect on quality I have been interested in audio and improving its quality for a while now and after researching for a while I found out how difficult it can get when you find the answer to a question and then find a contradictory statement to that and it just adds up to more questions.(my main source for testing atm is YouTube, I randomly picked a NCS song and tried working with it)
I am fairly new so these questions may seem easy but I am finding it very difficult to understand

*

*Is it true that you should download original audio from a source because converting it to other formats hurts quality?
the downloader I use ripped the audio to a .webm format at 128kbps

*If I convert this file to a wav (lossless) or mp3 (lossy) or any other format will the overall quality go down even if I increase the bitrate to  512 incase of wav  and 320 in case of mp3?

*does increasing projection rate have any effect on the audio itself usually i see its 44.1K or 48K, will going beyond that help of will it just diminish the existing quality after editing in case of the mp3. but incase of wav will it help because by my understanding wav is lossless so it wont effect the existing quality but will it improve ?

*I also saw 16 24 and 32 bit in wav and flac what do these represent and which one would be better

*what would you suggest would be the best way to extract audio without losses or at least minimizing them from such sites and once done is editing the projection rate or bitrate (I use audacity) preferred
or should i just search for a file which has a better bitrate to begin with

*which audio format in-between flac and mp3 would be better considering that I want to save space, keep the files compatible with most systems and not going down on quality a lot.
I was thinking Flac or m4a but advice would be appreciated

A: There are too many questions here to be able to answer fully in just one page.
One suggestion I might make is not to trust YouTube for any information reference. There is no bar to entry & anybody with a webcam can spout as much misinformation as they care to.
Briefly, once a file has been downsampled, data has been thrown away. No amount of upsampling will ever get that back.
So, again very briefly…

*

*Yes, highest rate available, even if that is just the official aac/mp3 from iTunes or any official source.
No unofficial source can be trusted to have not already done what you propose, upsample from a lower quality. (There is almost no way to accurately discern this after the fact, whatever YouTube might try to tell you)

*Nope. No amount of upsampling will ever recover the data already lost.

*None whatsoever. See 2.
In professional use, "music" uses 44.1, "video" uses 48. Youtubers might use anything, who knows what or why :P

*Flac is lossless compression, maintaining an exact copy of the original WAV in a smaller form.
The only place to get FLAC is from the record company or trusted distributor. Pretty much anything else has suffered upsampling from people with no clue.

*Get it from the original source. It's the only thing you can trust. An AAC file from Apple, for instance, has been through one downsample from the original master file, which would have been at 24bit 44.1kHz WAV. This is the modern standard for master delivery to distributors.
Though not absolutely perfect, this is the best you can generally access as a consumer.

*Depending on your source, MP3 @320k or AAC @256k (AAC gives better quality at lower data sizes).
FLAC only if it comes from a recognised distributor.
ALAC, again if you can get it direct. This is going to be rare & as likely from unrecognised sources to have been upsampled from an inferior format.
In short… if it didn't come from a recognised distributor, you have no quality control. if you did, that's the best quality available at consumer level.
One other thing (amongst many)
Ripping from a CD to any format is already downsampled. Masters these days are produced at 24 bit, CD is 16 bit, you you already lost a tiny fraction of the full quality by buying the CD.
I have never tested whether a high bitrate AAC from 24 bit is "better" than a CD at 16 bit WAV. (Life is too short ;)
One last note: "increase the bitrate to 512 incase of wav and 320 incase of mp3" This is more YouTube misinformation. WAV does not have a bitrate like mp3. Bitrate only ever applies to compressed formats.
Late edit
One other thing to consider is that if you only ever listen off your phone, with earbuds, or in the car, from laptop speakers, or some cheap 70 buck 2.1 or 5.1 desktop computer speakers, then it's not going to make the slightest bit of difference to you.
A lot of the fine detail in audio can only be heard if you have the right equipment to play it back from.
For my iPhone I deliberately reduce all audio to 128kpbs AAC, as that's as good as you ever need if you're on the move.
I'm speaking as a sound engineer of over 40 years' experience, btw ;)

redpajama_set_name: RedPajamaStackExchange


Janelle Neyron is pretty humble when talking about her past sports accomplishments.
Graduating from Mennonite Brethren Collegiate in Winnipeg, Manitoba, she calmly mentions that the Hawks, in her Grade 11 year, won the Manitoba High Schools Athletic Association (MHSAA) Girl's AAAA Volleyball provincials.
In her Grade 12 year, they would spike their way to second place, falling to the Lord Selkirk Regional Comprehensive Secondary School Royals.
Also in Grade 12, she was ranked No. 9 for the best girl's high school volleyball players in the province In the Winnipeg Suns annual coaching poll.
In a single line statement, it capsuled her play, "Incredible skill … positive attitude … thrives in tough situations."
Teammate Katie Friesen was ranked No. 1. Friesen went on to play with the Florida International University Panthers.
Neyron also dribbled her way onto the Hawks basketball and soccer teams.
The 5-foot-9 all-around athlete also competed at the national level in beach volleyball.
But she forgot to mention that she threw the discus 19.93 metres, which places her in the MHSAA track and field record books.
Looking back, it was more than just the practices, games and trophies.
"The highlight is just the people you meet along the way and becoming friends," said Neyron, 22, now a member of the Medicine Hat Rattlers women's volleyball team in Alberta Colleges Athletic Conference (ACAC) action.
A team in which she led in spikes 198 and second in digs 212 while adding 13 service aces 14 blocks.
Her third year in ACAC play, this was her first year with the Rattlers, having played for the Olds College Broncos from 2015-2017.
Her stats for 2016-2017 were a team high 253 kills to go along with 22 service aces, 174 digs and 22 blocks. Her rookie year 2015-2016 saw an impressive 137 kills, 21 service aces, 176 digs and 23 blocks for the Broncos.
For the 2017-2018, she would settle for intramural volleyball while attending the University of Alberta.
Three different post-secondary institutions in three consecutive years?
"After my course at Olds (Land & Water Resources Diploma) I decided to further my education (University of Alberta) but then I felt that my volleyball career was not over, so I am here (Medicine Hat, University Studies: Education)," said the native of East St. Paul, Manitoba.
Of the unpacking-and-packing, "It was different. I got some different experiences. I went from the town of Olds, a small town, to a very large city Edmonton and now at Medicine Hat, I am somewhere in-between.
"All three have been awesome. I have met so many good people and I have a lot of good memories and made some life-long friends. I was also so grateful that my parents could help out financially and emotionally. It was an experience that I would not trade."
Part of the experience, is that next year 2019-2020, she plans to enroll at the University of Winnipeg in order to continue her education in pursuit of becoming a teacher.
"My plans are to become a teacher...hopefully in elementary or middle school. It is important to have an impact on the future of children. Every summer when I go back home, I work at a daycare. I have been there the last three years and I have had the opportunity to see them grow-up. It is enough for me to know that it is somewhere I want to be in the future. Teaching children."
Did we mention that during the summers back in sunny Manitoba she is an ultimate disc star.


Artists from a variety of disciplines will come together February 22nd to 25th, 2018 to showcase their work at the 11th instalment of the Artist Project – a contemporary art fair hosted in Toronto at the Better Living Centre. This year's event will take collectors and curators, gallerists and designers #BehindTheArt for an intimate 'shoppable' experience, connecting them with over 250 curated Canadian and International artists. In addition, visitors will enjoy interactive installations, live performances, artist competitions and engaging talks on the industry's hot topics.
The four-day show commences with a ticketed, Opening Night Party celebrating the diverse world of art, and will feature music by Matthew Romeo and Flavia Abadia. As guests enter, they will be welcomed by an illuminative installation from Nathalie Sanche. SHINE ON will feature carefully manipulated paper shapes that resemble a chrysalis or a shell or a trumpet, arranged in large, eye-catching sculptures. The reflective aluminum sculptures are pure form – light, white and ephemeral – but at the same time, possess a density and a fluidity that will catch the viewer by surprise.
Installation Zone — A main attraction for visitors, the Installation Zone highlights work from a variety of artists working in different mediums. A must-see participant this year is Take A Picture; Toronto by Max Hart Barrnwell – a 10-foot mural that will bring to life a collection of images captured by Torontonians via disposable cameras found around the city's streets as part of an interactive art experiment.
Art Chats — The Artist Project's Art Chats engages guests and offers an insider's look into the art industry through the lens of experts in the field. A curated selection of special guests will share their knowledge from a variety of sectors in the creative community, imparting fresh perspectives and invaluable advice. This popular seminar series of interactive discussions will be hosted by some of the industries brightest minds and explore today's prevalent subject matter.
Art Battle — Back by popular demand, Art Battle #638 returns to the exhibition floor on the evening of Friday February 23rd from 7:00 p.m. to 10:00 p.m. This interactive, live painting competition will showcase 14 artists selected from the fair to create the best work they can in 20 minutes. As they paint, visitors can move around the easels, closely watching the creative process #BehindTheArt, and are encouraged to vote for their favourite painting and bid in a silent art auction.
UNTAPPED Emerging Artists Competition — Dedicated to supporting the development and success of students, new graduates and self-taught artists, the UNTAPPED Emerging Artist Competition, presented by DeSerres, is a juried competition that awards 20 emerging artists from all mediums the opportunity to exhibit at a professional-level art fair at no charge in a dedicated feature space. This program aims to provide a platform for young artists to launch their artwork to a public audience, make connections within the arts industry and gain experience in the contemporary art world.
TIME FLIES — Presented by Swatch, this year artists are invited to submit an original work based on their interpretation of the theme "TIME FLIES". All competition entries will be presented in a feature exhibit at the show for guests to enjoy. Winners will be selected by a panel of jurors to receive a cash prize. Show-goers can also vote for their favourite entry in the competition to receive the People's Choice Award and be automatically entered to win $250 towards a work of art and a pair of tickets to the Opening Night Party at Artist Project 2019.
Performance Art — OCAD University's Centre for Emerging Artists & Designers partners with Artist Project to present Under Construction by James Knott. This installation explores the notion of "constructed realities", particularly from a queer perspective, with the use of absurdity and camp theatrics as a coping mechanism.
Drawing inspiration from the paintings of Mike Smalley (a 10-year veteran of Artist Project), Ariel Adkins, Art & Social Media Maven and Founder of , will paint garments on live models creating a juxtaposition between art and life, fashion and function. Sponsored by Art Collectif, 10 per cent of sales raised through the auction of completed garments will be donated to Red Door Shelter – an organization providing safe shelter for women and families in need.
Ticket Information — Tickets are now on sale for the Early Access Preview and the Opening Night Party held on Thursday February 22, 2018. Early Access visitors will be among the first to preview and collect works of art, while indulging in specialty cocktails, complimentary hors d'oeuvres, music and art performances. Artist Project has partnered with Artbound's Creative Deeds Program, a charitable organization that helps build and support arts-focused community initiatives, to donate a portion of ticket sales proceeds to the organization.
Ticket information is available via the Artist Project website, linked .


