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A fully up-to-date guide to the Numeracy Skills Test for Teachers, providing support and guidance plus hundreds of sample questions and full practice papers to ensure success.
The complete and up-to-date guide to the Professional Skills Tests for Teachers, providing support and guidance plus hundreds of sample questions and full practice papers to ensure your success.
Essential reading for all those undertaking a policing or other law enforcement professional degree within higher education, providing study support, skills and strategies to ensure success.


Maybe you remember: Back in December, locally based Business Resources Corp. sued Dallas County in district court, claiming the commissioners awarded a seven-year, $17.3-million documents-preservation contract to Virginia-based GTSI without ever getting one other bid -- a violation of state law. Which Maureen Dickey seemed to understand in July 2009, when she made a motion to kill the deal. But the rest of the commissioners court didn't agree; they failed to vote for a do-over.
Of course, there have been a few filings and court orders since, but nothing as significant as Judge Bruce Priddy's ruling handed down Monday.
The judge granted Business Resources Corp.'s request for a temporary injunction and told the county to stop doing business with and paying money to GTSI immediately. Writes Priddy, "The competitive bidding requirements called for by Section 262.023 of the Texas County Purchasing Act have not been followed by Dallas County as to the Book Preservation Services contract entered into with GTSI in April 2009." Nor did the commissioners follow "proper procedures." He also set a trial date: February 2011. Priddy's ruling follows.


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Urmel voll in Fahrt' es una película de género animación, aventura, comedia y familiar alemana, estrenada en 2008. La película fue dirigida por Reinhard Klooss y Holger Tappe. Fue producida por Martin Moszkowickz y el guion fue de Oliver Huzly. El tiempo de la película es de 84 minutos y es la segunda de la saga "Isla de los Dinosaurios".

Sinopsis
Impy (Urmel) para su cumpleaños recibe un regalo, un hermanito que resulta ser un panda. Impy se siente triste porque Peg (la cerda), al parecer quiere más la recién nacido panda llamada Babú. Poco después de que el Profesor Tibberton y Tim van a una conferencia, llega el malvado y corrupto Barnaby a la isla Titiwu. Barnaby llega con un propósito, capturar a Impy. Barnaby engaña al dinosaurio, diciendo que sería una estrella e Impy de forma voluntaria viaja con él. Cuando Impy aborda, Babú se va con ellos en la parte de atrás sin que nadie se diera de cuenta. Mientras que Barbaby e Impy, están en un parque de atracciones que no ha abierto aún, Pingu, Monty, Shoe y Peg son enviados a rescatar a Impy y a Babú. Impy y babú, en el parque tienen éxito, pero Barbaby secuestra a Impy, al final se fugan con sus amigos. Impy, Babú, Peg, Shoe, Monty y Pingu, vuelven a la isla Titiwu y deciden no contarle nada de lo que pasó a Tibberton.

Reparto

Enlaces externos

Películas de 2008
Películas de Alemania
Películas cómicas
Películas sobre animales
Secuelas de películas
Películas de animación por computadora

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Home » The Religious Village Blog » Good Lutheran Hymns For A Funeral
Good Lutheran Hymns For A Funeral
The Religious Village Blog March 24, 2019 Author 0 Comments
Lutheran Service Book Prepared by The Commission on Worship of The Lutheran Church—Missouri Synod CONCORDIA PUBLISHING HOUSE • SAINT LOUIS hee ateria a e rerouce or uroe o revie on
died Wednesday, March 20, in Battle Lake Good Samaritan Center. at Glende-Nilson Funeral Home in Ashby. Visitation will continue from 1-2 p.m., followed by a funeral at 2 p.m., Monday, March 25, at.
The Church Of The First Born Though not widely celebrated, it preserves a rich tradition of the Church. If you count 40 days after the celebration. and again corresponds to an ancient Jewish practice of presenting the. Mr. LeBaron was also convicted in 1980 of plotting to kill his brother. The brother, Verlan LeBaron, led another polygamy sect, the Church of
Christian Hymns and Songs Online Christian songs including religious song lyrics and words suitable for all occasions. Lyrics and words to Wedding songs, National and Patriotic songs, Wedding songs, Funeral songs, Christmas Carols and songs, Patriotic Hymns, Easter songs.
He loved the outdoors, camping and listening to hymns. Survived by wife. Harold (Georgia) Mueller. The funeral will be 10:30 a.m. Friday, June 29, at Good Shepherd Lutheran Church in Fremont. The.
The Bible FAQs. What is the LCMS position regarding the age of the earth? Animals in Heaven? Are Bible stories true? Is there a translation the LCMS prefers?
St. Paul's Lutheran Church Prime Time Senior Ministry Click HERE for more information about the Prime Time Senior Center. Our Prime Time Members participating in a.
Aug 9, 2013. 11 great hymns that changed the Church | incourage.me. to be sure to sing it at my funeral because I can't think of a better way to go out:. I love our traditional Lutheran church with organ and hymns every Sunday.
. Suggested Scripture Readings for Christian Funerals · Suggested Hymns and. Wedding and Funeral Services, Life Passages and Events during Construction. Lutheran Church facility will be undergoing major renovation and restoration.
Good morning, troops. other area congregations joined the Rev. Steven Tibbetts, the Zion Lutheran pastor, in celebration. The bishop was there, too. By all accounts, it was quite a funeral. For a.
The service features hymns, scripture readings, prayers, homily, and a. will be a time to remember our loved one and to boldly proclaim the Good News of.
Occasion, funeral. Text, Lina Sandell. Language, Swedish. Meter, 10.9.10.9 D. Melody, "Blott en dag" by Oscar Ahnfelt. Day by Day, is a Christian hymn written in 1865 by Lina Sandell several years after she had. In Sweden, it is popular at funerals. Swedish-language songs · Carola Häggkvist songs · Lutheran hymns.
Feb 23, 2012. Listening to samples for these wonderful hymns and inspirational melodies will, God So Loved the World (John Stainer, The National Lutheran Choir). Guide Me, O Thou Great Redeemer (Choir Of Westminster Abbey)
Funeral Hymns Protestant Hymns, Lutheran Hymns, Anglican, Methodist, Baptist Hymns and Protestant Hymns are all detailed in the above list of funeral hymns.
The Rev. Jim Darchuk, pastor of King of Glory Lutheran Church. for we are God's work of art made for good works — to be good-deed doers — which God prepared to be the way we simply live. Favorite.
Bernette Ewert, 84, of Columbus, Nebraska, died Saturday, June 13, 2015, at Brookstone Acres in Columbus. The funeral service will be on Wednesday, June 17 at 10:30 AM at Gass Haney Funeral Home with Rev. Doug Zurek officiating.
Site provided by: The Rev. Michael McCoy, Pastor of Redeemer Lutheran Church in Emmett, ID. Banner graphics by Sharon Geiser.
A Christian funeral is a celebration of baptism, resurrection, and new life in Christ. Our baptismal covenant. After a pall is placed over the coffin or cremains, the first hymn begins and the. I have fought the good fight, I have finished the race.
Or how could our funeral hymns, which all breathe of positive Christian. A Lutheran pastor certainly cannot with a good conscience officiate at such a burial. 8.
Zingg, age 90 of Leland, Iowa, died on Thursday, March 21, 2019 at the Good. Mittelstadt Funeral Home, 902 East Main St., Lake Mills, Iowa with Pastor Josh Skogen of Center Lutheran Church.
Traditional Hymns. How Great Thou Art: LBW 532.. For the Lord is good; his steadfast love endures forever, and his faithfulness to all generations.
After 70 years of funerals, a church held a funeral for itself Sunday. North Heights Lutheran, the former megachurch of Arden. and after she said the last tearful goodbye, she left for good. "I am.
Book Concern. Books, hymnals and Sunday School materials produced by the Apostolic Lutheran Church of America Federation.
He smiled and said his company "had a good marketing person" — end of answer. say not to tell mom or dad because they would be so angry and disappointed. — Funeral Scams: Hard to believe, but true,
May 03, 2012 · I was surprised to find tonight ( my mother died earlier this week) that the tune writer for a very fundamentalist non worldly song that I sung at my dad's funeral in 1995 was Arthur S. Sullivan the Broadway composer.
About Luther: A Christian Sermon Over the Body and At the Funeral of the Venerable Dr. Martin Luther, preached by Mr. Johann Bugenhagen Pomeranus, (1546)
Thursday evening, across town, mourners waited patiently in the chilly November air to enter Our Saviour's Lutheran Church for a service for. community 90 miles east of Minneapolis, when a funeral.
Anderson, 91, New Rockford, died Saturday, March 16, in Lutheran Home of the Good Shepherd. Visitation will be from noon to 7 p.m., with a prayer service at 7 p.m., Wednesday, March 20, at Evans.
Classical music for funerals and memorial services Many thanks to John S. Rigney for correcting my many original errors (for example, one piece by Handel which was more appropriate for a wedding than a funeral is no longer listed).
Ave Ave Ave Maria Hymn Lyrics Spiritual Motherhood Quotes "I alone cannot change the world, but I can cast a stone across the water to create many ripples." — Mother Teresa Many people believe that they can't make a real difference in this world because they. May 2, 2018. Share these loving mother daughter quotes with Mom this Mother's Day. "
Growing up in my little Lutheran church, hymn singing was not the exuberant experience I now. was driven into my ears, in a good way. I think about heaven a lot. I don't know if perfect in heaven.
A service at 10:30 a.m. Sunday will include a baptism at Good Shepherd Lutheran Church, 4201 Stoudt's Ferry Bridge. The half- hour service will include hymns, scripture readings, prayer and a brief.
. that your relationship is in trouble, but is a great way to strengthen your relationship. Funerals today are held in various places outside the church, but seldom. The hymns should reflect such themes as the invocation of the Holy Spirit, the.
In reality, he was a lapsed Lutheran who became a pastor at a mega-church. As the Jonestown victims had chillingly reminded me, my faith is only as good as the one in whom it's invested. So why don.
Grace Lutheran Church of Dawson, Minnesota (ELCA) Welcome to Grace!  The people of Grace Lutheran welcome you to our community, congregation, and this webpage We are a people who share a common faith in God. We come together because we are a.
Current Obituaries (click here for the archived obituaries; 2011-2017) Obituaries in the Star Tribune. Obituaries in the Pioneer Press. Ferguson, Rodney Duane
Jan 5, 2009. Salem Lutheran Church – Funeral Planning Form. Funeral Service suggested Scripture Readings and Hymns. Great Is Thy Faithfulness.
Keywords: hymns, Evangelical Lutheran Church, hymnology, funerals. During the time of the Great Migration gospel music was at its peak. At this time ap-.
A Requiem or Requiem Mass, also known as Mass for the dead (Latin: Missa pro defunctis) or Mass of the dead (Latin: Missa defunctorum), is a Mass in the Catholic Church offered for the repose of the soul or souls of one or more deceased persons, using a particular form of the Roman Missal.It is usually, but not necessarily, celebrated in the context of a funeral.
Their good life together ended when Joan died of. Visitation will be held from 10-11 a.m. Friday, Mar. 22, 2019, at Our Saviour's Lutheran Church in Iron Mountain followed by an 11 a.m.
Ruth Carlson, 100, 10:30 a.m., Good Shepherd Lutheran Church, Bismarck. (Eastgate Funeral Service, Bismarck) Evelyn Herdt, 93, Garrison, 11 a.m., St. Paul Lutheran Church, Garrison. (Thompson Funeral.
Sunday's closing service at Grace Lutheran was old-style in its formal hymns, scripted prayers. "This is not Grace Lutheran's funeral, but its transformation, its metamorphosis into something new.
Funerals/Memorial Services @ Fj✟Lc – Funerals And Memorial Services Are. well as pick meaningful Scripture readings, hymns and ask people to speak at the.
Henry Kopczynskie family, McNulty Funeral. John's Lutheran Church, St. Johns, invites everyone each Sunday for adult Bible study and Sunday school at 8:45 a.m. and worship with Holy Communion at 10.
Christ Lutheran Church, 222 Niantic Road, Niantic, Montgomery County: Prayer shawls and quilts will be blessed, 7:45 and 10:15. Good Shepherd United Church. will play bluegrass music at 12:30 with.
Interment will be in Rosehill Cemetery in Wells in the spring. Memorials are preferred to hospice, Good Shepherd Lutheran Church or the donor's choice. Bruss-Heitner Funeral Home in Wells is assisting.
Most of all, I knew that this gentle and well loved man, who dedicated over 50 years serving his community as an undertaker, should have his funeral conducted with the care and love he deserved.
Faith Chapel Jekyll Island Ga St. Simons Island, GA www.stsimonsumc.com. 5:30 PM-solo recital. Faith Chapel 375 Riverview Drive Jekyll Island, GA www.friendsofhistoricjekyll.org. learn all about Historic Jekyll Island on our guided bus tour of Jekyll Island GA. Historic Faith Chapel is an architectural wonder in the Historic District that. Airline chicken Airline chicken can be several things, depending upon
Frequently Asked Questions. The worship staff receives a number of similar inquires on worship-related topics from across the church. The responses you find here should not be considered the final word on the topic, but rather as useful guides to be considered with sensitivity to the local context.
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Good Old Christian Hymns – Lyrics & Music: Start Page and Titles List 1400+ Core Hymns from Ecumenical Hymnody, with lyrics, sheet-music, midis, mp3 audio, & PDF.
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Last night and tonight begins the second half of the season with some real marquee games on tap. Here are the results from last night and tonight's schedule.
It's that time again. Time for local high schools football teams to gear up for the annual Jamborees in the area.
The undefeated Welsh Greyhounds and the defending 2A state champions Kinder Yellow jackets will lock up tonight for the 4-2A district title in Welsh, La.
Usually Thursday night there are just a couple of high school football games on tap but this week, seven games are on the schedule that involve lake area teams.
The second week of the high school football season begins tonight and several Southwest Louisiana teams will be in action tonight.


