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The Walls Of Benin, Africa's Wonder Now Lost Without Trace
Two drawings of the walls of Benin
Almost every African who swims in the waters of Africa's history knows that the Kingdom Of Benin was one of the greatest, oldest and most civilized kingdom in west Africa.
But most do not know about the walls of Benin city unless they go deeper in the "waters". Though the walls of Benin city might not be popular like the Great Walls Of China, it was "the world's largest earthworks prior to the mechanical era".
The Walls Of Benin
Constructed from around 800 to around 1400 AD, The Walls Of Benin were a series of earthworks made up of moats and ramparts known as "Iya" in the Edo language in the area around present-day Benin City, the capital of present-day Edo state in Nigeria.
Situated at the southern outskirt of the defunct Benin Kingdom, The Walls Of Benin stood for over 400 years shielding the Benin kingdom, her traditions, civilization and people from attacks and what have you.
On the 11th of September 1999, popular science writer who had reported on the environment, popular science and development issues from 64 countries over the past 20 years, Fred Pearce, talked about the Walls Of Benin which he published in an article in the widely read science magazine, The New Scientist. He stated that:
"They extend for some 16,000km in all, in a mosaic of more than 500 interconnected settlement boundaries. They cover 2, 510 sq. miles (6, 500 square kilometers) and were all dug by the Edo people."
The science writer also said that the Walls Of Benin were four times longer than the Great Wall of China and took about 150 million hours of digging during construction. In his words:
"In all, they are four times longer than the Great Wall of China and consumed a hundred times more material than the Great Pyramid of Cheops. They took an estimated 150 million hours of digging to construct and are perhaps the largest single archaeological phenomenon on the planet."
Professor in the School of Information at the University of Michigan, Ron Eglash who studies relationship between mathematics and culture observed and made research about the Walls of Benin, he came to a conclusion that: "When Europeans first came to Africa, they considered the architecture disorganised and thus primitive. It never occurred to them that the Africans might have been using a form of mathematics that they hadn't even discovered yet." The Ethnomathematician agrees that Africans might have been using a form of mathematics that the Britain hadn't even discovered yet.
The Walls Of Benin, A Wonder Lost
The Benin Kingdom was a highly civilized and organized Kingdom, this fact is agreed by many scholars. Dutch writer, Olfert Dapper who wrote books about world history and geography had this to say about the Great Kingdom Of Benin: "Houses are built alongside the streets in good order, the one close to the other. Adorned with gables and steps … they are usually broad with long galleries inside, especially so in the case of the houses of the nobility, and divided into many rooms which are separated by walls made of red clay, very well erected."
"[The walls are] as shiny and smooth by washing and rubbing as any wall in Holland can be made with chalk, and they are like mirrors. The upper storeys are made of the same sort of clay. Moreover, every house is provided with a well for the supply of fresh water" This proves that the Benin City was a well structured, and designed city.
Benin's social structure was a complex, sophisticated yet developed one. It was governed by a monarch called the "Oba" who resided in an extremely well fortified and masterfully designed palace at the center. The Benin kingdom had a wonderful relationship with Portugal, they traded goods like pepper, ivory, palm oil, bronze, etc amongst themselves. A Portuguese captain called Lourenco Pinto visited the Benin kingdom in the 17th century then he wrote from his observations: "Great Benin, where the King resides, is larger than Lisbon, all the streets run straight and as far as the eyes can see. The houses are large, especially that of the king which is richly decorated and has Fine columns. The city is wealthy and industrious. It is so well governed that theft is unknown and the people live in such Security that they have no door to their houses".
Drawing of Benin City made by an English officer in 1897. Source : Wikipedia
12 Facts About The Nile River, Including Secrets You Never Knew
Having a strong economic and military structure, the Benin kingdom was an independent one. They followed no regulations by other empires and kingdoms as they traded. The British Government hated this fact as they wanted to colonize the region, a subtle way of saying they wanted to control the region. The British Government, in 1897 sent out a small troop of 10 soldiers to the Benin kingdom, the intention of this troop is not really known but most scholars say it was a troop to the Oba carrying a message from Britain. This message is said to have the British Government's intention of governing Benin. But something went wrong, the soldiers were attacked and killed, the killers spared only two of the British soldiers. The killers were the Oba's soldiers but most Binis maintain that the order wasn't from the Oba himself but some of his Elders, this isn't proven yet.
On hearing this, the British Government sent out 1,200 soldiers to ravage the Benin kingdom, this didn't go easily though as the Benin kingdom soldiers resisted the attack for 17 days until the British Government finally won and took over the kingdom. They looted the Oba's palace and stole everything in it, they blew up and destroyed the Walls Of Benin. The then Oba of the Benin kingdom, Oba Ovoramwen Nogbaisi was forced to live in exile. This right here, led to the gradual lost of the African wonder. With this act, the British government destroyed one of the earliest civilizations of man. This act by the British Government is called the "Benin Expedition of 1897 ". It was one of the punitive expedition by the UK.
The Walls Of Benin, described in the 1974 edition of the Guinness Book of Records as being "the world's largest earthworks prior to the mechanical era." now exists only in its ruins. In 1995, UNESCO World Heritage Tentative List listed the Walls Of Benin in the cultural category. Most of the remains of the wall are constantly pulled down for construction purposes, while some of the ruins lie undiscovered in the bushes of Nigeria.
A Ruin Of The Wall Found In Benin
Keep visiting vocalafrica.com to discover more African stories, thank you!
Poem : Fireman's Jargons By Yusuf Alabi Balogun


As some of you may know, we have two Pembroke Welsh corgis named Frankie and Remi. They are brother and sister from the same litter. We adopted them when they were two years old. They are joyful and exuberant (although they were quite tired on that long drive home seven years ago).
As seen in this Vanity Fair piece, corgis are Queen Elizabeth's favorite dog.
They are also super smart and athletic. Because they are herding dogs, they need to be kept busy. We have taken many agility classes over the years and even once took them to a ranch in Malibu to herd sheep. That experience set us back $150, but I got lots of exercise chasing the sheep while Frankie and Remi barked at me.
To celebrate Frankie and Remi's 9th birthday this year, we decided to have dog friends, Kona and Kaleia, over for a Dog Party! (or Bark Fest in this case (herding dogs, they bark a lot).
Preheat the oven to 325°. Line two cookie sheets with parchment paper. [Ina's recipe says to use an electric mixer with a paddle attachment, but as I don't have one, a hand mixer worked just as well.] In a large bowl, combine the two flours, powdered milk, oats, peanut butter, and wheat germ. With the mixer on low speed, add the egg and 1 cup of water and mix until it just forms a slightly sticky ball.
Dump the dough out on a well-floured board and knead it into a ball. Roll the dough out ½ inch thick (if these biscuits are for smaller dogs, roll the dough a little thinner, so they are easier to bite into). Dip a dog bone-shaped cookie cutter in flour and cut out shapes. Collect the scraps, knead lightly, roll out again, and cut more dog biscuits.
Place the biscuits on the prepared sheet pans and brush with the egg wash. Sprinkle with oats and bake for 1 hour, until completely hard. Cool and store in an airtight container. Use within one week as they contain no preservatives.
…while Frankie especially loves them after a good run.
…and love you even more.


Buyamba is a non-profit organized to support the orphaned and disadvantaged children of Uganda. Florence Dongo and her late husband Bethuel's mission is to provide for the physical needs of these children and empower them through education and spiritual discipleship. Our team will visit several church partners throughout Kampala by reaching out to their communities. We will come alongside the needs of these communities by distributing water filters, setting up eye glass clinics and other small-scale medical stations, holding conferences for women and men, distributing Bibles, and visiting households to share the Gospel and pray for people. The team also spends time at God Cares Primary and High School leading chapel services, encouraging teachers and staff, and spending relational time with the students. If you sponsor a child at God Cares School, you will have the chance to meet them!


B-12 MC Spray is so convenient - no worries about taking more pills. Can be used anytime anywhere. My naturopath recommended this to me to maintain acceptable Vitamin B levels.
B-12 MC Spray by DaVinci Labs was recommended by my ND after I tired of giving myself the B-12 shot. Excellent product.
I was prescribed DaVinci B-12 spray several years ago by my health-care practitioner. I have stayed on it ever since, as I know it's easy to get deficient in B-12.
B-12 Spray is a dietary supplement that helps support energy as well as healthy blood and nerve cells. B-12 Spray combines 1000 mcg Vitamin B12 with the active form of vitamin B6 and folic acid in an easy to use spray.
• Individuals who have trouble absorbing vitamin B12 from foods.
• Ongoing fatigue and weakness.
• People needing GI tract support.
Vitamin B12 is a water-soluble vitamin. It is required for proper red blood cell formation' neurological function' and DNA synthesis. Vitamin B12 functions as a cofactor for the enzyme methionine synthase which causes the conversion of homocysteine to methionine. Methionine is required for the formation of S-adenosylmethionine (SAMe)' a universal methyl donor for almost 100 different substrates' including DNA' RNA'hormones' neurotransmitters' proteins' and lipids. Deficiency of vitamin B12 may occur as a result of an inability to absorb B12 from food. It can also occur in individuals with dietary patterns that exclude animal or fortified foods.
Other ingredients: glycerin' water' potassium citrate.
Vegetarian / Gluten Free / Soy Free. Made with Non GMO Ingredients.
As a dietary supplement' hold nozzle 1" from mouth' spray once and swallow. Use once daily or as directed by your health care practitioner. Shake well before each use.
If you are pregnant or nursing' consult your health care practitioner before taking this product. Keep out of reach of children. Store in a cool' dry place.
The spray is so easy to use; just a spray under the tongue. It doesn't have a lot of additives, as some others do, and it's is easier to absorb than capsules or tablets. It is a little more expensive than some, but I still prefer it for the aforementioned reasons.
B-12 MC Spray by DaVinci Labs is the perfect product if you remove or replace the folic acid with a different form. (methylfolate! and/or folinic) The prevalence of those with MTHFR genetic variations can be high 45-70% depending on ethnicity, so you're unnecessarily limiting your market. This WOULD BE my go to for everyone. Pray you can reformulate!
If I could only read the directions!
A very nice friend gave me a bottle of B12 MC Spray by DaVinci Labs, and I'm not sure how much it helped, but thought I'd try another bottle. I'm recovering from cancer treatment and hope it helps. However the directions must be in a 1/2 point type, as I couldn't read them unless I had a magnifying glass. Good thing the friend told me what to do!
Can't read the directions, type point too small.
Help! Get rid of folic acid!
Have been using B-12 MC Spray by DaVinci Labs product for a while. Was the purest I could find. Now I find out that I should not have folic acid due to my MTHRF gene mutation! Can't find a replacement that doesn't have junk in it.
Was the purest formula I could find.
I can't have the folic acid! See above!
doctor recommended and it does its job fantastic without all the additives. i have a tough time absorbing B-12 so this product was a welcomed surprise!!! fast shipment (as always) with pure formulas .. thank you!!!
it WORKS convenient and pure!


Keiryu Sure never been there so why not.
Keiryu I am, the more or less human personafication of INSANITY. I am her loyal servant, and i am the spreader of her might.
I AM, THE MASTER OF INSANITY!!!
Sometimes known as, that one a**hole.