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Maxine's Tweet Storm To Trump: 'It's Now The White Supremacists' House'… Forgot About Hillary's KKK 'MENTOR' (Video)
Maxine Waters' went on a Twitter rampage against President Trump, saying 'It's now the White Supremacists' House'… someone should have shown her THIS video of Hillary and her 'mentor' KKK 'Exalted Cyclops.'
It's time to add Rep. Maxine Waters name to the growing list of Democrat race-baiters along side Al Sharpton, Jesse Jackson and Barack Obama.
Waters blamed President Donald Trump for the deadly clash between white supremacist protesters and "anti-fascist" counter-protesters over the removal of a statue of Confederate General Robert E. Lee in Charlottesville, Virginia, on Saturday.
In a series of tweets on Sunday, Waters warned people to be "careful" and called the White House the "White Supremacists' House."
"Trump refuses to condemn white supremacists & terrorists who showed up in Charlottesville," Waters tweeted. "Is he sending a signal?
"Everyone must be careful," the tweet said.
Trump refuses to condemn white supremacists & terrorists who showed up in Charlottesville. Is he sending a signal? Everyone must be careful.
— Maxine Waters (@RepMaxineWaters) August 13, 2017
"Trump has made it clear – w/ Bannon & Gorka in the WH, & the Klan in the streets, it is now the White Supremacists' House," Waters tweeted, using the #Charlottesviille hashtag.
Trump has made it clear – w/ Bannon & Gorka in the WH, & the Klan in the streets, it is now the White Supremacists' House. #Charlottesviille
Waters also associated the president with former Imperial Wizard of the Ku Klux Klan David Duke.
Trump claimed he didn't know D. Duke, but Duke said white supremacist rally was done to fulfill Trump's promises. Do you know him now,Trump?
Perhaps Maxine needs a reminder that Hillary Clinton praised her "mentor" Robert Byrd, a Democrat, who was a recruiter for the Klan while in his 20s and 30s, rising to the title of Kleagle and Exalted Cyclops of his local chapter.
Byrd claimed that being part of the Klan was a mistake from his youth – he was in his 30's, he never publicly denounced them, and it was only when he ran for public office that he said he regretted it.
"@foxnation: Flashback: Hillary Clinton Praised Former KKK Member Robert Byrd as 'Friend and Mentor': https://t.co/e0Hb2rLb1X"
Here is President Trump disavowing David Duke and the KKK from 1991 to 2016, and calling Duke a "bigot" and "a problem".
On Saturday, the president tweeted his condemnation of the violence.
"We condemn in the strongest possible terms this egregious display of hatred, bigotry, and violence on many sides," Trump said and Fox Insider reported on Sunday. "When I watch Charlottesville to me it's very, very sad."
"We ALL must be united & condemn all that hate stands for. There is no place for this kind of violence in America. Lets come together as one!" Trump tweeted.
We ALL must be united & condemn all that hate stands for. There is no place for this kind of violence in America. Lets come together as one!
President Trump did denounce the hate and violence that took place in Charlottesville – what he did not do was name them all; Neo-Nazi's, BLM and ANTIFA because had he named the latter two, they would have rioted nationwide which in hindsight, would have proven his point and put an end to the Left's fake news rhetoric.
Newer PostPolice Stand And WATCH As Mob Toppled Confederate Statue In North Carolina (Video)
Older PostNancy Pelosi Blames Bannon After Charlottesville Clashes, DEMANDS Trump Take Immediate Action
July 18th, 2019 Liberty Unyielding

redpajama_set_name: RedPajamaCommonCrawl


The good news about Sony PlayStation's new online series POWERS, it is a fun series with a great cast. Now the bad news, it is only available online via Sony PlayStation. That is right: if you do not have a Sony Playstation or a Sony Playstation online account, you cannot watch POWERS — though the first episode will be made available on YouTube to entice new viewers to continue watching on the Sony PlayStation platforms.
POWERS is based on the best selling comic book series of the same name, created by writer Brian Michael Bendis and artist Michael Avon Oeming, and stars Sharlto Copley ("District 9"), Susan Heyward ("The Following"), Michelle Forbes ("The Returned," "The Killing," "Battlestar Galactica"), Eddie Izzard ("Hannibal," "The Riches"), Noah Taylor ("Game Of Thrones"), Olesya Rulin, Logan Browning ("Hit The Floor"), Adam Godley ("Manhattan," "Suits"), Max Fowler ("Wolf Hall"), Aaron Farb, Justice Leak and Sterling Beaumon ("Red Widow").
The basic premise of POWERS is that in the POWERS world there are those with special abilities (such as, flying, teleportation) and those without powers. It is a battle between those that want to do whatever they please with their powers versus those who want to do what they can to help protect the rest of the world from power-infused criminals. Heroes versus villains. It is a familiar story, but with a slight twist.
In Powers, the lead character is Christian Walker (Sharlto Copley), a homicide detective in the Powers Division of the LAPD, who used to be a "power" superhero until his powers were stolen from him. After the death of his partner and subsequent murder of a former hero teammate, Walker finds himself teamed up with a gung-ho new recruit, Deena Pilgrim (Susan Heyward) and together they attempt to track down the elusive criminal mastermind, Johnny Royalle (Noah Taylor) — a "power" who had been previously thought dead. Johnny and Walker go way back, all the way to a time when they were childhood friends. In fact, they both mentored under a super villain criminal, known as Wolfe (Eddie Izzard). Alas, fate intervened and sent all of them in vastly different paths for their lives — Walker was stripped of his "powers," Wolfe ended up in prison, and Royalle simply disappeared. But now, Royalle is back and that bodes badly for Walker.
Following the story outlined in the comic books, Powers jumps straight into the fast-paced world of the "powers" versus the non-powered and the complex interpersonal relationships that Walker has with both sides. Fortunately, star Sharlto Copley easily carries the show with his charismatic charm and viewers will soon fall under his spell. Adding to the show's appeal, getting to know the "powers" and the actors who portray the off-beat, zany and downright diabolical characters is a fun process. As each character is introduced, and as their place in Walker's world is explored, POWERS starts to take shape and and by the end of the first episode, viewers will be clamoring for more.
POWERS is available starting Tuesday, March 10th on PS3 and PS4. In addition, it will be made available to those with PlayStation Plus membership for viewing online via computer.


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Q: SQL - How to change a varchar column into date type in format yyyy-mm-dd I have a SQL Server table with some data imported from a .csv file. One of the columns RegDate is of type varchar and contains a date in format ddmmyyyy.
I need to convert the column to date datatype and in the format yyyy-MM-dd. So the value 17112011 should be converted to 2011-11-17.
Thanks:)

A: Check out the CONVERT function in T-SQL:
SELECT CONVERT(DATETIME, RegDate, 103) FROM myTable

Converts the VARCHAR field in your table to a DateTime type.
An option could be to add an extra column to your table which is of type DateTime.
Import the data from the CSV as is, and update the data afterwards:
UPDATE myTable SET ExtraDateTimeColumn = CONVERT(DATETIME, RegDate, 103)

I would consider this approach if this is a one-time import.
The format on how you want your DateTime to be represented, is just a representation form which you should handle in your UI/View logic imho

A: I think the easiest way to do this is to use SUBSTRING to re-arrange the import string value to a valid date format, which you can then CAST to datetime. So something like this:
SELECT
    RegDate, -- the import value

    SubString(RegDate, 5, 4) + '-' +  -- year
    SubString(RegDate, 3, 2) + '-' +  -- month
    SubString(RegDate, 1, 2) -- day
    as RegDate_str, -- the import value as YYYY-MM-DD

    CAST (
        SubString(RegDate, 5, 4) + '-' +  -- year
        SubString(RegDate, 3, 2) + '-' +  -- month
        SubString(RegDate, 1, 2) -- day
        as DateTime
    ) as RegDate_dt -- the import value cast as DateTime
FROM
    MyImportTable

I don't know which datetime column you want to update based on values in RegDate. But you could add a new datetime column to your import table, and then update that new column like so:
UPDATE
    MyImportTable
SET
    MyDateTimeColumn =
    CAST (
        SubString(RegDate, 5, 4) + '-' +  -- year
        SubString(RegDate, 3, 2) + '-' +  -- month
        SubString(RegDate, 1, 2) -- day
        as DateTime
    )
WHERE
    len(RegDate) = 8 -- optionally, check length to make sure value is ok