Let you guess what Bangkok Heightz is? From its name, you may already know it is a place on a high level of a building; you may also know it is a place in Bangkok. You may not feel surprised to know that it is also a sky bar, but I am sure you will be amazed that it is a Thai restaurant. It could be my own ignorance, but I really can't think of any authentic Thai restaurant that is located on a high floor offering spectacular bird's eye view of the city centre in Sukhumvit area and magic moments of sunset. Bangkok Heightz combines the charm of authentic Thai cuisine, magnificent city view and innovative Thai-culture-inspired cocktails, it is a brand new Thai restaurant opened recently at The Continent Hotel, which has received, not long ago, the World Luxury Restaurant Award 2016 and Thailand's Leading Boutique Hotel Award.
Thai street food is very well-known throughout the world for its complex blend of spices, herbs, and flavours. Bangkok Heightz has taken these traditional, old-age recipes and further developed them for better flavours and presentations, elevating authentic Thai street food to a completely new level of taste and dining experience. The concept of enjoying popular street food such as Phad Thai in a refined dining ambience offers diners a special dining experience for Thai cuisine.
Why will you like Bangkok Heightz?
There are many Thai restaurants by the river or in traditional Thai houses; Bangkok Heightz offers a totally different dining ambience for Thai cuisine, rendering diners a magnificent view of the vibrant city centre. I especially like the magic moment of sunset witnessed at Bangkok Heightz, making it one of the best romantic dining venues.
An experienced mixologist has created a unique cocktail menu, of which many cocktails show the influence of Thai culture and traditional ingredients.
We have tried Muay Thai Mule that contains house gin infused chili, lime juice, fresh pimento ginger. The presentation fully expresses its name. The chili-infused gin was like a sudden, beautiful strike to the taste buds. Together with other traditional Thai cuisine ingredients, this cocktail is a lovely starter for a romantic night.
The a la carte menu at Bangkok Heightz offers the most popular kinds of traditional Thai dishes such as Phad Thai, Thai Green Curry and Tomyum Kung. Twists on these dishes come when a number of options for the main ingredients are available for choosing. Take, Thai Green Curry, for example, you may choose pork, chicken, beef, and even Australian lamb rack as the main ingredient. Of course, it also denotes a slight change in the price.
You may feel excited to learn that Bangkok Heightz is also a sky bar. Not only are unique cocktails served there, but a professional house DJ also plays cheerful, upbeat music to create happy vibes in the restaurant.
What dishes do we recommend?
The green curry paste was made by the chef in-house using fresh ingredients, so the taste of the green curry was thick and flavourful. The Australian lamb rack was cooked just right to keep its tenderness and juice! To eat in a street style, eat the lamb rack with your hands and savour the juicy lamb rack with green curry. The portion of this dish is rather big, so it suits for sharing. The green curry sauce tasted flavoursome when eating with rice. Rice is served free of charge to all diners. When the main dish is served, choices for white and/or brown rice will be offered at the dining table for guests to enjoy their meal.
A Thai dinner will not be perfect without the traditional, well-known soup of Thailand – Tomyum Koong (Sour and spicy soup with prawns). This may look spicy to you, but the tastes of spiciness, saltiness, sourness and sweetness from all the ingredients were blended well. The coconut milk did not overpower the soup. It's best to enjoy it while it's still hot.
I am visiting next month! May be I try it! Do they have any discount or special offer?
I don't think they are offering any special discount now, but stay tuned with our website or Facebook fanpage https://www.facebook.com/GourmetBangkok, we will update latest status when special offer is on.
I have been to The Continent for the Italian meal, it was not bad at all! Is this Thai restaurant expensive??
Not expensive at all. The Australian Lamb rack green curry costs only THB 690. Portion is big too.
I will try this restaurant when I come to Bangkok next month!
Better go around 5-6 pm to see the sunset!
The food looks yummy! Is it always full? Do I need to make reservation?
If you would like a table by the windows so as to get the best view of the city, advance booking is recommended. As there are limited tables, you may consider making a reservation at least 3 days in advance.


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'Counting On': The Return of Jim Bob and Michelle Duggar Causes Mixed Reactions from Fans
Andrea Francese
Earlier in the month, TLC officially announced the return of Counting On, the show that revolves around the Duggar kids as they get married and start families of their own. As more siblings join the marriage club, there is no shortage of new footage. That footage isn't exactly fresh and unique though. Over the last couple of seasons, fans have suggested the production house is reaching for storylines, and the most recent trailer might be proof of that. Jim Bob and Michelle Duggar appear to be returning to the show in a big way, and fans aren't really sure how they feel about it.
Where were Jim Bob and Michelle cut from the lineup
Jim Bob and Michelle were the targets of much ire when it was revealed that their then-teenaged son, Joshua Duggar, had molested several of his siblings. The way the parents of 19 children dealt with the situation and subsequent fallout called their parenting into question, and TLC made the difficult decision to nix the family's reality TV show, 19 Kids and Counting. It wasn't long before the Duggar family was back on television, but a few familiar faces were missing from the reimagined lineup. Josh was ousted from the cast, as were his parents, Jim Bob and Michelle.
Michelle Duggar and Jim Bob Duggar | Peter Kramer/NBC/NBCU Photo Bank via Getty Images
Jim Bob and Michelle seemingly sacrificed themselves to ensure the family's media brand wouldn't completely disintegrate. That has worked out well. In the years since Josh was revealed as deeply troubled, several more Duggar kids have gotten married and joined the lineup up of the reimagined show, Counting On. The dust has also, seemingly, settled for the network and it appears as though they are ready to bring Jim Bob and Michelle back into the fold in a much more significant role.
The Season 10 trailer indicated Jim Bob and Michelle will be much more visible
TLC recently released the trailer for Counting On's 10th season. While the show looks like it will cover most of the heartbreaking experiences that the Duggar family has endured over the last several months, eagle-eyed fans noticed that the trailer was a little heavy on Jim Bob and Michelle.
I am so thankful for my mom Mary, my sister Deanna & my wife Michelle. These 3 ladies are great mothers, spiritual encouragers, business advisors and great examples for other women. Happy Mother's Day! -Jim Bob
A post shared by The Duggar Family (@duggarfam) on May 12, 2019 at 11:32am PDT
In fact, several episodes of the new season seem to revolve around the parents who started the media empire in the first place. The show will cover the accidental death of Mary Duggar, Jim Bob's mother. It makes sense that the pair would appear in that episode, but there are a few other incidents that make fan think the couple will be returning in a full castmember capacity.
Jim Bob and Michelle appear in a segment about babysitting and Michelle also appears in an interview segment regarding Jinger Duggar's decision to wear pants. In short, the pair are seemingly making a full-time comeback to television, but fans aren't exactly sure how to feel.
Fans have mixed feelings about their return
Fans were quick to take to the internet to discuss the upcoming season of Counting On. While many were excited about the next season, the most prominent topic of conversation was the appearance of Jim Bob and Michelle. Some fans were oddly happy to see the pair returning to the show, while other's are troubled by what their reemergence could mean for the future of the series.
It's Michelle's birthday and the whole family is heaping love on the birthday girl! Here's Jim Bob's birthday wish: "Happy 53rd Birthday to my best friend! I love you, Michelle!! You are the sweetest wife, a loving mother, and a fun grandmother. I have really enjoyed our special get away the last couple of days for your birthday at @thekeetercenter in Branson! I love spending time with you. You are my #1 encourager, you are my business advisor, and my spiritual accountability partner. You're my best friend. I am so thankful for the wonderful 35 years of marriage, I look forward to spending the rest of my life with you."
A post shared by The Duggar Family (@duggarfam) on Sep 13, 2019 at 8:51am PDT
One Reddit user noted that it looks like the family is desperately trying to get everyone back on TV. The user said, "its interesting in this trailer JB & Meech were so present. They're working on getting the whole family back on the show.. Anna was super promoted in this trailer too I found, so, who knows what they have up their sleeve. Most of the commentary n the trailer was JB & M." Another user suggested that the family has been testing the water for months by adding Josh back into background shots.
2018 has been a year full of blessings! We are thankful for all that God has done this year! Some highlights include the addition of two Godly, wonderful daughters-in-law, one precious granddaughter, and two precious grandsons! We can't wait to see what the Lord will do in 2019! Be blessed and have a wonderful new year!
A post shared by The Duggar Family (@duggarfam) on Dec 31, 2018 at 3:47pm PST
The addition of Jim Bob and Michelle may be a test by TLC to see how the whole family will do in future seasons. Ratings are allegedly slipping for the long-running reality series, so the network really doesn't have much to lose.