Dr. Christian Harisch belongs to a hotelier family in Kitzbühel and runs the hotels Weisses Rössl and Hotel Schwarzer Adler, which have been owned by the family for over 100 years. He studied law after completing his apprenticeship as a tourism manager. He has been managing director and co-owner of Lanserhof since 1998. Harisch is regarded as a pioneer in holistic medicine combined with naturopathic treatment. His passion for cycling is reflected in his support for professional sports, and with Lanserhof he has been supporting the Tour de France team "Bora-hansgrohe" for years.
Why enjoyment and renunciation are mutually dependent. Why Seneca is right and why asceticism is underestimated as a fine form of culture.


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Persian Wonders Mode Off
The Cyrus Cylinder
Study Of The Object | According to John Curtis of the British Museum
Translation Line By Line
The Cyrus Cylinder Translation
1-19: Associating Cyrus with the god Marduk Translate Line 1-19
20-22: Peaceful entry to Babylon Translate Line 20-22
23-34: Cyrus's policy of restoring Babylon Translate Line 23-34
34-37: Cyrus let people to live in peace Translate Line 34-37
38-45: Building Activities Orered by Cyrus In Babylon Translate Line 38-45
Associating Cyrus with the god Marduk
1. [When ... Mar]duk, king of the whole of heaven and earth, the ....... who, in his ..., lays waste his.......
2. [........................................................................] broad? in intelligence, ...... who inspects (?) the wor]ld quarters (regions)
3. [..............................................................…] his [first]born (=Belshazzar), a low person, was put in charge of his country,
4. but [..................................................................................] he set [a (…) counter]feit over them.
5. He ma[de] a counterfeit of Esagil, [and .....….......]... for Ur and the rest of the cult-cities.
6. Rites inappropriate to them, [impure] fo[od-offerings ….......................................................] disrespectful […] were daily gabbled, and, as an insult,
7. he brought the daily offerings to a halt; he inter[fered with the rites and] instituted […....] within the sanctuaries. In his mind, reverential fear of Marduk, king of the gods, came to an end.
8. He did yet more evil to his city every day; … his [people ................…], he brought ruin on them all by a yoke without relief.
9. Enlil-of-the-gods became extremely angry at their complaints, and […] their territory. The gods who lived within them left their shrines,
10. angry that he had made (them) enter into Shuanna (Babylon). Ex[alted Marduk, Enlil-of-the-Go]ds, relented. He changed his mind about all the settlements whose sanctuaries were in ruins,
11. and the population of the land of Sumer and Akkad who had become like corpses, and took pity on them. He inspected and checked all the countries,
12. seeking for the upright king of his choice. He took the hand of Cyrus, king of the city of Anshan, and called him by his name, proclaiming him aloud for the kingship over all of everything.
13. He made the land of Guti and all the Median troops prostrate themselves at his feet, while he shepherded in justice and righteousness the black-headed people
14. whom he had put under his care. Marduk, the great lord, who nurtures his people, saw with pleasure his fine deeds and true heart,
15. and ordered that he should go to Babylon. He had him take the road to Tintir (Babylon), and, like a friend and companion, he walked at his side.
16. His vast troops whose number, like the water in a river, could not be counted, were marching fully-armed at his side.
17. He had him enter without fighting or battle right into Shuanna; he saved his city Babylon from hardship. He handed over to him Nabonidus, the king who did not fear him.
18. All the people of Tintir, of all Sumer and Akkad, nobles and governors, bowed down before him and kissed his feet, rejoicing over his kingship and their faces shone.
19. The lord through whose help all were rescued from death and who saved them all from distress and hardship, they blessed him sweetly and praised his name.
Peaceful entry to Babylon
20. I am Cyrus, king of the universe, the great king, the powerful king, king of Babylon, king of Sumer and Akkad, king of the four quarters of the world,
21. son of Cambyses, the great king, king of the city of Anshan, grandson of Cyrus, the great king, ki[ng of the ci]ty of Anshan, descendant of Teispes, the great king, king of the city of Anshan,
22. the perpetual seed of kingship, whose reign Bel (Marduk)and Nabu love, and with whose kingship, to their joy, they concern themselves. When I went as harbinger of peace i[nt]o Babylon
Cyrus's policy of restoring Babylon
23. I founded my sovereign residence within the palace amid celebration and rejoicing. Marduk, the great lord, bestowed on me as my destiny the great magnanimity of one who loves Babylon, and I every day sought him out in awe.
24. My vast troops were marching peaceably in Babylon, and the whole of [Sumer] and Akkad had nothing to fear.
25. I sought the safety of the city of Babylon and all its sanctuaries. As for the population of Babylon […, w]ho as if without div[ine intention] had endured a yoke not decreed for them,
26.I soothed their weariness; I freed them from their bonds(?). Marduk, the great lord, rejoiced at [my good] deeds,
27. and he pronounced a sweet blessing over me, Cyrus, the king who fears him, and over Cambyses, the son [my] issue, [and over] my all my troops,
28. that we might live happily in his presence, in well-being. At his exalted command, all kings who sit on thrones,
29. from every quarter, from the Upper Sea to the Lower Sea, those who inhabit [remote distric]ts (and) the kings of the land of Amurru who live in tents, all of them,
30. brought their weighty tribute into Shuanna, and kissed my feet. From [Shuanna] I sent back to their places to the city of Ashur and Susa,
31. Akkad, the land of Eshnunna, the city of Zamban, the city of Meturnu, Der, as far as the border of the land of Guti - the sanctuaries across the river Tigris - whose shrines had earlier become dilapidated,
32. the gods who lived therein, and made permanent sanctuaries for them. I collected together all of their people and returned them to their settlements,
33. and the gods of the land of Sumer and Akkad which Nabonidus – to the fury of the lord of the gods – had brought into Shuanna, at the command of Marduk, the great lord,
34. I returned them unharmed to their cells, in the sanctuaries that make them happy. May all the gods that I returned to their sanctuaries,
Cyrus has enabled the people to live in peace
35. every day before Bel and Nabu, ask for a long life for me, and mention my good deeds, and say to Marduk, my lord, this: "Cyrus, the king who fears you, and Cambyses his son,
36. may they be the provisioners of our shrines until distant (?) days, and the population of Babylon call blessings on my kingship. I have enabled all the lands to live in peace."
37. Every day I increased by [… ge]ese, two ducks and ten pigeons the [former offerings] of geese, ducks and pigeons.
Building Activities Orered by Cyrus In Babylon
38. I strove to strengthen the defences of the wall Imgur-Enlil, the great wall of Babylon,
39. and [I completed] the quay of baked brick on the bank of the moat which an earlier king had bu[ilt but not com]pleted its work.
40. [I …… which did not surround the city] outside, which no earlier king had built, his workforce, the levee [from his land, in/int]o Shuanna.
41. [… ......................................................................with bitum]en and baked brick I built anew, and [completed] its [work].
42. […...........................................................] great [doors of cedar wood] with bronze cladding,
43. [and I installed] all their doors, threshold slabs and door fittings with copper parts. [….......................]. I saw within it an inscription of Ashurbanipal, a king who preceded me;
44. […................................................] in its place. May Marduk, the great lord, present to me as a gift a long life and the fullness of age,
45. [a secure throne and an enduring rei]gn, [and may I …... in] your heart forever. a. [Written and check]ed [from a…]; (this) tablet (is) of b. Qishti-Marduk, son of […].
The Shape of Cylinder
The shape of Cylinder was traditionally used in ancient Mesopotamia for foundation places – inscriptions buried under large structure such as city walls or temples. As a foreign conqueror, Cyrus used the cylinder shape to establish his respect for local tradition. The text on cylinder never starts and never finishes, It's endlessly revolving. You come to the end go seamlessly again onto the beginning. It's a rather ingenious object. It's a different concept from a sheet of paper, with a start and finish point. It gives more majesty and authority to the document itself. The interesting point is that, even though it's meant to be read by turning, when you stand in front of it, you're looking at it right away up. If you go around to the back of the case, you're looking at it upside down. [11]
Meant To Be Read Before Buried
The object is partly a religious document, and was buried to ask for the ongoing protection of the god of Babylon. Although at the same time, we know it contains a declaration, and [recently discovered] tablet fragments make clear that three were copies of It sent all around the Persian empire. It's very likely that there were other cylinders buried by Cyrus in Babylon, it's just that they haven't been found yet.[11]
The Two Tablet fragments
The significance of the discovery was that cylinders were made to be buries privately but tablets were made for public announcements.
This discovery showed that Cyrus wanted to publicise what he did in Babylon. He made press releases to tell the empire that he brought peace to Babylon and allowed gods to return to their own sanctuaries and late people how worshipped those gods go back to their lands and temples.
Line 1-2 and 44-45 are restored on the basis of the two clay fragments from a late Babylonian tablet, inscribed with text which duplicates that of the Cyrus cylinder
The Cyrus Cylinder Restorations
As the Cyrus Cylinder, which is permanently exhibited at the British Museum, sometimes removed from the exhibition and subjected to contemporary conservation. There were several generations of old restorations done. In addition, this object has been subjected to at least one moulding process, some of whose residues were still found in depressions of the object. The bonds between two fragments were softened and undone by acetone compresses. After removing most of the old fillings and cleaning the surface, the two loose fragments were re-glued using acrylic resin. The smaller fragment needed a relining made from a mixture of acrylic resin. Also The British museum re fire their clay tablets for long lasting purposes.[11]
Video From The British Museum
Persian Wonders is a cultural, non profit, apolitical team and focused on the subject of ancient Persia, based in Cambridge.
© 2006 - 2023 - ©PersianWonders.com v4.0.0.0 | Archaeological update: 02/11/2022
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*PW - Persian Wonders (based on our conclusion and study)
1. Majidzadeh, Yousef. "The Land of Aratta." Journal of Near Eastern Studies 35, no. 2 (1976): 105-13. Accessed August 10, 2020. www.jstor.org/stable/545195.
2. The British Museum. 2020. collection. [ONLINE] Available at: https://www.britishmuseum.org/collection/object/W_1936-1217-2. [Accessed 10 August 2020].
3. Madjidzadeh, Youssef & Pittman, Holly. (2008). Excavations at Konar Sandal in the region of Jiroft in the Halil basin: First preliminary report (2002-2008). Iran. 46. 69-103. 10.2307/25651436.
4. Geoffrey,B. Olivier,J. Youssef,M. ARTE France.; Gedeon Programmes. Special Broadcasting Service Corporation. SBS-TV. (2005). Unearthing the lost kingdom of Aratta. [Video file]. Retrieved from https://www.terranoa.com/product/product.php?code=125
6. Francfort H.-P., Tremblay X. Marhaši et la civilisation de l'Oxus // Iranica Antiqua, vol. XLV (2010), pp. 51–224. doi: 10.2143/IA.45.0.2047119.
8. Desset, Francois. (2014). A new writing system discovered in 3rd millennium bce iran: The konar sandal 'geometric' tablets. Iranica Antiqua. 49. 83-109. 10.2143/IA.49.0.3009239.
10. Geoffrey,B. Olivier,J. Youssef,M. ARTE France.; Gedeon Programmes. Special Broadcasting Service Corporation. SBS-TV. (2005). Unearthing the lost kingdom of Aratta. [Video file]. Retrieved from https://www.terranoa.com/product/product.php?code=125
11. Curtis, J. Finkel,I (Ed.). (2013). The Cyrus Cylinder: The Great Persian Edict from Babylon.
12. Curtis, J. (2013). The Cyrus Cylinder and Ancient Persia: A New Beginning for the Middle East.
13. Farzin, R. (2007). Iran: Seven Faces of Civilization.