Also, to quickly lookup any incorrect datevalues in your import table, you can use ISDATE to do something like this:
SELECT
    RegDate
FROM
    MyImportTable
WHERE ISDATE(
        SubString(RegDate, 5, 4) + '-' +  -- year
        SubString(RegDate, 3, 2) + '-' +  -- month
        SubString(RegDate, 1, 2) -- day
    ) = 0 -- 0=invalid date, 1=valid date


text:
Attorney General nominee William Barr departs after a meeting with Sen. John Cornyn, R-Texas, on Capitol Hill, Wednesday, Jan. 9, 2019 in Washington. (AP Photo/Alex Brandon)
Trump's AG Nominee: 'Vitally Important' Mueller Finish Work
WASHINGTON (AP) — President Donald Trump's nominee for attorney general will tell senators at his confirmation hearing "it is vitally important" that special counsel Robert Mueller be allowed to complete his Russia investigation. That's according to a transcript of William Barr's prepared remarks...
President Donald Trump's attorney general nominee, William Barr, meets with Senate Judiciary Committee member and Trump confidant Sen. Lindsey Graham, R-S.C., on Capitol Hill in Washington, Wednesday, Jan. 9, 2019. Barr, who served in the position in the early 1990s, has a confirmation hearing before the Senate Judiciary Committee next week and could be in place at the Justice Department as soon as February when Deputy Attorney General Rod Rosenstein leaves after Barr is confirmed. (AP Photo/J. Scott Applewhite)
Ag Pick To Reassure Senators He Backs Sentencing Overhaul
WASHINGTON (AP) — President Donald Trump's pick to be attorney general will assure lawmakers he supports a recent criminal justice overhaul that eases federal sentencing rules, even though he pushed tough-on-crime policies for decades, a person close to the confirmation process told The Associated...
Attorney General Pick Barr Expresses Confidence In Mueller
WASHINGTON (AP) — The new chairman of the Senate Judiciary Committee said Wednesday that attorney general nominee William Barr has confidence in special counsel Robert Mueller and will let him complete his Russia investigation. Sen. Lindsey Graham, R-S.C., said after meeting with Barr, who led the...
FILE - In this July 13, 2018 file photo, Deputy Attorney General Rod Rosenstein speaks during a news conference at the Department of Justice in Washington. Rosenstein is expected to leave his position soon after William Barr is confirmed as attorney general. That's according to a person familiar with the plans who was not authorized to discuss them on the record and spoke to The Associated Press on condition of anonymity. (AP Photo/Evan Vucci)
Rosenstein, A Frequent Trump Target, Will Leave Justice Dept
WASHINGTON (AP) — Deputy Attorney General Rod Rosenstein, the most visible Justice Department protector of special counsel Robert Mueller's Russia investigation and a frequent target of President Donald Trump's wrath, is expected to leave his position soon after Trump's nominee for attorney general...
President Donald Trump's attorney general nominee, William Barr, left, meets with Senate Judiciary Committee member and Trump confidant Sen. Lindsey Graham, R-S.C., on Capitol Hill in Washington, Wednesday, Jan. 9, 2019. Barr, who served in the position in the early 1990s, has a confirmation hearing before the Senate Judiciary Committee next week and could be in place at the Justice Department as soon as February when Deputy Attorney General Rod Rosenstein leaves after Barr is confirmed. (AP Photo/J. Scott Applewhite)
The Latest: Rosenstein Expected To Leave Justice Dept. Soon
WASHINGTON (AP) — The Latest on Deputy Attorney General Rod Rosenstein's expected departure from the Justice Department (all times local): 6 p.m. Deputy Attorney General Rod Rosenstein is expected to leave his position soon after President Donald Trump's nominee for attorney general is confirmed...
FILE - In this Feb. 21, 2018, file photo, Sen. Orrin Hatch, R-Utah, waves after addresses the Utah Senate while Senate President Wayne Niederhauser, R-Sandy, looks on at the Utah State Capitol, in Salt Lake City. Hatch is ending his tenure as the longest-serving Republican senator in history, Thursday, Jan. 3, 2019, capping a unique career that positioned him as one of the most prominent conservative voices in the United States. (AP Photo/Rick Bowmer, File)
Orrin Hatch Ends 4-Decade Senate Run As Unique GOP Voice
SALT LAKE CITY (AP) — Orrin Hatch ended his tenure Thursday as the longest-serving Republican senator in history, capping a unique career that positioned him as one of the most prominent conservatives in the United States. The departure of the vocal supporter of President Donald Trump ushers in...
FILE - In this Sept. 21, 2018, file photo, the Supreme Court is seen in Washington. The Supreme Court term has steered clear of drama since the tumultuous confirmation of Justice Brett Kavanaugh. The next few weeks will test whether the calm can last. (AP Photo/J. Scott Applewhite, File)
Low-Key Days At Supreme Court May Be Ending Soon
WASHINGTON (AP) — The Supreme Court began its term with the tumultuous confirmation of Justice Brett Kavanaugh, followed by a studied avoidance of drama on the high court bench — especially anything that would divide the five conservatives and four liberals. The justices have been unusually...
Supreme Court Keeps A Lower Profile, But For How Long?
The Capitol is seen in Washington, Friday morning, Dec. 14, 2018. Parties and Christmas cookies only soothe so much in the chilly Capitol after two years of President Donald Trump's provocations, dramas like Supreme Court Justice Brett Kavanaugh's confirmation and the elections that flipped the House majority to Democrats. Everyone wants to go home, yet both chambers were scheduled to be in session next week over hefty matters, including the budget and criminal sentencing reform. (AP Photo/J. Scott Applewhite)
December 14, 2018 - 7:43 am
Are We Done Here? Nope. Cranky Congress Still Has Work To Do
WASHINGTON (AP) — Nothing says, "Is it over yet?" quite like Senate Democratic leader Charles Schumer propping up his feet on the chair next to him. The casual vibe in the normally stuffy Senate was just one sign that the end of an ugly 115th Congress can't come soon enough, even for its own...
November 16, 2018 - 9:24 am
Graham Poised To Lead Judiciary Panel After Grassley Switch
WASHINGTON (AP) — Sen. Charles Grassley of Iowa is giving up the chairmanship of the Senate Judiciary Committee, paving the way for Sen. Lindsey Graham to take over. Grassley says he plans to become chairman of the Senate Finance Committee next year. To do that, he'll have to give up the gavel of...


A primary reason that stays pending reexamination are rarely granted at the ITC is that the ITC has a statutory mandate to expeditiously process its docket. See Certain Semiconductor Chips (Inv. No. 337-TA-605), Comm'n Op at 6. Since patent reexamination proceedings can often take 4-5 years to come to an ultimate resolution, the ITC has been reluctant to stay its relatively fast investigations while the PTO resolves a drawn-out reexamination.
However, the new post-grant proceedings allowed under the AIA are designed to conclude within 12-18 months of initiation. The speed of these proceedings as compared to traditional reexamination could significantly alter the calculus used to determine whether a stay is appropriate at the ITC. Since a stay pending a post-grant proceeding under the AIA would likely not last nearly as long as a stay pending reexamination, the justification for denying a stay based on the relative slowness of PTO proceedings may be significantly weakened in the future. Moreover, since the estoppel provisions under the AIA will extend to the ITC, the ITC may have more of an incentive to allow the PTO to come to a determination as to an asserted patent's validity in the first instance.
The ITC will likely take a wait-and-see approach in the short term based on its historical practice of rarely granting motions to stay pending traditional reexamination. However, if it becomes clear that the PTO is actually concluding trials within the mandated 12-18 month time frame, motions to stay ITC actions pending post-grant proceedings at the PTO stand a chance of gaining traction.
We will continue to monitor developments in this area. For more information on the AIA and the new post-grant proceedings, please visit the Patents Post-Grant Blog.


text:
Die Autoroute A 52 ist eine französische Autobahn mit Beginn in Aix-en-Provence und dem Ende in Aubagne. Sie hat eine Länge von insgesamt 26 km.

Geschichte
 29. August 1974: Eröffnung La Bouillardisse – Pont-de-l'Etoile (Ausfahrt 33 – A 501)
 16. Dezember 1975: Eröffnung Pont-de-l'Etoile – Aubagne-sud-est (A 501 – A 50)
 21. März 1978: Eröffnung Châteauneuf-le-Rouge – La Bouillardisse (A 8 – Ausfahrt 33)

Großstädte an der Autobahn
 Châteauneuf-le-Rouge
 Aubagne

Weblinks
 Autoroute A 52 in deutscher und französischer Fassung des SARATLAS
 Autoroute A 52 auf WikiSara (frz.)

52
Straße in Provence-Alpes-Côte d'Azur
Autoroute A052

redpajama_set_name: RedPajamaWikipedia


text:
\section{Introduction}\label{sec:one}
This paper considers Bayesian modeling of an unknown function  $f_0:\mathcal{X} \rightarrow \mathbb{R},$
where it is known that $f_0$ has at most $H$ local extrema, or change points, interior to $\mathcal{X}$,
and one wishes to estimate the function subject to constraints or test the hypothesis the function has a specific shape. For example,
one may wish to consider a monotone function as compared to a function having an  `N' shape.
We propose a novel spline construction that allows for nonparametric estimation of shape
constrained functions having at most $H$ change points. The approach places a novel prior
over a knot set that is dense in $\mathcal{X}$ while developing Markov chain Monte Carlo
algorithms to sample between models. The method allows for nonparametric hypothesis testing of
different shapes within the class of functions considered using Bayes factors.

The shape constrained regression literature focuses primarily on functions that
are monotone, convex, or have a single minimum, that is, cases with $H \leq 1$.
\citet{ramgopal1993}, \citet{lavine1995}, and \citet{bornkamp2009} consider
priors over cumulative distribution functions used to model
monotone curves. Alternatively, \citet{holmes2003}, \citet{neelon2004}, \citet{meyer2008}, and \citet{shively2009}
develop spline based approaches for monotone functions.
\citet{hans2005} design a prior for umbrella-shaped functions, while \citet{shively2011} propose
methods for fixed and free knot splines that model continuous segments having a single unknown  change
point.

Extending these approaches to broader shape constraints is not straightforward computationally.  For example,
to obtain $H=3$ change points, one could define a prior over B-spline bases
(\citet{deBoor2001}, page 87) having four monotone segments alternating between increasing and decreasing.
Even for a moderate number of pre-specified knots and a known number of change points, allowing for uncertainty in
the locations of the change points leads to a daunting computational problem.  For example, Bayesian computation
via Markov chain Monte Carlo is subject to slow mixing and convergence rates in alternating between updating
the spline coefficients conditionally on the change points and vise versa.  It is not clear how to devise algorithms that
can efficiently update change points and coefficients simultaneously.  These difficulties are
compounded by allowing for the possibility that some of the change points should be removed, which is commonly
the situation in applications.   By defining a new spline basis based on the number of change points, we
bypass these issues.

Also, little work has been done on nonparametric Bayesian testing of curve shapes.
Recently, \citet{salomond2014} and \citet{scott2015} consider Bayesian nonparametric
testing for monotonic versus an unspecified nonparametric alternative, but do not
consider shapes beyond monotonicity. Our approach is different because it allows
for testing of all shapes, where shape is defined as the type and sequence of extrema.
For example, one can use this approach to test for an
umbrella shape verses an `N' shaped curve and use the same procedure
to test the umbrella shape against monotone alternatives.

We propose a fundamentally new approach to incorporating shape constraints based on splines that are carefully constructed to induce curves having a particular number of extrema.  This is similar in spirit to the I-spline construction of \citet{ramsay1988} or the C-spline construction for convex splines
\citep{meyer2008, meyer2011}, which both create a spline construction based upon the derivative of the spline.
Our spline construction, when paired with positivity constraints on the spline coefficients, enforces shape
restrictions on the curve of interest by limiting the number of change points.