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Miss Suki Is Kooky! PDF Free Download
Download eBooks from Booktopia today. Miss Suki Is Kooky! EBook Instant Download. Warriors Secrets of the Clans. EBook Instant Download. My Weird School 17 Miss Suki Is Kooky Book Description: Something weird is going on! Miss Suki is a famous children's book author—and she's coming to A.J.' She lives in the rainforest and writes about endangered animals. But when her pet raptor gets loose in the classroom, it's the kids who are going to be endangered!
Unlocked The Life and Crimes of a Mafia Insider Louis Unlocked The Life and Crimes of a Mafia Insider Louis Ferrante on FREE shipping on qualifying offers From Louis Ferrante a onetime mafia thug and federal prison inmate comes this remarkable and moving memoir of his journey from a life of crime to that of a promising writer Up until his incarceration. Miss Lazar Is Bizarre! Docker Is Off His Rocker! Kormel Is Not Normal! Miss Holly Is Too Jolly! My Weirdest SchoolMr. Miss Suki Is Kooky! Yonkers Is Bonkers! Carbles Is Losing his Marbles! Louie Is Screwy! Miss Suki is Kooky! - read free eBook by Dan Gutman in online reader directly on the web page. Select files or add your book in reader.
This is one weird summer vacation special you won't want to miss!
Author: Dan Gutman
Category: Juvenile Fiction
With more than 23 million books sold, the My Weird School series really gets kids reading! School's almost out for the summer, and A.J. is dreaming about all the fun things he's going to do on vacation. But A.J.'s dream quickly turns into a nightmare when three familiar spirits appear to show him summers past, present, and yet to come. Will they be able to convince him to leave his bad ways behind? Or will this summer end up being a total bummer? Bestselling author Dan Gutman brings his kid-friendly sense of humor to this special series of after-school chapter books featuring hilarious stories plus thirty-two pages of games, puzzles, and more. This is one weird summer vacation special you won't want to miss!
My name is A.J. and I hate school.
It was Monday morning, and all the girls were playing with these fake makeup kits that they got at some birthday party over the weekend. I thought I was gonna throw up.
"Picture Day is in three weeks," said my teacher, Miss Daisy, as she handed us each a piece of paper. "A photographer is going to come and take pictures of every student in school. So make sure your parents fill out this form if they want to order pictures."
getting my picture taken!" said this annoying girl with curly brown hair named Andrea Young. (The girl's name is Andrea Young, that is. Not her hair. Hair doesn't have a name.)
"Me too," said this crybaby girl named Emily, who always agrees with anything Andrea says.
"They should take your pictures," I
suggested, "and burn them."
My friends Ryan and Michael laughed. Emily looked like she was going to cry.
"It just so happens that Emily and I are very photogenic," Andrea told us.
"Wow!" I said. "You can read minds?"
"'Photogenic' means you look good in pictures, dumbhead."
"That's good," I said, "because you're ugly in real life."
"Oh, snap!" said Michael.
"Do you know where they should put your picture, Arlo?" asked Andrea.
"Where?" I asked. I hate when she calls me by my real name.
"In the post office," she said, "with all
those pictures of criminals and bank robbers and murderers."
"Oh, snap!" said Ryan.
"So is your face," I told Andrea. Any time somebody says something mean to you, always say, "So is your face." Even if it doesn't make any sense. That's the first rule of being a kid.
"Enough chitchat," said Miss Daisy. "We have library now with Mrs. Roopy."
"Yay!" said all the girls.
"Boo!" said all the boys.
Bummer in the summer! Libraries are boring. Do you know why? Because they're filled with books! And there's nothing more boring than a book. Why are you even reading this one?
Library would be even more boring if we didn't have a librarian like Mrs. Roopy. She's always dressed up like somebody else, whether it's Little Bo Peep or Johnny Appleseed. Mrs. Roopy is loopy.
When we got to the library, we saw Mrs. Roopy dressed up like a giant bird, with lots of feathers and a beak.
"Why are you dressed up like a bird, Mrs. Roopy?" asked Neil, who we call the nude kid even though he wears clothes.
"Squawk! Squawk! Squawk!" shouted Mrs. Roopy as she flapped her wings. "Who's Roopy? My name is Rappy. I'm a peregrine falcon, the main character in
The Fearless Falcon
It's a wonderful book written and illustrated by the famous children's book author Miss Suki Kabuki."
Mrs. Roopy read us a few chapters of the book. It's about this falcon that sees its reflection in a window and thinks it's an enemy. So it attacks its own reflection
by flying right into the glass.
Man, was that bird dumb.
"That's the saddest story I ever heard!" Emily said, with tears in her eyes. That girl will cry over any old thing.
After library we went to the art room. Ms. Hannah, our art teacher, was waiting for us.
"Today we're going to draw pictures of Rappy, the peregrine falcon in
," said Ms. Hannah. "It was written and illustrated by the famous children's book author Miss Suki Kabuki."
Hmm, that was strange. Why were we
doing something with the
book in both library
After we finished drawing our pictures and cleaning up the art room, it was time to go to music with Mr. Loring.
"Today we're going to sing a song about a falcon named Rappy," said Mr. Loring. "He's the main character in
, which was written and illustrated by Miss Suki Kabuki."
Miss Suki Is Kooky Pdf Free Download Free
This was getting really weird!
After music class was over, we went to the computer lab.
"Good morning," said Mrs. Yonkers, our computer teacher. "Today we're going to visit www.sukikabuki.com. That's the
website of children's book author Miss Suki Kabuki."
What the heck was going on?! How come
the teachers were talking about this dumb children's book author? It was the weirdest thing in the history of the world.
After we finished computer lab, we went back to our class to get ready for lunch. Suddenly I heard a knock at the door. Miss Daisy answered it.
It was Mr. Klutz, the principal! He has no hair at all.
"I have big news!" Mr. Klutz announced. "Guess who will be coming to visit our school in three weeks?"
"Who?" we all asked.
"A famous children's book author," Mr. Klutz said. "Her name is Miss Suki Kabuki!"
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Simon Vanrie
Françoiz Breut
Taking part in
October 29, 8:30pm - 11:59pm - Concerts - + Afterparty with VICE
Trained at the School of Fine Arts in Caen, it was in Nantes that Françoiz Breut first settled down to practice plastic art. There she met Dominique A and accompanied him on vocals for several pieces, before setting down roots in Brussels. Her plastic works, most often drawings, boxes and art videos, have toured many cities. Fascinated by everyday life, she deconstructs life and tinkers with it and, giving the audience the opportunity to discover a joyous mess. She illustrates children's books, and with her affinity with the musical world growing, she is beginning to illustrate a few records. She released her first self-titled album in 1997, starting a musical career that immediately met with international success. Five albums then followed, Vingt à trente mille jours (2000), Une Saison volée (2005), À l'aveuglette (2008), La Chirurgie des sentiments (2012), Zoo (2016), and as many journeys and poetic explorations. There is no link between these two parallel lives, image and sound, she says. And yet.
With her new album Flux flou de la foule, she tells of her anger, her curiosity and her appetite. She summons Fela and Sun Ra, evokes seventies space pop as much as deep dub, and makes you dance to obsessive, electronic loops. She denounces a world caught in perpetual (vicious) movement made up of upheavals and repeated explosions. Minimalist in form, complex and lively in content, it invites us laugh, rather madly, to cross the battlefields, to enjoy a moment of pleasure before the flood.


text:
Case Name NAACP Legal Defense & Education Fund v. Trump PR-NY-0003
Docket / Court 1:17-cv-05427 ( S.D.N.Y. )
State/Territory New York
Case Type(s) Presidential Authority
Attorney Organization NAACP Legal Defense Fund
On July 18, 2017, the NAACP Legal Defense & Education Fund (NAACP) filed this lawsuit in the U.S. District Court for the Southern District of New York. The NAACP joined with a number of non-profit organizations to sue President Donald J. Trump, members of the executive branch in their official ... read more >
On July 18, 2017, the NAACP Legal Defense & Education Fund (NAACP) filed this lawsuit in the U.S. District Court for the Southern District of New York. The NAACP joined with a number of non-profit organizations to sue President Donald J. Trump, members of the executive branch in their official capacities, and the Presidential Advisory Commission on Election Integrity (Commission) under the Federal Advisory Commission Act (FACA) and the Administrative Procedure Act (APA). The NAACP sought declaratory and injunctive relief as well as a writ of mandamus. The case was originally assigned to Judge Gregory H. Woods but was reassigned to Judge Andrew L. Carter, Jr. on July 27, 2017.
The NAACP filed this case to enjoin the operation of the Commission because they alleged the President had neither constitutional nor statutory authority to create a new executive organ for the purpose of launching an investigation that targets individual or groups of voters. The NAACP claimed that this Commission was created to manufacture evidence supporting President Trump's false claim of widespread voter fraud in the 2016 Presidential Election. The creation and operation of the Commission allegedly violated FACA, the APA, and the Fifth and Fifteenth Amendments.
On September 5, 2017, the NAACP filed its first amended complaint, requesting new declaratory relief and adding additional factual allegations. On October 20, 2017, the NAACP filed a second amended complaint, leaving the bulk of the complaint the same.
On November 3, 2017, the defendants filed a letter with the court in response to the plaintiff's letter requesting a scheduling conference. Judge Carter construed the letter as a motion to stay and on November 17, 2017, stayed all proceedings until resolution of the motion to dismiss filed that day. The defendants asked the court to dismiss the case because the plaintiff lacked standing and failed to state a claim upon which relief could be granted.
On February 28, 2018, the NAACP filed a motion of voluntary dismissal. That same day, the court granted the motion and dismissed the case without prejudice. Parties beared their own costs and expenses. There has been no other activity on the docket, so the case is presumably closed.
Jake Parker - 07/19/2018
Constitutional Clause
Non-profit NON-religious organization
Causes of Action Administrative Procedure Act, 5 U.S.C. §§ 551 et seq.
Ex Parte Young (Federal) or Bivens
Defendant(s) United States
Plaintiff Description NAACP Legal Defense & Education Fund
Indexed Lawyer Organizations NAACP Legal Defense Fund
Prevailing Party Defendant
Nature of Relief None
Source of Relief None
Form of Settlement Voluntary Dismissal
Case Ongoing No reason to think so
See this case at CourtListener.com (May provide additional documents and, for active cases, real-time alerts)
1:17-cv-5427 (S.D.N.Y.)
PR-NY-0003-9000.pdf | Detail
Complaint [ECF# 1]
Second Amended Complaint [ECF# 66]
Order Granting Plaintiffs' Motion for Voluntary Dismissal [ECF# 94] (S.D.N.Y.)
Judges Carter, Andrew Lamar Jr. (E.D.N.Y., S.D.N.Y.) show/hide docs
PR-NY-0003-0003 | PR-NY-0003-9000
Plaintiff's Lawyers Cartagena, Juan (New York) show/hide docs
PR-NY-0003-0002
Chin, Jackson (New York) show/hide docs
Gomez Hernandez, Julia Alejandra (California) show/hide docs
Ifill, Sherrilyn (New York) show/hide docs
PR-NY-0003-0001 | PR-NY-0003-0002 | PR-NY-0003-9000
Ingram, Joanna Elise Cuevas (New York) show/hide docs
Kleinman, Rachel Miriam (New York) show/hide docs
Lopez, Burth (District of Columbia) show/hide docs
Merle, Natasha C. (New York) show/hide docs
Nelson, Janai S. (New York) show/hide docs
Perez, Jose-Luis (New York) show/hide docs
Saenz, Thomas A. (California) show/hide docs
Senteno, Andrea E. (District of Columbia) show/hide docs
Spital, Samuel (New York) show/hide docs
Defendant's Lawyers Borson, Joseph Evan (District of Columbia) show/hide docs
Federighi, Carol (District of Columbia) show/hide docs
Shapiro, Elizabeth J. (District of Columbia) show/hide docs
Wolfe, Kristina Ann (District of Columbia) show/hide docs