redpajama_set_name: RedPajamaCommonCrawl


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May 4, 2018 January 7, 2020 Simon Pettet
Allen Ginsberg – Photograph by Allan Tannenbaum
Continuing today in New York, the inaugural St Mark's Poetry Project Allen Ginsberg Symposium – For more on that (proposed annual event) – see here
On public television this week, (presented by WGBH Boston and distributed by American Public Television) the beginning of a new tv series and multi-platform digital initiative, Poetry In America. Allen's poems ("Hymmnn" (from "Kaddish") and "Hum Bom!" are featured in the opening program
From the program credits:
"Although we think of a poem as something read from a book, poet Allen Ginsberg knew that poetry's power did not depend upon print, and he drew on the traditions of religious and ritual communities in writing verse that would elevate the spirit, knit together community and even, when necessary, soothe and console the mourner. Joined by rock star Bono former United States Poet Laureate Juan Felipe Herrera, and by a chorus of clergy and religious practitioners, in this episode we read two of Ginsberg's most emotionally transporting poems"
We've already previewed this program (at least, one of the two main poetry readings) – here
Musician Peter Case has some stories to tell – about busking outside of City Lights in San Francisco, and bumping into Allen ("My name's Allen, mind if I sit in with you?".."Can you guys play some country blues?"), improvising, while people walked on by, oblivious, unaware that it was the famous Allen Ginsberg playing free for them in the street.
And, driving around the next day with Allen and Peter Orlovsky in their VW van ("Hey, you guys need a ride?"), and Allen name-dropping ("Well, Dylan told me.."). And a contrasting encounter the next day with (self-described) Satanist, Anton LaVey! ("going from Ginsberg who seemed like a benevolent, you know, sort of hipster to this guy that seemed like a malevolent hipster"..)
"These guys were important", Case goes on, "all those Beats, they were like your big brothers or something, teachers, you know, they were almost like father-figures, I suppose – but they weren't like anybody's father, so, old big brothers, you know, (or), yeah, weird uncles ..and City Lights (City Lights Bookstore) was so important.
Barry Miles on William Burroughs – Opening on Monday (May 7), and on show through to June 2nd, in London, at the Westminster Arts Library, an exhibition, drawn from his own personal archives, chronicling the time Burroughs' spent living in London – (Interviewer (Stephen Coates): "What brought William S Burroughs to London?" – Barry Miles: "He came to London because he was.. he had an affair with this guy Ian Sommerville who was a mathematican, who was still studying at Cambridge, and so, at the end of the summer, Ian came back to London, and Bill simply followed him.." – "And then, in 1967, I think it was, he rented a place on Duke Street, St James, and lived there until 1974, so he was there (in London) for quite a long time…" ). For more of this illuminating interview – see here
Miles will be formally interviewed later in the month (May 30), by Frank Rynne, as part of the Salon For The City's Naked London Lunches series. There will also be a guided walk of Burroughs' London on May 26 with writer Antony Clayton and esoteric scholar Dr. William Redwood. Miles also speaks to Richie Troughton of The Quietus – here
Jack Kerouac's recently re-released 1959 Blues and Haikus album (re-released last month on Real Gone Music) is reviewed by William Nesbitt on PopMatters – here
Speaking of PopMatters – here's Megan Volpert's review of the recently-released live-from-the-St-Marks-Poetry-Project-1971 Lou Reed recording – Do Angels Need Haircuts?
Allan Tannenbaum
Barry Miles
Beat History
Hum Bom
Juan Felipe Herrera
Megan Volpert
William Nesbitt
Previous The St Mark's Poetry Project's Allen Ginsberg Symposium
Next Wichita Vortex Sutra (Automobile Poesy to Nebraska, 1967)


The time has come for women to reclaim their roles as deacons in the Catholic Church.
That was the assertion of a panel of scholars who came together on Tuesday, Jan. 15 at Fordham's Lincoln Center campus.
The issue of whether women can become deacons is one that the Vatican had studied twice since the early 1990s. In 2016, Pope Francis announced a third commission, made up of six women and six men, to study its feasibility.
Phyllis Zagano, Ph.D., and Bernard Pottier, S.J., two members of that commission, spoke Tuesday at a Fordham panel event, The Future of Women Deacons: Views from the Papal Commission and the American Pews.
Zagano, a senior research associate-in-residence at Hofstra University and author of Women Deacons? Essays with Easy Answers (Michael Glazier, 2016), said evidence of the existence of women deacons, who share many responsibilities with priests, in the churches' earliest days is indisputable.
Documents available in Vatican libraries from the fourth and fifth centuries make clear the existence of a position that was separate and distinct from the priesthood, and was therefore open to all, she said, and specifically referenced women.
"The earliest ordination for deacons is in the apostolic constitution, which directs the bishop to lay hands on [a woman being ordained]in the presence of the presbyterate, the male deacons, and the woman deacons, and to pray a prayer that parallels the ordination of the deacon, including the Epiclesis, which is the calling down of the Holy Spirit," she said.
"God is asked to bless her in regard to her ministry. The ordaining bishop places a stole around her neck. As I've said to many people, 'If she wasn't a deacon, they would call her something else.'" she said, but the responsibilities would have been the same.
In the middle of the 18th century, she said, scholars began rejecting the idea of a female deacon, and quibbled over whether these women had been "ordained" or "blessed." Zagano said the words were used interchangeably at the time.
"For me, if a bishop was laying hands on a woman, invoking the Holy Spirit, putting a stole on her, giving the chalice, and calling her a deacon, I don't know what else to say," she said.
So why did women deacons disappear? Father Pottier, a faculty member at the Institute D'Etudes Théologiques in Brussels, said the Great Schism of 1054, when what is now the Catholic Church and the Eastern Orthodox churches split, was key to the change.
"The Western church began to think by its own, without the mystical spirituality of the East, that rationality and legalistic thought was more important," he said.
The upside of this was the rise of immensely influential philosophers such as St. Thomas Aquinas, he said.
"On the other side, we lost a little bit of what the sacrament is. What is the spirituality and the grace of the sacrament? The West wanted to do everything clear, and everything simple. So the sacrament of ordination became very simple. You have cursus honorum, a sort of scale you have to pass by all the steps, and not miss one. A deacon became only a step to priesthood," he said, and therefore, something reserved for men. But he cautioned that this needn't be the end of the story.
"Our faith has roots in the Bible, in the New Testament, in the person of Jesus Christ, and in what the church has done. We do not have to be afraid of history. In history, we do not have a source of rigidity and immobility," he said, but rather an example that change is possible.
Panelist Donna Ciangio, O.P., said conversations she's had with lay members of the Archdiocese of Newark, where she is chancellor, have convinced her that parishes need women deacon now.
"I asked a few parishioners about the possibility of women deacons, and the first answer I got was, "Aren't you and Sister Sandy deacons already?" she said.
Where the issue really rears its head is when she works with couples who want to have their child baptized in the church.
"We ask them, is there anything that keeps you from embracing the church wholly? One woman said to me, 'My children ask me, 'Why can't women be priests or deacons?' I have no answer that satisfies them,'" she said.
Sister Ciangio also recently oversaw the creation of a study guide to help Catholics better understand this issue, titled Women Deacons: Past, Present, Future, (Paulist Press, 2012), which Zagano co-wrote. She invited 12 parishioners from the diocese to come together to read it.
"As we discussed each chapter, they became more and more interested, but they became more and more agitated," she said, noting that none were aware of the existence of women deacons in the past.
What if Pope Francis decides this is not the right time to let women become deacons again?
The panel has presented its report to the pontiff and is waiting for a response. Zagano said that given the church's dire need for those who can minister to the faithful, even a delayed answer will be a negative answer.
"I think it's up to the church to make noise. The pope has said in other cases, make noise. Well, make noise," she said.
The panel event was sponsored by Fordham's Center on Religion and Culture. David Gibson, the center's director, said the topic is a timely one given the upheaval the church has faced recently.
"Elevating and broadening the role of the women in the church, as Pope Francis has said we must do, is especially critical today if we're to answer the call of the spirit in this time of epochal change and challenge for the Catholic church," said Gibson.
The panel was moderated by Thomas Rosica, C.S.B., president of Salt & Light Media, and was streamed live on Salt & Light.


A friend of mine whom is constantly on the road making his living in a sales field once told me of how much he hates airports. Between the line-ups, the paper work and the hauling of luggage to kingdom come (or the next terminal at DFW), he has associated these hubs of long range travel with the same ill-will that the average commuter would place upon a big city highway at 5:30pm. This couldn't be further from how I feel about airports.
I don't work in sales and I have never had to travel for work. Also because of my job (which is steady, well-paying and one that I consider myself lucky to have) I don't have the opportunity to jet-set around the world like some of the "digital nomads" we all love to read about online. The vacation time I have accrued allows me to take maybe two major trips per year. The good part about such infrequent travel is for one, the time I have on my side to plan the perfect vacation, and maybe more importantly the scarcity allows me to fully appreciate all that contributes to the magic of travel, of which the airport experience is an integral part.
…and leaving the house well before sunrise. I don't do this when I go to work. I surely don't do this on the weekend. I only do this when I'm going to the airport. Thus 4am wake-up call = vacation!
Call me weird but sometimes I just love to stand in front of this thing and imagine all of the different places I could get to in a matter of hours. I could be in Lima for lunch or Delhi for dinner.
Remember all those times sitting at your desk eating leftovers, reading about who's about to takeoff to Europe? Well now it's my turn, and you're getting an Eiffel Tower emoji with that too!
So what if I will have no shortage of opportunity to buy cheap booze while at my destination. I'm at the airport, I'm on vacation and dammit I'm going to at least look at all of the bottles and cigars.
Similar to the destination board, look at all the places you can go! Beautifully illustrated with hub-and-spoke airports all over the map. I also enjoy the layout maps of the hub airports and info about the airline's fleet. Other than Skymall, this is the pinnacle of inflight reading. Oh ya, Skymall!
No real explanation required. I will never buy a cat house or a Boston Red Sox themed BBQ set, but these are fun to look at for 5 minutes from the window seat.
I know, the major portion of an 8-hour trans-Atlantic flight is pretty damn boring, but man those views from above during take-off and descent are stunning.
This is really sweet! I've never met anyone who enjoys airports before - they are to be endured rather than enjoyed. You would love some of the splendid Middle Eastern airports such as Abu Dhabi.
Thanks for the comment! I have never been to the Middle East but I have heard there are some pretty epic airports in that part of the world. Cheers!


When you are sad, I will dry your tears.
When you are scared, I will comfort your fears.
When you are worried, I will give you hope.
When you are confused, I will help you cope.
I shall be your beacon, shinning ever so bright.
This is my oath., I pledge 'till the end.


