text:
123 → Next
Colpoys Bay WI Tweedsmuir Community History, Volume 2
Colpoys Bay Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1972] - [2010] FWIO Do You Know? Brochure Newspaper Articles Colpoy W.I.,1972,1973,1975,1976,1977,1978,1979,1981,1982,1983,1986,1952, 99th Birthday - Mary Rydall Bruce County W.I. Articles Colpoy's Bay Community Banquet Oct. 4,1946 Obituary - Annie Laura Parrot Pruder, June 6,1946 50th Anniversary - Clifford & Revenia Barfoot 50th Anniversary - Dave & Kathleen Caudle 50th Anniversary - Lil ...
Colpoys Bay Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1972] - [2010] FWIO Do You Know? Brochure Newspaper Articles Colpoy W.I.,1972,1973,1975,1976,1977,1978,1979,1981,1982,1983,1986,1952, 99th Birthday - Mary Rydall Bruce County W.I. Articles Colpoy's Bay Community Banquet Oct. 4,1946 Obituary - Annie Laura Parrot Pruder, ...
Bervie WI Tweedsmuir Community History, Volume 15
Bervie Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [2007] - [2011] W.I. Pictures Obituaries - Katherine E. Patterson Collins,January 22, 2004 - Elizabeth Pearl Griffith, May 18,2005 - Marjorie Louise Ferris Shewfelt, August 14, 2005 - Edbert Thompson Bushell, Oct. 31, 2004 - Lexie Bell, November 2, 2004 - Harold Quinn, August 27,2005 - Muriel Phyllis Dawson Eskrick, January 30,2005 - ...
Bervie Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [2007] - [2011] W.I. Pictures Obituaries - Katherine E. Patterson Collins,January 22, 2004 - Elizabeth Pearl Griffith, May 18,2005 - Marjorie Louise Ferris Shewfelt, August 14, 2005 - Edbert Thompson Bushell, Oct. 31, ...
Elsinore WI Scrapbook, 1975-1976
Elsinore Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1915] - [1976] Misc. Newspaper Articles Marriages - Colleen Lillian Harron & Murray James Miller, Sept.27,1975 - Phyllis Ruth Gowanlock & Wayne Gordon Stevens,October 18,1975 - Lynn Marie Nelson & Dave John White, July 12,1975 - Kathy Leagh Nickason & William Gary McDougald,Sept.26,1975 - Patricia Ann McCulloch & Michael John Smith - Phyllis ...
Elsinore Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1915] - [1976] Misc. Newspaper Articles Marriages - Colleen Lillian Harron & Murray James Miller, Sept.27,1975 - Phyllis Ruth Gowanlock & Wayne Gordon Stevens,October 18,1975 - Lynn Marie Nelson & Dave John White, ...
Stoney Creek Women's Institute Scrapbook 1940-59
Stoney Creek WI Scrapbook, 1940-59 - "Five-year Farm Recreation Plan" article with caption "What a united community can do" - Newspaper clippings related to various local WI branches: - St. George - Troy - Community Beach - Caledonia - Rockton - Binbrook - Woodburn - Ira Brock - Patricia - ...
Stoney Creek WI Scrapbook, 1940-59 - "Five-year Farm Recreation Plan" article with caption "What a united community can do" - Newspaper clippings related to various local WI branches: - St. ...
Vinemount WI Tweedsmuir Community History, Volume 5
Vinemount Women's Institute, (19140102), [1992]-[1999] Vinemount WI Tweedsmuir Community History, Volume 5 - Photos from a fashion show of historic garments - Article about Myrtle Sturch's 100th birthday - Article about Vinemount 4-H club planting a Catalpa tree at the Erland Lee Museum, 1995 - Article about Adelaide Hoodless stamp - Life memberships presented to ...
Vinemount Women's Institute, (19140102), [1992]-[1999] Vinemount WI Tweedsmuir Community History, Volume 5 - Photos from a fashion show of historic garments - Article about Myrtle Sturch's 100th birthday - Article about Vinemount 4-H club planting ...
Stoney Creek Women's Institute Scrapbook (Rogers) 1967-1979
This is a scrapbook compiled between 1967 and 1979 by Lorna M. Rogers, President of the Stoney Creek branch of the Women's Institutes. It contains: - Invitation to Stoney Creek Jubilee Banquet, 1947 - Photo of Charter Members (?) in 1947 (?) - "Stoney Creek W.I. Annual Dinner" article, no ...
This is a scrapbook compiled between 1967 and 1979 by Lorna M. Rogers, President of the Stoney Creek branch of the Women's Institutes. It contains: - Invitation to Stoney Creek ...
Bervie WI Tweedsmuir Community History, Volume 8
Bervie Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1999] - [2004] Obituary - Lynwood Geddes, Sept. 24,2001 Sports - Jeff Alcombrack Kincardine Scottish Pipe Band Medical Missionary, Rev. George Sach, Jan. 18,1995 95th Birthday - Gladys Arnold, 2000 Various Newspaper Articles Graduation - Murray Needham, May 16,1991 90th Birthday - Mary MacKenzie Sheane,Nov.18,1998 Various Poems Tribute to Princess Diana 25 Years ...
Bervie Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1999] - [2004] Obituary - Lynwood Geddes, Sept. 24,2001 Sports - Jeff Alcombrack Kincardine Scottish Pipe Band Medical Missionary, Rev. George Sach, Jan. 18,1995 95th Birthday - Gladys Arnold, 2000 Various Newspaper Articles ...
Lake Dore WI Tweedsmuir Community History, Volume 1
Lake-Dore Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), March 1992 Lake Dore Women's Institute Table of Contents Acknowledgements Historical Research & Current Events Mrs. Leslie Davis "Foreword" written by Lady Tweedsmuir Mrs. Adelaide Hunter Hoodless Presidents 1934 - 1992 Lake Dore W.I. Branch History, compiled by Averil Moore for 50th Anniversary Celebration, Sept. 12, 1984 In Memoriam, Lake Dore W.I. ...
Lake-Dore Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), March 1992 Lake Dore Women's Institute Table of Contents Acknowledgements Historical Research & Current Events Mrs. Leslie Davis "Foreword" written by Lady Tweedsmuir Mrs. Adelaide Hunter Hoodless Presidents 1934 - 1992 Lake ...
Brooksdale WI Tweedsmuir Community History: 2003-2004
Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [2003]-[2004] Brooksdale WI Tweedsmuir Community History, 2003-2004 Women's Institute Activities, 2003 - Brooksdale WI 80th Anniversary Celebration, January 16, 2003: Theme of "Hats off to BWI" - List of branch Presidents, Secretaries, and Treasurers from 1922-2002 - Brooksdale WI member Helen Piett receives Queen Elizabeth Golden Jubilee Medals - Brooksdale WI ...
Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [2003]-[2004] Brooksdale WI Tweedsmuir Community History, 2003-2004 Women's Institute Activities, 2003 - Brooksdale WI 80th Anniversary Celebration, January 16, 2003: Theme of "Hats off to BWI" - List of branch Presidents, ...
Bluebell WI Tweedsmuir Community History, Volume 2a
Bluebell Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1990] - [2002] Meeting notes Bluebell W.I. Pictures of W.I. Members Marriages - Jeannette Margaret Gilbert & Aaron Christopher Stronge, March 23,1991 - Bonnie Miller & Kelly Hellyer, Aug.17,1991 - Mr & Mrs Peter Norris, May 4,1991 Farming in Ottewell & Boat Lake Communities,1991 Obituaries - William Wayne Henry Rouse, Sept.15,1991 - David ...
Bluebell Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1990] - [2002] Meeting notes Bluebell W.I. Pictures of W.I. Members Marriages - Jeannette Margaret Gilbert & Aaron Christopher Stronge, March 23,1991 - Bonnie Miller & Kelly Hellyer, Aug.17,1991 - Mr & Mrs ...
Winona Tweedsmuir History, Volume 4 1972-1980
Winona Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1972]-[1980] - History of Winona WI - Several short poems/verses - Article on the Lewis house, Stoney Creek - Articles on opening of the Erland Lee Museum, 1972 - Death notice of Mrs. Carscallen (WI member) - Typewritten article, "Federated Women's Institutes of Ontario: Background History of the Lee Family and ...
Winona Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1972]-[1980] - History of Winona WI - Several short poems/verses - Article on the Lewis house, Stoney Creek - Articles on opening of the Erland Lee Museum, 1972 - Death notice ...
Castleton WI Scrapbook, 1999, Volume 2
Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1999] Newspaper Articles Obituaries - Dr. William John Dymoke Eberlie, March 26, 1999 - Alfred William Thrower, March 24, 1999 - Robert Gibson (Bob) Eakins, April 4, 1999 - Grace Hobbs Allchurch, April 2, 1999 - William Jeremiah "Bill" Purdy, March 28, 1999 - Elizabeth Jean Hetherington Teal, March 31, 1999 ...
Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1999] Newspaper Articles Obituaries - Dr. William John Dymoke Eberlie, March 26, 1999 - Alfred William Thrower, March 24, 1999 - Robert Gibson (Bob) Eakins, April 4, 1999 - Grace Hobbs ...
Vinemount Tweedsmuir History, Volume 6 1940-90
Vinemount Women's Institute, (19150723), [1940]-[1981] - Article, "At Lee Homestead: Unveiling Ceremony Honors Women's Institute Founder," 1967 - Program, "The Stoney Creek Women's Institute (The First in the World) Celebrates its 70th Birthday at "The Pines" February, 1967" - Pamphlet entitled "This is the Site of Squires Hall Stoney Creek where was formed the First ...
Vinemount Women's Institute, (19150723), [1940]-[1981] - Article, "At Lee Homestead: Unveiling Ceremony Honors Women's Institute Founder," 1967 - Program, "The Stoney Creek Women's Institute (The First in the World) Celebrates its 70th Birthday at "The ...
Brooksdale WI Tweedsmuir Community History: Volume 3, Activities
Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1984]-[2011] Brooksdale WI Tweedsmuir Community History, Volume 3: WI Activities This volume contains photos with captions and writeups about various Brooksdale WI events in the 1980s-2000s - Mayor's (Wallis Hammond) welcome address from the presentation of Youngsville historical plaque, 1984 - Photos of the ceremony and reception for the Youngsville plaque ...
Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1984]-[2011] Brooksdale WI Tweedsmuir Community History, Volume 3: WI Activities This volume contains photos with captions and writeups about various Brooksdale WI events in the 1980s-2000s - Mayor's (Wallis Hammond) welcome ...
Pinkerton WI Scrapbook, Volume 2
Pinkerton Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1970]-[1986] Pinkerton WI Scrapbook, Volume 2 (1974) Newspaper clippings from local newspapers relating to: - Pinkerton WI meetings - Bruce East District Annual, 1970 - Bruce Trail - Local birth/death announcements - Bruce County WI Rally, 1979 - Chickenfest - New Walkerton Community Centre, 1972 - Paisley Pioneer Village - Prime ...
Pinkerton Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1970]-[1986] Pinkerton WI Scrapbook, Volume 2 (1974) Newspaper clippings from local newspapers relating to: - Pinkerton WI meetings - Bruce East District Annual, 1970 - Bruce Trail - Local birth/death announcements ...
Honeydale WI Tweedsmuir Community History, Volume 7
Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1990] - [1992] Official Opening S.A. Cawker Public School, May 10,1990 Newspaper Articles Photographs Obituary - Philip Figary, Apr. 23, 1925 - J.J. Gibson, Aug. 7, 1985 - Eleanor Wood, June 16, 1987 - Storey Esmond Beare, July 20, 1990 - Caroline Katherine Naples, Feb. 16, 1990 - Arthur W. Brock, Nov. 30, ...
Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1990] - [1992] Official Opening S.A. Cawker Public School, May 10,1990 Newspaper Articles Photographs Obituary - Philip Figary, Apr. 23, 1925 - J.J. Gibson, Aug. 7, 1985 - Eleanor Wood, June 16, 1987 ...
Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [2011] Newspaper Articles Obituaries - Eleanor Jean McCubbin Dudley, March 31, 2011 - Donald James Newlands, March 25, 2011 - John Peter de Graauw, April 5, 2011 - Linda Ann Boucher Cotton, April 8, 2011 - Lois Emeline Linton, April 12, 2011 - Lillian McMahon, Feb. 4, 2011 - Finn Erik ...
Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [2011] Newspaper Articles Obituaries - Eleanor Jean McCubbin Dudley, March 31, 2011 - Donald James Newlands, March 25, 2011 - John Peter de Graauw, April 5, 2011 - Linda Ann Boucher ...
Sunshine WI Tweedsmuir Community History, Volume 7
Sunshine Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1953]-[1986] Sunshine Women's Institute,Fournier, Ontario, Tweedsmuir History, Book 7 Obituary - Alma Catherine MacGillivray, March 5, 1953 Letterhead Sunshine Women's Institute List of Curators Obituary - Minnie Isabel (Harkin) McGowan, May 11, 1998 Sunshine W.I. Branch - Table of Contents Picture - District Annual held in Riceville, June 14, 1946 Picture ...
Sunshine Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1953]-[1986] Sunshine Women's Institute,Fournier, Ontario, Tweedsmuir History, Book 7 Obituary - Alma Catherine MacGillivray, March 5, 1953 Letterhead Sunshine Women's Institute List of Curators Obituary - Minnie Isabel (Harkin) McGowan, May ...
Dunchurch WI Tweedsmuir Community History, Volume 5
Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [2005] - [2011] Newspaper Articles Dunchurch WI Programme - 2001-2002 - 2002-2003 - 2003-2004 - 2004-2005 - 2005-2006 Photographs Parry Sound District WI Life Membership - Jewell Crossman, May 2003 Agenda - Northern Area W.I. Convention, Oct. 4, 2003 Northern Area WI Financial Report 2002-2003 90th Anniversary Dunchurch WI June 19, 2003 Parry ...
Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [2005] - [2011] Newspaper Articles Dunchurch WI Programme - 2001-2002 - 2002-2003 - 2003-2004 - 2004-2005 - 2005-2006 Photographs Parry Sound District WI Life Membership - Jewell Crossman, May 2003 Agenda - Northern ...
Horton North WI Tweedsmuir Community History, Volume 6
Horton North Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1811] - [2003] Mary Stewart Collect, Institute Grace Ode written by Mrs. Eva Wallace, North Horton W.I. The Women's Institute - Do you know that? North Horton Women's Institute By-Laws, March 15,2001 Branch Program for the Centennial Celebration, February 19,1997 FWIO Honouring an Older Member, International Year of Older Persons Renfrew South District ...
Horton North Women's Institute, Tweedsmuir Community History Collections (Stoney Creek, ON: Federated Women's Institutes of Ontario), [1811] - [2003] Mary Stewart Collect, Institute Grace Ode written by Mrs. Eva Wallace, North Horton W.I. The Women's Institute - Do you know that? North Horton Women's Institute By-Laws, March 15,2001 Branch ...
Bervie Women's Institute (2)
Blackstock Women's Institute (1)
Bluebell Women's Institute (1)
Brooksdale Women's Institute (2)
Bruce Centre District (1)
Calvin Women's Institute (1)
Castleford Women's Institute (4)
Castleton Women's Institute (6)
Cobden Women's Institute (1)
Colpoy's Bay Women's Institute (1)
Dunchurch Women's Institute (1)
Elsinore Women's Institute (1)
Falkenburg Women's Institute (1)
Gillies Hill Women's Institute (2)
Holyrood Women's Institute (1)
Honeydale Women's Institute (1)
Horton North Women's Institute (2)
Kinloss Kairshea Women's Institute (1)
Lake Dore Women's Institute (1)
Lucknow Women's Institute (2)
Monteith Women's Institute (1)
Pinkerton Women's Institute (1)
Queen's Line Women's Institute (2)
Ross, Allie, Miss (2)
Shirley Women's Institute (1)
Snake River Women's Institute (1)
Stoney Creek Women's Institute (2)
Sunderland Women's Institute (2)
Sunshine Women's Institute (5)
Tweedsmuir Community History Collections (55)
Tweedsmuir Histories (55)
Vinemount Women's Institute (2)
Walkerton Young Women's Evening Women's Institute (3)
Waters Women's Institute (1)
Westmeath Women's Institute (1)
Westwood Women's Institute (1)
Winona Women's Institute (1)
Women's Institutes Documents (58)
Woodville Women's Institute (2)
Centenarians (59)
Women's Institutes (59)
Aged persons (28)
Hospitals (26)
Galleries & museums (23)
Ice hockey (14)
Villages (14)
Banquets (13)
Retirements (13)
Committees (11)
Stores & shops (9)
Google Earth [help]
Funding for this project was provided by the Government of Canada
Please consider a donation to our Tweedsmuir Fund to help us continue digitizing and providing this content for free
Learn more about the Federated Women's Institutes of Ontario by visiting our website