text:
Q: rasterio.fill.fillnodata doesn't work as expected I have a DEM of a lake bottom, that contains a few holes (nodata) which I'd like to fill. For that purpose i'm using rasterio's fillnodata with a mask. Unfortunatly, I don't get the results I am expecting. Namely, that the holes within the lake are filled, but no changes at the 'lakeshore' are made. I'm creating a mask in the process, to indicate where the interpolation should happen and where it shouldn't but that doesn't seem to work. Any suggestions on what I might be doing wrong?
Here's my code:
import os
import numpy as np
import rasterio as rio
from rasterio.fill import fillnodata
from rasterio.features import sieve

path_in = r'Z:\..\dhms\Lake_process_test\raw'
path_out = r'Z:\...\dhms\Lake_process_test\filled'
path_msk = r'Z:\...\dhms\Lake_process_test\msk'

with rio.open(os.path.join(path_in, 'Lake.tif'), "r") as src:

    # collect metadata for output file
    profile = src.profile

    # create array which will be filled
    arr = src.read(1)
    # create mask indicating valid data area
    msk = src.read_masks(1)
    # fill holes in valid data area
    sieved_msk = sieve(msk, size=2000)
    # sieved_msk_inv = np.where((sieved_msk == 255), 0, 255)

    # fill nodata areas
    arr_filled = fillnodata(arr, mask=sieved_msk, max_search_distance = 1, smoothing_iterations=0)

    # write filled file
    with rio.open(os.path.join(path_out,'Lake_filled.tif'), "w", **profile) as filled:
         filled.write(arr_filled, 1)

    # write mask file
    with rio.open(os.path.join(path_msk,'Lake_mask.tif'), "w", **profile) as mask:
         mask.write(sieved_msk, 1)

Oh, and as you can see, I tried also inverting the mask, but that doesn't seem to be the problem.
EDIT: I've experimented a bit further: Inverting the mask leads to actually 'shrinking' the lake, whereas if I don't, it 'grows' but then the holes aren't filled.

A: So i solved it by just clipping back to the original extent with the mask created in the beginning. I'm still confused though, because the mask in the 'fillnodata' step doesn't do what i'd expect. So further hint's on whats going on are still welcome ;).
with rio.open(os.path.join(path_in, 'Lake.tif'), "r") as src:

    # collect metadata for output file
    profile = src.profile

    # read band which should be filled as array
    arr = src.read(1)

    # create mask indicating valid data area
    msk = src.read_masks(1)
    # fill holes in valid data area
    sieved_msk = sieve(msk, size=2000)

    # fill nodata areas
    arr_filled = fillnodata(arr, mask=src.read_masks(1), max_search_distance = 50, smoothing_iterations=0)

    # use mask to clip back to original extent
    arr_clipped = np.where((sieved_msk == 255), arr_filled, np.nan)

    with rio.open(os.path.join(path_out, 'Lake_filled.tif'), "w", **profile) as filled:
        filled.write(arr_clipped, 1)

redpajama_set_name: RedPajamaStackExchange


text:
\section{\label{sec:level1}Introduction}

Synchronization of interacting chaotic oscillators is one of the most
interesting nonlinear phenomenon and is an inherent part of many natural
systems ~(cf.\cite{asp2001,sbjk2002}). The concept of synchronization is
receiving a central importance in recent research in nonlinear dynamics due to
its potential applications in diverse areas of science and technology.  Since
the identification of chaotic synchronization \cite{hfty1983,hfty198370,
lmptlc1990}, several works have appeared in identifying and demonstrating
basic kinds of synchronization both theoretically and experimentally
\cite{asp2001,sbjk2002,hfty1983,hfty198370,lmptlc1990}.  There are also
attempts to find a unifying framework for defining the overall class of chaotic
synchronizations \cite{rblk2000,sblmp2001,aehaak2004}.

One of the interesting synchronization behaviors of unidirectionally coupled
chaotic systems is the generalized synchronization (GS), which was conceptually
introduced in Ref.~\cite{nfrmms1995}. Generalized synchronization is observed in
coupled nonidentical systems, where there exists some functional relation
between the  drive $X(t)$ and the response $Y(t)$ systems, that is,
$Y(t)=F(X(t))$.  With GS, all the response systems coupled to the drive lose
their intrinsic chaoticity (sensitivity to initial conditions) under the same
driving and follow the same trajectory. Hence the presence of GS can be detected
using the so called auxiliary system approach \cite{hdianfr1996}, where an
additional system (auxiliary system) identical to  the response system is
coupled to the drive in similar fashion. Auxiliary system approach is
particularly appealing since it can be implemented directly in an experiment
and, in addition, this method allows one to utilize analytical approaches for
studying GS.  However, one  has to be aware that if there are multiple basins of
attraction for the coupled drive-response system, then the auxiliary system
approach can  fail.

Generalized synchronization (GS) has been well studied and
understood in systems with few degrees of freedom and for discrete maps
~\cite{nfrmms1995,hdianfr1996,rb1998,lkup1996,kp1996,brheo1997,nfrctl2001}.
The concept of GS has  also been extended to  spatially extended
chaotic systems such as coupled Ginzburg-Landau equations~\cite{aehaakpre2005}.
Recently, the terminology intermittent generalized synchronization (IGS)
\cite{aehaak2005} was introduced in diffusively coupled R\"ossler systems in
analogy with  intermittent lag synchronization (ILS) \cite{sbdlv2000,dlvsb2001}
and intermittent phase synchronization (IPS) \cite{apgo1997,apmz1997,kjlyk1998},
and also  experimentally  in coupled Chua's circuit.  Very recently, it has been
shown \cite{lzycl2005} that the transition to intermittent chaotic
synchronization (in the case of complete synchronization) is characteristically
distinct for geometrically different chaotic attractors.  In particular, it has
been shown that for phase coherent chaotic attractors (R\"ossler attractor) the
transition occurs immediately as soon as the coupling strength is increased from
zero and for non-phase-coherent attractors (Lorenz attractor),  the transition
occurs slowly as the coupling is increased from zero.

Time-delay systems form an important class of dynamical systems and recently
they are receiving central importance in investigating the phenomenon of chaotic
synchronizations in view of their infinite dimensional nature and feasibility of
experimental realization~\cite{mzxw2003,emskas2005,dvskmlpre2006,dvskml2005}.
While the concept of GS has been well established in low dimensional systems, it
has not yet been studied in detail in coupled time-delay systems and  only very
few recent studies have been dealt with GS in time-delay
systems~\cite{mzxw2003,emskas2005}.  In particular, the mechanism of onset of GS
in coupled time-delay systems and its characteristic properties have not yet
been clearly understood and require urgent attention.

In this paper, we investigate the characteristic properties of nature of
onset of GS from asynchronous state in unidirectionally coupled piece-wise
linear time-delay systems exhibiting highly non-phase coherent hyperchaotic
attractors~\cite{dvskmlpre2006}. We find that the onset of GS is preceded by
on-off intermittency mechanism from the desynchronized state. We have also
identified that the intermittency transition to GS exhibits characteristically
distinct behaviors for different coupling schemes.  In particular, the
intermittency transition occurs in a broad range of coupling strength for error
feedback coupling configurations and in a narrow range of coupling strength for
direct feedback  coupling configurations, beyond certain threshold value of
coupling strength. In addition, the intermittent dynamics is characterized by
periodic bursts away from the temporal synchronized state with period equal to
the delay time of the response system in the case of broad range intermittency
transition whereas it is characterized by random time intervals in the case of
narrow range intermittency transition.  We have also confirmed these dynamical
behaviours in both linear and nonlinear coupling configurations. We have
analyzed these transitions analytically using Krasvoskii-Lyapunov functional
approach and numerically by the probability of synchronization and by the
\emph{sub}Lyapunov exponents.  We have also addressed the reason behind these
transitions using periodic orbit theory. The robustness of these transitions
with the system parameters in both the linear and nonlinear, error feedback and
direct feedback coupling configurations, are also studied.

\begin{figure}
\centering
\includegraphics[width=0.5\columnwidth]{fig1}
\caption{\label{chaos} The hyperchaotic attractor of the system~(\ref{eq.onea})
 for the parameter values $a=1.0, b=1.2$ and $\tau=15.0$.}
\end{figure}

The plan of the paper is as follows. In Sec.~II, we will point out the existence
of broad range intermittency transition to GS for linear error feedback
coupling  proportional to ($x_1(t)-x_2(t)$) while in Sec.~III the existence of
narrow range intermittency transition is shown for the linear direct feedback
coupling of the form $x_1(t)$, where $x_1(t)$ and $x_2(t)$ are the drive and
response signals, respectively (see below for details). In Sec.~IV we will
discuss the existence of broad range intermittency transition for nonlinear
error feedback coupling of the form $(f(x_1(t-\tau_2))-f(x_2(t-\tau_2)))$, where
$f(x)$ is an odd piece-wise linear function. The existence of narrow range
intermittency transition is discussed in Sec.~V for nonlinear direct feedback
coupling of the form $(f(x_1(t-\tau_2))$.  Finally in Sec.~VI, we will summarize
our results.

\section{Broad range (slow/delayed) intermittency transition to GS for linear
error feedback coupling of the form $(x_1(t)-x_2(t))$}

We consider the following first order delay differential equation introduced
by Lu and He~\cite{hlzh1996} and discussed in detail by Thangavel et
al.~\cite{ptkm1998},
\begin{eqnarray}
\dot{x}(t)&=&-ax(t)+bf(x(t-\tau)),
\label{eq.onea}
\end{eqnarray}
where $a$ and $b$ are parameters, $\tau$ is the time-delay and $f$ is an
odd piecewise linear function defined as
\begin{eqnarray}
f(x)=
\left\{
\begin{array}{cc}
0,&  x \leq -4/3  \\
            -1.5x-2,&  -4/3 < x \leq -0.8 \\
            x,&    -0.8 < x \leq 0.8 \\
            -1.5x+2,&   0.8 < x \leq 4/3 \\
            0,&  x > 4/3. \\
         \end{array} \right.
\label{eqoneb}
\end{eqnarray}

Recently, we have reported ~\cite{dvskmlijbc}  that the system
~(\ref{eq.onea}) exhibits hyperchaotic behavior for suitable parametric values.
For our present study, we find that for the choice of the parameters $a=1.0,
b=1.2$ and $\tau=15.0$ with the initial condition $x(t)=0.9, t\in(-5,0)$,
Eq.~(\ref{eq.onea}) exhibits hyperchaos.  The corresponding pseudoattractor is
shown in Fig.~\ref{chaos}. The hyperchaotic nature of Eq.~(\ref{eq.onea})
is confirmed by the existence of multiple positive Lyapunov exponents.   The
first ten maximal Lyapunov exponents for the above choice of parameters as a
function of delay time $\tau$ is shown in Fig.~\ref{fig1} (spectrum of Lyapunov
exponents in this paper are calculated using the procedure suggested by Farmer
\cite{jdf1982}).