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Home Seynani Sugar Relapse: What It Is and How to Avoid It
Sugar Relapse: What It Is and How to Avoid It
Sugar is addictive. It's something that our bodies crave and we're not happy until we get it. That's why many people are opting to quit sugar once and for all. It's the key to leading a healthier life. Hidden sugars are in a lot of foods that you wouldn't even think. That's why it's important to read labels, come up with a plan, and ditch the sugar once and for all.
However, just like with any other addictive substance, quitting cold turkey can be hard. A sugar relapse can be easily instigated by a trigger. In fact, the parallels between addiction to sugar and addiction to drugs or alcohol are so similar that many of the triggers and treatments are the same. Let's zoom in on some of these triggers and how to avoid them so that you don't have to risk a sugar relapse:
Avoid Situations With Sugary Snacks
If you're going to quit sugar once and for all, then you need to avoid situations where there will be sugary snacks. Does the break room at work have doughnuts? Don't go in there. Does your friend invite you to a fast food place for lunch? Say no until you're strong enough. With sugar lurking almost anywhere, you don't want to put yourself in situations where you know you'll splurge.
Don't Fall Into the Just One "Mentality"
When you're quitting sugar, you need to quit once and for all. You can't go back and forth between the two extremes. It will throw your body out of whack, your skin will break out, and you'll never get over the sugar addiction. Many people think that they can have one without gaining weight or causing any damage. The problem is that just one turns into two, three, four, or more and suddenly you're back to old habits. If you're going to cut out all sugar then you need to stay on that path until you break the addiction.
Stress triggers can be anything from people, to smells, to situations, or any other stimulus that causes stress. Any of these may cause people to overeat and grab a sugar snack. In order to avoid sugar, you need to avoid stress. That's because many people think of food as comforting when they're feeling stressed out. There are other options, however. If you're feeling stressed, sing a song, take a walk, write some poetry, or draw a picture instead of grabbing a candy bar. Your body will feel better.
Stay Stocked with Healthy Snacks
If you're trying to quit sugar completely, have other snacks on hand instead. Many people are prone to snacking throughout their day and that's okay. There are so many healthy options out there. Instead of going to the vending machine, stay stocked with eggs, nuts, raw veggies, and other snacks that don't include added sugar.
Slay the Sugar Dragon with Sweet Zap
You can free yourself from sugar's addictive hold over you. Sweet Zap naturally, safely, and temporarily blocks your ability to taste sweet from both sugar and artificial sweeteners. The reward mechanism is never triggered. Sugar that tastes no more sweet than sand is easy to say no to. Sweet Zap's ability to block sweet turns addicting sweets into undesirable food.
Quitting sugar will be one of the best things you do for your body. You will no longer feel tired, sluggish, or cranky. After your body detoxes and you see how good you feel, you might not want to ever go back to eating that way again.
Tags: addiction, snacks, sugar
The Science Behind Sugar Cravings
4 More Reasons You Should Cut Sugar Out of Your Diet
What Diabetics Need to Know About Ketoacidosis
If You're an Athlete, It's Time to Bench the Sugary Drinks and Snacks


Upscale Suits and Shirts for Men at Bryn Keith Clothing Company (Up to 50% Off). Three Options Available.
Promotional value expires 120 days after purchase. Amount paid never expires. Limit 1 per person, may buy 1 additional as gift. Limit 1 per visit. Valid only for option purchased. Alterations only valid on items of clothing purchased at time of redemption. Not valid with other offers or in-house specials. By appointment only. Some colors and suit styles may be charged extra. May be repurchased every 30 days. Merchant is solely responsible to purchasers for the care and quality of the advertised goods and services.
Bryn Keith Clothing Company takes its name from Bryn Johnson, who founded the company to provide fine clothing for his family and friends. Now he reaches an international client base with collections of high-end suits, shirts, and accessories. His fabrics—which come from Italy, England, Egypt, and Switzerland—rotate regularly so that clients can follow fashion trends, dress for the season, or start a suit-of-the-month club.
In Bryn Keith Clothing Company's showroom, specially curated music wafts around browsers as they pick all-cotton or all-silk pieces with as much or as little staff assistance as they desire. After clients choose the fabrics and cut, a Hong Kong tailoring service assembles the pieces and provides custom alterations in case of the sudden sprouting of a third arm. Peruse some frequently asked questions online.


A number of players will be missing against the Germans. Ali Boussaboun and Pascal Bosschaart have both trained with the squad this week, but for them the game has come to early. The same goes for Cory Gibbs, who underwent a knee operation in the summer and has yet to rejoin training. Christian Gyan's knee keeps him out too, whereas Shinji Ono and Patrick Mtiliga are both in rehab in their home countries.
Feyenoord will certainly be starting with a defensive midfielder, confirmed Koeman. 'That's the best thing for the organisation in midfield. We will then always have the same number of people in midfield or a man more. That breeds confidence and I hope that will get us playing easier.' Alfred Schreuder is likely to take on the role.


Possible systematic errors in determining the solar radius from the f-mode frequencies are studied to find that the input physics governing the structure of outermost layers of the Sun has significant influence on the estimated radius. It is investigated how treatment of convection and low temperature opacity may influence the determination of radius and it is found that it may be changed by as much as 100 km. The best estimate of the solar radius is found to be 695.77±0.1 Mm, where the error bars represent estimate of systematic errors, while the statistical errors are very small (≈1 km).


Sweet Romances include all romance that exclude titillating descriptions and sexual content. Inspirational or Christian romance falls into that category so these tips work for both secular and faith-based sweet romances.
Many novelists begin the plot with the focus on the heroine, but occasionally the hero gets that opportunity. No matter, the heroine and hero are equal in the importance to develop a clear characterization. The points below can serve as a guide on keeping the romance sweet and yet providing good descriptions and attributes that arouse the interest and enjoyment for the reader.
So what attributes and characteristics make a romantic hero? Does he have broad shoulders tapering to a trim waist? Is he tall and dark? Is he blond and witty? Each author and each reader has her own answer to these questions. Yet in creating a hero, authors are wise to know the more defined guidelines of most Christian publishing houses.
The past creates who he is today. The past formulates his present needs, goals, and weaknesses. Even if he is a Christian, he has flaws, sorrows, and shames. Christian's sin and so does the hero. He's behaved in ways that makes him feel unworthy or makes him feel unforgiven. A perfect hero is a cartoon, not a believable, compelling character. Give your hero an event in his life that he wants to forget, deeds he fears others will learn, secrets that smother his growth. Then love moves into his heart through the heroine and the workings of his faith, and the character will grow.
In Loving Ways, Love Inspired, the hero's present life is paralyzed by his past.
Ken winced. Annie's attitude jarred his memory. He'd been a drinker, created fear in others, embarrassed his family, and caused them shame. For better or worse. Annie's words crept like tendrils through his conscience. His life had been worse not better. Since running into Gordon, the old days kept niggling at him and brought back fear of discovery. He wished the guy hadn't remembered him.
Though physical attributes are highlighted in most romances, Christian romances tend to focus mainly from the chest upward. The hero might have broad shoulders, a square jaw, raven black hair, mesmerizing blue eyes and an expansive chest, but references to the lower extremities is avoided.
Any physical description is most effective when it appears for a greater purpose: drawing out emotion, deepening characterization, or providing details important to the story. Kate Davis sees her friend the arms of a stranger in Secrets of the Heart is jolted by his appearance which brings back unwanted memories and serving an important purpose to the stories conflict.
Not his near six foot stature, but his broad, square frame like a football player. Thick neck, powerful chest, strong muscular legs, and bulging arms she saw wrapped around Phyllis.
In the novella "Better To See You," the heroine recalls her earlier relationship with the hero.
The arm holding her dropped to his side, and he raised the other, running his fingers through his thick, wavy blond hair. His near-center part tugged at her memory—-the way she'd kissed his forehead just below his hairline.
No matter how tall, dark, and handsome the hero is in Christian fiction, the physical attributes are not the most important characteristic to the heroine.
The qualities that are appreciated by most people are: compassion, kindness, thoughtfulness, and generosity. The qualities are faith based and ones a heroine looks for in a hero. In the romantic suspense, Adam's Promise, Adam is depicted as a handsome, arrogant surgeon, but Kate's description deepens the characterization.
Kate's heels clicked along the hallway as her thoughts swung from her frustration with Adam to her admiration. The man could be self-centered one minute and filled with compassion the next. . .when it involved the patients. Beneath her irritation, she admired the man. He'd come from a prestigious family in Colorado Springs. His father was the mayor, and yet, here he was in Venezuela providing health care to the poor in the rustic community so many miles from the comforts of home.
Notice what is important to Kate—his compassion, his willingness to leave family wealth behind—attributes most women would cherish in a husband.
In "Christmas Moon ," a two-in-one release in That Christmas Feeling, the hero sees the heroine with new eyes.
The truth settled over him. For the first time since Della died, he was looking forward to Christmas. Rose had been the catalyst. They'd become friends. Their lives had become entwined. Blest be the ties that entwine. The words twisted in his head.
As they'd spent more time together, Paul sensed a kind of like-minded spirit they shared. The painting came to mind. They'd both been drawn to it immediately. But it was more than that. He felt comfort in her presence. She exuded compassion and evoked from him a new tenderness.
Must the hero be a believer? Sometimes novels present a weak Christian, one who believed but allowed his faith to waver. Part of his journey is returning to his faith through his own growth and change. Being repentant and seeking forgiveness is often part of a hero's struggle. A flawed Christian hero makes a Christian novel realistic as in this selection from Adam's Promise.
If a hero is not a Christian, he must be by the end of an inspirational romance, but a full conversion must be through the hero's own struggle, and not the result of the heroine's "missionary" dating. In "Better To See You," the hero learns through th heroine's example of living her faith.
Was this God's work? He wondered. He'd been such a difficult person back then, not only disbelieving, but scorning those who believed…except Lucy. She had made her faith so desirable, so sincere that he had a difficult time taunting her.
Still, her happy heart and open arms had instilled a small seed of question, of wonder about her beliefs. And he'd done the rest, fertilized by memories of her joy in living, he'd stumbled along until one day, alone in a motel room, he'd picked up a Bible. That day was only the beginning. Lucy would never believe how much he'd changed.
Make the hero realistic. Give him flaws and give him a past that shows his weaknesses, flaws and mistakes. Show how the past molds the hero's goals and motivations, then how overcoming them changes him for the better. No matter what qualities and characteristics you give your hero, limit the physical description to above the waist and give the hero spiritual gifts that arouses the heroine's love and respect for him.


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Blog: More providers than previously thought accept Medicaid patients
Virgil Dickson
A long-running belief may have just been refuted: There may be more providers willing to see Medicaid patients than previously estimated.
Patient advocates argue that providers are often unwilling to take on Medicaid enrollees because reimbursement rates can be as little as 60% of the costs of care. That concern has even led to lawsuits. In 2015, the U.S. Supreme Court ruled that private healthcare providers cannot sue state Medicaid agencies over low reimbursement rates.
Idaho providers had argued in the case, Armstrong v. Exceptional Child Center Inc. that suing over low rates is sometimes the only way to enforce federal payment requirements. Otherwise, low rates could lead to fewer providers agreeing to participate in Medicaid, and thus less access to care for Medicaid patients.
Physicians, meantime, have argued that with only so many hours in a day, why would they devote time to serving the lowest-paying patients?
In 2013, the last time Health Affairs published a physician survey on the question, the researchers found nearly 1 out of 3 doctors refused to see new Medicaid patients. That was compared to just 17% of physicians who refused to see new Medicare patients&msash;and those were the ones who admitted it.
But a new analysis by the Medicaid and CHIP Payment and Access Commission (MACPAC) could be turning that belief on its head.
Still, while more physicians than previously believed take on Medicaid patients, MACPAC found that many physicians only serve five or fewer Medicaid patients in their practice. Among specialists, there were some states where as many as 61% of psychiatrists had five or fewer Medicaid patients. And as many as 53% of OB-GYNs in some states reported the same patient numbers.
The Commission was quick to point out that its findings were preliminary, and that additional validation and refinement are still needed.
MACPAC's findings are important because most estimates on the willingness of providers to see Medicaid patients come from national surveys. The National Ambulatory Medical Care Survey is considered the leading resource.
However, that survey is limited in that responses are self-reported by physicians who tend to be in an office versus an outpatient setting, according to MACPAC. The survey also doesn't track specialists' patient uptake.
Every provider who bills a third-party program like Medicaid receives a national provider identifier (NPI). To get a more accurate sense of care access for Medicaid beneficiaries, MACPAC did a retroactive analysis of NPI claims data in the national database called the Medicaid Statistical Information System.


development/THE: Add optional dep PDCurses.
-THE is a highly configurable and versatile editor.
+key bindings and a prefix area to operate.
-THE: that THE is a highly configurable and versatile editor.
+THE: key bindings and a prefix area to operate.