text:
Young and the Restless Spoilers
Perhaps one of the most iconic soap operas in history. The day-to-day drama and the vast number of plots. That the series spews out over the course of a year can fill a loyal fan's lifetime.
Y&R spoilers keep wanting us to believe that Ashland Locke's days are numbered, and he couldn't possibly be plotting anything. Except no one around Victoria Newman believes that these two crazy kids could possibly be experiencing the real thing. A true love story for the ages. (Source: soaphub.com)
Ashland Fake Army Planning to Save Themselves
While the last few seasons of Young and the Restless left many fans heartbroken and disappointed. The fans who managed to hold on were rewarded with an even more mysterious and intriguing storyline: the fake army of Ashland. Insider sources tell us that the network's plan for the season is to have the fake army save the town of Oakdale. They are then revealed to be fakes.
The Y&R spoilers for Wednesday, September 15, 2021, once again center on Ashland Locke's past. After coming completely clean with Victoria Newman (he says), Ashland offers an abbreviated version to the rest of her family. Victoria pleaded with them to respect Ashland's – and her – privacy. But Billy Abbott isn't feeling it. And he intends to make a move that even Lily Winters can't condone. (Source: soaphub.com)
Ashland announces threats to Billy's father, who says it will never marry Victoria if Billy goes through with the wedding.
Ashland's players make a plan to bring on a fake army on the show. To save themselves from the vicious plans of Billy and Victoria. The fake army becomes a huge problem for the citizens of Ashland.
Look for Young and the Restless spoilers and news every day at Soap Dirt. (Source: soapdirt.com)
This Will Be Ashland Locke's Next Big Moment
As we all know, this is a pivotal moment for Ashland. And it is this key event that might finally win over the town and fans of the show. Nevertheless, this was a crucial conversation and with any luck, we will see it escalate in the upcoming episode.
Young and the Restless spoilers hint Sally Spectra designs a stunning wedding dress. That will have a big impact on one lucky lady and redeem the redhead too… (Source: soapdirt.com)
Victoria and Billy's Future This Week on Young and Restless
The Week in Young and the Restless spoilers this week include huge moments in the Ashland/Billy/Victoria triangle. Victoria let Billy know in no uncertain terms that she's no longer interested in marrying him. Billy's father, Ashland Locke, held a press conference at the Ashland compound to announce. The threats he will make if Billy goes through with the wedding. In the meantime, Ashley hired a fake army of tough guys to save themselves from being married.
Bragging About Spoilers to Friends on Facebook
Viewers of the Young and the Restless seemed surprised to see the duo reunited on Thursday, but not everyone's disappointed. The change in dynamic can be attributed to the spoilers for this week's episode, which will feature the introduction of Ashland Locke. After splitting up for so long, viewers will be excited to see their favorite couple together again.
The Golden Globes Are Returning to NBC in January 2023
How to Tour Tyler Perry Studios in 2023
Who Streams Married at First Sight 2023?
5 Ways to Create Videos Online
How Can I Get Verified on YouTube?
How to Get the Most Out of Twitter
Black Friday 50 Inch TV Deals 2022 346
Why Rex Orange County is Trending on Twitter
Richa Moorjani - A Beautiful Indian-American Beauty Queen
Now You See Me 3.
How old is piper Rochelle
How Many Episodes of Real Housewives of Potomac Season 6 2023 Will Be Out?
When is Real Housewives of Potomac Season 7 Coming Out 2023?
Free Movies at Lincoln Center
Why is Caitlin Johnstone a Popular Face on Facebook?
Posted on September 16 , 2021

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Why does cat <<< $VAR1 lose newlines? Example 1: Print two lines from the shell
$ cat <<< $'Line 1\nLine 2'
Line 1
Line 2

Example 2: Does not print two lines, why?
$ VAR1=$'Line 1\nLine 2'
$ cat <<< $VAR1
Line 1 Line 2

Checking the value of VAR1 to see if it is exactly what I set it to:
set | grep VAR1

Output:
VAR1=$'Line1\nLine2'

So, if VAR1 is what I set it to, why does variable expansion produce a result different from the literal string - the \n is replaced with a space?

A: Although the parameter expansions in a here string are not supposed to undergo word-splitting, that wasn't actually true until bash 4.4. The newline in the expansion is treated as arbitrary whitespace, which the shell replaces with a single space before passing the result into cat's standard input.
Quoting the expansion preserves the literal newline in earlier versions of bash:
bash-4.3$ VAR1=$'Line 1\nLine 2'
bash-4.3$ cat <<< $VAR1
Line 1 Line 2
bash-4.3$ cat <<< "$VAR1"
Line 1
Line 2

but the unquoted expansion works as intended in bash 4.4:
bash-4.4$ VAR1=$'Line 1\nLine 2'
bash-4.4$ cat <<< $VAR1
Line 1
Line 2

redpajama_set_name: RedPajamaStackExchange


text:
Italian Army Growing Medical Cannabis to Help Drive Down Prices
July 26, 2016 by Anthony Martinelli
By Gabriel Samuels, The Independent
The Italian army is growing large crops of cannabis in order to force the price of the drug down to about €8 per gram, according to the colonel overseeing production.
In September 2014, the country's government announced the army would help increase the production of medical marijuana, with the first secure growing facility unveiled in Florence in April last year.
It is hoped the sterile chamber will produce up to 100kg of cannabis every year, strictly for use by cancer patients, multiple sclerosis sufferers and those with other medical conditions which could be alleviated by the drug.
Colonel Antonio Medica is in charge of the Florence military base, which currently houses around 135 cannabis plants in carefully maintained conditions.
"My mission is to produce the best-quality cannabis on an industrial scale at a low price," he told The Times. "We think we can get that down to €8 [per gram]".
The colonel confirmed the army had been entrusted with the task due to the guarantee of tight security and because it has been involved in pharmaceutical matters since the 1800s, providing medicines and treatments for injured soldiers.
He said the purity of the drug was a crucial factor in its production, adding: "The police offered us cannabis they had seized but it was not up to the standards we want."
The cost of medical marijuana is not covered by the Italian government, meaning patients are frequently left unable to pay the prohibitive costs of the drug.
The substance has been clinically proven to benefit sufferers of a variety of conditions, particularly those involving chronic pain and damage to the nervous system.
Like in the UK, the possession, cultivation and sale of cannabis in Italy are illegal, with the latter crime punishable by imprisonment.
However, Italian government may be about to legalise the home-growth of small quantities of marijuana if a law being debated next week is approved, according to the Local.
According to the law, Italian people would be permitted to grow up to five cannabis plants for personal use and keep up to 15 grams of marijuana at home and five grams on their person.
Categories News Tags colonel antonio medica, gabriel samuels, italian army, italy, italy medical cannabis, italy medical marijuana, the independent, the times Post navigation
King County, WA Lifts Ban on Cannabis Businesses
Marijuana Popsicles
1 thought on "Italian Army Growing Medical Cannabis to Help Drive Down Prices"
Douglas Curtis
They want maximum terpene and cannabinoid production and retention? They should read my book. Seriously.
https://www.amazon.com/dp/B01HZWMCEC
"Secrets to Growing Trichome Dense Cannabis"