To be specific, we first consider the following unidirectional, linearly
coupled systems with drive $x_1(t)$, response $x_2(t)$ and an auxiliary
$x_3(t)$,
\begin{subequations}
\begin{align}
\dot{x}_1(t)=&\,-ax_1(t)+b_{1}f(x_1(t-\tau_1)),  \\
\dot{x}_2(t)=&\,-ax_2(t)+b_{2}f(x_2(t-\tau_2))\nonumber \\
&\,+b_{3}(x_1(t)-x_2(t)),\\
\dot{x}_3(t)=&\,-ax_3(t)+b_{2}f(x_3(t-\tau_2))\nonumber \\
&\,+b_{3}(x_1(t)-x_3(t)),
\end{align}
\label{eqonea}
\end{subequations}
where $b_1, b_2$ and $b_3$ are constant parameters, and $\tau_1$ and $\tau_2$
are constant delay parameters. Note that when $b_1\ne b_2$ or $\tau_1 \ne
\tau_2$ or both, corresponding to parameter mismatches, we have
unidirectionally coupled nonidentical systems (Eq.~(\ref{eqonea}a) and
(\ref{eqonea}b)), while the auxiliary system is given by (\ref{eqonea}c) and
$f(x)$ is the odd piece-wise linear function (\ref{eqoneb}). The coupling in
(\ref{eqonea}b) may be also called a linear error feedback coupling.

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig2}
\caption{\label{fig1} The first ten maximal Lyapunov exponents $\lambda_{max}$
 of the scalar time-delay system  for the parameter values
 $a=1.0,b_1=1.2, \tau\in(2,29)$ (which is the same as Eq.~(\ref{eq.onea}) with
 $b_1$ replaced by $b$) (\ref{eqonea}a).}
\end{figure}

For simplicity, we have chosen $b_1=b_2$ so that the time-delays $\tau_1$ and
$\tau_2$ alone introduce a simple form of parameter mismatch between the drive
$x_1(t)$ and the response $x_2(t)$.  We have chosen the values of parameters as
$a=1.0, b_1=b_2=1.2, \tau_1=20$ and $\tau_2=25$.  For this parametric choice,
in the absence of coupling, all the three systems (\ref{eqonea}) evolve
independently and exhibit hyperchaotic attractors, which is confirmed by the
existence of multiple positive Lyapunov exponents (Fig.~\ref{fig1}). The actual
value of the positive Lyapunov exponents for $\tau=20$ are
$0.00916$, $0.00759$, $0.00565$, $0.00283$ and $0.00073$ and for $\tau=25$ they are
$0.01234$, $0.01067$, $0.00886$, $0.00658$, $0.00386$, $0.00229$, $0.00123$
and $0.00033$.
\subsection{Stability Condition}
With GS, as all the response systems under the same driving follow the same
trajectory, it is sufficient to identify the existence condition for
establishment of complete synchronization (CS) between the response $x_2(t)$
and the auxiliary $x_3(t)$ systems in order to achieve GS between the drive
$x_1(t)$ and the response $x_2(t)$ systems.

Now,  for CS to occur between the response $x_2(t)$ and the auxiliary $x_3(t)$
variables, we consider the time evolution of the difference system with the
state variable $\Delta=x_3(t)-x_2(t)$. It can be written for small values of
$\Delta$ as
\begin{eqnarray}
\dot{\Delta}=-(a+b_3)\Delta+b_2f^\prime(x_2(t-\tau_{2}))\Delta_{\tau_2},
\label{eq.difsys}
\end{eqnarray}
where
\begin{eqnarray}
f^\prime(x)=
\left\{
\begin{array}{cc}
            -1.5,&  -4/3 < x \leq -0.8 \\
            1,&    -0.8 < x \leq 0.8 \\
            -1.5,&   0.8 < x \leq 4/3. \\
         \end{array} \right.
\label{eqonec}
\end{eqnarray}
\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig3}
\caption{\label{fig2} Dynamics in the phase space of the systems
(\ref{eqonea}). (a) and (b): Approximate GS and CS, respectively, for the value
of the coupling strength $b_3=0.4$. (c) and (d): Perfect GS and CS,
respectively, for the value of the coupling strength $b_3=0.9$.}
\end{figure}

The synchronization manifold, $x_2(t)=x_3(t)$, is locally attracting if the origin
of this equation is stable.  Following  Krasovskii-Lyapunov functional
approach, we define a positive definite  Lyapunov functional of
the form \cite{nnk1963,kp1998,dvskml2005} (details of stability
analysis are given in appendix~\ref{a1})
\begin{eqnarray}
V(t)=\frac{1}{2}\Delta^2+\mu \int_{\tau_2}^0\Delta^2(t+\theta)d\theta,
\label{eq.lfunc}
\end{eqnarray}
where $\mu$ is an arbitrary positive parameter, $\mu>0$.  The solution of
Eq.~(\ref{eq.difsys}), namely $\Delta=0$, is stable if the derivative of the
functional along the trajectory of Eq.~(\ref{eq.difsys}) is negative.  This
negativity condition is satisfied if $b_3+a>\frac{b_2^2f^{\prime
2}(x_2(t-\tau_2))}{4\mu}+\mu$, from which it turns out that the sufficient
condition for asymptotic stability is
\begin{eqnarray}
a+b_3>\left|b_2f^{\prime}(x_2(t-\tau_2))\right|.
\label{eq.asystab}
\end{eqnarray}
Now from the form of the piecewise linear function $f(x)$ given by
Eq.~(\ref{eqoneb}),
we have,
\begin{eqnarray}
\left|f^{\prime}(x_2(t-\tau_2))\right|=
\left\{
\begin{array}{cc}
1.5,&  0.8\leq|x_2|\leq\frac{4}{3}\\
1.0,&  |x_2|<0.8. \\
\end{array} \right.
\end{eqnarray}
Consequently the stability condition (\ref{eq.asystab}) becomes
$a+b_3>\left|1.5b_2\right|>\left|b_2\right|$.  Thus one can take
\begin{eqnarray}
a+b_3>\left|b_2\right|
\label{eq.ls}
\end{eqnarray}
as the less stringent or approximate stability condition (as the synchronization
dynamics of the coupled systems  (\ref{eqonea}) can occur even beyond the inner
region, $|x_2|<0.8$) for (\ref{eq.asystab}) to be valid, while
\begin{eqnarray}
a+b_3>\left|1.5b_2\right|
\label{eq.gc}
\end{eqnarray}
can be considered as the most general or stringent or exact stability condition
(as the full synchronization dynamics of the coupled systems  (\ref{eqonea})
lies within the outer region $0.8<|x_2|\le\frac{4}{3}$) specified by
(\ref{eq.asystab}) for asymptotic stability of the synchronized state
$\Delta=0$.

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig4}
\caption{\label{fig3} The intermittent dynamics of the response $x_2(t)$ and
auxiliary $x_3(t)$ systems for the value of the coupling strength $b_3=0.4$. (a)
Time traces of the difference $x_2(t)-x_3(t)$ corresponding to Fig.~\ref{fig2}b,
(b) Enlarged in x scale to show bursts at periodic intervals when bursts of
larger amplitudes $\Delta>|0.01|$ are considered and (c) Enlarged in y scale to show random
bursts when bursts of smaller amplitudes $\Delta<|0.01|$ are considered.}
\end{figure}

\subsection{Approximate (Intermittent) Generalized Synchronization}
In order to understand the mechanism of transition to synchronized state, it
will be important to follow the dynamics from the parameter values at which the
less stringent condition is satisfied. Figure~\ref{fig2}a shows the approximate
GS (which may also be termed as intermittent generalized synchronization (IGS)
in analogy with intermittent lag synchronization (ILS)) between the drive
$x_1(t)$ and the response $x_2(t)$ systems, whereas Fig.~\ref{fig2}b shows the
approximate CS between the response $x_2(t)$ and the auxiliary $x_3(t)$ systems
for  the values of the parameters $a=1.0, b_1=b_2=1.2, \tau_1=20,  \tau_2=25$
and  $b_3=0.4$ satisfying the less stringent condition (\ref{eq.ls}). Perfect GS
and perfect CS are shown in Figs.~\ref{fig2}c and ~\ref{fig2}d respectively for
$b_3=0.9$ satisfying the general stability condition  (\ref{eq.gc}). Time traces
of the difference $x_2(t)-x_3(t)$ corresponding to approximate CS
(Fig.~\ref{fig2}b) are shown in Fig.~\ref{fig3}, which show periodic bursts with
period between two consecutive bursts approximately equal to the  time-delay of
the response system $t\approx 25$ when 'on' states of amplitude greater than
$|0.01|$ are considered. Fig.~\ref{fig3}b shows an enlarged (in x scale)
part of Fig.~\ref{fig3}a to view the bursts at periodic intervals when bursts
of larger amplitudes ($\Delta>|0.01|$) are considered, while Fig.~\ref{fig3}c is
an enlarged (in y scale) version of  Fig.~\ref{fig3}b to show random bursts when
bursts of smaller amplitude $\Delta<|0.01|$ are considered.

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{nfig5}
\caption{\label{fig4} The statistical distribution of laminar phases
corresponding to the Fig.~\ref{fig3}. (a) For threshold value $\Delta=|0.1|$ and
(b) for the threshold value of $\Delta=|0.0001|$.}
\end{figure}

Usually the intermittent dynamics is characterized by the entrainment of the
dynamical variables in random time intervals of finite duration
\cite{npsmh1994,jfhnp1994}.  But from  Fig.~\ref{fig3}b, it is evident that the
intermittent dynamics displays periodic bursts from the synchronous state with
period approximately equal to the delay time of the response system, when
amplitudes of the state variable $|\Delta|=|x_3(t)-x_2(t)| > 0.01$ are
considered, for the values of the coupling strength at which the less stringent
stability condition (\ref{eq.ls}) is satisfied. The statistical features
associated with the intermittent  dynamics is analyzed by calculating the
distribution of laminar phases $\Lambda(t)$ with amplitude less than a threshold
value to $\Delta$.  A universal asymptotic power law distribution $\Lambda(t)
\propto t^{-\alpha}$ is observed for the threshold value $\Delta=|0.0001|$ with
the value of the exponent $\alpha=-1.5$ as shown in Fig.~\ref{fig4}b, which is
quite typical for on-off intermittency.  On the other hand the distribution of
laminar phases $\Lambda(t)$ for the value of the threshold value of
$|\Delta=0.1|$ shows a periodic structures (Fig.~\ref{fig4}a), where the peaks occur
approximately at $t=nT, n=1,2,...$, where $T\approx \tau_2$ is the period of the
lowest periodic orbit of the uncoupled system (\ref{eqonea}b). Note that $-3/2$
power law is observed for the intermittent dynamics shown in Fig.~\ref{fig3} for
laminar phases $\Lambda(t)$ with amplitude less than  $\Delta=|0.0001|$ (as an
illustrative example), which is also evident from Fig.~\ref{fig3}c, while
periodic bursts are observed for 'on' state of amplitude greater than $|0.01|$.
It is to be noted that such periodic bursts of period approximately equal to
the  time-delay of the response system for larger threshold value of $\Delta$
along with the on-off intermittency behavior for larger threshold value of
$\Delta$ has also been observed by Zhan \emph{et al} \cite{mzxw2003}  in
unidirectionally coupled Mackey-Glass systems , where the authors discussed
relation between two modes of synchronization, namely, CS and GS.