Are you looking for the idyllic luxury villa to rent or let in Marbella? Then you have come to the right place.
Our villas & homes are carefully selected and vetted to ensure that you can be confident that when you arrive you will not be disappointed.
Prior to each and every rental each villa is subjected to a thorough pre-inspection & during your stay you have the comfort of knowing that we have a team of over 25 staff who are at hand to assist you.
If you have specific requirements and cannot find the villa you are looking for on our website then let please us know; with our in-depth knowledge of Marbella we will more than likely know where to locate it.
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"Wasted" is a song by Polish singer Margaret. It was included on her debut studio album, Add the Blonde (2014), and released as its lead single in Poland on 15 January 2014 by Magic Records. On 28 April 2014, the single was released in Scandinavia by Warner Music Sweden and Extensive Music. The song was written by Boris Potemkin, Anthony Whiting, Emily Philips, Robert Uhlmann and Thomas Karlsson. It samples Edita Piekha's 1967 song "Our Neighbour" (Russian: "Наш сосед" nash sosed).

Margaret debuted "Wasted" at the Sylwestrowa Moc Przebojów ("New Year's Eve Power of Hits") concert in Gdynia, Poland on 31 December 2013. The single reached number six on the Polish Airplay Chart.

Music video
The song's music video premiered on Orange Poland website on 14 January 2014, and was uploaded to YouTube on 30 January 2014. The video was directed by Julia Bui Ngoc. It was filmed in Warsaw, and draws inspirations from the Jean-Pierre Jeunet's 2001 film Amélie and the work of Andy Warhol.

Track listing
Digital single
 "Wasted" (Radio Version) – 3:21

Digital single – Remixes
 "Wasted" (Esquire Remix) – 4:43
 "Wasted" (Esquire Radio) – 3:08

Accolades

Charts

Weekly charts

Year-end charts

Release history

References

2014 singles
2014 songs
Margaret (singer) songs
Songs written by Ant Whiting
Songs written by Robert Uhlmann (composer)
Songs with lyrics by Thomas Karlsson
Magic Records singles

redpajama_set_name: RedPajamaWikipedia


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Heart Essex
Tiptree: Jam factory Plans Move Forward
A new Wilkin and Sons factory in Tiptree has moved a step closer after outline plans were approved.
Colchester Borough Council approved the plans last night (Thursday, April 11).
The project would see a new facility built on Factory Hill with old one demolished and almost 250 homes built on the site, bringing around 200 new jobs to the area.
In a statement, the company - famed for its Tiptree Jam - said: "We could not have reached this stage without the support of the village. Now we must ensure we live up to expectations.
"Intense local scrutiny of our plans has without doubt produced a better solution - the petition including over 6,000 names in support of new homes to enable the factory to be built was the strongest indication possible that there is a place for our business in the village."


When you start working on a new project, there are usually a couple of steps you'll need to follow to get up and running. This process is called on-boarding. One of the steps in this process is getting your local development environment setup.
On every team I've worked we've used Vagrant. Any provisioning is done using Ansible, a simple configuration based provisioner. Ansible Galaxy is to Ansible what Composer is to PHP; A tools to make it easy to re-use code or, in Ansible's case, roles.
If you don't know what Ansible is, I highly recommend you check out the blogs from Erika Heidi. She's got enough blog posts to get you up and running.
While I had been publishing all my code on packagist to enable re-use of my efforts across projects, I found myself still copying over Ansible roles. I was even googling roles I had previously used, downloading zip files and copying over the required roles into my project. This, of course, is super silly. If you're doing that still now: STAHP. There is a better way. Let's stop doing things the old-school way and hop on the Ansible Galaxy train, or spaceship.
Ansible Galaxy is divided into two things; A role repository (and discovery) tool, and an installer. The installer can be compared to composer, while the role repository (the website) is like Packagist.
On the Ansible Galaxy website it's pretty easy to find roles for commonly required dependencies like node.js or something like ElasticSearch. Installing roles is super easy. For example, the following command installs the node.js role.
Using the role is as easy as adding it to your playbook.
By default roles are installed globally. The install path depends on which platform you are on, but what's more important to know is; all roles installed globally are available for every project. While this is nice, this is not always desired.
Global dependencies are on-boarding hurdles.
In order to onboard new people on your project as quickly as possible, we want to eliminate every hurdle a new developer on our team can encounter. Having a vagrant box and Ansible provisioning is already a step in the right direction. Things get a little more tricky when a project is dependant on globally installed roles. It's much easier if they could just vagrant up without needing to go through a 10 step process to get up and running. Luckily there is a way to set the install path to determine where the required roles are installed.
In order to install Ansible roles locally we need to alter some configurations. Project configuration for Ansible settings can be done in the ansible.cfg file which you can create in your project root. This ini-like file allows you to alter the behaviour of Ansible on a per-project basis. One of the configuration options is the roles_path option, which allows you to specify where roles are installed when executing the ansible-galaxy install command.
Now, when we run the ansible-galaxy install [role] command from the project root, the desired role will be installed inside the project. This allows you to check the role into source controle, and share them amongst your team members.
During on-boarding you want there to be as little friction as possible. Getting people started with a simple vagrant up is immensely powerful. Removing steps, shortening the process, benefits the experience and lets people be productive faster.
For me, knowing how to remove the dependency on globally installed roles made the on-boarding process smoother and less error-prone. Using freely available roles also removed the need for me to invest into creating my own. Have you got projects depends depending on globally installed roles? Perhaps convert them to local roles instead and improve your on-boarding experience.


Just as I thought my knee was fixed and I made to a whole 25 minutes of running, my knee started to hurt again. I couldn't run to the end of the road without pain and had to have the whole week off running.
This is a list of things that I've used and bought over the last 12 months or are things that are on my own Wish List. I'm not sponsored by any of these retailers and I've bought and paid for all of these products.
Help – my life is crazy – how can I stick to a training plan?
It can be really hard to stick to a training programme when you don't have a regular routine due to work or family life.


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2015 Tesla Model S P90D: Quickest Sedan Ever?
The first sub-3.0-second sedan we've ever tested. So that's something.
By Don Sherman Published: Jan 29, 2016
MICHAEL SIMARI, MARC URBANO
From the February 2016 issue
Tesla's product architect, Elon Musk, must have been watching a Mel Brooks marathon on TNT when he picked "Ludicrous Speed," straight out of Spaceballs, as the tag for the fastest acceleration mode in his Model S P90D. And indeed, one must have balls from outer space to fully exploit this car's launch performance. To sort heroic acts from hype, we ran this electric missile through our test gantlet with, shall we say, shocking results.
Cutting to the chase, it's the first production car with four doors to crack the 3.0-second zero-to-60-mph barrier, doing it in 2.8 seconds. In 30-to-50-mph passing acceleration, it trumps the Tesla Roadster Sport's all-time record run of 1.5 seconds, also by two-tenths of a second. The P90D's 11.1-second, 121-mph quarter-mile run, achieved with no hint of tire smoke or exhaust ruckus, merits VIP parking at NHRA headquarters. The Model S P85D in Insane mode, formerly the quickest Tesla, was a half-second slower to 60 and 0.7 second and 7 mph pokier in the quarter-mile.
Due care is necessary to achieve these results. Options that add ballast, including the Model S's huge sunroof, rear-facing seats, and second battery charger, must be avoided. It's a $38,000 upgrade from a base Model S 70 rear-drive version to obtain the most-potent electric motors, the four-wheel drive, and the long-range 90-kWh battery pack. Then add the $10,000 Ludicrous Speed option to enable the on-demand disappearing services. A full cardiac work-up is recommended for anyone interested in experiencing Tesla's latest abuse of common sense.
Maximum acceleration is available only when the battery's state of charge is above 95 percent and "max battery performance mode" is set on the control screen. When we test, we average two acceleration runs in opposite directions to eliminate wind and grade effects. Normally that's no issue, but because the Model S's performance deteriorates with heat build-up in the battery pack, controllers, wiring, and electric motors, pausing at least three minutes between acceleration runs is necessary.
This Tesla's exploitation of Newtonian physics tops anything you're likely to encounter this side of an amusement park or the Navy's flight school. Nailing the right pedal vents a massive torque gush, and weird, wonderful, and addictive bursts of dopamine flood your brain's pleasure center when this tsunami sloshes the juice in your inner ear.
GOLLY G's
Checking our data bank for outliers, we found this Tesla ranks fourth among five cars capable of averaging more than 1.0 g during the first second of acceleration:
Porsche 911 Turbo S ................................. 1.25
Lamborghini Huracán LP610-4 ................ 1.19
Porsche 918 Spyder .................................. 1.14
Tesla Model S P90D .................................. 1.12
Audi R8 V-10 Plus ...................................... 1.08
And we'd add an honorable mention for the Bugatti Veyron 16.4 at 0.95 g.
That's the beauty of chambering 713 pound-feet of torque into a four-wheel-driver weighing 4842 pounds. Sir Isaac didn't lie when he told you great things are possible without bending or bruising his second law of motion. You hope the rush lasts to orbital escape velocity but, alas, it soon peters out. Roll alongside a Dodge Charger SRT Hellcat at 40 mph, for example, and the Mopar beats the Tesla to 150 mph by more than six seconds.
An interesting consolation race would be to see whether the Hellcat or the P90D would be the first to deplete its fuel supply. For now, we are satisfied in the knowledge that this is the quickest production four-door ever conceived.
VEHICLE TYPE: front- and rear-motor, 4-wheel-drive, 5-passenger, 4-door hatchback
PRICE AS TESTED: $134,200 (base price: $119,200)
MOTOR TYPE: 2 asynchronous AC
Power: F: 259 hp R: 503 hp
Combined: 532 hp
Torque: F: 244 lb-ft R: 469 lb-ft
Combined: 713 lb-ft
TRANSMISSION: 1-speed direct drive
Width: 77.3 in Height: 56.5 in
Passenger volume: 95 cu ft
Cargo volume: 32 cu ft
Curb weight: 4842 lb
C/D TEST RESULTS:
Zero to 60 mph: 2.8 sec
Zero to 100 mph: 7.1 sec
Zero to 150 mph: 21.8 sec
Rolling start, 5-60 mph: 3.0 sec
Top gear, 30-50 mph: 1.3 sec
Standing ¼-mile: 11.1 sec @ 121 mph
Top speed (governor limited): 155 mph
Braking, 70-0 mph: 159 ft
Roadholding, 300-ft-dia skidpad: 0.90 g
EPA city/highway driving: 89/98 MPGe
C/D observed: 66 MPGe
TEST NOTES: Reaping the optimum acceleration reported here required minor adjustments to our usual procedures (noted in text).
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Organic purple mangosteen (Garcinia mangostana) and Star Apple (Chrysophyllum cainito) for breakfast in Vientiane, Laos. Chrysophyllum cainito is known in Lao language as Mak Nam Nom.
We bought the mangosteen and star apple fruits from the Organic Farmer's Market at That Luang esplanade. I love to eat fresh fruits for breakfast. For a fraction of the cost in Holland, I can eat as much organic fresh fruits while visiting Vientiane, Laos.