With almost three decades of experience in the cash handling industry, we are familiar with cash processing challenges faced in the areas of education, healthcare, the public sector, charities and private organisations. In confidence, we can speak to you and your staff to analyse your processes and existing machines. By combining our experience and knowledge with this information we can provide you with a detailed recommendation for process improvements and equipment & software upgrades.
We know that being able to reduce the time and effort spent counting and sorting cash is crucial. You can do this by implementing some simple changes. Technology can do all of these tasks faster, more accurately and also provide you with comprehensive, real-time reports.
In addition to this, by using our proprietary software, Cashman Connect, you can link up your equipment and create customised reports that suit YOUR requirements.
No matter what size your budget is, we will work with you to find the best-fit solution for your business.
Take manual counts, rechecks and human error out of the picture and you can considerably reduce the time spent counting, reconciling and sorting cash.
Security is an important concern for any business that handles cash. We understand that accurately and securely processing your cash, while keeping costs down can be a challenge.
Automating your cash handling processes also results in less shrinkage, enabling you to manage your cash more efficiently and profitably. This is where the right cash management system can make all the difference. We provide solutions of all sizes from point of sales smart safes right through to back office cash depositing & recycling equipment, allowing you to track transactions with real time reporting and potentially reduce cash holdings through onsite cash recycling.
Automating your cash handling processes saves you both time and money and results in a more streamlined process where you and your staff can focus more on revenue generating activities.
"Money Point has enabled us to cut our cash handling time in half."
"Money Point provided us with exactly what we needed and to top it all off, our return on investment was less than 20 weeks!"


Its been four years since popular gospel group M.O.G broke up leaving their fans in shock.
According to Kenti one of the members disclosed that they had achieved all they had planned as a group and were now working on solo projects.
Sionce then fans have been hoping for a reunion of the guys that gave us bangers like Papa God, Heart Breaker and Tosheka.
Well according to Boss of the group while speaking in an interview with one of the radio stations said, a M.O.G reunion might be a tall order. This is because among other issues, Tony of the group couldn't sing and some members of the group felt like he was leeching off them as the money was shared equally.
"It will take a lot of things for us to come back together. Because kuna vitu ambavyo zilifanya tukosane. For example Tony alikuwa na shida ya kuimba, mafans hawajui. Mafans walikuwa wanatuona pale mbele sisi sote tunaimba, sote tunashika microphone wanaona vitu ziko sawa. Ikafika mahali mmoja wetu akaona aah mbona huyu haimbi ila tunagawana pesa the same measure? Ikakuwa issue. Kuna uwezekano tutarudi pamoja but there are some factors to be considered before we come back together," he explained on Mambo Mseto.


text:
\section{Introduction}
In \cite{bessis}, while studying partition functions of quantum
mechanical systems, a conjecture was made regarding a positivity
property of traces of matrices.  If this property holds, explicit
error bounds in a sequence of Pad\'e approximants follow.
Recently, in \cite{Lieb}, and as previously communicated to us
\cite{JH}, the conjecture of \cite{bessis} was reformulated as a
question about the traces of certain sums of words in two positive
definite matrices.
\begin{conj}[BMV]\label{conjecture}
The polynomial $p(t) = \text{\rm{Tr}}\left[(A+tB)^m\right]$ has all
positive coefficients whenever $A$ and $B$ are $n$-by-$n$ positive
definite (PD) matrices.
\end{conj}
The coefficient of $t^k$ in $p(t)$ is the trace of $S_{m,k}(A,B)$,
the sum of all words of length $m$ in $A$ and $B$, in which $k$
$B$'s appear (sometimes called the $k$-th Hurwitz product of $A$
and $B$).  In \cite{JH}, among other things, it was noted that,
for $m <6$, each constituent word in $S_{m,k}(A,B)$ has positive
trace.  Thus, the above conjecture is valid for $m < 6$ and
arbitrary positive integers $n$.  It was also noted in \cite{JH}
that the conjecture is valid for arbitrary $m$ and $n < 3$.  Thus,
the first case in which prior methods do not apply and the
conjecture is in doubt, is $m = 6$ and $n = 3$.  Even in this
case, all coefficients, except
$\text{Tr}[S_{6,3}(A,B)]$, are known to be positive (also as shown
in \cite{JH}).  Our purpose here is to show that the remaining
coefficient $\text{Tr}[S_{6,3}(A,B)]$ is nonnegative when $A$ and $B$
are 3-by-3 positive definite matrices, which requires notably
different methods (some summands of $S_{6,3}(A,B)$ can have
negative trace \cite{JH}).  It follows that the conjecture is
valid for $m= 6$, $n=3$, our new result.  A key tool is that it
suffices to prove the conjecture for singular (positive
semidefinite) matrices.

The coefficients $S_{m,k}(A,B)$ may be generated via the
recurrence: \[S_{m+1,k+1}(A,B) = S_{m,k}(A,B)B + S_{m,k+1}(A,B)A\]
(variants are available).  The following lemma will be useful for
computing the $S_{m,k}$.  We give an algebraic proof although a purely combinatorial proof is also available.
\begin{lem}\label{easytracelemma}
For any two $n$-by-$n$ matrices $A$ and $B$, we have
\[\text{\rm{Tr}}\left[S_{m,k}(A,B)\right] = \frac{m}{m-k}
\text{\rm{Tr}}\left[AS_{m-1,k}(A,B)\right].\]
\end{lem}
\begin{proof}
\begin{equation*}
\begin{split}
0 = & \text{Tr}\left[ {\sum\limits_{i = 1}^m {\left( {A + tB}
\right)^{i - 1} \left( {A - A} \right)\left( {A + tB} \right)^{m -
i} } } \right] \hfill \\
= &\text{Tr}\left[ {m A\left({A + tB} \right)^{m - 1}}\right]  -
\text{Tr} \left[\sum\limits_{i = 1}^m {\left( {A + tB} \right)^{i
- 1} A\left( {A + tB} \right)^{m - i} }  \right] \hfill \\
= & \text{Tr}\left[ {mA\left( {A + tB} \right)^{m - 1} } \right] -
\left. {\text{Tr}\left[ {\frac{d} {{dy}}\left( {Ay + tB} \right)^m
} \right]\;} \right|_{y = 1}  \hfill \\
= & \text{Tr}\left[ {mA\left( {A + tB} \right)^{m - 1} } \right] -
\left. {\frac{d} {{dy}}\left[ {\text{Tr}\left( {Ay + tB} \right)^m
} \right]\;} \right|_{y = 1}. \\
\end{split}
\end{equation*}
Since $S_{m,k}(Ay,B) = y^{m-k}S_{m,k}(A,B)$, it follows that the
coefficient of $t^k$ in the last expression above is just
\[m\text{Tr}[AS_{m-1,k}(A,B)] - (m-k)\text{Tr}[S_{m,k}(A,B)],\]
which proves the lemma.
\end{proof}

\section{Reduction to the Singular Case}

Of course, when $A$ and $B$ are Hermitian, $S_{m,k}(A,B)$ is
Hermitian, but even when $A$ and $B$ are $n$-by-$n$ real symmetric PD matrices, $n > 2$, $S_{m,k}(A,B)$ need not be PD.  Examples are
easily generated, and computational experiments suggest that it is
usually not PD. We want to show that Tr[$S_{6,3}(A,B)]$ is
nonnegative for $3$-by-$3$ positive definite $A$, $B$.  This is subtle as $S_{6,3}(A,B)$ need not have positive eigenvalues, and as some words within the $S_{6,3}(A,B)$ expression can have negative trace \cite{JH}.  A main component of our argument is based on the following technical observation.

\begin{thm}\label{mainlemma}
Let $B$ be any real $n$-by-$n$ matrix, and let $A =
\text{\rm{diag}}(1,x_1,\ldots,x_{n-1})$.  Suppose that $\mathbf{a} =
(a_1,\ldots,a_{n-1}) \in [0,1]^{n-1}$, and let $D =
\text{\rm{diag}}(1,d_1,\ldots,d_{n-1})$ be such that $d_i = 0$ if $a_i
= 0$, and $d_i = 1$ otherwise.  If $\mathbf{a}$ achieves the
minimum of the function $f: [0,1]^{n-1} \to \mathbb R$ given by
$f(x_1,\ldots,x_{n-1}) = \text{\rm{Tr}}[S_{m,k}(A,B)]$, then, with $A'
= \text{\rm{diag}}(1,a_1,\ldots,a_{n-1})$, we have
\[f(a_1,\ldots,a_{n-1}) = \text{\rm{Tr}}[S_{m,k}(A',B)] = \frac{m}{m-k}
\text{\rm{Tr}}\left[DS_{m-1,k}(A',B)\right].\]
\end{thm}

\begin{proof}
Let $A'$, $B$, $D$, and $\mathbf{a} = (a_1,\ldots,a_{n-1}) \in
[0,1]^{n-1}$ be as in the hypotheses of the theorem. First suppose
that $A' = D$. Then, it is clear that the formula in the theorem
reduces to the identity in Lemma \ref{easytracelemma}.  When $A'
\neq D$, consider the differentiable function $g: [-1/2,1] \to
\mathbb R$ given by
\[g(z) = \text{Tr}\left[S_{m,k}\left(\frac{A'+zD}{1+z},B \right)\right].\]
By hypothesis, ${\bf a} \in [0,1]^{n-1}$ achieves the
minimum for $f$.  Consequently, it follows (from basic variational techniques) that
\begin{equation}\label{derivzero}
\left. {\frac{{dg(z)}} {{dz}}\;} \right|_{z = 0}  = 0.
\end{equation}
Next, notice that, \[\frac{d} {{dz}}\left[ {\text{Tr}\left(
{\frac{{A' + zD}} {{1 + z}} + tB} \right)^m } \right] =
\text{Tr}\left[ {\frac{d} {{dz}}\left( {\frac{{A' + zD}} {{1 + z}}
+ tB} \right)^m } \right]
\]
\[=  \text{Tr}\left[ {\sum\limits_{i = 1}^m {\left( {\frac{{A' + zD}}
{{1 + z}} + tB} \right)^{i - 1} \frac{d} {{dz}}\left( {\frac{{A' +
zD}} {{1 + z}} + tB} \right)\left( {\frac{{A' + zD}} {{1 + z}} +
tB} \right)^{m - i} } } \right].\]  In particular, at $z= 0$, the
above expression evaluates to
\[\text{Tr}\left[ {\sum\limits_{i = 1}^m {\left( {A' + tB} \right)^{i - 1} \left( {D - A'} \right)\left( {A' + tB} \right)^{m - i} } } \right]
\hfill\]
\[=\text{Tr}\left[ {m D\left({A' + tB} \right)^{m - 1}}\right]  - \text{Tr} \left[\sum\limits_{i = 1}^m {\left( {A' + tB} \right)^{i - 1} A'\left( {A' + tB} \right)^{m - i} }  \right]
\hfill\]
\[=\text{Tr}\left[ {mD\left( {A' + tB} \right)^{m - 1} }
\right] - \left. {\text{Tr}\left[ {\frac{d} {{dy}}\left( {A'y +
tB} \right)^m } \right]\;} \right|_{y = 1}  \hfill\]
\begin{equation}\label{traceeqn}
=\text{Tr}\left[ {mD\left( {A' + tB} \right)^{m - 1} } \right] -
\left. {\frac{d} {{dy}}\left[ {\text{Tr}\left( {A'y + tB}
\right)^m } \right]\;} \right|_{y = 1}.
\end{equation}