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig6}
\caption{\label{fig5} (a) The probability of synchronization $\Phi(b_3)$
between the response $x_2(t)$  and the auxiliary $x_3(t)$ systems and (b)
Largest Lyapunov exponents of the coupled drive $x_1(t)$ and response $x_2(t)$
systems (\ref{eqonea}a) and (\ref{eqonea}b).}
\end{figure}

\subsection{Characterization of IGS} Now we characterize the intermittency
transition to GS by using (i) the notion of the probability of synchronization
$\Phi(b_3)$ as a function of the coupling strength $b_3$~\cite{lzycl2005}, which
can be defined as the fraction of time during which $\left|x_2(t)-x_3(t)\right|<
\epsilon$ occurs, where $\epsilon$ is a small but arbitrary threshold, and (ii)
from the changes in the sign of \emph{sub}Lyapunov exponents (which are nothing
but the Lyapunov exponents of the subsystem) in the spectrum of Lyapunov
exponents of the coupled time-delay systems. Fig.~\ref{fig5}a shows the
probability of synchronization $\Phi(b_3)$ as a function of the coupling
strength $b_3$ calculated from the variables of the response $x_2(t)$ and the
auxiliary $x_3(t)$ systems for CS between them. For the range of
$b_3\in(0,0.39)$, there is absence of any entrainment between the systems
resulting in asynchronous behavior and the probability of synchronization
$\Phi(b_3)$ is practically zero in this region.  However, starting from the
value of $b_3=0.39$ and above, there appear  oscillations in the value of the
probability of synchronization $\Phi(b_3)$ between zero and some finite values
less than unity, exhibiting intermittency transition to GS in the range of
$b_3\in(0.4,0.62)$ for which the less stringent stability condition
(\ref{eq.ls}) is satisfied. Beyond $b_3=0.62$, $\Phi(b_3)$ attains unit value
indicating perfect GS. Note that the above intermittency transition occurs in a
rather wide range of the coupling strength (this can also be termed as slow or
delayed intermittency transition in analogy with the terminology used in
~\cite{lzycl2005}), which has also been confirmed from the transition of
successive largest \emph{sub}Lyapunov exponents in the corresponding range of
the coupling strength.

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig7}
\caption{\label{fig6} The probability of synchronization $\Phi(b_3)$ in
3-dimensional plots (a) as a function of the system parameter $b_2$ and the
coupling strength $b_3$ and (b) as a function of the coupling delay $\tau_2$
and the coupling strength $b_3$, exhibiting broad range intermittency transition
to GS for linear error feedback coupling.}
\end{figure}

The spectrum of the first fifteen largest Lyapunov exponents $\lambda_{max}$ of
the coupled  drive $x_1(t)$ and response $x_2(t)$ systems  are shown in
Fig.~\ref{fig5}b. From the general stability condition (\ref{eq.asystab}), it is
evident that for the chosen value of the parameter $a=1.0$, the less stringent
stability condition (\ref{eq.ls}) is satisfied for the values of coupling
strength $b_3>0.2$.   Correspondingly, the least positive \emph{sub}Lyapunov
exponent of the response system (\ref{eqonea}b) gradually becomes negative from
$b_3>0.2$. Subsequently, the remaining positive \emph{sub}Lyapunov exponents
gradually become negative and attain saturation in the range of
$b_3\in(0.2,0.8)$.  This is in accordance with the fact that the less stringent
stability condition is satisfied only in the corresponding range of coupling
strength $b_3$. This is a strong indication of the broad range intermittency
(IGS) transition to GS.  For $b_3>0.8$, the general stability condition
(\ref{eq.gc}) is satisfied, where one can observe perfect GS as is evidenced by
both the probability of synchronization approaching unit value and by the
negative saturation of \emph{sub}Lyapunov exponents calculated between the drive
and response systems. The inference is that the correlation between the
oscillations of the systems eventually becomes stronger with the strength of the
coupling, and this is indicated by the successive transition of
\emph{sub}Lyapunov exponents to negative values.

It is a well established fact that a chaotic attractor can be considered as a
pool of infinitely many unstable periodic orbits of all periods.
Synchronization between two coupled systems is said to be asymptotically stable,
if all the unstable periodic orbits of the response system are stabilized in the
transverse direction of the synchroniation manifold. Consequently, all the
trajectories transverse to the synchronization manifold converge for suitable
values of coupling strength and this is reflected in the negative values of the
transverse Lyapunov exponents (\emph{sub}Lyapunov exponents) upon
synchronization~\cite{lzycl2005}. From our results, we find that the
\emph{sub}Lyapunov exponents gradually become negative in a broad range of
coupling strength $b_3$ after certain threshold value and this is in accordance
with the known results on gradual stabilization of unstable periodic orbits of
the response system in the complex synchronization manifold of low dimensional
systems~\cite{lzycl2005}. Unfortunately, methods for locating UPO's and
calculating their transverse Lyapunov exponents have not been well established
for time-delay systems and hence a quantitative proof for the gradual
stabilization of UPO's has not been given here.  However, the gradual
stabilization of UPO's along with their transverse Lyapunov exponent in the
range of intermittency transition have been reported for the case of coupled
R\"ossler and Lorenz systems in Ref.~\cite{lzycl2005}. It can then be inferred
from these studies that the broad range intermitteny transition in the case of
error feedback coupling configuration is due to the fact that the strength of
the coupling $b_3$ contributes only less significantly  to stabilize the UPO's
as the error $x_1(t)-x_2(t)$ gradually becomes smaller from the transition
regime after certain threshold value of the coupling strength.

The robustness of the intermittency transition in a broad range of coupling
strength with the system parameter $b_2 \in (1.1,1.6)$  and with the coupling
delay $\tau_2 \in (10,20)$ has also been confirmed. Fig.~\ref{fig6}a shows the
3-dimensional plot of the probability of synchronization as a function of the
system parameter $b_2$ and the coupling strength $b_3$, while Fig.~\ref{fig6}b
shows the 3-dimensional plot of $\Phi(b_3)$ as a function of the coupling delay
$\tau_2$ and the coupling strength $b_3$. The above figures (Fig.~\ref{fig6})
clearly reveal the broad range intermittency transition to GS in the case of
linear error feedback coupling scheme.

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig8}
\caption{\label{fig7} Dynamics in the phase space of the systems (\ref{lin2}):
(a) and (b) Approximate GS and CS, respectively, for the value of the coupling
strength $b_3=0.64$ and (c), (d) Perfect GS and CS, respectively, for the value of
the coupling strength $b_3=0.8$.}
\end{figure}

\section{\label{lin_narrow}Narrow range (immediate) intermittency transition to
 GS for linear direct feedback coupling of the form $x_1(t)$}
To illustrate the narrow range intermittency transition to GS, we consider the
unidirectional linear direct feedback coupling of the form
\begin{subequations}
\begin{eqnarray}
\dot{x}_1(t)&=&-ax_1(t)+b_{1}f(x_1(t-\tau_1)),  \\
\dot{x}_2(t)&=&-ax_2(t)+b_{2}f(x_2(t-\tau_2))+b_{3}x_1(t),\\
\dot{x}_3(t)&=&-ax_3(t)+b_{2}f(x_3(t-\tau_2))+b_{3}x_1(t),
\end{eqnarray}
\label{lin2}
\end{subequations}
where $f(x)$ is of the same odd piece-wise linear form as in
Eq.~(\ref{eqoneb}). Assuming the same values of the parameters as before
and proceeding in the same way as in the previous case, one can obtain the
sufficient condition for asymptotically stable CS between the response $x_2(t)$
(\ref{lin2}b) and the auxiliary $x_3(t)$ (\ref{lin2}c) systems as
\begin{eqnarray}
a>\left|b_2f^{\prime}(x_2(t-\tau_2))\right|.
\label{lin2stab}
\end{eqnarray}

It is to be noted that the above stability condition holds good only for the
case when coupling is present, that is $b_3\ne0$.  When there is no coupling
($b_3=0$), by definition, there will be a desynchronized chaotic state. As soon
as the value of the coupling strength is increased from zero, the stability
condition (\ref{lin2stab}) always lead to synchronized state even for very
feeble values of $b_3$ for  parameters satisfying the stability condition, as
it  is independent of the coupling strength $b_3$. As the values of the
parameters satisfying the stability condition (\ref{lin2stab}) rapidly leads to
immediate transition to synchronized state as soon as the coupling is switched
on, it is difficult to identify the possible transitions to synchronized state.
In addition, as the stability condition  is independent of the coupling strength
$b_3$, one is not  able to explore the dynamical transitions as a function of
coupling strength for the parameter values satisfying the stability condition
(\ref{lin2stab}). Hence we study the synchronization transition by choosing the
parameters violating the stability condition as $a=1.0, b_1=1.2, b_2=1.1,
\tau_1=\tau_2=20$ and varying the coupling strength $b_3$ in order to identify
the mechanism of synchronization transition. Here, in this case $b_1$ and $b_2$
alone introduce the parameter mismatch while $\tau_1=\tau_2$ (It may be added
that the qualitative nature of the dynamical transitions remain the same even
when the mismatch is either in time delays alone, that is  $\tau_1\neq\tau_2$,
$b_1=b_2$ or in both the system parameters and time delays, $b_1\neq b_2$,
$\tau_1\neq \tau_2$, as confirmed below in the three dimensional plots of
Figs.~\ref{fig11}).