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text:
\section{Introduction}

Quantum computation is a most challenging project involving research both
by physicists and computer scientists. The principles of quantum
computation differ from the principles of classical computation very much.
The classical computation is based on classical mechanics while
quantum computation attempts to exploit phenomena specific to
quantum physics.

One of features of quantum mechanics is that a quantum process can be
in a combination (called {\em superposition}) of several states and these
several states can interact one with another.
A computer scientist would call this {\em a massive
parallelism}.
This possibility of massive parallelism is very important for
Computer Science. In 1982, Nobel prize winner physicist Richard Feynman
(1918-1988) asked what effects the principles of quantum
mechanics can have on computation\cite{Fe 82}. An exact simulation of quantum
processes demands exponential running time.
Therefore, there may be other computations
which are performed nowadays by classical computers but might be
simulated by quantum processes in much less time.

R.Feynman's influence was (and is) so high that rather soon this
possibility was explored both theoretically and practically.
David Deutsch\cite{De 89} introduced quantum Turing machines,
quantum physical counterparts of probabilistic Turing machines.
He conjectured that they may be more efficient that classical
Turing machines. He also showed  the existence of a universal quantum
Turing machine. This construction was subsequently improved
by Bernstein and Vazirani \cite{BV 97} and Yao \cite{Ya 93}.

Quantum Turing machines might have remained relatively unknown
but two events caused a drastical change.
First, Peter Shor \cite{Sh 94} invented surprising polynomial-time
quantum algorithms for computation of discrete logarithms and for
factorization of integers.
Second,
unusual quantum circuits having no
classical counterparts (such as quantum bit teleportation) have
been physically implemented. Hence, there is a chance that
universal quantum computers may be built.
Moreover, since the modern public-key
cryptography is based on intractability of discrete logarithms and
factorization of integers, building a quantum computer implies
building a code-breaking machine.

In this paper, we consider quantum finite automata (QFAs),
a different model of quantum computation.
This is a simpler model than quantum Turing machines and
and it may be simpler to implement.

Quantum finite automata have been studied in \cite{AF 98,BP 99,KW 97,MC 97}.
Surprisingly, QFAs do not generalize deterministic finite automata.
Their capabilities are incomparable.
QFAs can be exponentially more space-efficient\cite{AF 98}.
However, there are regular languages that cannot be recognized by quantum
finite automata\cite{KW 97}.

This weakness is caused by reversibility.
Any quantum computation is performed by means of unitary
operators. One of the simplest properties of these operators
shows that such a computation is reversible. The result always determines
the input uniquely. It may seem to be a very strong limitation.
Luckily, for unrestricted quantum algorithms (for instance,
for quantum Turing machines) this is not so.
It is possible to embed any irreversible computation in an appropriate
environment which makes it reversible\cite{Be 89}.
For instance, the computing agent
could keep the inputs of previous calculations in successive order.
Quantum finite automata are more sensitive to the reversibility requirement.

If the probability with which a QFA is required to be correct
decreases, the set of languages that can be recognized increases.
In particular\cite{AF 98}, there are languages that can be recognized
with probability 0.68 but not with probability 7/9.
In this paper, we extend this result by constructing a hierarchy of
languages in which each next language can be recognized with
a smaller probability than the previous one.

\section{Preliminaries}

\subsection{Basics of quantum computation}
\label{basics}

To explain the difference between classical and quantum mechanical
world, we first consider one-bit systems.
A classical bit
is in one of two
classical states $true$ and $false$.
A {\em probabilistic} counterpart of the
classical bit can be $true$ with a
probability $\alpha $ and $false$ with probability $\beta $, where
$\alpha + \beta = 1$.
A {\em quantum bit (qubit)} is very much like to it
with the following distinction.
For a {\em qubit} $\alpha $ and $\beta $ can be
arbitrary complex numbers with the property
$\|\alpha \|^2 + \|\beta \|^2 = 1$.
If we observe a qubit, we get $true$ with probability
$\|\alpha\|^2$ and $false$ with probability $\|\beta\|^2$, just like
in probabilistic case.
However, if we modify a quantum system without observing it
(we will explain what this means), the set of transformations
that one can perform is larger than in the probabilistic case.
This is where the power of quantum computation comes from.

More generally, we consider quantum systems with $m$ basis states.
We denote the basis states $\ket{q_1}$, $\ket{q_2}$, $\ldots$,
$\ket{q_m}$. Let $\psi$ be a linear combination of them
with complex coefficients
\[ \psi=\alpha_1\ket{q_1}+\alpha_2\ket{q_2}+\ldots+\alpha_m\ket{q_m} .\]

The $l_2$ norm of $\psi$ is
\[  \|\psi\|=\sqrt{|\alpha_1|^2+|\alpha_2|^2+\ldots+|\alpha_m|^2}. \]

The state of a quantum system can be any $\psi$ with $\|\psi\|=1$.
$\psi$ is called a {\em superposition} of $\ket{q_1}$, $\ldots$, $\ket{q_m}$.
$\alpha_1$, $\ldots$, $\alpha_m$ are called {\em amplitudes} of
$\ket{q_1}$, $\ldots$, $\ket{q_m}$.
We use $l_2(Q)$ to denote the vector space consisting
of all linear combinations of $\ket{q_1}$, $\ldots$, $\ket{q_m}$.

Allowing arbitrary complex amplitudes is essential for physics.
However, it is not important for quantum computation.
Anything that can be computed with complex amplitudes can be done
with only real amplitudes as well.
This was shown for quantum Turing machines in \cite{BV 93}\footnote{For
unknown reason, this proof does not appear in \cite{BV 97}.}
and the same proof works for QFAs.
However, it is important that {\em negative} amplitudes are allowed.
For this reason, we assume that
all amplitudes are (possibly negative) reals.

There are two types of transformations that can be performed
on a quantum system. The first type are unitary transformations.
A unitary transformation is a linear transformation $U$ on $l_2(Q)$
that preserves $l_2$ norm. (This means that any $\psi$ with $\|\psi\|=1$
is mapped to $\psi'$ with $\|\psi'\|=1$.)

Second, there are measurements.
The simplest measurement is observing
$\psi=\alpha_1\ket{q_1}+\alpha_2\ket{q_2}+\ldots+\alpha_m\ket{q_m}$
in the basis $\ket{q_1}, \ldots, \ket{q_m}$.
It gives $\ket{q_i}$ with probability $\alpha_i^2$.
($\|\psi\|=1$ guarantees that probabilities of different outcomes sum to 1.)
After the measurement, the state of the system changes to $\ket{q_i}$
and repeating the measurement gives the same state $\ket{q_i}$.

In this paper, we also use {\em partial measurements.}
Let $Q_1, \ldots, Q_k$ be pairwise disjoint subsets of $Q$ such that
$Q_1\cup Q_2 \cup \ldots \cup Q_k=Q$.
Let $E_j$, for $j\in\{1, \ldots, k\}$, denote the
subspace of $l_2(Q)$ spanned by $\ket{q_j}$, $j\in Q_i$.
Then, a {\em partial measurement} w.r.t. $E_1, \ldots, E_k$
gives the answer $\psi\in E_j$ with probability $\sum_{i\in Q_j} \alpha_i^2$.
After that, the state of the system collapses to the projection
of $\psi$ to $E_j$.
This projection is $\psi_j= \sum_{i\in Q_j}  \alpha_i \ket{q_i}$.

\subsection{Quantum finite automata}

Quantum finite automata were introduced twice. First this was done by C.
Moore and J.P.Crutchfield \cite{MC 97}. Later in a different and
non-equivalent way these automata were introduced by A. Kondacs and J.
Watrous \cite{KW 97}.

The first definition just mimics the definition of
1-way probabilistic finite automata
only substituting {\em stochastic} matrices by {\em unitary} ones.
We use a more elaborated definition  \cite{KW 97}.

A QFA is a tuple
$M=(Q;\Sigma ;V ;q_{0};Q_{acc};Q_{rej})$ where $Q$ is a finite set
of states, $\Sigma $ is an input alphabet, $V$ is a transition function,
$q_{0}\in Q$ is a starting state, and $Q_{acc}\subset Q$
and $Q_{rej}\subset Q$ are sets of accepting and rejecting states.
The states in $Q_{acc}$ and $Q_{rej}$ are called {\em halting states} and
the states in $Q_{non}=Q-(Q_{acc}\cup Q_{rej})$ are called
{\em non halting states}.
$\kappa$ and $\$$ are symbols that do not belong to $\Sigma$.
We use $\kappa$ and $\$$ as the left and the right endmarker,
respectively. The {\em working alphabet} of
$M$ is $\Gamma = \Sigma \cup \{\kappa ;\$\}$.

The transition function $V$ is a mapping from $\Gamma\times l_2(Q)$
to $l_2(Q)$ such that, for every $a\in\Gamma$, the function
$V_a:l_2(Q)\rightarrowl_2(Q)$ defined by $V_a(x)=V(a, x)$ is a
unitary transformation.

The computation of a QFA starts in the superposition $|q_{0}\rangle$.
Then transformations corresponding to the left endmarker $\kappa$,
the letters of the input word $x$ and the right endmarker $\$$ are
applied. The transformation corresponding to $a\in \Gamma$ consists
of two steps.

1. First, $V_{a}$ is applied. The new superposition $\psi^{\prime}$
is $V_{a}(\psi)$ where $\psi$ is the superposition before this step.

2. Then, $\psi^{\prime}$ is observed with respect to
$E_{acc}, E_{rej}, E_{non}$ where
$E_{acc}=span\{|q\rangle:q\in Q_{acc}\}$,
$E_{rej}=span\{|q\rangle :q\in Q_{rej}\}$,
$E_{non}=span\{|q\rangle :q\in Q_{non}\}$
(see section \ref{basics}).

If we get $\psi^{\prime} \in E_{acc}$, the input is accepted.
If we get $\psi^{\prime} \in E_{rej}$, the input is rejected.
If we get $\psi^{\prime} \in E_{non}$, the next transformation is applied.

We regard these two transformations as reading a letter $a$.
We use $V'_a$ to denote the transformation consisting of
$V_a$ followed by projection to $E_{non}$.
This is the transformation mapping $\psi$ to the non-halting part
of $V_a(\psi)$.
We use $\psi_y$ to denote the non-halting part of
QFA's state after reading the left endmarker $\kappa$ and the
word $y\in\Sigma^*$.