Finally, observe that $S_{m,k}(A'y,B) = y^{m-k}S_{m,k}(A',B)$ so
that the coefficient of $t^k$ in (\ref{traceeqn}) is
\[m\text{Tr}[DS_{m-1,k}(A',B)] - (m-k)\text{Tr}[S_{m,k}(A',B)].\]
It follows, therefore, from (\ref{derivzero}) that
\[\text{Tr}[S_{m,k}(A',B)] = \frac{m}{m-k}
\text{Tr}\left[DS_{m-1,k}(A',B)\right].\]  This completes the
proof.
\end{proof}

\begin{ex}
As an example of the theorem, let $m = 4$, $n = 3$, $k = 2$, and
\[B = \left[
\begin {array}{ccc} -2&1&0\\\noalign{\medskip}-1&2&3
\\\noalign{\medskip}1&-1&3\end {array} \right], \
A = \left[ \begin {array}{ccc}
1&0&0\\\noalign{\medskip}0&x_1&0\\\noalign{\medskip}0&0&x_2\end
{array} \right] .\]  A straightforward computation gives us that
\begin{equation*}
\begin{split}
\text{\rm{Tr}}[S_{4,2}(A,B)] = & \
20-4\,x_1+8\,{x_1}^{2}-12\,x_1x_2+42\,{x_2}^{2}, \\
\text{\rm{Tr}}[S_{3,2}(A,B)] = & \ 9 + 18x_2. \\
\end{split}
\end{equation*}
The minimum of $\text{\rm{Tr}}[S_{4,2}(A,B)]$ is achieved by $x_1 = 7/25$, $x_2 = 1/25$, and one has \[\text{\rm{Tr}}[S_{4,2}(A',B)] = 2\text{\rm{Tr}}[S_{3,2}(A',B)] =
\frac{486}{25}.\]
\end{ex}

Let $A$, $B$, and $f$ be as in Theorem \ref{mainlemma}. If we are
fortunate enough that $f$ achieves a minimum $f(\mathbf{a})$ with
$\mathbf{a} \in (0,1]^{n-1}$, then $D$ is the identity matrix and the theorem statement simplifies to the following.

\begin{cor}\label{maincor}
Suppose that $f$ as in Theorem \ref{mainlemma} achieves a minimum
$f(\mathbf{a})$ with $\mathbf{a} \in (0,1]^{n-1}$.  Then, the
nonnegativity of $\text{\rm{Tr}}[S_{m-1,k}(A',B)]$ implies the
nonnegativity of $\text{\rm{Tr}}[S_{m,k}(A',B)]$.
\end{cor}

To see the importance of this corollary, we next examine the real version of Conjecture \ref{conjecture}.  Suppose we know that the conjecture is true for
the power $m-1$ and also suppose (by way of contradiction) that
there exist $n$-by-$n$ real positive definite matrices $A$ and $B$
such that $\text{Tr}[S_{m,k}(A,B)]$ is negative.  Then, in
particular, (by homogeneity) there are real positive definite $A$
and $B$ with norm 1 such that $\text{Tr}[S_{m,k}(A,B)]$ is
negative (here, we use the spectral norm \cite[p. 295]{HJ1} so
that for positive semidefinite $A$, it is just the largest
eigenvalue of $A$). Let $M$ be the (compact) set of real positive
semidefinite matrices with norm 1 and choose $(A,B) \in M\times M$
that minimizes $\text{Tr}[S_{m,k}(A,B)]$; our goal is to show that
this minimum is 0. By a uniform (real) unitary similarity we may assume
that $A = \text{diag}(1,a_1,\ldots,a_{n-1})$ is diagonal with $1
\geq a_1 \geq \cdots \geq a_{n-1} \geq 0$.

Corollary \ref{maincor} then tells us that $A$ must be singular,
because by induction, $\text{Tr}[S_{m-1,k}(A,B)]$ will be
nonnegative for all positive semidefinite $A$ and $B$.  By
symmetry, it also follows that $B$ is singular.  We combine these
observations into the following theorem.

\begin{thm}\label{singthm}
Suppose that $\text{\rm{Tr}}\left[(A+tB)^{m-1}\right]$ has all positive
coefficients for each pair of $n$-by-$n$ real
positive definite matrices $A$ and $B$.  If $p(t) = \text{\rm{Tr}}\left[(A+tB)^m\right]$ has all positive coefficients whenever $A, B \neq 0$ are singular $n$-by-$n$ real
positive definite matrices, then $p(t)$ has all positive
coefficients whenever $A$ and $B$ are arbitrary $n$-by-$n$ real
positive definite matrices.
\end{thm}

\section{Symbolic Real Algebraic Geometry}

In this section, we discuss the symbolic algebra preliminaries
necessary for solving the $m = 6$, $n=3$ case of Conjecture
\ref{conjecture}. Let $R = \mathbb Q[x_1,\ldots,x_n]$, and let $I,J$ be
two ideals of $R$. The \emph{quotient ideal} of $I$ by $J$ is the
ideal of $R$ given by \cite[p. 23]{Cox2} \[(I:J) = \{f \in R :
fg \in I \text{ for all $g \in J$}\}.\]  We can iterate this
process to get the increasing sequence of ideals \[I \subseteq
(I:J) \subseteq (I:J^2) \subseteq (I:J^3) \subseteq \cdots.\] This
sequence stabilizes to an ideal called the \emph{saturation} of
$I$ with respect to $J$ (see \cite[p. 15]{PolySystems}):
\[(I,J^{\infty}) = \{f \in R :  \exists m\in \mathbb N \text{
with } f^m \cdot J \subseteq I\}.\] If $I$ is any ideal in $R$,
let $V(I)$ denote the set, \[V(I) = \{(a_1,\ldots,a_n) \in \mathbb
C^n :  f(a_1,\ldots,a_n) = 0 \text{ for all $f \in I$}\}.\]
From these definitions, it is easily verified that for any two
ideals, $I,J \subseteq R$, \[V(I) \setminus V(J) \subseteq
V(I:J^{\infty}).\]

For our particular application, we will be interested in proving
that $V(I) \setminus V(J)$ contains no elements in $(0,1)^n$.  Let
$P$ denote the saturation ideal $\left( I: J^{\infty} \right)$. If
we are fortunate enough to find that $P = \left\langle 1
\right\rangle = \mathbb Q[x_1,\ldots,x_n]$, then there are no
points in $V(I) \setminus V(J)$ (and hence none in $(0,1)^n$). One
difficulty with this approach is that these new saturations do not
always produce unit ideals.  One more idea is needed, which we
describe below.

If $K$ is an ideal of $R$, the \emph{elimination ideal} \cite[p.
25]{Cox2} of $K$ with respect to $x_i$ is $K_i = \mathbb Q[x_i]
\cap R$.  The $x_i$-coordinates of elements in $V(K)$ are elements
in $V(K_i)$.  For our purposes, we need only verify that for a
saturation $P$, there is an elimination ideal $P_i$ of $P$ such
that $V(P_i)$ contains no numbers in $(0,1)$.

Normally, a procedure such as the one outlined above would be
relatively intractable (the symbolic algorithms are doubly exponential in
nature).  Our reductions give us enough efficiency to complete a proof computationally.  We performed our computations using the symbolic algebra system Macaulay 2.

\section{The Case $m = 6$, $n=3$}

The remainder of this article is devoted to a technical
consideration of the case $m = 6$, $k = 3$, $n=3$ which is the
content of the theorem below.

\begin{thm}
The polynomial $p(t) = \text{\rm{Tr}}[(A+tB)^m]$ has positive coefficients when $m =
6$ and $A$ and $B$ are any two $3$-by-$3$ positive definite
matrices.
\end{thm}

\begin{proof}
Suppose that there exist $3$-by-$3$ (complex Hermitian) positive definite
matrices $A$ and $B$ such that $\text{Tr}[S_{6,3}(A,B)]$ is
negative; we will derive a contradiction.  Performing a uniform unitary similarity and using homogeneity, we may assume that $A$ and $B$ are of the form, \[
A = \left[ {\begin{array}{*{20}c}
   { 1 } & 0 & 0  \\
   0 & { r } & 0  \\
   0 & 0 & {s}  \\
\end{array}} \right],\;\;B = \left[ {\begin{array}{*{20}c}
   {a} & x & z  \\
   \overline{x} & {b } & y  \\
   \overline{z} & \overline{y} & {c}  \\
\end{array}} \right],
\] in which $1 \geq r \geq s$, $a,b,c \geq 0$, and $x,y,z \in \mathbb C$.  If $x,y,z \geq 0$, then we clearly have a contradiction. Otherwise, perform a simultaneous diagonal unitary similarity on $A$ and $B$ (a similarity by a diagonal matrix with entries on the unit disc) making $x,y \geq 0$. This does not change the trace of $S_{6,3}(A,B)$.

We next show that we may assume $z \in \mathbb R$.  A computation of Tr[$S_{6,3}(A,B)$] reveals that it has the form $w = \alpha z\overline{z}+\beta z + \gamma \overline{z}+\delta$, in which $\alpha,\beta,\gamma,\delta \geq 0$.  Since $w$ is real, we have
\begin{equation*}
\begin{split}
w = \text{Re}(w) = & \ \alpha z\overline{z}+\beta \text{Re}(z) + \gamma \text{Re}(\overline{z})+\delta \\
\geq & \ \alpha \text{Re}(z)^2+\beta \text{Re}(z) + \gamma \text{Re}(z)+\delta. \\
\end{split}
\end{equation*}
Consequently, it follows that we can assume $z$ is real and negative.  Theorem \ref{singthm} now applies, so that it is enough to verify the claim with $s = 0$ and det$(B) = 0$.

Since $B$ is positive semidefinite, we have $ab-x^2 \geq 0$.  If $b = 0$, then $x = 0$, and an
easy computation shows that \[\text{Tr}[S_{6,3}(A,B)] =
6\,{z}^{2}c+24\,a{z}^{2}+20\,{a}^{3}+6\,{r}^{3}{y}^{2}c \geq 0,\]
a contradiction.  Therefore, we must have $b > 0$.  A similar
computation also shows that $a,x,y > 0$.

Next, we prove that $c > 0$.  Since \[\text{det}(B) =
2\,xzy+abc-a{y}^{2}-{x}^{2}c-{z}^{2}b = 0,\] it follows that when
$c = 0$, we have $2xyz = bz^2+ay^2$.  From this, it is clear
that $z < 0$ is impossible, and therefore $z = 0$, a
contradiction.  Finally, if $ab = x^2$, then from $\text{det}(B) =
0$, we have that $2xyz = bz^2+x^2y^2/b$.  This implies again that  $z
= 0$, another impossibility.  Hence, $ab-x^2 > 0$.

Summarizing these observations, we may assume that \[B = \left[
{\begin{array}{*{20}c}
   {\frac{x^2+u^2}{b}} & x & -z  \\
   x & {b } & y  \\
   -z & y & {{\frac {{x}^{2}{y}^{2}+u^2{y}^{2}+2\,xbzy+{z}^{2}{b}^{2}}{u^2b}}}  \\
\end{array}} \right]
\] in which $u,b,x,y > 0$ and $z > 0$.  Furthermore, if $r = 1$ or $r = 0$,
then \cite[Theorem 4]{HJS} (along with a straightforward
continuity argument) implies that $\text{Tr}[S_{6,3}(A,B)]$ is
nonnegative.  Therefore, we may assume that $0 < r < 1$.

A direct computation shows that $b^3u^2\text{Tr}[S_{6,3}(A,B)]$ is a polynomial $p(r,x,y,z,u,b)$ $\in \mathbb Z[r,x,y,z,u,b]$. The negative terms in $p$ factor as
\begin{equation}\label{negterms}
-12\,{b}^{3}{u}^{2}xzy \left({r}^{2}+ r+1 \right).
\end{equation}
We shall verify that the minimum of $p(r,x,y,z,u,b)$ over
$r,x,y,z,u,b \in [0,1]$ is 0, which will prove the claim (by
homogeneity of the matrix $B$ in the variables $x,y,z,u,b$).