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig9}
\caption{\label{fig8} The intermittent dynamics of the response $x_2(t)$
(\ref{lin2}b) and  auxiliary $x_3(t)$ (\ref{lin2}c) systems for the value of the
coupling strength $b_3=0.64$. (a) and (b) Time traces of the difference
$x_2(t)-x_3(t)$ corresponding to Fig.~\ref{fig7}b.}
\end{figure}

As $b_3$ is varied from zero, transition from desynchronized state to
approximate GS occurs for $b_3>0.6$. Approximate GS (IGS) between the  drive
system $x_1(t)$ specified by Eq.~(\ref{lin2}a), and the response system
$x_2(t)$ represented by  Eq.~(\ref{lin2}b), is shown in Fig.~\ref{fig7}a whereas
the approximate CS between the response $x_2(t)$ (Eq.~(\ref{lin2}b)) and the
auxiliary $x_3(t)$ (Eq.~(\ref{lin2}c)) systems is shown in  Fig.~\ref{fig7}b for
the value of the coupling strength $b_3=0.64$. Prefect GS and CS are shown in
Figs.~\ref{fig7}c and \ref{fig7}d, respectively, for the value of the coupling
strength $b_3=0.8$. The intermittent dynamics at the transition regime
corresponding to the value of the coupling strength $b_3=0.64$ is shown in
Figs.~\ref{fig8}, in which Fig.~\ref{fig8}b shows the enlarged part of
Fig.~\ref{fig8}a. It is clear from this figure that the intermittent dynamics
displays intermittent bursts at random time intervals.  The statistical
distribution of the laminar phases again shows a universal asymptotic $-1.5$
power law behavior for the threshold value $\Delta=|0.0001|$, which is  typical
for on-off intermittency transitions, as shown in Fig.~\ref{fig9}.

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig10}
\caption{\label{fig9} The statistical distribution of laminar phases for the
Fig.~\ref{fig8}.}
\end{figure}

Now we characterize the intermittency transition to GS in the present case,
again by using the notion of the probability of synchronization $\Phi(b_3)$ and
from the changes in the sign of \emph{sub}Lyapunov exponents of the coupled
system. The probability of synchronization is shown in Fig.~\ref{fig10}a as a
function of the coupling strength, again calculated from the response $x_2(t)$
and  the auxiliary $x_3(t)$ systems, Eqs. (\ref{lin2}b) and (\ref{lin2}c),
respectively, which remains zero in the range of $b_3 \in (0,0.60)$ and
oscillates between its maximum and minimum values in a narrow range of $b_3 \in
(0.60,0.68)$ confirming the existence of approximate CS in the later range.
Above $b_3=0.68$ the probability of synchronization acquires its maximum value
depicting perfect CS between the response $x_2(t)$  and the auxiliary $x_3(t)$
systems. Correspondingly there exists perfect GS between the drive $x_1(t)$  and
the response $x_2(t)$ systems. Fig.~\ref{fig10}b shows the first twelve  maximal
Lyapunov exponents of the coupled drive $x_1(t)$   and the response $x_2(t)$
systems. The least positive \emph{sub}Lyapunov exponent of the response system
starts to become negative from $b_3>0.60$. Subsequently, all the other positive
\emph{sub}Lyapunov exponents become negative and reach saturation in a rather
narrow range of $b_3 \in (0.60,0.68)$.  Thus the narrow range intermittency
(IGS) transition (this can also be termed as  immediate intermittency transition
in analogy with the terminology used in ~\cite{lzycl2005}) is confirmed from
both the probability of synchronization, calculated from the response and the
auxiliary systems, and negative saturation of \emph{sub}Lyapunov exponents,
calculated from the drive and the response systems.

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig11}
\caption{\label{fig10} (a) The probability of synchronization $\Phi(b_3)$
between the response $x_2(t)$ (\ref{lin2}b) and the auxiliary  $x_3(t)$
(\ref{lin2}c) systems and (b) Largest Lyapunov exponents of the coupled drive
$x_1(t)$ and response $x_2(t)$ systems (\ref{lin2}a) and (\ref{lin2}b).}
\end{figure}

As discussed in the previous section, the narrow range intermittency transition
is in accordance with the stabilization of all the unstable periodic orbits of
the response system  in a narrow range as a function of the coupling strength
$b_3$ and this is reflected in the immediate transition of all the
\emph{sub}Lyapunov exponents (Fig.~\ref{fig10}b) to negative values.  It is also
to be noted that the narrow range intermitteny transition in the case of direct
feedback coupling configuration can be attributed to the fact that the strength
of the coupling $b_3$ contributes significantly proportional to the strength of
the signal $x_1(t)$ to stabilize all the UPO's  immediately at  the transition
regime after certain threshold value of the coupling strength as in the case of
low-dimensional systems~\cite{lzycl2005}.

The robustness of the intermittency transition in a narrow range of the coupling
strength $b_3$ for a range of values of the parameter $b_2 \in (1.1,1.6)$  and
the  delay $\tau_1=\tau_2 \in (10,20)$ is shown in Fig.~\ref{fig11}. The
3-dimensional plot of the probability of synchronization as a function of the
system parameter $b_2$ and the coupling strength $b_3$ is shown in
Fig.~\ref{fig11}a, while Fig.~\ref{fig11}b shows the 3-dimensional plot of
$\Phi(b_3)$ as a function of the coupling delay $\tau_2$ and the coupling
strength $b_3$.

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig12}
\caption{\label{fig11} The probability of synchronization $\Phi(b_3)$ in
3-dimensional plots (a) as a function of the system parameter $b_2$ and the
coupling strength $b_3$ and (b) as a function of the coupling delay $\tau_2$
and the coupling strength $b_3$, exhibiting narrow range intermittency
transition to GS for linear direct feedback coupling}
\end{figure}

\section{Broad range intermittency transition to GS for nonlinear error feedback
coupling of the form $(f(x_1(t-\tau_2))-f(x_2(t-\tau_2)))$}
Next we demonstrate the existence of the above types of distinct characteristic
transitions for nonlinear coupling configurations as well.  For this purpose,
we consider the  unidirectional nonlinear error feedback coupling of the form
\begin{subequations}
\begin{align}
\dot{x}_1(t)=&\,-ax_1(t)+b_{1}f(x_1(t-\tau_1)),  \\
\dot{x}_2(t)=&\,-ax_2(t)+b_{2}f(x_2(t-\tau_2)) \nonumber \\
&\, +b_{3}(f(x_1(t-\tau_2))-f(x_2(t-\tau_2))),\\
\dot{x}_3(t)=&\,-ax_3(t)+b_{2}f(x_3(t-\tau_2))\nonumber \\
&\, +b_{3}(f(x_1(t-\tau_2))-f(x_3(t-\tau_2))),
\end{align}
\label{nlin1}
\end{subequations}
where $f(x)$ is again of the same piece-wise linear form as in
Eq.~(\ref{eqoneb}). The parameters are now fixed as $a=1.0,b_1=b_2=1.2,
\tau_1=20$ and the coupling delay $\tau_2=25$, where the delays alone form the
parameter mismatch between the drive and response systems in Eqs.~(\ref{nlin1}). Following
Krasvoskii-Lyapunov theory, for  complete synchronization so that the manifold
$\Delta=x_3(t)-x_2(t)$ between the response $x_2(t)$ and the auxiliary
$x_3(t)$ approaches zero, one can obtain the stability
condition  as
\begin{eqnarray}
a>\left|(b_2-b_3)f^{\prime}(x_2(t-\tau_2))\right|.
\label{nlinasystab}
\end{eqnarray}
Consequently from the form of the piecewise linear function (\ref{eqoneb}),
the stability condition (\ref{nlinasystab}) becomes
$a>\left|1.5(b_2-b_3)\right|>\left|(b_2-b_3)\right|$. Thus one can take
\begin{eqnarray}
a>\left|b_2-b_3\right|
\label{nlin.ls}
\end{eqnarray}
 as less stringent condition for (\ref{eq.asystab}) to be valid, while
\begin{eqnarray}
a>\left|1.5b_2-1.5b_3\right|
\label{nlin.gc}
\end{eqnarray}
can be considered as the most general condition specified by
(\ref{nlinasystab}) for asymptotic stability of the synchronized state
$\Delta=x_2(t)-x_3(t)=0$. For the chosen values of the parameters, the less
stringent stability condition (\ref{nlin.ls}) is satisfied for the values of the
coupling strength $b_3\in(0.2,0.535)$ and the general stability condition
(\ref{nlin.gc}) is satisfied for $b_3>0.535$.

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig13}
\caption{\label{fig12} Dynamics in the phase space of the systems
(\ref{nlin1})). (a) and (b): Approximate GS and CS, respectively, for the value of the coupling
strength $b_3=0.37$. (c) and (d): Perfect GS and CS, respectively, for the value of the coupling
strength $b_3=0.8$.}
\end{figure}

As the coupling strength is increased from zero, approximate GS occurs from
$b_3>0.2$. Figure \ref{fig12}a shows the approximate GS (IGS) between the drive
$x_1(t)$ (Eq.~(\ref{nlin1}a)) and the response $x_2(t)$ (Eq.~(\ref{nlin1}b))
systems for the value of the coupling strength $b_3=0.37$, while  the
approximate CS between the response $x_2(t)$ (Eq.~(\ref{nlin1}b)) and the
auxiliary $x_3(t)$  (Eq.~(\ref{nlin1}c))  systems  is shown in
Fig.~(\ref{fig12}b). Perfect GS and perfect CS are shown in  Figs.~\ref{fig12}c
and \ref{fig12}d respectively for $b_3=0.8$. The intermittent dynamics exhibited
by the coupled systems at the transition regime is shown in Fig.~\ref{fig13},
which shows  bursts at the period approximately equal to the delay time of the
response system $x_2(t)$ for bursts of amplitude greater than $|0.01|$
(Fig.~\ref{fig13}b). The statistical distribution of the laminar phases away
from the intermittent bursts shows an asymptotic $-1.5$ power law behavior for
the threshold value $\Delta=|0.0001|$ (see Fig.~\ref{fig13}c), typical for
on-off intermittency, which is shown in Fig.~\ref{fig14}b. On the other hand for the
threshold value  $\Delta=|0.1|$ Fig.~\ref{fig14}a shows periodic structures
similar to Fig.~\ref{fig4}a with peaks occuring approximately at $t=nT,
n=1,2,...$, where $T\approx \tau_2$ is the period of the lowest periodic orbit
of the uncoupled system (\ref{nlin1}b).