Another key aspect of our approach is that we place a prior over a model space that can grow to a
countably dense set of knots. This bypasses  the sensitivity to choice of the number of knots,
while facilitating computation and theory on consistency.
In particular, we propose a prior over nested model spaces where the location of the knots is known for each model.
This allows for a straightforward reversible jump
Markov chain Monte Carlo algorithm \citep{green1995} based upon \citet{godsill2001}. This is different from much of the previous Bayes
literature allowing unknown numbers of knots \citep{biller2000,dimatteo2001}. In these methods,
the knot locations are unknown, and the reversible jump Markov chain Monte Carlo
proposal must propose a knot to add or delete as well as its location.  Such algorithms are notoriously inefficient.

\section{Model}
\subsection{Local Extrema Spline Construction}
Let $\mathcal{F}^{H}$ be a set of functions defined on the closed set $\mathcal{X} \subset \mathbb{R},$
such that for $f_0\in \mathcal{F}^{H},$  $f_0$ is continuously differentiable and has
$H$ or fewer local extrema interior to $\mathcal{X}.$
Such functions can be modeled using B-spline approximations of the form
\begin{align}
	f(x)  = \sum_{k=1}^{K+j-1} \beta_k B_{(j,k)}(x), \label{BX:splineapprox}
\end{align}
Here, $\beta_k$ is a scalar coefficient, and $B_{(j,k)}(x)$ is a B-Spline
function of order $j$ defined on the knot set $\mathbf{\mathcal{T}} = \{\tau_k\}_{k=1}^{K},$
$\tau_1 \leq \tau_2 \leq \ldots \leq \tau_K,$ which includes end knots.
\citet{deBoor2001}, page 145, showed that for any knot set there exists
spline approximations such that $||f-f_0||_{\infty} \leq \Delta||f_0||_{\infty},$
where $\Delta$ is  the  maximum difference between adjacent knots.
Though this construction can be used to model $f_0$ with arbitrary accuracy,
it does not guarantee the approximating function $f$ is itself in $\mathcal{F}^{H}.$

We force $f \in \mathcal{F}^{H}$  to have at most
$H$ local extrema by defining a new spline basis
\begin{align}
	B_{(j,k)}^{\ast}(x) = M \int_{-\infty}^{x} \bigg\{ \prod_{h=1}^H (\xi - \alpha_h) \bigg\} B_{(j,k)}(\xi) d\xi, \label{BX:splineconstruction}
\end{align}
where, as above, $B_{(j,k)}(x)$ is a B-spline that is
constructed using the knot set $\mathcal{T},$  $\{\alpha_1,\ldots,\alpha_h\}$ are distinct change points
and the scalar $M$ is a fixed integer. Letting
$B_{(j,0)}^{\ast}(x) = 1,$  if $\beta_k \geq 0$, for all $k \geq 1,$
then any linear combination of local extrema spline basis functions for any
distinct values of $\alpha_1,\ldots,\alpha_H$ in (\ref{BX:splineconstruction})
will be in $\mathcal{F}^{H}.$

\begin{prop}
Letting $f(x) = \sum_{k=0}^{K+j-1} \beta_k B^{\ast}_{(j,k)}(x)$ for any $K \geq 1$
with $M \in \{-1,1\},$ $j \geq 1,$ and $\beta_k \geq 0$ for all $k \geq 1,$ then $f \in \mathcal{F}^{H}.$
\end{prop}

This result follows from the constraint on the $\beta_k$ coefficients.  By forcing $\beta_k \geq 0$ for $k \geq 1$,
the sign of the derivative is controlled by the polynomial $M\prod_{h=1}^H(x-\alpha_h),$
which forces a maximum of  $H$ local extrema located at the change points $\{\alpha_1,\ldots,\alpha_H\}$.
 When $\beta_k =\ldots = \beta_{k+j} = 0$ and $\alpha_h \in [\tau_{k+j},\tau_{k+j+1}],$ $\alpha_h$ does not define unique extrema.  In this case, there is a flat region
and multiple configurations of the change point parameters can result in the same curve.
Otherwise, the extrema are uniquely defined for all $\alpha_h \in \mathcal{X},$ and
fewer than $H$ extrema can be considered if $\alpha_h \notin \mathcal{X}.$

\begin{thm}
For any $f_0 \in \mathcal{F}^{H}$ and $\epsilon > 0$ there exists a knot set $\mathcal{T}$ and a local extrema spline $f^{LX}$ defined
on this knot set such that
\begin{align*}
	\| f_0 - f^{LX}\|_\infty < \epsilon.
\end{align*}
\end{thm}

The flexibility of local extrema splines is attributable to the B-splines used in their construction.
The proof of this theorem assumes that $M$ can be chosen to be positive or negative, which allows
all functions in $\mathcal{F}^{H}$ to be approximated.
If $M$ is fixed, then any function with $H-1$ extrema can be modeled. For functions with exactly $H$ extrema, one is limited to modeling functions that are either initially increasing or initially decreasing, and this depends on the sign of $M$.

\textit{Remark:} Though the polynomial
weighting does not affect the ability of the local extrema spline to model arbitrary functions
in $\mathcal{F}^{H},$ it does impact the magnitude of the spline, that is, $\sup_{x\in \mathcal{X}} |B^{\ast}_{(j,k)} (x)|,$
which may cause difficulty in the prior specification.
To minimize this effect it is often beneficial to construct the splines on
the interval $(-0{\cdot}5,0{\cdot}5).$ Additionally, it is often beneficial to multiply M by a fixed constant
to aid in prior specification.

\subsection{Infill Process Prior}
Bayesian methods for automatic knot selection \citep{biller2000,dimatteo2001}
commonly define  priors over the number and location of knots.  Using free knots presents computational
challenges while fixed knots are too inflexible; we address this by defining a prior over a branching process
where the children of each generation represent knot locations that are binary infills of the previous
generation.  This defines a nested set of spline models such that successive generations
produce knot sets  that are  arbitrarily close.

To make these ideas explicit, define  $\mathcal{T}_N = \{{a}/{2^{N+1}}: a = 1,3,\ldots,2^{N+1}-1\}$
with $N \in \{0,1,2,3,\ldots\}.$ Assume $\mathcal{X} = [0,1]$ for the sake of exposition,
and consider an infinite complete binary tree.
In this tree, each node at a given depth $N$ is uniquely labeled using
an element from $\mathcal{T}_N.$ Given the node's label is
${a}/{2^{N+1}},$  its  children are labeled
${(2a-1)}/{2^{N+2}}$ and ${(2a+1)}/{2^{N+2}}.$
For example,  the node labeled ${3}/{8}$ at $N=2$ has children labeled ${5}/{16}$
and ${7}/{16},$ and the root node labeled ${1}/{2}$ has children labeled ${1}/{4}$
and ${3}/{4}.$

We induce a prior on the set of local extrema spline basis functions through a branching process over this tree. The process starts at the root node $N=0$ where the generation of children occurs via
two independent Bernoulli experiments having probability of success $\zeta.$
On each success, a child is generated, and its label is added to the knot set. This process repeats until it dies out.  If $\zeta < 0{\cdot}5$, the probability of extinction is $1$
(\citet{feller1974}, page 297).  To favor parsimony in the tree, we define the
probability of success for a node at a given depth $N$ to be $0{\cdot}5^{N+1},$ which
decreases the probability of adding a new node the larger the tree becomes.
The tree $\mathcal{M}$ generated from this process corresponds to a knot set  $\mathcal{T}_{\mathcal{M}}$.
We complete the knot set by adding end knots $\{0,1\}.$

Letting $K = |\mathcal{T}_{\mathcal{M}}|$ be the number of knots for tree $\mathcal{M}$ including end knots,
there are $K+j-1$ basis functions.
Letting $\beta_k \in \beta_{\mathcal{M}}$ denote the coefficient on $B^{\ast}_{(j,k)}(x),$ we choose the prior:
\begin{align}
	p(\beta_k | \mathcal{M}) =  \pi1_{(\beta_k = 0)} + (1-\pi) \text{Exp}(\beta_k; \lambda),\quad 1 \leq k \leq K+j-1, \label{PRI:1}
\end{align}
where $\text{Exp}(\lambda)$ is an exponential distribution with rate parameter $\lambda$, $\pi$  is the prior probability of $\beta_k =  0$,
and the $\beta_k$ are drawn independently conditionally on $\mathcal{M}, \pi, \lambda$.
For the intercept, we let $\beta_0 \sim N(0,c)$, and we allow for greater adaptivity to the data through hyperpriors, $\pi \sim \mbox{Be}(\nu,\omega)$ and $\lambda \sim \mbox{Ga}(\delta,\kappa)1(\lambda > \epsilon),$ which
is a truncated gamma distribution, truncated slightly above zero to guarantee posterior consistency. In
practice, this value is set to $1e-5$ making the prior indistinguishable from the Gamma distribution.

To allow uncertainty in locations of the change points, we choose the prior
\begin{align}
	p(\alpha) = \prod_{h=1}^{H}\text{TN}\{\alpha_h; (b-a)/2,1,a,b\} \label{PRI:3}
\end{align}
where  $\text{TN}\{(b-a)/2,1,a,b\}$ is truncated normal with mean $(b-a)/2,$ variance $1$, and is
truncated below by $a$ and above by $b$ with $\mathcal{X} \subset [a,b].$  If $\alpha_h \leq \inf \mathcal{X}$
or $\alpha_h \geq \sup \mathcal{X}$, then the change point is removed.
We assume $M$ is pre-specified corresponding to prior knowledge of whether the function is initially
increasing or decreasing, though generalizations to place a prior on $M$, for example a Bernoulli prior on $M,$ are straightforward.