If any of $x,y,z,u,$ or $b$ is zero, then we are done
by (\ref{negterms}); therefore, we begin by determining the
critical points of $p$ in $(0,\infty)^6$.  This amounts to a
calculation of
\begin{equation}
D = \left\langle  \frac{{\partial p}} {{\partial
r}},\frac{{\partial p}} {{\partial
x}},\frac{{\partial p}} {{\partial y}},\frac{{\partial p}}
{{\partial z}},\frac{{\partial p}} {{\partial u}},\frac{{\partial
p}} {{\partial b}} \right\rangle,
\end{equation}
which is an ideal in the ring $\mathbb Q[r,x,y,z,u,b]$.  We are
interested in verifying that the set of points $V(D) \setminus
V(rxyzub)$ contains no element in $(0,1)^6$. From the discussion
in the previous section, it suffices to verify this claim
for $V(D: \langle rxyzub \rangle^{\infty})$.

Let $P = \left( D: \left\langle rxyzub\right\rangle^{\infty}
\right)$.  Using Macaulay 2, it can be checked that $P$ is the
unit ideal $\mathbb Q[r,x,y,z,u,b]$.  It follows that the minimum of
the function $p$ above must occur when one of the $x,y,z,u,b$ is 1
(in other words, on the ``boundary'').

This process now continues, recursively, by next finding the critical points of
the functions $p(r,1,y,z,u,b), \ldots, p(r,x,y,z,u,1)$, and checking
that they either do not occur in $(0,1)^5$ or that the function is
nonnegative when they do.  As noted before, a difficulty is that
these new saturations do not always produce unit ideals.
Therefore, we finish by showing that for each saturation $P$,
there is an elimination ideal $P_i$ of $P$ such that $V(P_i)$
contains no positive numbers in $(0,1)$. Since each $P_i$ is
generated by a single-variable polynomial, we use Sturm's
algorithm to verify such a claim symbolically.  These computations were also performed in Macaulay 2.  This completes the proof of the theorem.
\end{proof}

As a final remark, we should note that there are some good tools
for the numerical exploration of such problems. Namely, the
program SOSTOOLS written by Prajna, Papachristodoulou, and Parrilo is an excellent resource for
investigating real algebraic
systems.\footnote{http://www.cds.caltech.edu/sostools/}

redpajama_set_name: RedPajamaArXiv


Cancer patient receives stem cell-made windpipe, first in U.S.
(CBS) In only the second operation of its kind, a Baltimore man has received an artificial windpipe made from stem cells to replace one destroyed by cancer.
Christopher Lyles, 30, had tracheal cancer that had progressed so far it was considered inoperable, the New York Times reported. In November, doctors made him a new windpipe - or trachea - made out of tiny plastic fibers seeded with stem cells from his own bone marrow.
Two months after his successful operation, Lyles arrived home in Md. last week.
Surgeon Paolo Macchiarini, a professor of regenerative surgery at Karolinska Institute in Stockholm, performed the surgery. He's also the doctor who performed the first surgery of this kind on a 31-year-old Eritrean man last July. Both surgeries were done in Stockholm.
"What we did is surgically remove his malignant tumor," Dr. Macchiarini told the Times. "Then we replaced the trachea with this tissue-engineered scaffold." The scaffold was placed in a container called a bioreactor and soaked in a solution that allows the cells to be fully absorbed. Once the windpipe was implanted, the cells continued to grow. "We're using the human body as a bioreactor to promote regeneration," Macchiarini said.
Is the operation fail-safe? "Time will tell what the longevity of these devices is, how long they last," Dr. Harald C. Ott, an instructor in surgery at Massachusetts General Hospital and Harvard Medical School, told the Boston Globe. Ott is unsure how the artificial material will integrate into the recipients' bodies, with both the biology of the body and the outside air that passes through the windpipe.
Researchers have used stem cell-seeding techniques to create other organs, including bladders and a urethra created at Wake Forest University.


text:
Tigers and Twins keep their distance
DETROIT —
Justin Verlander kept the Detroit Tigers on top in the American League Central, pitching eight innings in a 6-5 win Tuesday over the Minnesota Twins that salvaged a split of a day-night doubleheader.
The Tigers restored their two-game division lead over the Twins, who won the day game, 3-2, in 10 innings. There are two games left in the series and five in the regular season.
Verlander (18-9) gave up four runs and eight hits. Fernando Rodney pitched the ninth for his 36th save in 37 chances, overcoming some shaky defense that allowed Minnesota to pull within a run.
Brian Duensing (5-2) gave up five runs over 4 2/3 innings for the Twins, who had a chance to at least tie the score in the eighth and ninth innings.
Delmon Young started the ninth with an infield single. Rodney retired the next two batters and Nick Punto followed with a fly ball to center field that Curtis Granderson misjudged, allowing it to go over his head and helping the Twins pull within a run. Rodney then got Denard Span to hit a game-ending fly to left field.
Orlando Cabrera hit a go-ahead single in the 10th inning of the opener. Jon Rauch (4-1) earned the win and Joe Nathan picked up his career-high 45th save.