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig14}
\caption{\label{fig13} The intermittent dynamics of the response $x_2(t)$
(\ref{nlin1}b) and  auxiliary $x_3(t)$ (\ref{nlin1}c) systems for the the value
of the coupling strength $b_3=0.37$ for nonlinear error feedback coupling. (a)
Time traces of the difference $x_2(t)-x_3(t)$ corresponding to
Fig.~\ref{fig12}b, (b) Enlarged in x scale to show bursts at periodic intervals
when bursts of larger amplitudes $\Delta>|0.01|$ are considered and (c) Enlarged in y scale to
show random bursts when bursts of smaller amplitudes $\Delta<|0.01|$ are considered.}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{nfig15}
\caption{\label{fig14} The statistical distribution of laminar phases
corresponding to  the
Fig.~\ref{fig13}. (a) For threshold value $\Delta=|0.1|$ and
(b) for the threshold value of $\Delta=|0.0001|$.}
\end{figure}

Now, the intermittency transition is again characterized using the probability
of synchronization and the \emph{sub}Lyapunov exponents as in the previous
cases. Fig.~\ref{fig15}a shows the probability of synchronization  $\Phi(b_3)$,
the value of which remains zero in the range $b_3 \in (0,0.2)$ due to the fact
that there lacks any entrainment between the response $x_2(t)$ and the auxiliary
$x_3(t)$ systems, whereas  it fluctuates between the two extreme values in a
rather broad range of the coupling strength  $b_3 \in (0.2,0.42)$, depicting the
existence of intermittency transition in the corresponding range of  $b_3$.
Perfect CS exists for $b_3>0.42$ as evidenced from the maximum value of
$\Phi(b_3)$.  Correspondingly there exists perfect GS between the drive $x_1(t)$
and the response $x_2(t)$ systems. Figure \ref{fig15}b shows the transition of
\emph{sub}Lyapunov exponents of the spectrum of Lyapunov exponents of the
coupled drive $x_1(t)$ (Eq.~(\ref{nlin1}a)) and the response $x_2(t)$
(Eq.~(\ref{nlin1}b)) systems. The \emph{sub}Lyapunov exponents become negative
in the range  $b_3 \in (0.2,0.42)$ confirming the broad range intermittency
(IGS) transition in a rather wide range of the coupling strength and this is
again due to the gradual stabilization of the unstable periodic orbits of the
response systems because of the less significant contribution of the coupling
strength $b_3$ as the error becomes gradually smaller from the transition regime
beyond certain threshold value of the coupling strength as discussed in Sec.~II.
The robustness of the intermittency transition with the system parameter $b_2$
and the coupling delay $\tau_2$ as a function of coupling strength $b_3$ is
shown as 3-dimensional plots in Figs.~\ref{fig16}.

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig16}
\caption{\label{fig15} (a) The probability of synchronization $\Phi(b_3)$
between the response $x_2(t)$ (\ref{nlin1}b) and the auxiliary  $x_3(t)$
(\ref{nlin1}c) systems and (b) Largest Lyapunov exponents of the coupled drive
$x_1(t)$ and response $x_2(t)$ systems (\ref{nlin1}a) and (\ref{nlin1}b).}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig17}
\caption{\label{fig16} The probability of synchronization $\Phi(b_3)$ in
3-dimensional plots (a) as a function of the system parameter $b_2$ and the
coupling strength $b_3$ and (b) as a function of the coupling delay $\tau_2$ and
the coupling strength $b_3$ for the case of nonlinear error feedback coupling
configuration given by Eq.~(\ref{nlin1}), showing broad range intermittency
transition.}
\end{figure}
\section{Narrow range intermittency transition to GS for nonlinear direct
feedback coupling of the form $f(x_1(t-\tau_2))$}

Now we consider the unidirectional nonlinear coupling of the form
\begin{subequations}
\begin{align}
\dot{x}_1(t)=&\,-ax_1(t)+b_{1}f(x_1(t-\tau_1)),  \\
\dot{x}_2(t)=&\,-ax_2(t)+b_{2}f(x_2(t-\tau_2))\nonumber \\
&\,+b_{3}f(x_1(t-\tau_2)),\\
\dot{x}_3(t)=&\,-ax_3(t)+b_{2}f(x_3(t-\tau_2))\nonumber \\
&\,+b_{3}f(x_1(t-\tau_2)).
\end{align}
\label{nlin2}
\end{subequations}

Choosing the values of the parameters  as in the previous case and
following Krasvoskii-Lyapunov functional approach for the asymptotically stable
synchronized state $\Delta=x_3(t)-x_2(t)=0$, one can obtain
the sufficient condition for asymptotic stability for complete synchronization
of the response $x_2(t)$ and the auxiliary $x_3(t)$ systems as
\begin{eqnarray}
a>\left|b_2f^{\prime}(x_2(t-\tau_2))\right|.
\label{nlin2asystab}
\end{eqnarray}

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig18}
\caption{\label{fig17} Dynamics in the phase space of the systems
(\ref{nlin2})). (a) and (b): Approximate GS and CS, respectively, for the value
of the coupling strength $b_3=0.78$. (c) and (d): Perfect GS and CS,
respectively, for the value of the coupling strength $b_3=0.9$.}
\end{figure}

The above stability condition rapidy leads to immediate transition to
synchronized state even for very feeble values of the coupling strength $b_3$
for the parameter values satisfying the stability condition
(\ref{nlin2asystab}) as the stability condition is independent of
$b_3$ as in the previous linear coupling case (Sec.~\ref{lin_narrow}). Hence
it is difficult to identify the possible dynamical transitions to synchronized
state as a function of the coupling strength $b_3$.  Hence we study the
synchronization transition as a function of the coupling strength $b_3$ by
choosing the parameters  violating the stability condition as $a=1.0,
b_1=1.2,b_2=1.1$ and $\tau_1=\tau_2=15$.

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig19}
\caption{\label{fig18} The intermittent dynamics of the response $x_2(t)$
(\ref{nlin2}b) and  auxiliary $x_3(t)$ (\ref{nlin2}c) systems for the the value
of the coupling strength $b_3=0.78$. (a) and (b) Time traces of the difference
$x_2(t)-x_3(t)$ corresponding to Fig.~\ref{fig17}b.}
\end{figure}

As $b_3$ is varied from zero for the above values of the parameters, transition
from desynchronized state to approximate GS occurs for $b_3>0.74$. The
approximate GS (IGS) between the drive  $x_1(t)$  and the response $x_2(t)$
variables described by Eqs.(\ref{nlin2}a) and (\ref{nlin2}b) is shown in
Fig.~\ref{fig17}a, whereas Fig.~\ref{fig17}b shows the approximate CS between
the response $x_2(t)$  and the auxiliary $x_3(t)$  variables
(Eqs.~(\ref{nlin2}a) and (\ref{nlin2}c)) for  the value of the coupling strength
$b_3=0.78$. Perfect GS and perfect CS are shown in Figs.~\ref{fig17}c and
~\ref{fig17}d respectively for $b_3=0.9$. Time traces of the difference
$x_2(t)-x_3(t)$ corresponding to approximate CS (Fig.~\ref{fig17}b) is shown in
Fig.~\ref{fig18}, which shows intermittent dynamics with the entrainment of the
dynamical variables in random time intervals of finite duration.
Fig.~\ref{fig18}b shows the enlarged picture of part of Fig.~\ref{fig18}a. The
statistical distribution of the laminar phases again shows a universal
asymptotic $-1.5$ power law behavior for the threshold value $\Delta=|0.0001|$,
typical for on-off intermittency, as shown in Fig.~\ref{fig19}.

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig20}
\caption{\label{fig19} The statistical distribution of laminar phase for the
Fig.~\ref{fig18}.}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig21}
\caption{\label{fig20} (a) The probability of synchronization $\Phi(b_3)$
between the response $x_2(t)$ (\ref{nlin2}b) and the auxiliary $x_3(t)$
(\ref{nlin2}c) systems and (b) Largest Lyapunov exponents of the coupled
drive $x_1(t)$ and response $x_2(t)$ systems (\ref{nlin2}a) and
(\ref{nlin2}b).}
\end{figure}

As in the previous cases, now we characterize the intermittency transition to GS
using  the notion of  probability of synchronization $\Phi(b_3)$ and  from the
changes in the sign of \emph{sub}Lyapunov exponents in the spectrum of Lyapunov
exponents of the coupled time-delay systems~(\ref{nlin2}). Fig.~\ref{fig20}a
shows the probability of synchronization $\Phi(b_3)$ as a function of the
coupling strength $b_3$ calculated from the response $x_2(t)$ and the auxiliary
$x_3(t)$ variables (Eqs.~(\ref{nlin2}b) and (\ref{nlin2}c)) for CS between
them.  In the range of $b_3\in(0,0.74)$, the probability of synchronization
remains approximately zero. Upon increasing the value of $b_3$, $\Phi(b_3)$
oscillates in the narrow range of  $b_3\in(0.74,0.78)$ depicting the existence
of intermittency transition. This  narrow range transition is also confirmed
from the transition of successive largest \emph{sub}Lyapunov exponents. The
spectrum of the first nine largest Lyapunov exponents $\lambda_{max}$ of the
coupled  drive $x_1(t)$  and response $x_2(t)$ variables (Eqs. (\ref{nlin2}a)
and  (\ref{nlin2}b)) is shown in Fig.~\ref{fig20}b. It is also evident from the
spectrum that the \emph{sub}Lyapunov exponents suddenly become negative in the
narrow range of $b_3\in(0.74,0.78)$, and then reach saturation values for
$b_3>0.78$. This confirms the narrow range intermittency (IGS) transition to GS.
This is also in accordance with the immediate stabilization of all the UPO's of
the response system as discussed in Sec.~(\ref{lin_narrow}).

The robustness of the transition with the system parameter $b_2$ and the delay
time $\tau_2$ as a function of coupling strength  $b_3$ is shown as
3-dimensional plots in Fig.~\ref{fig21}.

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{fig22}
\caption{\label{fig21} The probability of synchronization $\Phi(b_3)$ in
3-dimensional plots (a) as a function of the system parameter $b_2$ and the
coupling strength $b_3$ and (b) as a function of the coupling delay $\tau_2$
and the coupling strength $b_3$ for the case of nonlinear direct feedback
coupling configuration given by Eq.~(\ref{nlin2}) showing narrow range intermittency transition to GS.}
\end{figure}

\section{Conclusion}

In conclusion, we have studied intermittency transition to generalized
synchronization from desynchronized state in unidirectionally coupled scalar
piecewise linear time-delay systems for different coupling configurations using
the auxiliary  system approach. We have shown that the intermittency transition
to GS occurs in a  broad range of coupling strength  for both linear and
nonlinear error feedback coupling configurations whereas it occurs in a narrow
range of coupling strength for both the linear and nonlinear  direct feedback
coupling configuration. It has also been shown that the intermittent dynamics
displays periodic intermittent bursts of period equal to the delay time of the
response systems in the former cases and it takes place in  random time
intervals in the latter cases. The robustness of the intermittent dynamics with
the system parameters and the delay time  is also studied as a function of the
coupling strength for both  error feedback and direct feedback (linear and
nonlinear) coupling configurations. Universality of these intermittent behaviors
\cite{dvskml2006} (periodic and random) and their (broad and narrow range)
transitions are also confirmed for different forms of linear and nonlinear
coupling configurations in other time-delay systems such  as Mackey-Glass and
Ikeda systems. These distinct characteristic behaviors are analyzed using the
analytical stability condition for synchronized state, probability of
synchronization $\Phi(b_3)$ between the response and the auxiliary systems, and
by the changes in the sign of \emph{sub}Lyapunov exponents in the spectrum of
Lyapunov exponents of the drive and the response systems in both the linear and
nonlinearly coupled time-delay systems.  In spite of the fact that both the
probability of synchronization and the \emph{sub}Lyapunov exponents have been
calculated from different systems, we have found good agreement between them in
showing intermittency transition in all the cases. We hope this study will
contribute to the basic understanding of the nature of transition to  GS in
coupled time-delay systems and we are now investigating the experimental
verification of these findings in nonlinear electronic circuits.

\begin{acknowledgments}
The work of D. V. S and M. L has been supported by a Department of Science and
Technology, Government of India sponsored research project. The work of M. L is
supported by a DAE-BRNS Raja Ramanna Fellowship award, India.
\end{acknowledgments}

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