\comment{For probabilistic computation, the probability
of correct answer can be easily increased
by executing several copies of an automaton (or Turing machine)
in parallel. Hence, if a language can be recognized by a probabilistic

Hence, it is not surprising that \cite{KW 97} wrote
"with error probability bounded away from $1/2$", thinking
that all such probabilities are equivalent.
However, mixing reversible (quantum computation) and non-reversible
(measurements after each step) components in one model
makes it impossible.}
We compare QFAs with different probabilities of correct answer.
This problem was first considered by A. Ambainis
and R. Freivalds\cite{AF 98}. The following theorems were proved there:

\begin{theorem}
\label{T1}
Let $L$ be a language and $M$ be its minimal automaton.
Assume that there is a word $x$ such that $M$
contains states $q_1$, $q_2$ satisfying:
\begin{enumerate}
\item
$q_1\neq q_2$,
\item
If $M$ starts in the state $q_1$ and reads $x$,
it passes to $q_2$,
\item
If $M$ starts in the state $q_2$ and reads $x$,
it passes to $q_2$, and
\item
$q_2$ is neither "all-accepting" state, nor "all-rejecting" state.
\end{enumerate}
Then $L$ cannot be recognized by a 1-way quantum finite automaton with
probability $7/9+\epsilon$ for any fixed $\epsilon>0$.
\end{theorem}

\begin{theorem}
\label{T2}
Let $L$ be a language and $M$ be its minimal automaton.
If there is no $q_1, q_2, x$ satisfying conditions of Theorem \ref{T1}
then $L$ can be recognized by a
1-way reversible finite automaton (i.e. $L$ can be recognized by a 1-way
quantum finite automaton with probability 1).
\end{theorem}

\begin{theorem}
\label{T4}
The language $a^{*}b^{*}$ can be recognized by a 1-way QFA
with the probability of correct answer $p=0.68...$ where
$p$ is the root of $p^3+p=1$.
\end{theorem}

\begin{corollary}
\label{C1}
There is a language that can be recognized by a 1-QFA with probability
$0.68...$ but not with probability $7/9+\epsilon$.
\end{corollary}

For probabilistic automata, the probability of correct answer can be
increased arbitrarily and this property of probabilistic computation
is considered as evident. Theorems above show thatits counterpart
is not true in the quantum world! The reason for that is that the model
of QFAs mixes reversible (quantum computation) components with
nonreversible (measurements after every step).

In this paper, we consider the best probabilities of acceptance by 1-way
quantum finite  automata the languages $a^{*}b^{*}\dots z^{*}$. Since the
reason why the language $a^{*}b^{*}$ cannot be accepted by 1-way
quantum finite  automata is the property described in the Theorems
\ref{T1} and \ref{T2}, this new result provides an insight on what the
hierarchy
of languages with respect to the probabilities of their acceptance by
1-way quantum finite automata may be.
We also show a generalization of Theorem \ref{T4} in a style similar
to Theorem \ref{T2}.

\section{Main results}

\begin{lemma}
\label{lemma}
For arbitrary real $x_1>0$, $x_2>0$, ..., $x_n>0$, there exists
a unitary $n\times n$ matrix $M_n(x_1,x_2,...,x_n)$ with elements $m_{ij}$
such that
$$
m_{11}=\frac{x_1}{\sqrt{x_1^2+...+x_n^2}},\
m_{21}=\frac{x_2}{\sqrt{x_1^2+...+x_n^2}},\ ...,
m_{n1}=\frac{x_n}{\sqrt{x_1^2+...+x_n^2}}.
$$
\end{lemma}
\hspace*{118mm} $\Box$

Let $L_n$ be the language $a_1^*a_2^*...a_n^*$.
\begin{theorem}
\label{part1}
The language $L_n$ ($n>1$) can be recognized by a 1-way QFA
with the probability of correct answer $p$ where $p$ is the root of
$p^\frac{n+1}{n-1}+p=1$ in the interval $[1/2, 1]$.
\end{theorem}
{\bf Proof:}
Let $m_{ij}$ be the elements of the matrix $M_k(x_1,x_2,...,x_k)$
from Lemma \ref{lemma}.
We construct a $k\times (k-1)$ matrix $T_k(x_1,x_2,...,x_k)$
with elements $t_{ij}=m_{i,j+1}$.
Let $R_k(x_1,x_2,...,x_k)$ be a $k\times k$ matrix
with elements $r_{ij}=\frac{x_i\cdot x_j}{x_1^2+...+x_k^2}$
and $I_k$ be the $k \times k$ identity matrix.

For fixed $n$,
let $p_n\in[1/2, 1]$ satisfy $p_n^\frac{n+1}{n-1}+p_n=1$
and $p_k$ ($1\leq k<n$) = $p_n^\frac{k-1}{n-1}-p_n^\frac{k}{n-1}.$
It is easy to see that $p_1+p_2+...+p_n=1$ and
\begin{equation}
1-\frac{p_n(p_k+...+p_n)^2}{(p_{k-1}+...+p_n)^2}=
1-\frac{p_np_n^\frac{2(k-1)}{n-1}}{p_n^\frac{2(k-2)}{n-1}}=
1-p_n^\frac{n+1}{n-1}=p_n.
\end{equation}

Now we describe a 1-way QFA accepting the language $L_n$.

The automaton has $2n$ states:
$q_1$, $q_2$, ... $q_{n}$ are non halting states,
$q_{n+1}$, $q_{n+2}$, ... $q_{2n-1}$ are rejecting states
and $q_{2n}$ is an accepting state.
The transition function is defined by unitary block matrices
$$V_\kappa=
\left (
\begin{array}{cc}
M_n(\sqrt{p_1},\sqrt{p_2},...,\sqrt{p_n})&{\bf 0}\\
{\bf 0}&I_n
\end{array}
\right ),
$$
$$V_{a_1}=
\left (
\begin{array}{ccc}
R_n(\sqrt{p_1},\sqrt{p_2},...,\sqrt{p_n})&
T_n(\sqrt{p_1},\sqrt{p_2},...,\sqrt{p_n})&{\bf 0}\\
T_n^T(\sqrt{p_1},\sqrt{p_2},...,\sqrt{p_n})&{\bf 0}&{\bf 0}\\
{\bf 0}&{\bf 0}&1
\end{array}
\right ),
$$
$$
V_{a_2}=
\left (
\begin{array}{ccccc}
0&{\bf 0}&1&{\bf 0}&0\\
{\bf 0}&R_{n-1}(\sqrt{p_2},...,\sqrt{p_n})&
{\bf 0}&T_{n-1}(\sqrt{p_2},...,\sqrt{p_n})&{\bf 0}\\
1&{\bf 0}&0&{\bf 0}&0\\
{\bf 0}&T_{n-1}^T(\sqrt{p_2},...,\sqrt{p_n})&
{\bf 0}&{\bf 0}&{\bf 0}\\
0&{\bf 0}&0&{\bf 0}&1
\end{array}
\right ),
$$
$$...,$$
$$
V_{a_k}=
\left (
\begin{array}{ccccc}
{\bf 0}&{\bf 0}&I_{k-1}&{\bf 0}&{\bf 0}\\
{\bf 0}&R_{n+1-k}(\sqrt{p_k},...,\sqrt{p_n})&
{\bf 0}&T_{n+1-k}(\sqrt{p_k},...,\sqrt{p_n})&{\bf 0}\\
I_{k-1}&{\bf 0}&{\bf 0}&{\bf 0}&{\bf 0}\\
{\bf 0}&T_{n+1-k}^T(\sqrt{p_k},...,\sqrt{p_n})&
{\bf 0}&{\bf 0}&{\bf 0}\\
{\bf 0}&{\bf 0}&{\bf 0}&{\bf 0}&1
\end{array}
\right ),
$$
$$...,$$
$$
V_{a_n}=
\left (
\begin{array}{cccc}
{\bf 0}&{\bf 0}&I_{n-1}&{\bf 0}\\
{\bf 0}&1&{\bf 0}&{\bf 0}\\
I_{n-1}&{\bf 0}&{\bf 0}&{\bf 0}\\
{\bf 0}&{\bf 0}&{\bf 0}&1
\end{array}
\right ),
$$
$$
V_\$=
\left (
\begin{array}{cc}
{\bf 0}&I_n\\
I_n&{\bf 0}
\end{array}
\right ).
$$

{\it Case 1.} The input is $\kappa a_1^*a_2^*...a_n^*\$$.

The starting superposition is $\ket{q_1}$.
After reading the left endmarker
the superposition becomes
$\sqrt{p_1}\ket{q_1}+\sqrt{p_2}\ket{q_2}+\ldots+\sqrt{p_n}\ket{q_n}$
and after reading $a_1^*$ the superposition remains the same.

If the input contains $a_k$ then
reading the first $a_k$ changes the non-halting part of the superposition to
$\sqrt{p_k}\ket{q_k}+\ldots+\sqrt{p_{n}}\ket{q_{n}}$
and after reading all the rest of $a_k$
the non-halting part of the superposition remains the same.

Reading the right endmarker maps $\ket{q_{n}}$ to $\ket{q_{2n}}$.
Therefore, the superposition after reading it contains
$\sqrt{p_n}\ket{q_{2n}}$.
This means that the automaton accepts with probability $p_n$
because $q_{2n}$ is an accepting state.\\

{\it Case 2.} The input is $\kappa a_1^*a_2^*...a_k^*a_ka_m...\ (k>m)$.

After reading the last $a_k$ the non-halting part of the superposition is
$\sqrt{p_k}\ket{q_k}$\\ $+\ldots+\sqrt{p_{n}}\ket{q_{n}}$.
Then reading $a_m$
changes the non-halting part to\\
$\frac{\sqrt{p_m}(p_k+...+p_n)}{(p_m+...+p_n)}\ket{q_m}+\ldots+
\frac{\sqrt{p_n}(p_k+...+p_n)}{(p_m+...+p_n)}\ket{q_n}.$
This means that the automaton accepts with probability
$\leq \frac{p_n(p_k+...+p_n)^2}{(p_m+...+p_n)^2}$ and rejects
with probability at least
$$1-\frac{p_n(p_k+...+p_n)^2}{(p_m+...+p_n)^2}
\geq 1-\frac{p_n(p_k+...+p_n)^2}{(p_{k-1}+...+p_n)^2}=p_n$$
that follows from (1).
$\Box$

\begin{corollary}
\label{cor1}
The language $L_n$ can be recognized by a 1-way QFA with
the probability of correct answer at least $\frac{1}{2}+\frac{c}{n}$,
for a constant $c$.
\end{corollary}

\noindent
{\bf Proof:}
By resolving the equation $p^{\frac{n+1}{n-1}}+p=1$, we get
$p=\frac{1}{2}+\Theta(\frac{1}{n})$.
$\Box$

\begin{theorem}
\label{part2}
The language $L_n$ cannot be recognized by a 1-way QFA with probability
greater than $p$ where $p$ is the root of
\begin{equation}
\label{e1}
(2p-1)=\frac{2(1-p)}{n-1}+4\sqrt{\frac{2(1-p)}{n-1}}
\end{equation}
in the interval $[1/2, 1]$.
\end{theorem}

\noindent
{\bf Proof:}
Assume we are given a 1-way QFA $M$.
We show that, for any $\epsilon>0$, there is a word
such that the probability of correct answer is less than $p+\epsilon$.

\begin{lemma}
\cite{AF 98}
\label{LT1}
Let $x\in \Sigma^{+}$.
There are subspaces $E_1$, $E_2$ such that $E_{non}=E_1\oplus E_2$ and
\begin{enumerate}
\item[(i)]
If $\psi\in E_1$, then $V_x(\psi)\in E_1$,
\item[(ii)]
If $\psi\in E_2$, then $\| V'_{x^k}(\psi)\|\rightarrow 0$ when
$k\rightarrow\infty$.
\end{enumerate}
\end{lemma}

We use $n-1$ such decompositions: for $x=a_2$,
$x=a_3$, $\ldots$, $x=a_n$.
The subspaces $E_1$, $E_2$ corresponding to $x=a_m$ are
denoted $E_{m, 1}$ and $E_{m, 2}$.

Let $m\in\{2, \ldots, n\}$, $y\in a_1^* a_2^* \ldots a_{m-1}^*$.
Remember that $\psi_{y}$ denotes the superposition after reading $y$
(with observations w.r.t. $E_{non}\oplus E_{acc}\oplus E_{rej}$
after every step).
We express $\psi_y$ as $\psi^1_{y}+\psi^2_{y}$, $\psi^1_{y}\in E_{m, 1}$,
$\psi^2_{y}\in E_{m, 2}$.