text:
Episodes and Videos
Friday Nights on PBS
FULL EPISODE: Recapping President Donald Trump's trip to Europe
Donald Trump,
Republicans,
Democrats,
The panelists discussed the president's recent trip to Europe, where he commemorated the 75th anniversary of D-Day and pledged a "phenomenal" post-Brexit trade deal with the United Kingdom.
The group also discussed President Trump's call for tariffs on Mexico.
NOTE: At 8:31 p.m. EST on June 7, the president tweeted the United States had reached an agreement with Mexico and the impending tariffs set to take effect June 10 would instead be "'indefinitely suspended."
ROBERT COSTA: A migrant surge and a trade standoff. I'm Robert Costa. Welcome to Washington Week.
PRESIDENT DONALD TRUMP: (From video.) Something pretty dramatic could happen. We've told Mexico the tariffs go on, and I mean it, too.
MR. COSTA: President Trump vows to impose tariffs on Mexico and dismisses Republican critics.
PRESIDENT DONALD TRUMP: (From video.) They have no idea what they're talking about when it comes to tariffs. They have absolutely no idea.
SENATE MAJORITY LEADER MITCH MCCONNELL (R-KY): (From video.) Well, there is not much support in my conference for tariffs.
MR. COSTA: Democrats say the president is reckless.
HOUSE SPEAKER NANCY PELOSI (D-CA): (From video.) This is dangerous territory. It's not a way to deal with immigration. It's not a way to deal with humanitarian needs at the border.
MR. COSTA: And global leaders remember D-Day, next.
ANNOUNCER: This is Washington Week. Once again, from Washington, moderator Robert Costa.
MR. COSTA: As migrant issues mount at the U.S.-Mexico border, President Trump is pressing ahead with his planned 5 percent tariff on all Mexican imports starting on Monday. Talks continued on Friday between the two nations, and the president in a tweet from Air Force One wrote that there is, quote, "a good chance" of a deal. But Trump administration officials cautioned that the U.S. could still issue notice late Friday and formally begin the tariff process.
Joining me tonight, Mark Landler, White House correspondent for The New York Times; Vivian Salama, White House reporter for The Wall Street Journal; Anna Palmer, senior Washington correspondent for POLITICO and co-author of The Hill to Die On; and Joshua Green, national correspondent for Bloomberg Businessweek.
Vivian, where do these talks stand? Will Mexican President Lopez Obrador buckle and cut a deal?
VIVIAN SALAMA: I mean, it certainly seems like they are willing to come to the table to discuss. They're very eager, obviously, to avoid these tariffs. But really, we've been on pins and needles waiting for President Trump to get back in country. He's been out of the country for this entire week where all of this has been unfolding – meetings at the White House, meetings at the State Department where they seem to be breaking ground on a number of the immigration
issues that the Trump administration is demanding, particularly adhering to the asylum system, the stay in Mexico policy and the safe third country policy. Those are the three major issues. The Mexicans came to the table wanting to put troops on their southern border and make other concessions, but at the end of the day President Trump from Europe said it wasn't enough and he wanted to see more from the Mexicans, and so –
MR. COSTA: How many troops would be on the southern border for Mexico?
MS. SALAMA: That is a part of the discussion, and they haven't really even determined that much as far as our reporting has gone. The numbers go back and forth, and it's not something that the Trump administration has been so focused on as much as it is securing the U.S. southern border. And so that's where we stand, but a lot of the advisors – including people who were in the room with the Mexicans this week – say ultimately it doesn't matter where the talks stand because President Trump is going to come back at the end of the day and he's going to make a decision, and even though he said there has been progress and a number of White House officials have indicated as much, he still says that those tariffs are going into effect on Monday as he said.
MR. COSTA: The metrics don't seem clear, Mark. What's the president's strategy?
MARK LANDLER: Well, the president loves tariffs. Tariffs are his preferred weapon. He's used them in his view quite successfully with China. He's gotten China to move further, maybe, than many people thought it would. He's used steel and aluminum tariffs around the world. He's in a bilateral trade negotiation with Japan that he would argue was – in a way the door was opened by tariffs. So I think that they – it's the weapon that he has. It's a unilateral weapon. It doesn't depend on congressional support, although it's worth noting in this case Congress might well override – veto him and then override him. So this is – you know, as Vivian has said, he's called tariff man for a reason. This is something that he really values. He thinks it works. He makes this rather incredible argument that American consumers don't pay for it, that it's money the American Treasury takes in. That's an argument most economists knock down. But he is really fastened to it. He feels it's worked for him in the past and I think he figures he has one more chance to show that with Mexico in the – in the coming days.
MR. COSTA: He may like using tariffs as a political tool. Is he also under pressure from his base?
JOSHUA GREEN: I think Trump feels that he's under pressure from his base, because the thing that really got him elected was this promise that he would build a wall on the southern border and then stop the inflow of migrants, and that very much has not happened. We got reports this week that the migrant border surge is six times as large as it was a year or so ago. Clearly, things are going badly. This is a weapon, I think – tariffs – that Trump thinks he can use to force concessions from the Mexican government, and at least the indications we've gotten today – of course, nothing is settled – is that the Mexicans realize there's some real pain here for them if Trump goes ahead with these tariffs.
MR. COSTA: What would the pain be for the Mexicans?
MR. GREEN: Well, it would be an escalating series of tariffs. So beginning on Monday, if Trump goes ahead with this, it would be 5 percent tariffs, which would certainly spook the stock market and cause a fall. And then they would go up in increments of 5 percent, hitting a top level, I believe, of 25 percent by October. That could be enough to send the Mexican economy into a recession. It could certainly mess up the U.S. supply chain, could slow down growth here. There are all sorts of dire economic effects, and I would argue political effects for Trump, that could stem from this policy. But for right now he's got the upper hand.
MR. COSTA: And one of those political effects could play out on Capitol Hill because many Republicans, even Trump allies, are speaking out against the proposed tariffs.
SENATOR TED CRUZ (R-TX): (From video.) Millions of jobs in Texas depend on international trade, and in particular trade with Mexico. This is the wrong solution to the crisis.
SENATOR JOHN CORNYN (R-TX): (From video.) Tariffs, on the other hand, would be a massive tax.
MR. COSTA: Others say the president's tariffs are necessary.
REPRESENTATIVE MARK MEADOWS (R-NC): (From video.) One more tool to be able to control the flow of illegal immigrants coming across our southern border.
MR. COSTA: According to federal data, more than 144,000 migrants, many of them from Central America, were taken into custody in May. U.S. Customs and Border Protection said it was the highest monthly figure in more than a decade. Democrats have sharply criticized the president's response.
HOUSE SPEAKER NANCY PELOSI (D-CA): (From video.) This is dangerous territory. It's not a way to deal with immigration. It's not a way to deal – meet the humanitarian needs at the border.
MR. COSTA: That's the scene, Anna, in Congress, but will Republicans actually try to block the president?
ANNA PALMER: I think it's a real possibility. Mark Meadows, who was speaking there defending the president, is really an outlier. I think what you really need to focus on is the Senate – Mitch McConnell, others saying they don't want this to go into effect, and this could be the first time that you have Republicans in the Senate issue a veto – override a veto of the president's. I mean, that would be a pretty stunning rebuke for this president.
MR. COSTA: But we don't know if the Republicans are just complaining or they're actually willing to take action. You've been on the Hill all week. What do you hear about actually moving on Monday should these tariffs go into effect?
MS. PALMER: It feels different, I will say. I think sometimes the Republicans kind of try to, you know, tap the president a little bit and rap him and say, hey, you know, this is going to be – you know, don't go that far, right? But this feels like there's a coalescing, really, of a majority of the majority of Republicans, and when there is that that's a dangerous, I think, formula for the president because all of a sudden you have Republicans saying we're going to take him on. And this is an issue where they think they feel they are right on and it's not just politics; they can go back to their states and say the president's wrong on this.
MR. COSTA: What does this mean, Vivian, for the USMCA, the new version of NAFTA? You've been tracking that.
MS. SALAMA: Absolutely. So U.S. Trade Representative Robert Lighthizer was one of the people who was very much against imposing these punitive tariffs against Mexico because he felt like it could jeopardize efforts to get the USMCA through Congress, which has already been a bumpy road so far, Democrats really not cooperating and Republicans raising certain concerns about certain clauses. The vice president was in Canada the very same day that the president made this announcement of tariffs on Mexico talking with Justin Trudeau, prime minister of Canada, to see how they could get it through their parliament, and the Mexicans were doing the same that very same day – everyone, obviously, having to sort of juggle the political elements of this to get it through their own parliaments and our Congress here, and suddenly this happens. It doesn't – a lot of folks concerned that it doesn't reflect goodwill in terms of their efforts to negotiate.
One other thing I want to add also to Anna's point is, remember, all this is coming on the heels of the China tariffs and the escalating dispute with China. And so a lot of these senators already concerned that folks in their states, especially farmers and others in the agriculture sector, were suffering. The U.S. has already – the Trump administration has already offered a form of bailout for farmers, especially soybean farmers, who were hurting from the China tariffs. And now you have the Mexicans threatening to go after certain Republican states and the farming sector, the agriculture sector specifically. It could just really make a bad situation worse.
MR. COSTA: So is there any chance, weighing all those factors laid out Vivian and Anna, you also have the jobs numbers on Friday. Seventy-five thousand up into the payroll, lower than expectations. Does the White House have any chance of delaying the tariffs on Monday?
MR. LANDLER: Well, I mean, the president would have appeared to lock himself in, in terms of when he's going to start with this. But I think that raising – you mentioned the job numbers. I think that's important. There's another fairly arcane thing that has started happening in recent weeks which is called an inversion of the yield on bonds. And that's important because every time – seven of the last 10 times this has happened it's been a pretty accurate predictor of the economy going into recession. So there had been for a long time a feeling that the economy was going to continue to grow at a fairly healthy rate well into 2020. Now you're beginning to hear people say: Well, maybe not. Maybe there'll be at least a slowdown. I don't think people are really talking about a recession.
So if you're the White House and President Trump, you have to weigh, you know, your strategy and your belief that tariffs allow you to make advances against the possibility that you go into your reelection campaign with a sharply slowing economy.
MR. GREEN: Well, one other factor too, you know, today the stock market soared in the wake of this bad jobs report, because in the somewhat perverse logic of market traders, bad news was good news because it increased the likelihood that the Federal Reserve will cut interest rates this year – essentially putting a safety net under what Trump is doing in terms of the trade war, which could be read as ushering Trump along, or at least giving him leeway to pursue these tariffs if he decides he wants to.
MR. COSTA: How would they affect consumers across the country, if they actually are affected?
MR. GREEN: Every economist I've talked to says that they will raise prices. And if these tariffs go on Mexico and hit the U.S. supply chain, it could raise auto costs by an average of $1,300 per car. So a real dent in the U.S. economy.
MS. PALMER: It also could be a big deal in terms of the holidays, right? In terms of spending when you have retailers. There's a lot of goods that go back and forth between the Mexico-U.S. border. So that is another issue where you're going to have a lot of people are the Trump supporters all of a sudden thinking, you know, what's actually – what's this president doing?
MR. GREEN: Well, and the real danger here is we talked about the hit that farmers have taken in some of the western and midwestern states. If the auto industry gets hit, then you're looking at the upper Midwest states, places like Michigan, Pennsylvania, and Ohio, that most analysts I think believe are going to be the critical states in 2020, where Trump is already struggling politically.
MR. COSTA: We saw Speaker Pelosi talk about the humanitarian crisis at the border. You have, just according to the Customs and Border Protection Agency, more than 19,000 migrants in custody right now, often in cells that are packed and dirty. Many children are arriving without a parent. And the Trump administration is cancelling English classes, recreational programs, legal aid for unaccompanied minors. Is there anything in motion to address those issues – those real issues at the border?
MS. SALAMA: Well, this is the struggle that the Trump administration continues with. Certainly one of the issues that led him to declare a national emergency late last year, and something that they haven't really figured out yet. The border wall funding is still an issue that continues to be very contentious between Congress and the president. And in general, you have an acting DHS secretary. And so nothing is really institutionalized there with him still uncertain as to the future of his role. You have a new ICE director. And so there's a lot of moving parts there.
And just this general consensus that DHS gradually was losing control over the situation because the White House tended to siphon off a lot of the decision-making process with regard to border security during the tenure of Kirstjen Nielsen, the former DHS secretary. There's a lot of sort of absent communication situation there that DHS and the White House are falling behind on getting that together.
MR. COSTA: We know that Republicans, President Trump, is pushing for the tariffs as a response to this influx of migrants at the southern border. What is the Democratic reaction, the hope, the plan?
MS. PALMER: I don't think they feel like they have to put up a plan, frankly. I mean, the president needs to lead on this. This is going to be an administration play. The big question to me is going to be what happens with federal funding, as you say. They have not – they are nowhere on the border wall. There's nowhere on kind of any kind of aid package that is going to add some relief to this –
MR. COSTA: That would add judges or something like that.
MS. PALMER: Right. I mean, there's really no talk of that right now at all on Capitol Hill. I mean, if anything, the president is tweeting against Nancy Pelosi, you know, when he's in the air on Air Force One. And Democrats are more unilaterally opposed to him than I've ever seen.
MS. SALAMA: Not to mention continuing to fight the courts on a lot of these issues too.
MR. COSTA: And, as you said, Anna, the president returned to Washington on Friday from a weeklong trip to Europe, where he marked the 75th anniversary of D-Day with other world leaders.
PRESIDENT DONALD TRUMP: (From video.) The blood that they spilled, the tears that they shed, the lives that they gave, the sacrifice that they made did not just win a battle. It did not just win a war. Those who fought here won a future for our nation.
MR. COSTA: He also toasted the queen in London and talked trade with outgoing British Prime Minister Theresa May. There were controversies too. In an interview with Fox News he called former special counsel Robert Mueller a, quote, "fool," and Speaker Pelosi a, quote, "disaster."
PRESIDENT DONALD TRUMP: (From video.) I think she's a disgrace. I actually don't think she's a talented person. I've tried to be nice to her because I would have liked to have gotten some deals done. She's incapable of doing deals. She's a nasty, vindictive, horrible person.
MR. COSTA: Mark, you began the day in Paris, and you ended up here at the Washington Week table. (Laughter.) We appreciate it.
MR. LANDLER: I'm still awake.
MR. COSTA: You've been traveling with this president throughout this entire trip. And when you listened to that speech in Normandy, what was your takeaway, especially in terms of how he talked about the nation and sovereignty?
MR. LANDLER: Well, you know, this is a – sort of a location, a locale, that American presidents have often delivered some of their most memorable speeches. President Reagan in 1984 talked about the boys of Pointe du Hoc. So this is a very hallowed ground. And President Trump gave a speech that I think his aides hoped would be very presidential. But it bore some very distinctively Trumpian touches. Rather than talk about the alliance system that the U.S. created in the ashes of World War II, he spoke about sovereignty. Rather than talk about the sacrifices that all of these countries made together, he really focused very much on American soldiers.
Now, to some extent that's understandable. He was standing in the American military cemetery. But what you heard in this speech was no particular reference to the great institutions that came out of World War II. And the reason for that is that President Trump has largely been an enemy of those institutions. He's ridiculed NATO. He has attempted to sabotage the European Union. And so on this day it fell to Emmanuel Macron, the French president, to actually get up and talk about the legacy the United States had left Europe in the wake of World War II. So that was one very noticeable thing about his time there.
MR. COSTA: Based on that analysis, Josh, you've written a book about Steve Bannon. The president met with Nigel Farage, the Brexit Party leader in London. When you listen to his speech in Normandy and see he's meeting with Farage, are you seeing a president who's underscoring his nationalism, or is it something a little different?
MR. GREEN: Very much so. I mean, Bannon is long gone from a position of influence in the Trump White House, and yet his ideas seem to resonate more than ever. If you look at what it is that Trump focuses on, it is issues like trade and immigration, precisely the things that Bannon had encouraged him to run on. Listening to Trump's speech today – yesterday, listening to the way he spoke about Brexit in the U.K., Trump seems to be the same guy he's been all along and is keyed on the same issues. I don't think that's going to change.
MR. COSTA: Constant fights with Speaker Pelosi, the president was even criticized for appearing in front of the graves at Normandy and talking about political enemies.
MS. PALMER: Yeah, and Nancy Pelosi didn't respond in kind. I think that is the real split screen there, where you have the president continuing his attacks, kind of focused – laser-focused on what's happening back home. And she basically trying to be the bigger person, be the leader, and say: That's not what we do on foreign soil. But you can't underscore how important him attacking her is for her base and getting her caucus behind her. There's been a lot of friction in the Democratic Caucus about whether to impeach the president, what's the right strategy? And every time he goes after her, all he does is unify Democrats. And she becomes stronger and stronger.
MR. COSTA: When you think about the president's fighting with the London mayor, the president's being compared to a fascist by the London mayor. Where is the special relationship with the U.K. coming away from this trip? There's a coziness with Theresa May, the prime minister. He's friendly with Boris Johnson. Yet, a lot of criticism and some protests.
MS. SALAMA: Well, coziness with Theresa May when she's one foot out the door, let's put it that way. (Laughter.) But certainly the friction with Sadiq Kahn, the mayor of London, goes back now a couple of years with the president, because he's been a very outspoken critic. And the president really hammered him this time, saying that's not how you treat a guest; you know, I'm a guest in your country. Of course, the president also has the tendency to, you know, attack people back, and so it was a little bit ironic. Certainly, the president was very happy to remind people that he was against – that he was promoting Brexit from the start, and he didn't really feel that Theresa May took his advice, and that's why the entire thing basically is crashing and burning with her – two days away from her final day in office he reminded that he actually recommended to her that she should sue the EU and then settle with them, and that was the best way to sort out the Brexit issues. And so the special relationship sort of with an inserted element of I am Trump and here is what I have offered to this whole entire thing, so it was interesting to watch.
MR. COSTA: A debatable special relationship, perhaps, but what a moment for history to be there and to see the planes flying overhead, to think about 75 years ago what happened there. Beyond President Trump, what did it tell us?
MR. LANDLER: Well, I mean, I think it really reminded us of the tremendous personal sacrifice the United States made on the behalf of a free and peaceful Europe. I mean, there is really no greater, more glorious demonstration of that. And I think that's why, when President Reagan went and President Obama and President Clinton, all of whom spoke in the same place, they really presented the United States as being squarely in the center of the European experiment. And I think not hearing that message from President Trump was – once again, it's not a new thing with him – he's been very clear on this – but it was really vivid not hearing from him on this hallowed ground.
I think the other major sort of takeaway I had from this week was the degree to which President Trump really valued the relationship he built up with Queen Elizabeth, the rapport they had. In speaking to Laura Ingraham in that interview, he said that folks had told him that people had never seen her so animated before.
MS. PALMER: She was great, great. (Laughter.)
MR. LANDLER: Yeah. And every day he would increase the superlatives he used – she was a great woman, she was a spectacular woman. (Laughter.) And so, you know, clearly that for him was maybe the biggest takeaway.
MS. PALMER: Yeah, I mean, I think it was pretty stunning. I mean, what was also very interesting, too, was just to see he had the trappings of his entire family there, right, something
that you don't always see, and really saw that kind of friction between, you know, the family and business and all of those things.
MR. COSTA: Thanks, everybody. We have to leave it there.
But stay tuned for a special message from your PBS station, then watch our Washington Week Extra on our website, Facebook, or YouTube.
I'm Robert Costa. Have a great weekend.
National Correspondent
Mark Landler
White House Correspondent
Vivian Salama
White House Reporter
Anna Palmer
Senior Washington Correspondent
Watch the Webcast Extra:
United States and Mexico reach agreement, avoid tariffs
Tariffs on the country were to begin June 10.
Audio Podcast | Video Podcast
Trump Fans the Flames of a Racial Fire
President Trump woke up on Sunday morning, gazed out at the nation he leads, saw the dry kindling of race relations and decided to throw a match on it. It was not the first time, nor is it likely to be the last.
'Go Back' Message Deepens Immigration-Debate Wounds
President Trump tweeted out his already-famous, incendiary declaration that young Democratic congresswomen criticizing America should "go back" to the "totally broken and crime infested places from which they came." In his message, Mr.
How Donald Trump conquered the Republican Party
President Trump knows he can say whatever he likes and face no consequences from the party he has conquered.
Rep. Pressley Among Targets Of Trump's Tweets Telling Congresswomen To Leave The U.S.
Massachusetts Congresswoman Ayanna Pressley is part of a group of Democratic representatives, all women of color, who are the focus of presidential tweets that are being called racist.
Robert Mueller public hearing to be delayed one week
Robert Mueller's long-awaited testimony has been delayed a week, until July 24, to allow more time for Mueller to testify, House Democrats said in a statement late Friday.
House Votes to Extend 9/11 Fund for Lifetimes of First Responders
The House on Friday approved legislation to replenish a depleted federal fund to compensate emergency workers and others who became ill as a result of their work in the ruins of the World Trade Center in Lower Manhattan, extending it for the lifetime
Treasury Department warns the US could hit debt ceiling in early September
Treasury Secretary Steven Mnuchin is calling on Congress to lift debt ceiling before the August recess.
#WashWeekPBS Extra: United Kingdom Ambassador Kim Darroch resigns after criticism of Trump surfaces
The panelists discussed the resignation of British Ambassador to the United States Kim Darroch after cables leaked in which he called the Trump administration "inept" and "dysfunctional."
Full Episode
#WashWeekPBS full episode: Labor Secretary Alexander Acosta resigns
President Donald Trump accepted Labor Secretary Alexander Acosta's resignation Friday.
Support provided by:
Get Washington Week Updates
Follow @washingtonweek'
@NewsHour
Follow @NewsHour
Asylum seekers who pass through another country first will be ineligible for asylum at the U.S. southern border, ac… t.co/lFRdz04Dky
21 min 21 sec ago.
Seung Min Kim
@seungminkim
Follow @seungminkim
—> t.co/jsj8V1c5Ny
1 hour 27 min ago.
@maggieNYT
Follow @maggieNYT
Via @yashar t.co/vLzypsjwAv
"In Iowa, South Bend Mayor Pete Buttigieg said Democrats need to stand their own ground," reports @LisaDNews t.co/DrewMLOqKg
Carol Leonnig
@CarolLeonnig
Follow @CarolLeonnig
Democratic hopeful Beto O'Rourke raises a lackluster $3.7 million in second quarter, via the late-working, die hard… t.co/zKKVXB6AaD
@AshleyRParker
Follow @AshleyRParker
Tonight, over roughly two hours, my sister's boyfriend crushed four (!) Spindrift seltzers, along w some… t.co/2kClDPln8O
"Washington Week" is a production of WETA Washington, D.C.
Copyright © 2019 WETA. All rights reserved.
Major funding is provided by:
LIVE: Watch the #WashWeekPBS Extra here
EXTRA: Recapping this week in the 2020 presidential race
Analyzing SCOTUS season