\textit{Remark:} The prior for the change point parameters is defined such that $\mathcal{X} \subset [a,b].$
When a change point is placed outside of $\mathcal{X}$, this allow for the derivative of $f$ to be non-zero at
$\inf \mathcal{X}$ or  $\sup \mathcal{X}.$
In practice, results are insensitive to the choice of $a$ and $b.$
In what follows, we chose $a=\inf (\mathcal{X}) - \Delta$ and $b = \sup (\mathcal{X}) + \Delta$ where
$\Delta = \{\sup (\mathcal{X}) - \inf (\mathcal{X})\}/2.$

\subsection{Prior Properties}
Define $\mathcal{F}^{H+}$ as the space of
continuously differentiable functions with $H$ or fewer local extrema, such that, for all
$f_0 \in \mathcal{F}^{H+}$
having exactly $H$ extrema, the first extrema from the left is a maximum, and, for all functions in
$f_0 \in \mathcal{F}^{H+}$   having less than $H$ extrema, the function is also in  $\mathcal{F}^{H-1}.$
Conversely, define $\mathcal{F}^{H-}$  as the set of continuously differentiable functions with $H$ or fewer local extrema,
such that, for all functions having exactly $H$ extrema the first from the left is a minimum,
and for all functions $f_0 \in \mathcal{F}^{H-}$  having less than $H$ extrema they  are also in $\mathcal{F}^{H-1}.$  The prior places positivity in $\epsilon-$neighborhoods of any $f_0$ in $\mathcal{F}^{H-}$ or $\mathcal{F}^{H+}$ depending on the sign of $M$.

\begin{lmma}
	Letting $f^{LX}$ be a randomly generated local extrema spline from the prior defined in $\S 2{\cdot}2$
        for all $f_0\in \mathcal{F}^{H-1}:$
	\begin{align*}
		   \mbox{pr}(||f^{LX} - f_0||_{\infty} < \epsilon) > 0.
	\end{align*}
This holds for all $f_0 \in \mathcal{F}^{H+}$ if $H$ is odd and $M<0$ or $H$ is even and $M>0$.  Otherwise, if $H$ is even and $M>0$ or $H$ is odd and $M<0$, this holds for all $f_0 \in \mathcal{F}^{H-}$.
\end{lmma}

Using this result we can show posterior consistency.
Assume $Y = (y_1,\ldots,y_n)^T$ are observed at locations
$(x_1,\ldots,x_n)$ such that $y_i \sim \text{N}\{f_0(x_i),\sigma_0^2\}.$ Following
\citet{choi2007}, assume that the design points
are drawn independent and identically distributed from some probability distribution $Q$ on the interval $\mathcal{X},$ or observed
using a fixed design such that $\max(|x_i - x_{i+1}|) < (K_1 n)^{-1}$ where $0 < K_1 < 1$ and
$i < n.$ Also,  define the neighborhoods $W_{\epsilon,n} = \{(f,\sigma): \int |f(x)-f_0(x)| dQ_n(x) < \epsilon, |\sigma/\sigma_0 - 1 | < \epsilon\}$
and $U_{\epsilon} = \{(f,\sigma): d_Q(f,f_0) < \epsilon, |\sigma/\sigma_0 - 1 | < \epsilon\}$ where
$d_Q(f_1,f_2) = \inf\{\epsilon > 0: Q(\{x:|f_1(x)-f_2(x)| > \epsilon\}) < \epsilon \}.$ Under
the assumption that the  prior over $\sigma$ assigns positive probability to every $\epsilon-$neighborhood
of $\sigma_0,$ one has:

\begin{thm}
    Let $f^{LX}$ be a randomly generated curve from the prior defined in $\S 2{\cdot}2$
         with $f_0\in \mathcal{F}^{H-1}.$ If $P_{f_0,\sigma_0}$ is the joint distribution of $\{y_i\}_{i=1}^{\infty}$
         conditionally on $\{ x_i \}_{i=1}^{\infty}$,
	$\{\mathcal{Z}_i\}_{i=1}^{\infty}$ is a sequence of open subsets in $\mathcal{F}^{H-1}$ that is defined by
       $W_{\epsilon,n}$ for fixed designs or by $U_\epsilon$ for random designs, and $\Pi_n$
	is the posterior distribution of $f_0$ given
	$\{y_i\}_{i=1}^{n},$ then
	\begin{align*}
		\Pi_n(f \in \mathcal{Z}_{n}^{C}|y_1,\ldots,y_n) \rightarrow 0 \hspace{10mm} \textit{almost surely} \hspace{2 mm}  [P_{f_0,\sigma_0}].
	\end{align*}
		Further, for all $H$ odd if  $M < 0,$  this relation holds for $f_0 \in \mathcal{F}^{H+},$
		otherwise it holds for  $f_0 \in \mathcal{F}^{H-}.$ Similarly, for $H$ even if
		$M  > 0,$ then  $f_0 \in \mathcal{F}^{H+},$ otherwise it holds for $f_0 \in \mathcal{F}^{H-}.$
\end{thm}

The proof of this consistency result follows from
\citet{choi2007} and the prior positivity result above.  The condition on the
prior over $\sigma^{2}$  can be satisfied with an inverse-Gamma prior.

\subsection{Bayes Factors for Testing Curve Shapes}

A key feature of our approach is that it allows one to explicitly define the shape
of the curve through the $\alpha$ vector and place prior probability on
a class of functions having a given shape.  We use the term shape to correspond
only to the number and type of extrema in $\mathcal{X},$ which
is parametrized through $\alpha.$ When there are flat regions of $f_0$
the shape of the curve is not uniquely identifiable based upon the configuration of
the $\alpha,$ and all hypothesis tests may be inconclusive. For
an example of this, see the consistency arguments for monotone curve testing in \citet{scott2015}. In what follows, we assume that $|f_0'(x)| > 0$
at all points in $\mathcal{X}$ except at
the extrema to rule out the consideration of flat regions.

\textit{Remark} As posterior consistency is guaranteed when there are flat regions, the assumption that $|f_0'(x)| > 0$ is not required for model fitting.

Let $\mathbb{H}_1$ and $\mathbb{H}_2$ denote two distinct and non-nested sets of $\alpha$ values, corresponding to distinct shapes.  These sets are defined by the number of $\alpha_h \in \mathcal{X}$, the number of
$\alpha_h \leq \inf(\mathcal{X}),$ and the number of $\alpha_h \geq \sup(\mathcal{X}).$
One can compute $\mbox{pr}(Y | f_0 \in \mathbb{H}_1 )$ and $\mbox{pr}(Y| f_0 \in \mathbb{H}_2 ),$  with the corresponding Bayes factor between the two shapes being
\begin{align}
 BF_{12} = 	\frac{\mbox{pr}(Y|f_0 \in \mathbb{H}_1)}{\mbox{pr}(Y|f_0 \in \mathbb{H}_2)}. \label{bayesFac}
\end{align}
This quantity is not available analytically, but can be estimated through posterior simulation
by monitoring the $\alpha$ and $\beta$ vectors.

Any two possible shapes falling within $\mathcal{F}^{H}$ can be compared using this approach.
Alternatively,  one may be interested in the hypothesis that $f_0$ is in a class of functions with at least $K$ extrema.  For example, one may wish to assess whether or not the function is monotone. In this case, one can define $\mathbb{H}_1$ to correspond to functions in $\mathcal{F}^H$ with $F$ or more extrema and $\mathbb{H}_2 = \mathbb{H}_1^c$ to functions with less than $F$ extrema.  The value of $H$ can be elicited as an upper bound on the number of extrema to avoid highly irregular functions.  For such tests, the following result holds.

\begin{prop} \label{prop1}
	Let $\mathbb{H}_1$ be the class of functions in $\mathcal{F}^{H}$ with $F$ or more extrema and $\mathbb{H}_2 =
\mathbb{H}_1^c \bigcap \mathcal{F}^H$.  If $f_0 \in \mathbb{H}_1,$ then
	\begin{align*}
			B_{12} \rightarrow \infty
	\end{align*}
	as $n \rightarrow \infty.$
\end{prop}

This result is a direct application of Theorem 1 in \citet{walker2004}.
It follows from the fact that local extrema spline representations
having fewer than $F$ change  points can never be arbitrarily close to the
function of interest, and, consequently, $\mathbb{H}_1$ will be supported given more data.

\section{Posterior Computation}

We rely on \citet{godsill2001} to develop a reversible jump
Markov chain Monte Carlo algorithm to sample between models.
Consider moves between models
$\mathcal{M}$ and $\mathcal{M'},$ where the model $\mathcal{M'}$ has one extra
knot that is a child of a node also in $\mathcal{M}.$
As described further in the supplemental material,  most of the local
extrema spline basis functions for model $\mathcal{M}$ and $\mathcal{M'}$ are
identical, with only $j+2$ functions being different.
Let $\beta_{-\mathcal{M}}$ denote the coefficients on all the splines that are the same
as well as $\sigma^{2}, \pi$ and $\lambda$, which are parameters shared between both models.
The remaining spline coefficients are $\beta_{\mathcal{M}}$ and $\beta_{\mathcal{M}'}$
for models $\mathcal{M}$ and $\mathcal{M'}$, respectively.
As in Godsill, given the shared vector $\beta_{-\mathcal{M}}$, we
marginalize  $\beta_{\mathcal{M}}$ and $\beta_{\mathcal{M'}}$ out of the posterior
to compute $p(\mathcal{M}'|Y,\beta_{-\mathcal{M}})$ and $p(\mathcal{M}|Y,\beta_{-\mathcal{M}}).$
This marginalization requires numerical integration of multivariate normal distributions, which
are performed using \citet{genz1992} and \citet{genz2000}.
The probability of a move between two models is determined by the ratio
\begin{align}
		h &= \frac{q(\mathcal{M};\mathcal{M}')p(\mathcal{M}'|Y,\beta_{-\mathcal{M}})}{q(\mathcal{M}';\mathcal{M})p(\mathcal{M}|Y,\beta_{-\mathcal{M}})}, \label{metrat}
\end{align}
where a knot insertion is made with probability $\min(1,h),$ a knot deletion is made with probability $\min(1,1/h),$
and $q(\mathcal{M};\mathcal{M}')$ is the transition probability between $\mathcal{M}$ and $\mathcal{M}'.$

All proposals are made between  models that are nested and differ by only one knot.  When the current model has no children we propose a knot insertion with probability $1.$ Otherwise, the proposal adds or deletes a knot with probability $1/2,$ and the inserted or deleted knot is chosen with uniform probability.  For a knot insertion, that is, as we are going from model $\mathcal{M}$ to $\mathcal{M'},$
the available knots are represented by all failures in the branching process that generated $\mathcal{M}$.
For a knot deletion, that is one goes from model $\mathcal{M'}$ to $\mathcal{M},$
this represents all of the nodes in the branching process that generated $\mathcal{M'}$
that do not have any children.  All other parameters, including the spline coefficients,
are sampled in Gibbs steps described in the supplement.