{\em Case 1.}
$\|\psi^2_{y}\|\leq \sqrt{\frac{2(1-p)}{n-1}}$
for some $m\in\{2, \ldots, n\}$ and $y\in a_1^* \ldots a_{m-1}^*$.

Let $i>0$.
Then, $y a_{m-1}\in L_n$ but $y a_m^i a_{m-1}\notin L_n$.
Consider the distributions of probabilities on $M$'s answers ``accept"
and ``reject" on $y a_{m-1}$ and $y a_m^i a_{m-1}$.
If $M$ recognizes $L_n$ with probability $p+\epsilon$,
it must accept $y a_{m-1}$ with probability at least $p+\epsilon$
and reject it with probability at most $1-p-\epsilon$.
Also, $y a_m^i a_{m-1}$ must be rejected with
probability at least $p+\epsilon$
and accepted with probability at most $1-p-\epsilon$.
Therefore, both the probabilities of accepting and the probabilities of
rejecting must differ by at least
\[ (p+\epsilon)-(1-p-\epsilon)=2p-1+2\epsilon .\]
This means that the {\em variational distance} between two probability
distributions (the sum of these two distances) must be
at least $2(2p-1)+4\epsilon$.
We show that it cannot be so large.

First, we select an appropriate $i$.
Let $k$ be so large that $\|V'_{a_m^k}(\psi^2_{y})\|\leq \delta$ for
$\delta=\epsilon/4$.
$\psi^1_{y}, V'_{a_m}(\psi^1_{y}), V'_{a_m^2}(\psi^1_{y})$, $\ldots$
is a bounded sequence in a finite-dimensional space. Therefore, it
has a limit point and there are $i, j$ such that
\[  \|V'_{a_m^j}(\psi^1_{y})-V'_{a_m^{i+j}}(\psi^1_{y})\|<\delta.\]
We choose $i, j$ so that $i>k$.

The difference between the two probability distributions comes from two sources.
The first source is the difference between $\psi_{y}$ and
$\psi_{y a_m^i}$ (the states of $M$ before reading $a_{m-1}$).
The second source is the possibility of $M$ accepting while
reading $a_m^i$ (the only part that is different in the two words).
We bound each of them.

The difference $\psi_{y}-\psi_{y a_{m}^i}$
can be partitioned into three parts.
\begin{equation}
\label{eq5}
 \psi_{y}-\psi_{y a_{m}^i}=(\psi_{y}-\psi^1_{y})+
(\psi^1_{y}-V'_{a_m^i}(\psi^1_{y}))+
(V'_{a_m^i}(\psi^1_{y})-\psi_{y a_{m}^i}).
\end{equation}

The first part is
$\psi_{y}-\psi^1_{y}=\psi^2_{y}$ and
$\|\psi^2_{y}\|\leq\sqrt{\frac{2(1-p)}{n-1}}$.
The second and the third parts are both small.
For the second part, notice that $V'_{a_m}$ is unitary
on $E_{m, 1}$ (because $V_{a_m}$ is unitary and $V_{a_m}(\psi)$ does not
contain halting components for $\psi\in E_{m, 1}$).
Hence, $V'_{a_m}$ preserves distances on $E_{m, 1}$ and
\[ \|\psi^1_{y}-V'_{a_m^i}(\psi^1_{y})\|=
\|V'_{a_m^j}(\psi^1_{y})-V'_{a_m^{i+j}}(\psi^1_{y}) \| <\delta \]

For the third part of (\ref{eq5}), remember that
$\psi_{y a_m^i}=V'_{a_m^i}(\psi_y)$.
Therefore,
\[ \psi_{y a_{m}^i}-V'_{a_m^i}(\psi^1_y) = V'_{a_m^i}(\psi_y) -
V'_{a_m^i}(\psi^1_y) = V'_{a_m^i}(\psi_y-\psi^1_y) = V'_{a_m^i}(\psi^2_y) \]
and $\|\psi^2_{y a_{m}^i}\|\leq \delta$ because $i>k$.
Putting all three parts together, we get
\[ \|\psi_{y}-\psi_{y a_{m}^i}\|\leq \|\psi_{y}-\psi^1_{y}\|+
\|\psi^1_{y}-\psi^1_{y a_{m}^i}\|+
\|\psi^1_{y a_{m}^i}-\psi_{y a_{m}^i}\|\leq
\sqrt{\frac{2(1-p)}{n-1}}+ 2\delta.\]

\begin{lemma}
\cite{BV 97}
\label{BVTheorem}
Let $\psi$ and $\phi$ be such that $\|\psi\|\leq 1$, $\|\phi\|\leq 1$ and
$\|\psi-\phi\|\leq\epsilon$.
Then the total variational distance resulting from measurements
of $\phi$ and $\psi$ is at most $4\epsilon$.
\end{lemma}

This means that the difference between any probability distributions
generated by $\psi_{y}$ and $\psi_{y a^i_{m}}$ is at most
\[ 4\sqrt{\frac{2(1-p)}{n-1}}+ 8\delta.\]
In particular, this is true for the probability distributions obtained
by applying $V_{a_{m-1}}$, $V_{\$}$ and the corresponding measurements
to $\psi_{y}$ and $\psi_{y a_m^i}$.

The probability of $M$ halting while reading $a_m^i$ is at most
$\|\psi^2_{\kappa}\|^2=\frac{2(1-p)}{n-1}$. Adding it increases the
variational distance by at most $\frac{2(1-p)}{n-1}$.
Hence, the total variational distance is at most
\[ \frac{2(1-p)}{n-1}+4\sqrt{\frac{2(1-p)}{n-1}}+ 8\delta=
\frac{2(1-p)}{n-1}+4\sqrt{\frac{2(1-p)}{n-1}}+ 2\epsilon .\]
By definition of $p$, this is the same as $(2p-1)+2\epsilon$.
However, if $M$ distinguishes $y$ and $y a_m^i$ correctly,
the variational distance must be at least $(2p-1)+4\epsilon$.
Hence, $M$ does not recognize one of these words correctly.

{\em Case 2.}
$\|\psi^2_{y}\|> \sqrt{\frac{2(1-p)}{n-1}}$
for every $m\in\{2, \ldots, n\}$ and $y\in a_1^* \ldots a_{m-1}^*$.

We define a sequence of words $y_1, y_2, \ldots, y_m\in a_1^* \ldots a_n^*$.
Let $y_1=a_1$ and $y_{k}=y_{k-1} a_k^{i_k}$ for $k\in\{2, \ldots, n\}$ where
$i_k$ is such that
\[ \|V'_{a_k^{i_k}}(\psi^2_{y_{k-1}})\|
\leq \sqrt{\frac{\epsilon}{n-1}}.\]
The existence of $i_k$ is guaranteed by (ii) of Lemma \ref{LT1}.

We consider the probability that $M$ halts on
$y_n=a_1 a_2^{i_2} a_3^{i_3} \ldots a_n^{i_n}$
before seeing the right endmarker.
Let $k\in\{2, \ldots, n\}$.
The probability of $M$ halting while reading the $a_k^{i_k}$ part
of $y_n$ is at least
\[ \| \psi^2_{y_{k-1}}\|^2 -
\| V'_{a_k^{i_k}}(\psi^2_{y_{k-1}}) \|^2
> \frac{2(1-p)}{n-1}-\frac{\epsilon}{n-1} .\]
By summing over all $k\in\{2, \ldots, n\}$, the probability
that $M$ halts on $y_n$ is at least
\[ (n-1)\left(\frac{2(1-p)}{n-1}-  \frac{\epsilon}{n-1}\right)=
2(1-p)-\epsilon .\]
This is the sum of the probability of accepting and the probability
of rejecting. Hence, one of these two probabilities must be at least
$(1-p)-\epsilon/2$. Then, the probability of the opposite
answer on any extension of $y_n$ is at most $1-(1-p-\epsilon/2)=p+\epsilon/2$.
However, $y_n$ has both extensions that are in $L_n$ and extensions that are not.
Hence, one of them is not recognized with probability $p+\epsilon$.
$\Box$

By solving the equation (\ref{e1}), we get

\begin{corollary}
\label{cor2}
$L_n$ cannot be recognized with probability greater than
$\frac{1}{2}+\frac{3}{\sqrt{n-1}}$.
\end{corollary}

\noindent
{\bf Proof:}
The right-hand side of (\ref{e1}) is at most
$\frac{1}{n-1}+4\sqrt{\frac{1}{n-1}}$ because $p\geq 1/2$ and,
hence, $1-p\leq 1/2$. This implies
\[ 2p-1 \leq \frac{1}{n-1}+4\sqrt{\frac{1}{n-1}}, \]
\[ p\leq \frac{1}{2}+2\sqrt{\frac{1}{n-1}}+\frac{1}{2(n-1)}\leq
\frac{1}{2}+3\sqrt{\frac{1}{n-1}} \]
and $L_n$ cannot be recognized with probability greater than $p$
by Theorem \ref{part2}.
$\Box$

Let $n_1=2$ and $n_k=\frac{9n_{k-1}^2}{c^2}+1$ for $k>1$
(where $c$ is the constant from Theorem \ref{part1}).
Also, define $p_k=\frac{1}{2}+\frac{c}{n_k}$.
Then, Corollaries \ref{cor1} and \ref{cor2} imply

\begin{theorem}
For every $k>1$,
$L_{n_k}$ can be recognized with by a 1-way QFA with the probability
of correct answer $p_{k}$ but cannot be recognized with the
probability of correct answer $p_{k-1}$.
\end{theorem}

\noindent
{\bf Proof:}
By Corollary \ref{cor1}, $L_{n_k}$  can be recognized with
probability $\frac{1}{2}+\frac{c}{n_k}=p_k$.

On the other hand, by Corollary \ref{cor2}, $L_{n_k}$ cannot be
recognized with probability $\frac{1}{2}+\frac{3}{\sqrt{n_k-1}}$.
The definition of $n_k$ implies
$n_k-1=\frac{9n_{k-1}^2}{c^2}$, $\sqrt{n_k-1}=\frac{3 n_{k-1}}{c}$,
\[ \frac{1}{2}+\frac{3}{\sqrt{n_k-1}}=\frac{1}{2}+\frac{c}{n_{k-1}}=p_{k-1} .\]
$\Box$

Thus, we have constructed a sequence of languages $L_{n_1}$, $L_{n_2}$, $\ldots$
such that, for each $L_{n_k}$, the probability with which $L_{n_k}$
can be recognized by a 1-way QFA is smaller than for $L_{n_{k-1}}$.

Our final theorem is a counterpart of Theorem
\ref{T2}. It generalizes Theorem \ref{T4}.

\begin{theorem}
\label{T9}
Let $L$ be a language and $M$ be its minimal automaton.
If there is no $q_1, q_2, q_3, x, y$ such that
\begin{enumerate}
\item~
the states $q_1 , q_2 , q_3$ are pairwise different,
\item
If $M$ starts in the state $q_1$ and reads $x$,
it passes to $q_2$,
\item
If $M$ starts in the state $q_2$ and reads $x$,
it passes to $q_2$, and
\item
If $M$ starts in the state $q_2$ and reads $y$,
it passes to $q_3$,
\item
If $M$ starts in the state $q_3$ and reads $y$,
it passes to $q_3$,
\item
both $q_2$ and $q_3$ are neither "all-accepting" state, nor
"all-rejecting" state,
\end{enumerate}
then $L$ can be recognized by
a 1-way quantum finite automaton with probability $p=0.68... $.
\end{theorem}

redpajama_set_name: RedPajamaArXiv