Position Summary: Overall responsibility is to pull and/or receive product in an accurate manner, load and unload vehicles, operate warehouse equipment, and keep the work environment clean and safe.
• Process shipped and received orders. Prepare goods for shipment or storage (i.e., assemble or disassemble pallets of product). Accurately measure, weigh, and/or count product.
• Pull orders; pack, wrap, label, and ship product; load, unload, or stack containers, materials, or product.
• Verify incoming and outgoing stock for the purpose of ensuring specifications, quantity, and quality of orders are correct. Compare shipment and/or received contents to records.
• Abide by inventory control procedures.
• Maintain accurate and complete records.
• Operate and maintain warehouse equipment in a safe and prudent manner (e.g., forklifts, pallet jacks, dock levelers, hand trucks, etc.).
• Maintain a clean and orderly work area. Remove shrink wrap and tape from dock pallets, wipe cases and make presentable, and recommend the removal or transfer of product that is not picked up.
• Keep the facility and grounds clean (e.g., yard maintenance, sweeping, pressure washing, etc.).
High school diploma or equivalent. At least two years of experience assisting in the receipt, storage, and issuance of materials from a centralized stockroom or warehouse. Forklift certification a plus or experience operating a forklift with willingness to obtain certification.
• Ability to operate standard warehouse equipment including, but not limited to, pallet jacks, forklifts, dock levelers, and other materials-handling equipment.
• Knowledge of inventory management.
• Able to work in a physically-demanding environment which includes lifting and/or moving material weighing up to 50 pounds frequently, and heavier items occasionally.
• Basic computer knowledge helpful to complete select reports, electronic timecards, access email, etc.
• Ability to work in a results-oriented environment and perform against established performance standards.
Allowable Substitution: Combination of education, experience, and/or training that provides the required knowledge and skills for the position may be considered in lieu of education and/or experience at the company's discretion.
2. Type "Warehouse Specialist" as the only content in the subject line of your email.


Kevin Sorbo, Lisa Ryder, Laura Bertram, Gordon Michael Woolvett. Captain Dylan Hunt and his ragtag crew on the Andromeda Ascendant battle foes from within and without while trying to rebuild the fallen civilization known as Systems Commonweatlh in this thrilling sci-fi series created by Gene Roddenberry 110 episodes on 24 DVDs. 2000–05/color/78 hrs., 50 min/TV-PG/widescreen.


The only Underground Church in the World!
With Krakow Salt Mines Ticket you will see the very beginning of salt extraction. During the trip, you will hear a legend about Princess Kinga who is said to be the patron saint of salt miners in Poland and you will find out why.
Also: How the mine functioned during World War II? Who visited Wieliczka Salt Mine throughout the history? What is the title of the movie shot there? All those questions will be answered.
The microclimate of the mine has a beneficial impact on visitors who suffer from asthma and allergies, so breathe as deeply as you can!
Nowadays the mine serves not only as a monument of culture but also as a venue for underground concerts, theater shows, and various exhibitions.
Please await our Tour Leader at 7 Edwarda Dembowskiego Street, Wieliczka - Discover Cracow Tourist Information Point. Our Tour Leder will take the group up to the entrance when the guide will be waiting.
Sometimes the line to get a ticket can be overwhelming. With us you don't need to worry, your seat is secured.
Official Wieliczka Salt Mine guide will show around you the Mine in your language. Entrance fees are already paid so you don't have to worry about anything.
Please arrive at the designated pick- up point at least 5 minutes before departure time. Minor delays (circa 20 minutes) are possible due to traffic conditions.
The sightseeing itself takes around 2 hours.
The regular Salt Mine tour requires lots of walking and climbing stairs. If you have trouble walking you should consider taking the special route for physically challenged tourists. It is easier and shorter and we can organize it for you.
You just need to choose the Wieliczka Salt Mine tour with private transport and inform our booking department that you want to attend the shorter Route. If you are a person using a wheelchair it is the only possible way of visiting the Krakow Salt Mine.
How to get to Wieliczka Salt Mine?
We highly encourage you to read our blog post about How to Get to Wieliczka Salt Mine to Krakow - all your question are answered there.
If you are physically challenged, you have trouble climbing stairs and need to pick the Shorter Route choose Wieliczka Salt Mine with Private Transport - we will organize the Shorter Route especially for you. Also, this option will be best for you if you want to be picked up from a private apartment - our driver will pick you up from any point in Krakow.
If you want to travel to Wieliczka Salt Mine by yourself (by train or bus) and you don't need transportation from Krakow, but you want to book your ticket in advance and skip the line at the Salt Mine - pick the Wieliczka Salt Mine Ticket.
Great, well organised tour. Would definitely recommend!
The meeting point was easy to find, I didn't want to stand in line, so I bought the ticket online. everything went well.
The Salt Mine is a must visit if you're near Wieliczka/ Kraków. The mine is very impressive with beautiful statues and places of worship - all underground. Our guide (Daniel) was brilliant, full of knowledge about the Mine and very personable. I would definitely recommend!
The guide was funny and super nice! A lot of walking and stairs but all worth it. It's impressive what you can find so deep underground. Tour was professionally organized with no issues.


text:
Q: Code to perform an attack to a CNN with foolbox, what's wrong? I have to perform a simple FSGM attack to a convolutional neural network. The code for the CNN works correctly, and the model is saved without a problem, but when i try to perform the attack an error is shown.
HERE'S THE CODE FOR THE CNN
from keras.models import Sequential
from keras.layers import Dense, Conv2D, Flatten, MaxPooling2D
import matplotlib.pyplot as plt
from keras.datasets import mnist
from keras.utils import to_categorical
import json
import tensorflow as tf
#Using TensorFlow backend.