The posterior distribution is often multimodal, with the above sampler often getting stuck in a single mode.
This occurs when widely different parameter values have relatively large support by the data,
with low posterior density between these isolate modes.  To increase the  probability  of jumps
between modes, a parallel tempering algorithm \citep{geyer1991,geyer2011} is implemented, which is
fully described in the supplemental material.

\section{Simulation}
We investigate our approach through simulations for functions
having $0,1,$ or $2$ local extrema interior to $\mathcal{X}.$
For all simulations, we place a $Ga(1,1)$ prior over  $\sigma.$
For the hyper prior on $\pi$, we let $\nu = 2$ and $\omega = 18$
which puts a low probability of favoring flat curves. Additionally, for the hyper prior over $\lambda$,
we let $\delta = 0{\cdot}2$ and $\kappa = 2,$ which favors smaller values of $\beta.$
Finally, all local extrema splines were constructed using B-splines of order $2$ with $M = 100.$

The Markov chain Monte Carlo algorithm was implemented in the R programming
language with some subroutines written in C++ and is
available from the first author.  Depending on the complexity of the
function being fit, the algorithm took between $60$ and $90$ seconds per $50,000$ samples
using one core of a $3{\cdot}3$ gigahertz Intel i7-5830k processor.
Parallelizing the tempering algorithm on multiple cores may substantially
reduce the computation time.  Additional information
on the convergence of the algorithm, as well as impact of the B-spline
order used, is examined in the supplemental material.

\subsection{Curve Fitting}
We compare the local extrema spline approach to other
nonparametric methods, including Bayesian P-splines  \cite{lang2004},
a smoothing spline method described in \citet{green1993},
and a frequentist Gaussian process approach described in chapter $5$ of \citet{shi2011}.
We consider seven different curves each having between $0$ and $2$
extrema, and compare the fits of the other approaches to a
local extrema spline specified to have at most $H=2$ change points.
The following true curves are  investigated
\begin{align*}
	\begin{array}{rlrl}
	f_1(x) =& 10 x^{2}                         & f_2(x) =& 2+20\Phi\left\{(x-0{\cdot}5)/0{\cdot}071\right\}\\
	f_3(x) =& 5 \cos(\pi x)   & f_4(x) =& 10(x-0{\cdot}5)^2 \\
	f_5(x) =& -2{\cdot}5 + 10\exp\left\{-50(x-0{\cdot}35)^2\right\} &	 f_6(x) =& 1 + 2{\cdot}5 \sin\left\{2\pi(x+8)\right\}+10x \\
	f_7(x) =& 5 \sin(2\pi x)/(x+0{\cdot}75)^3 - 2{\cdot}5(x+10{\cdot}5)
	\end{array}
\end{align*}
We assume $y_i = f_j(x_i) + \epsilon_i$ with $\epsilon_i \sim \text{N}(0,\sigma^2).$
Functions $f_1,f_2$ and $f_3$ are monotone, functions $f_4$ and $f_5$ have one change point, and $f_6$ and $f_7$ have two change points. For each simulation, a total of $100$ equidistant points are sampled
across $\mathcal{X}=[0,1].$  In the simulation, we consider two variance conditions $\sigma^2  = 4$ and
$\sigma^2 = 1.$ For each simulation condition, $250$ data sets were generated, fit and compared using
the mean squared error, $n^{-1} \sum^n_{i=1} (\hat{f}(x_i)-f(x_i))^2,$  for the local extrema spline, smoothing spline, Bayesian P-spline, and Gaussian process approaches.

For the local  extrema approach, we collected $50,000$ Markov chain Monte Carlo samples, with the first
$10,000$ samples disregarded as burn in. For the parallel tempering algorithm,
we specify $12$ parallel chains with $\{\kappa_1,\ldots,\kappa_{12}\} = \{1/30,1/24,1/12,1/9,1/5,1/3{\cdot}5,1/2,1/1{\cdot}7,1/1{\cdot}3,1/1{\cdot}2,1/1{\cdot}1,1\},$ and monitor the target chain with $\kappa_{12}= 1.$ The P-spline approach was defined using $30$ equally
spaced knots, and the prior over the second order random walk smoothing parameter was given
a $\text{IG}(1$,0${\cdot}$0005) distribution, which  was one of the
recommended choices in \citet{lang2004}. In this approach,
$25,000$ posterior samples were taken disregarding
the first $5,000$ as burn in. For the smoothing spline method, the R
function `smooth.spline' was used. Finally, the Gaussian process approach
used a frequentist implementation given in the R package `GPFDA.'

Table  \ref{table1}  gives the integrated mean squared error
of the local extrema approach as compared to the  other approaches.
All numbers marked with an asterisk are significantly different
from the local extrema approach. In all conditions, the local
extrema approach has an integrated mean square error that is
numerically less than the other approaches, and, in most of these
conditions the value is significantly different at the 0${\cdot}$05
level, indicating the local extrema approach was superior, and, in some cases,
this improvement resulted in integrated mean square errors that were $40\%$
less than the closest competing method.  Generally, when there is
high signal to noise ratio the methods perform similarly.
However, in regions where the signal to noise ratio
decreases, specifically in flat regions, the local extrema approach was superior as
it removed artifactual bumps from the estimate.

\begin{table}
	\centering
	\caption{Integrated mean squared error for all functions. For each function, the top row
	represents the simulation condition $\sigma^2 = 4$ and the bottom row represents the
	simulation condition $\sigma^2 = 1.$ Asterisks signify the number is significantly
	different than the Local Extrema spline at the 0${\cdot}$05 level. For display purposes,
	all numbers are multiplied by 10. }
	\label{table1}

	\begin{tabular}{clllll}
						&    	        &	Local 	&	Smoothing       &Bayesian          &  Gaussian  \\
	True Function   	&     &   Extrema Splines &  Splines  &  P-Splines&              Process \\ [5pt]
\multirow{ 2}{*}{$f_1$}	&		        &	1$\cdot$60	&	2$\cdot$11$^*$	 &	2$\cdot$28$^*$	&	2$\cdot$15$^*$	\\
						&		        &	 0$\cdot$49	&	0$\cdot$58	&	0$\cdot$55	&	0$\cdot$71$^*$	\\ [3pt]

\multirow{ 2}{*}{$f_2$}	&		        &	2$\cdot$59	&	4$\cdot$19$^*$	& 3$\cdot$82$^*$		&	5$\cdot$26$^*$	\\
						&		        &	0$\cdot$09	&	0$\cdot$13$^*$	& 0$\cdot$11$^*$		&	0$\cdot$15$^*$	\\ [3pt]

\multirow{ 2}{*}{$f_3$}	&				&	 1$\cdot$57	&	2$\cdot$43$^*$	&	2$\cdot$26$^*$	&	2$\cdot$64$^*$	\\
						&				&	0$\cdot$49	&	0$\cdot$67$^*$	&	0$\cdot$92$^*$	&	0$\cdot$79$^*$	\\ [3pt]

\multirow{ 2}{*}{$f_4$}	&				&	1$\cdot$70   &	2$\cdot$10$^*$	& 2$\cdot$15$^*$		&  1$\cdot$90$^*$	\\
						&				&	0$\cdot$49	&	0$\cdot$56$^*$	& 0$\cdot$49		&  0$\cdot$59$^*$	\\ [3pt]

\multirow{ 2}{*}{$f_5$}	&				&	 2$\cdot$55	&	3$\cdot$69$^*$	&	3$\cdot$39$^*$	&	3$\cdot$90$^*$	\\
						&				&	0$\cdot$61	&	1$\cdot$12$^*$	&	0$\cdot$98$^*$	&	1$\cdot$14$^*$	 \\ [3pt]

\multirow{ 2}{*}{$f_6$}	&				&	2$\cdot$17	&	2$\cdot$57	&	5$\cdot$16$^*$	&	2$\cdot$44	\\
						&				&	0$\cdot$69	&	0$\cdot$72	&	0$\cdot$72	&	0$\cdot$79$^*$	 \\ [3pt]

\multirow{ 2}{*}{$f_7$}	&				&	2$\cdot$38	&	3$\cdot$39$^*$	&	3$\cdot$96$^*$	&	3$\cdot$30$^*$	\\
						&				&	0$\cdot$66	&	1$\cdot$05$^*$	&	0$\cdot$85$^*$	&	0$\cdot$90$^*$	\\

	\end{tabular}
\end{table}

\subsection{Hypothesis Testing}
We perform a simulation experiment investigating the method's ability to
correctly identify the shape of the response function. This is done for three
sets of hypotheses. In the first case, the null hypothesis is the
set of non-monotone functions and the alternative, $\mathbb{H}_1$, is the set of all
monotone increasing functions. In the second test, the null consists of all
monotone functions and the alternative, $\mathbb{H}_2$,
is all non-monotone functions. Finally, for the third test
the null hypothesis is the set of functions having at most one change point,
and the alternative, $\mathbb{H}_3,$ is the set of functions with two change points first having
a local maximum followed by a local minimum. Functions are defined on $\mathcal{X} \in [0,1].$
The nine functions used in this simulation are

\begin{align*}
	\begin{array}{rlrl}
					\multicolumn{4}{c}{\mathbb{H}_1} \\
		g_1(x)& =2+0{\cdot}5x +\Phi\{(x-0{\cdot}5)/0{\cdot}071\}   & g_2(x) &=0{\cdot}5 \sin\{2\pi (x+8)\} + 4{\cdot}75x \\[3pt]
		g_3(x)& \multicolumn{3}{l}{= 1 + 2{\cdot}25 x} \\   [3pt]
						\multicolumn{4}{c}{\mathbb{H}_2} \\
		g_4(x)& =-2(x-0{\cdot}75)^2     & 	g_5(x) &= 1+2x-1{\cdot}56 \exp\{-50(x-0{\cdot}5)^{2}\} \\[3pt]
		g_6(x)& \multicolumn{3}{l}{  = 15(x-0{\cdot}5)^31_{(x<0{\cdot}5)} +0{\cdot}3(x-0{\cdot}5)-\exp\{-250(x-0{\cdot}25)^2\}} \\[3pt]
					\multicolumn{4}{c}{\mathbb{H}_3} \\
		g_7(x)& = 0.85\sin\{2\pi(x+8)\} + 4{\cdot}75x   & g_8(x)&= g_5(x)\\   [3pt]
		g_9(x)&\multicolumn{3}{l}{=5\sin(2\pi x)/(x+0{\cdot}75)^3 - 2{\cdot}5(x+10{\cdot}5) + 2}.\\[3pt]
	\end{array}
\end{align*}

For the simulation, data are generated assuming $y_i = g_j(x)  + \epsilon_i$, where
$\epsilon_i \sim \text{N}(0,\sigma^2)$ and $\sigma^2=1.$
We consider sample sizes of $n = 100, 200, 300,$ and  $400,$ with
$50$ data sets constructed where points are sampled evenly across $\mathcal{X},$
for each sample condition. The local extrema approach
is specified as above except $150,000$ posterior samples are taken with the first $10,000$
disregarded as burn in.  For tests $\mathbb{H}_1$ and
$\mathbb{H}_2$, the local extrema approach
is compared against the Bayesian method of \citet{salomond2014} as well as
the frequentist methods of \citet{baraud2005} and \cite{wang2011}.  For the method
of Baraud et al. we use the test where $\ell_n = 25,$ and for the method of Wang and Meyer
we use $k=4$ splines, which were the most powerful tests presented in the respective articles.