#download mnist data and split into train and test sets

(X_train, y_train), (X_test, y_test) = mnist.load_data()

#plot the first image in the dataset
plt.imshow(X_train[0])
#check image shape
X_train[0].shape
#reshape data to fit model
X_train = X_train.reshape(60000,28,28,1)
X_test = X_test.reshape(10000,28,28,1)
#one-hot encode target column
y_train = to_categorical(y_train)
y_test = to_categorical(y_test)

y_train[0]
#create model
model = Sequential()
#add model layers
model.add(Conv2D(32, kernel_size=(5,5), activation='relu', input_shape= (28,28,1)))

model.add(MaxPooling2D(pool_size=(2,2)))
model.add(Conv2D(64, kernel_size=(5,5), activation='relu'))
model.add(MaxPooling2D(pool_size=(2,2)))
model.add(Flatten())
model.add(Dense(10, activation='softmax'))
#compile model using accuracy as a measure of model performance
model.compile(optimizer='adam', loss='categorical_crossentropy', metrics= ['accuracy'])

#train model
model.fit(X_train, y_train,validation_data=(X_test, y_test), epochs=5)

json.dump({'model':model.to_json()},open("model.json", "w"))
model.save_weights("model_weights.h5")

THEN I TRY TO PERFORM THE ATTACK WITH THE FOLLOWING CODE:
import json
import foolbox
import keras
import numpy as np
from keras import backend
from keras.models import load_model
from keras.datasets import mnist
from keras.utils import np_utils
from foolbox.attacks import FGSM
from foolbox.criteria import Misclassification
from foolbox.distances import MeanSquaredDistance
import matplotlib.pyplot as plt
from keras.models import Sequential
from keras.layers import Dense, Flatten, Conv2D, MaxPooling2D
import numpy as np
import tensorflow as tf
from keras.models import model_from_json
import os

############## Loading the model and preprocessing #####################

backend.set_learning_phase(False)

model = tf.keras.models.model_from_json(json.load(open("model.json"))["model"],custom_objects={})
model.load_weights("model_weights.h5")
fmodel = foolbox.models.KerasModel(model, bounds=(0,1))
_,(images, labels) = mnist.load_data()

images = images.reshape(10000,28,28)
images= images.astype('float32')
images /= 255

######################### Attacking the model ##########################

attack=foolbox.attacks.FGSM(fmodel, criterion=Misclassification())
adversarial=attack(images[12],labels[12]) # for single image
adversarial_all=attack(images,labels) # for all the images
adversarial =adversarial.reshape(1,28,28,1) #reshaping it for model prediction

model_predictions = model.predict(adversarial)
print(model_predictions)

########################## Visualization ################################
images=images.reshape(10000,28,28)
adversarial =adversarial.reshape(28,28)

plt.figure()
plt.subplot(1,3,1)
plt.title('Original')
plt.imshow(images[12])
plt.axis('off')

plt.subplot(1, 3, 2)
plt.title('Adversarial')
plt.imshow(adversarial)
plt.axis('off')

plt.subplot(1, 3, 3)
plt.title('Difference')
difference = adversarial - images[124]
plt.imshow(difference / abs(difference).max() * 0.2 + 0.5)
plt.axis('off')
plt.show()

this error is shown when the adversarial examples are generated:
    c_api.TF_GetCode(self.status.status))
InvalidArgumentError: Matrix size-incompatible: In[0]: [1,639232], In[1]: [1024,10]
[[{{node dense_4_5/MatMul}}]]
[[{{node dense_4_5/BiasAdd}}]]

What could it be?

A: here is my solution.
First of all modify the model code as follows
import tensorflow as tf
import json
# download mnist data and split into train and test sets
(X_train, y_train), (X_test, y_test) = tf.keras.datasets.mnist.load_data()
# reshape data to fit model
X_train = X_train.reshape(X_train.shape[0], 28, 28, 1)
X_test = X_test.reshape(X_test.shape[0], 28, 28, 1)
X_train, X_test = X_train/255, X_test/255
# one-hot encode target column
y_train = tf.keras.utils.to_categorical(y_train)
y_test = tf.keras.utils.to_categorical(y_test)
# create model
model = tf.keras.models.Sequential()
# add model layers
model.add(tf.keras.layers.Conv2D(32, kernel_size=(5, 5),
                                 activation='relu', input_shape=(28, 28, 1)))
model.add(tf.keras.layers.MaxPooling2D(pool_size=(2, 2)))
model.add(tf.keras.layers.Conv2D(64, kernel_size=(5, 5), activation='relu'))
model.add(tf.keras.layers.MaxPooling2D(pool_size=(2, 2)))
model.add(tf.keras.layers.Flatten())
model.add(tf.keras.layers.Dense(10, activation='softmax'))
# compile model using accuracy as a measure of model performance
model.compile(optimizer='adam', loss='categorical_crossentropy',
              metrics=['accuracy'])

# train model
model.fit(X_train, y_train, validation_data=(X_test, y_test), epochs=5)

json.dump({'model': model.to_json()}, open("model.json", "w"))
model.save_weights("model_weights.h5")

You just forgot to divide each pixel by the maximum value of RGB (255)
As for the attacker code
import json
import foolbox
from foolbox.attacks import FGSM
from foolbox.criteria import Misclassification
import numpy as np
import tensorflow as tf

############## Loading the model and preprocessing #####################
tf.enable_eager_execution()
tf.keras.backend.set_learning_phase(False)

model = tf.keras.models.model_from_json(
    json.load(open("model.json"))["model"], custom_objects={})
model.load_weights("model_weights.h5")
model.compile(optimizer='adam', loss='categorical_crossentropy',
              metrics=['accuracy'])

_, (images, labels) = tf.keras.datasets.mnist.load_data()
images = images.reshape(images.shape[0], 28, 28, 1)
images = images/255
images = images.astype(np.float32)

fmodel = foolbox.models.TensorFlowEagerModel(model, bounds=(0, 1))

######################### Attacking the model ##########################

attack = foolbox.attacks.FGSM(fmodel, criterion=Misclassification())
adversarial = np.array([attack(images[0], label=labels[0])])

model_predictions = model.predict(adversarial)
print('real label: {}, label prediction; {}'.format(
    labels[0], np.argmax(model_predictions)))

I used TensorFlowEagerModel instead of KerasModel for simplicty. The error you were encountering was due to the fact that model.predict expects a 4d matrix while you were passing a 3d matrix, so I just wrapped up the attack to the image example into a numpy array to make it 4d.
Hope it helps


text:
Woolwich, ME (View All Cities)
Sagadahoc County
43.96, -69.77
Woolwich, ME
ZIP code 04579 is located in southwest Maine and covers a slightly less than average land area compared to other ZIP codes in the United States. It also has a slightly less than average population density.
The people living in ZIP code 04579 are primarily white. The number of middle aged adults is extremely large while the number of people in their late 20s to early 40s is large. There are also a large number of families and a small number of single parents. The percentage of children under 18 living in the 04579 ZIP code is slightly less than average compared to other areas of the country.
88 people per sq mi
Male 83 81 88 91 54 66 71 103 138 135 130 128 112 100 59 42 24 14
Female 79 114 80 83 57 71 73 92 137 125 143 139 123 92 71 32 20 22
Total 162 195 168 174 111 137 144 195 275 260 273 267 235 192 130 74 44 36
Under 5 83 79 162
5-9 81 114 195
10-14 88 80 168
35-39 103 92 195
85 Plus 14 22 36
Owner 9 74 187 278 262 186 78 17
Renter 9 42 43 26 15 10 4 1
Total 18 116 230 304 277 196 82 18
75-84 78 4 82
85 Plus 17 1 18
Male 15 15 24 16 15 19 18 12 17 22 22 10 18 16 18 19 23 20 11 11
Female 17 13 15 20 18 28 26 19 23 11 16 18 18 17 15 16 30 13 9 10
Total 32 28 39 36 33 47 44 31 40 33 38 28 36 33 33 35 53 33 20 21
ZIP code 04579 has a slightly less than average percentage of vacancies.
The majority of household are owned or have a mortgage. Homes in ZIP code 04579 were primarily built in the 2000s or the 1990s. Looking at 04579 real estate data, the median home value of $192,600 is slightly higher than average compared to the rest of the country. It is also slightly less than average compared to nearby ZIP codes. 04579 could be an area to look for cheap housing compared to surrounding areas. Rentals in 04579 are most commonly 3+ bedrooms. The rent for 3+ bedrooms is normally $500-$749/month including utilities. 2 bedrooms are also common and rent for $1,000+/month. Prices for rental property include ZIP code 04579 apartments, townhouses, and homes that are primary residences.
3,072 100%
The median household income of $61,658 is compared to the rest of the country. It is also compared to nearby ZIP codes. So 04579 is likely to be one of the nicer parts of town with a more affluent demographic.
As with most parts of the country, vehicles are the most common form of transportation to places of employment. In most parts of the country, the majority of commuters get to work in under half an hour. A slightly higher than average number of commuters in 04579 can expect to fall in that range. There are a slightly smaller percentage of employees that have to travel over 45 minutes to reach their place of employment.
59 10.2%
ZIP Code 04579 is in the following school districts: Rsu 01 - Lkrsu School District and Private. There are 2 different elementary schools and high schools with mailing addresses in ZIP code 04579.
Woolwich Central School
137 Nequasset Road
District: Rsu 01 - Lkrsu School District
Chop Point School
425 Chopps Point Rd
Bowdoinham, ME
Dresden, ME
Georgetown, ME
Wiscasset, ME


text:
Tempel der Menschheit steht für:

 Tempel der Menschheit (theosophische Organisation)
 Tempel der Menschheit (positivistische Kirche), siehe Religion des Positivismus #Tempel der Menschheit

redpajama_set_name: RedPajamaWikipedia


text:
Q: Univariate multi-step prediction model for missing value imputation I have a dataframe with columns of timestamp and energy usage. The timestamp is taken for every min of the day i.e., a total of 1440 readings for each day. I have few missing values in the data frame.
I want to impute those missing values with deep neural networks, and for this, I have to frame the dataset for developing the neural network. Here's a example of the data:
    timestamp           mains_1
0   2013-01-03 00:00:00 155.0
1   2013-01-03 00:01:00 154.0
2   2013-01-03 00:02:00 155.0
3   2013-01-03 00:03:00 NaN
4   2013-01-03 00:04:00 153.0
5   2013-01-03 00:05:00 153.0
6   2013-01-03 00:06:00 153.0
7   2013-01-03 00:07:00 152.0
8   2013-01-03 00:08:00 152.0
9   2013-01-03 00:09:00 152.0
10  2013-01-03 00:10:00 152.0
10  2013-01-03 00:10:00 152.0
11  2013-01-03 00:11:00 NaN
12  2013-01-03 00:12:00 NaN
13  2013-01-03 00:13:00 NaN
14  2013-01-03 00:14:00 149.0
15  2013-01-03 00:15:00 150.0

For each NaN, I want to use the past five value as input for my model to predict the NaN
Right now I have this line of code:
def prp_data(df, ts, look_back=5, train_fraction=0.80):
"""
Create data for modelling
"""

# Convert an array of values into a dataset matrix
def create_dataset(dataset, look_back=5):
    """
    Create the dataset
    """
    dataX, dataY = [], []
    for i in range(len(dataset)-look_back-1):
        a = dataset[i-look_back:i, 0]
        dataX.append(a)
        dataY.append(dataset[i, 0])
    return np.array(dataX), np.array(dataY)

# Get dataset
dataset = df[ts].values
dataset = dataset.astype('float32').reshape(-1, 1)

# Split into train and test sets
train_size = int(len(dataset) * train_fraction)
test_size = len(dataset) - train_size
train, test = dataset[0:train_size,:], dataset[train_size:len(dataset),:]

# Reshape into X=t and Y=t+1
look_back = look_back
trainX, trainY = create_dataset(train, look_back)
testX, testY = create_dataset(test, look_back)

return trainX, trainY, testX, testY

What this does is reframes the data into something like this:
    y-5    y-4    y-3    y-2    y-1    y
0   NaN    NaN    NaN    NaN    NaN    155.0
1   NaN    NaN    NaN    NaN    NaN    154.0
2   NaN    NaN    NaN    NaN    NaN    155.0
3   NaN    NaN    155.0  154.0  155.0  NaN
4   NaN    155.0  154.0  155.0  NaN    153.0
5   155.0  154.0  155.0  NaN    153.0  153.0
6   154.0  155.0  NaN    153.0  153.0  153.0
7   155.0  NaN    153.0  153.0  153.0  152.0
8   NaN    153.0  153.0  153.0  152.0  152.0
9   153.0  153.0  153.0  152.0  152.0  152.0
10  153.0  153.0  152.0  152.0  152.0  152.0
11  153.0  152.0  152.0  152.0  152.0  NaN
12  152.0  152.0  152.0  152.0  NaN    NaN
13  152.0  152.0  152.0  NaN    NaN    NaN
14  152.0  152.0  NaN    NaN    NaN    149.0

I want to train a model for predicting these missing values using only lagged values. As you can see in the data, I have continues missing gaps with different sizes. Now, I think I have to predict the first NaN (for example row 11) and then plug it in the next row and use it for predicting row 12 and so forth. For training and testing the model, I think I need to use rows where y is available as training data and rows where y is NaN as the testing dataset.
Am I doing this correctly? If yes, what should the deep learning model look like? I have experience with Keras and Conv and LSTM layers and I prefer to develop a model that can handle multi-step prediction.