The Bayesian tests produce Bayes factors, while the frequentist tests have corresponding test statistics. An important question is how to choose thresholds for concluding in favor of the null or alternative so that the tests are calibrated in the same manner.  We compare the methods based upon area under a receiver operating curve. This approach allows an objective comparison between the testing
approaches.  For the simulation, the false positive rate was computed from the values of the
test statistics for the other functions not in the test set.  For example, when the functions in hypothesis
$\mathbb{H}_1$ were considered, the test statistics for functions in hypotheses $\mathbb{H}_2$ and $\mathbb{H}_3$ were used.

\begin{figure}
	\centering
		\includegraphics[width=0.8\textwidth]{ROC.pdf}
	 \caption{The receiver operating curve for the four tests defined for hypothesis $\mathbb{H}_1$ for all $1,400$ simulations. }
\label{fig:ROC}
\end{figure}

Figure \ref{fig:ROC} shows the receiver operating curve for hypothesis $\mathbb{H}_1.$
This figure shows that the local extrema approach is superior to the other three approaches
across all false positive rates.  Further, the estimated area under the receiver operating
curve is $0{\cdot}94,$ which is excellent and better than the approach of Salomond at $0{\cdot}86$,
Baraud at $0{\cdot}77,$ and Wang and Meyer at $0{\cdot}74.$ When looking at the impact of sample size on the tests,
the power of the local extrema approach increases as the sample size increases,
does so at a rate greater than competitors, and is similarly superior for hypothesis
$\mathbb{H}_2,$ data not shown.

For hypothesis $\mathbb{H}_3$ there is not an equivalent methodology in the literature, but performance of our
approach is excellent. The area under the receiver operator curve
is $0{\cdot}937.$ For the Bayes factor cut point of $6$, table  \ref{table3} gives results across all simulation conditions.
Our test achieves high power for function $g_7,$ even though this function is only slightly
different than $g_3$.  Function $g_8$ is the same as $g_5$,  and this simulation gives evidence that the departure from
monotonicity, which is concluded with high power hypothesis $\mathbb{H}_2$, may be due to the pronounced `U' shape in the data, and not necessarily due to the fact that there are two extrema. As evident by the observed power,
this feature requires more data to conclude $\mathbb{H}_3$.

\begin{table}

	\centering
	\caption{Percent of samples where the model was correctly chosen as having
	two extrema.}

	\label{table3}
	\begin{tabular}{ccccc}
Function		&	\multicolumn{4}{c}{n}							\\
		&	100	&	200	&	300	&	400	\\[5pt]
$g_7$		&	78	&	90	&	98	&	96	\\
$g_8$		&	14	&	32	&	22	&	46	\\
$g_9$		&	76	&	88	&	98	&	100	\\
\end{tabular}

\end{table}

\section{Applications}

\subsection{Estimating Muscle Force}

When studying the ability of a muscle to adapt to exercise protocols, muscle force tracings are
often used. One approach involves first activating the muscle and then after a short period of time
moving the joint through the range of motion \citep{baker2008}. It is expected
that the muscle force quickly obtains a maximum force with the observed force decreasing
until joint movement; however, the observed force may plateau and not decrease before
movement. When the joint is moved, there is an expected increase in the force output until the joint
reaches a specific angle, after which, the observed force decreases until the joint reaches
its original position.  When the joint returns to its original position, the muscle remains activated
and the force output is non-increasing until deactivation.
Estimation of this muscle force curve may allow better understanding of adaptation or maladaptation
following exercise, but it is important to include known biophysical constraints in curve estimation.

We model two force tracings ($n=96$ per tracing) using a local extrema spline having at most $H=3$ local extrema.  Consistent with prior knowledge of a very high signal to noise ratio, we place a $\text{Ga}(2000,1)$prior on $\sigma^{-2}.$ We also applied frequentist smoothing splines, Gaussian processes, and Bayesian P-splines. Competing methods are close to interpolating the data points, leaving unwanted artifactual bumps in the function estimate.
However, as seen in Fig. \ref{fig:MFFig}, the local extrema spline obtains an estimate restricted to the
known shape and robust to minor local fluctuations. Further, when the force tracing exhibits a single maxima, as in the left plot, the local extrema spline can readily distinguish between this shape,  and
a shape which has two maximum, as in the right plot, with no change in the model.

\begin{figure}
	\centering
	\includegraphics[width=0.8\textwidth]{./iso-sscfig.pdf}
		\caption{Fit of the local extrema spline,  black line, to observed muscle force data, solid triangles.}
		\label{fig:MFFig}
\end{figure}

\subsection{Seasonal Influenza and Pneumonia Death Rate}
	In temperate climates, the prevalence of influenza peaks in the
	winter months while dropping in the warmer months. Estimating this seasonal effect
	as well as departures from this effect, may be of interest
	when estimating the magnitude of an influenza epidemic. Here, we expect a peak in the
	winter months followed by a trough in the summer months. Parametric models
	for this pattern may not be adequate to model the observed phenomena, and smoothing
	approaches do not guarantee this pattern.  We use local extrema
	splines, setting $H = 2$, to estimate this trend for Virginia, North Carolina and South Carolina
	for data collected by the Centers for Disease Control and Prevention National Center
	for Health Statistics Mortality	surveillance branch.

	Figure \ref{fig:CFPFig} plots the estimated mortality rates. These
	rates are	estimated using an additive model defined by a
	quadratic trend representing a decrease in mortality over time, a
	seasonal component defined using local extrema spline, and a P-spline that represents
	departures from the overall trend. In this figure, the black curve represents the
	seasonally adjusted trend using the local extrema spline.   This seasonal component is different
	than the trend published by the Centers for Disease Control, gray line \citep{viboud2010}.
	The main difference between the two is the asymmetry in the local extrema
	approach during the winter months, which can not not be captured by a single
	sinusoidal function.

\begin{figure}
	\centering
	\includegraphics[width=0.8\textwidth]{./flu.pdf}
		\caption{Estimate of the expected rate of seasonal influenza and pnuemonia deaths using the local
		extrema spline, black line, compared to the observed rate of influenza and pnuemonia deaths
		estimated using the Center for Disease Control's standard approach, gray line. }
		\label{fig:CFPFig}
\end{figure}

\section*{Acknowledgement}
This research was partially supported by a grant from the National Institute of
Environmental Health Sciences of the United States National Institutes of Health.  The
authors would like to thank Brent Baker for sharing the isometric muscle force
data.

redpajama_set_name: RedPajamaArXiv


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The CIA was very focused on killing Fidel Castro.
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text:
Friedrich Heinrich Zinckgraf (* 30. Oktober 1878; † 7. Juni 1954) war ein deutscher Galerist, Kunsthändler und Philatelist aus München.

Zinckgraf war schon lange Mitarbeiter der im Besitz einer aus dem Judentum stammenden Familie befindlichen Galerie Heinemann in München. Als die Verfolgung der Judenverfolgung schlimmer wurde, sah Zinckgraf seine Zeit gekommen. Er eignete sich 1938/1939 die Galerie Heinemann am Lenbachplatz an. Die Besitzerin Franziska Heinemann war nach den Novemberpogromen 1938 am 9./10. November 1938 ins Gefängnis gesteckt worden. Sie wurde erst wieder freigelassen, nachdem sie einem "ausgesprochen unfairen" Kaufangebot ihres Mitarbeiters Zinckgraf zugestimmt hatte. Dabei war ihm sein Freund, der ehemalige Wirtschaftsminister und frühere Reichsbankpräsident Hjalmar Schacht als stiller Teilhaber durch Bereitstellung von Kapital behilflich.

Zinckgraf war ein engagierter, bekannter Philatelist und Förderer der philatelistischen Abteilung der Münchner Stadtbibliothek. Er war auch jahrzehntelang Präsident des Münchener Briefmarkenclub e.V. 1953 erhielt Zinckgraf das Verdienstkreuz (Steckkreuz) der Bundesrepublik Deutschland. Nach Zinckgrafs Tod stiftete der Club zu seinen Ehren eine nach Zinckgraf benannte Medaille, die an Nachwuchssammler vergeben wird. Bereits zwei Jahre nach seinem Tod widmete ihm die Stadt München im Stadtteil Großhadern eine Straße.

Literatur
 Nachruf. In: Die Sammler-Lupe Nr. 15 von 1954, Jahrgang Nr. 9, S. 227
Anja Heuß: Friedrich Heinrich Zinckgraf und die "Arisierung" der Galerie Heinemann in München. In: Anzeiger des Germanischen Nationalmuseums. Hrsg. von G. Ulrich Großmann, Nürnberg 2012, S. 85 – 94
Birgit Jooss: Ludwig Grote und die Galerie Zinckgraf (ehemals Heinemann) in den Jahren 1940–1946, in "Ludwig Grote und die Bauhaus-Idee", hrsg. von Peter Bernhard und Torsten Blume, Leipzig 2021, S. 117 – 129.
 Christopher Kopper: Hjalmar Schacht. Aufstieg und Fall von Hitlers mächtigstem Bankier. München 2006, ISBN 3-446-40700-6. (Schacht war mit Zinckgraf befreundet)

Weblinks

 http://heinemann.gnm.de/

Einzelnachweise

Galerist
Philatelist
Träger des Bundesverdienstkreuzes 1. Klasse
Deutscher
Person (München)
Geboren 1878
Gestorben 1954
Mann


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text:
By CoyotePrime (Reporter)
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Sunday, September 6, 2020 11:17
by The Zman
"Television is the great propaganda weapon of the liberal democratic state, so it is a useful window into the thinking of the oligarchs. Movies and television shows still have to attract an audience, so they are usually the trailing edge of whatever the oligarchs are trying to impose on society, but the ads are a different matter. They are the leading edge of the latest Progressive fads. They know people will not abandon a show or movie just because the ads are offensive.
That's what makes the ads a useful window into the black soul of our rulers. The ad makers are all from the ruling class. Look at the team photo of an ad agency and it looks like the faculty of an Ivy League college. There may be a little color in there for show, but otherwise it is all men with small hats and people who still write "Episcopalian" when asked about their religion. The advertising agencies that produce these ads are the special forces of the Judeo-Puritan ruling class.
This is why the ad makers were ready for the aggressive push to support the Black Lives Matter stuff after George Floyd died from an overdose. It is the thing that gets no attention, but should be the focus. Within days of the event, even before the rioters were in the streets, every global corporation was running diversity ads. The television services had all their blaxploitation films and shows ready. They even changed their graphical interfaces to feature black stuff.
It takes weeks and months to put together a simple ad. The concept has to be settled and the story boards created. Then there is filming, editing and final production. A corporate marketing program takes months to get ready. Changing the look and feel of the TV streaming service to feature blacks is no small feat. Creating a useful list of "black creators" should take a week or two, but they had it all ready to go. This pogrom was in the works for months.
In large part this is why Black Lives Matter initially had lots of white support, despite its record of murder and mayhem. Just four years ago BLM was executing cops, but thanks to a barrage of ads, most people forgot that and were initially inclined to support the cause. Then the black protesters reminded everyone why Africa is not the high point of human progress. The ad makers have now shifted the diversity message to feature homosexuals, deviants and girls playing male roles.
That's really where you get a clear look into the mind of the oligarchs. This ad for the Marine Corp is getting revived in time for the election. When the ad was produced three years ago, the official line was that the Marines made the ad because they were facing pressure from women to let the girls go into combat units. That's a lie, of course, as no women want to go into combat. Most men don't want to see combat. Lying, however, is the core of advertising and the modern media.
The ad, of course, is disgusting. The thought of sending mothers and daughters into combat should make a decent person wretch. People at the edge of extinction turn their future into weapons of war. The ancients defined the barbarians, in part, by their habit of bringing their women and children to the battle. Of course, the absurdity of this little girl in combat is impossible to miss. Ad makers can normalize just about anything, but even they are bounded by reality.
You'll note that the ad makers always use white women when they are trying to convince girls to be boys. Non-whites always get portrayed in traditional roles or they are cast as the natural leaders. The military ads always have the blacks in command positions or as the heroic example of the military code. That's what they are selling to the non-whites they are targeting. Apparently, the oligarchs think they can patrol the empire with a Tinkerbell army run by 90-IQ officers.
Obviously, that will never happen. It does, however, reveal that these people are not geniuses who have carefully thought this through. They are caught up in nutty fads of their own creation, that sweep them along like flotsam. You see that with the response to the riots this summer. These idiot mayors, in places like Minneapolis and Portland, really thought they would be the heroes of these stories. They believed the agit-prop produced by the cult of social justice.
Even so, there are long term consequences to the culture war waged on the television screens of America. White males have been mostly removed from advertising, unless they are the fool or the supplicant. Blacks have been turned into objects of worship, largely due to television and advertising. This absurd sense of entitlement by blacks is one consequence. The negrophilia by many whites is another. It is not beyond the pale to use the term "ethnic cleansing" for what we are seeing.
At the peak of the 1960's cultural revolution, Timothy Leary popularized the phrase, "Turn on, tune in, drop out" as a way to convince people to detach from the existing conventions and hierarchies in society. Of course, he was peddling degeneracy and self-abuse to whites, but the advice actually makes a lot of sense as an antidote to what the oligarchs are doing to us now. Disconnecting from the system as much as possible places you beyond the tractor beam of the propaganda organs.
This is the irony of this phase of the cultural revolution. What was initially pitched as a counter culture movement, was really a war on heritage America by the newly ascendant managerial class. The way to overthrow this decrepit and degenerate ruling class is to take their old advice. White people need to detach from the existing conventions and hierarchies that support the oligarchs. We need a counter culture that turns off, tunes out and eventually drops out."
- https://www.theburningplatform.com/
Source: http://coyoteprime-runningcauseicantfly.blogspot.com/2020/09/turn-off-tune-out-and-drop-out.html
TV commercials are just as nauseating
Sep 6, 2020, 3:01 pm 1 Reply
K¡llúḿ¡ńàṫ¡✝☪ ॐ ﷲ ✡
Katt Williams Now, that was just the shit they told us when we were little.
Now that we grown, these mXtherfuckers still think we stupid.
They got commercials on television where they lie and tell the truth at the same time.
Now, how fXcking stupid do I have to be for you to lie and tell the truth at the same time?
I'll just ignore the mainstream media, and, i don't even care what happens in the world.
I don't care about what happens to earth or anyone else. "Um. Excuse me?"
I stopped watching TV? you have no no solution?
Once a sheep, always a sheep! learn to follow the older members…
baehh baehh, baaa baaa, bè bè, mbeeek mbeeek, mæh-mæh, mae-ee, mäh, meh meh
Yes great advice to preserve your mental health ….and Murdochs MOCKINGbirdy Lies….of constant FEAR/ terror-terror-Terror!
BUT with Covid Corona crown CONjob……..they are changing all LAWS ,daily. If we dont know this knew "Covid rule=LAW,now" crap…
u might get SHOT by Police freemason Gestapo …for NOT wearing a mask….for NOT distancing enough….for 'inciting revolts on Facebook".
THE REAL PROBLEM…..is evryone doesnt know who the real enemy is.
Corona= latin CROWN…..Papal CORONAtions of Kings/Queens….Defenders of the VATICAN PEDOPHILE FAITH.
RCC= RAPE CHILDREN CULT……Eunech making Castration of CHOIRBOY occult= @CASTRATO….the origin of adreno BLOOD jesus juice.
the JESUITS that secretly run as all…will lose their hold and control once this becomes truth……JE$U$ = a MYTH….to hide Attis.
to control the not so easily fooled by Jesus ….they created FREEMASONS…(Judges,Police,Military, Charity organisations like SALVOS).
BUT BOTH….swear that evil Jesuit dagger OATH on BENDED KNEE…..virgin mary landers. Knights of COLOMBUS?= Columbine school
God's Word - Ezekiel Chapter 43
Biden Holds Press Conference In Fluent Alzheimer's
The Ancient Priest of Saturn - The Midnight Ride


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Film based on Indira Gandhi's Assassination cleared by Delhi High Court
August 30th, 2019 | by vBollywood Author
The Delhi High Court has given permission for the release of Punjabi film "Kaum De Heere" which was slated for release back in August 2014. The verdict sets aside CBFC's earlier order withdrawing the film's certification for public screening.
The Punjabi film is based on the lives of Satwant Singh, Beant Singh and Kehar Singh, allegedly, glorifies the assassination of former prime minister Indira Gandhi.
Referring to a Supreme Court verdict, Justice Vibhu Bakhru said once an expert body has considered the impact of a movie on the public and has cleared the film, it is no excuse to say that there may be a law and order situation.
"The reliance placed by the respondents upon Section 6(1) of the Cinematograph Act, is wholly misplaced. First of all, the said provision to the extent that it enables the Central Government to exercise revisional powers in respect of the decisions rendered by CBFC, has been held to be unconstitutional. Second, even if Section 6(1) of the Act was operative, the respondents had not followed the procedure as contemplated therein. The petitioner was not granted any opportunity to represent its views before the direction was issued," the high court said.
The film was initially granted 'A' certification but was latter barred from release in India by the government.
The film's producer, Sai Cine Productions, had challenged CBFC's August 2014 and Film Certification Appellate Tribunal's October 2014 orders by which the film's certification was withdrawn.
The company had contended the board "had no factual or legal basis for withdrawal of certificate" after granting permission for release.
The Ministry of Information and Broadcasting and CBFC had said the withdrawal of certification was done according to the provisions of the Cinematograph Act, 1952 and on the orders of the central government.
Senior advocate Colin Gonsalves, appearing for the petitioner, had challenged the orders saying that the Chairperson of CBFC had no power to review and cancel the certificate that was issued by the CBFC.
He also contended that the said certification was issued by CBFC after the Revising Committee had viewed the feature film on two occasions.
He submitted that there was no provision in the Act which empowered the Chairperson to override the decision of the Revising Committee.
Advocate Colin Gonsalves had appeared for the production house submitted that the feature film did not violate any guidelines and withdrawal of certification was violative of Article 19(1)(a) of the Constitution of India.
Photo courtesy: www.thenewindianexpress.com
Assassination Delhi High Court Indira Gandhi


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Q: Zend framework controller filenames containing "init"? Zend framework: what is the significance of controller filenames that have "init" in them? I have 3 files that seems to have exactly the same code, named:
TestController_init.php
TestController.init.php
TestController.php
?

A: In my opinion you should have onlu one TestController.php that contains all behaviours that this controller should have (init() method, etc).
Could you pase the content of 2 other files ?


But there is one big difference between 1889 Germany and the world we live in today: The average lifespan then was 70 years. Now we're all living much, much longer. And many of us would like to retire much earlier. But the scary headlines — and the realities that we see around us — cast doubt on our ability to ever retire. The entire concept of retirement is starting to feel flimsy at best.
They don't. They don't even have a word for it. Literally nothing in their language describes the concept of stopping work completely. Instead, one of the healthiest societies in the world has the word ikigai (pronounced like "icky guy"), which roughly translates to "the reason you wake up in the morning." It's the thing that drives you most.
Now, am I saying that if you're six weeks away from your final punch-out after 30 years on the job, you should suddenly skewer your dreams and ramp up for 30 more? Of course not. What I'm saying is that retirement is a Western invention from days gone by that's based on broken assumptions that we want — and can afford — to do nothing.
If you're already struggling to pay bills and your career's sitting on tectonic plates that are threatening to shift below the labor market, my recommendation is to dig deep into your natural passions to find a second act that aligns with your values. We know there are far more problems and opportunities on this spinning planet than there are people to help with them, so go solve some! If you feel lost, follow your heart, find your ikigai, and remember the 4 S's.
And stop worrying that you won't ever be able to retire. You'll be far better off if you don't.


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