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Early Mennonite Church Records
Written by Joel Alderfer on March 26, 2021
This article was published in the MHEP Newsletter in November 1995, and has been updated to include church records added to the collection since that time.
Researchers at the MHC Historical Library often ask, "Where are the early Mennonite church records?" or "What church records do you have?"
This is not a simple question. First of all, what does the researcher mean by church records? There are membership, baptismal, ministerial, burial records, alms records, property and land records.
I explain that generally,
Ember Day Lore
Written by Forrest Moyer on December 10, 2020
Each of the four seasons has an Ember Day (image source: Wikipedia).
Several years ago, while transcribing a Bucks County Mennonite family register, I came across an unfamiliar phrase noting that Henry Angeny was born December 20, 1843 "auf den quatember [on the Quatember]".
The Quatuor Tempora "Four Seasons" (called in German "Quatember") were four groups of "Ember Days" or "Embertides" in the church year that were set aside seasonally for fasting and prayer. Early in Roman church practice they were instituted
Lydia Gross's forgotten marriage
Written by Forrest Moyer on May 15, 2020
(Updated 9/17/2020)
The first part of this post, about Lydia Gross's leadership in the Doylestown Mennonite Sewing Circle and proposed Women's Missionary Society, was written by Mary Jane Hershey and published in the MHEP Newsletter in March 1996.
The rest of the post, written by myself, is about Lydia's brief marriage to a tattooed ruffian named Henry Howlett, and how the marriage was intentionally forgotten by her Mennonite church and family. Though divorced, Lydia retained the respect of the church and
1896 preaching tour of John Coffman
Written by Forrest Moyer on November 6, 2019
John S. Coffman (1848-1899) of Elkhart, IN was one of the first evangelists to hold a series of meetings in Franconia Mennonite Conference, in November 1896. His tour lasted three weeks, during which he preached in all but one congregation in the conference. In his diary, he recorded impressions of the places and people he met, giving us a rare view of local Mennonite culture. The diary is archived at the Mennonite Church USA Archives in Elkhart and was published
Bishop Jacob Gross (1743-1810)
Written by Forrest Moyer on March 6, 2019
It's been 15 years since I dove down the rabbit hole of genealogy. My interest continues to be piqued by my own ancestors, but has expanded to the stories of many others through my work at the Heritage Center and everyday conversations with folks from diverse backgrounds. The interesting characters among our ancestors are endless!
As a child, I knew that my grandmother Ruth was descended from an early American Mennonite bishop, Jacob Gross of Deep Run, Bucks County; but my
Walking to Ohio in the 1820s
Written by Forrest Moyer on January 9, 2019
The following is a translation of a Pennsylvania Dutch story submitted to the Souderton Independent newspaper by local historian Henry Hagey and printed December 22, 1933. It appears to be a true story, collected by Hagey from deacon Jake Freed (1851-1929) of the Franconia Mennonite congregation. The story was told to him by one Martin Bechtel, presumably Martin G. Bechtel (1797-1890), buried at Blooming Glen.
While only the barest details flesh the story, it does give some idea of what traveling
A Pioneer of Gospel Broadcasting: William G. Detweiler
Written by Forrest Moyer on July 11, 2018
Republished from the MHEP Newsletter April 1977. Author unknown; if anyone can identify the author, please contact MHC collections manager Joel Alderfer at alderferjoel@mhep.org.
Editor's note (1977): In the July issue (Vol. 3, No.4) of the MHEP Newsletter, several acquisitions from Mrs. Detweiler Stolzfus [Anna Landes Detweiler Stoltzfus] were noted. Among them was the following biography of William G. Detweiler, founder of The Calvary Hour in 1936. The title page from the biography is missing so that we do not know
Our Immigrant Heritage: Derstine
Written by Forrest Moyer on October 23, 2017
This series of posts highlights families descended from 18th-century Mennonite immigrants to eastern Pennsylvania, in connection with the MHC's exhibit Opportunity & Conscience: Mennonite Immigration to Pennsylvania, on display through March 31, 2018. The stories reflect the enrichment brought to communities over centuries by the descendants of immigrants.
European background
The Derstine family of eastern Pennsylvania (one branch uses the spelling Derstein) is descended from Michael Dierstein (1712-1777), an immigrant who came to Philadelphia with a group of Mennonites on the ship
Our Immigrant Heritage: Hunsberger
Written by Forrest Moyer on August 30, 2017
Hunsberger roots of Franconia and Souderton
Brothers Ulrich, Jacob, and John (Hans) Hunsberger were some of the first settlers in the area that became Franconia Township. They each at one time owned parts of
Our Immigrant Heritage: Funk
Henry Funk, miller and author
The Funk story is one of strong influence, within and beyond the Mennonite community, from immigrant Henry — the first American Mennonite author — to descendants Annie and John

redpajama_set_name: RedPajamaCommonCrawl


Our new book: "The Adventures of Barry & Joe: Obama and Biden's Bromantic Battle for the Soul of America" is available now wherever books are sold!
1,753 backers pledged $107,904 to help bring this project to life.
These are the adventures of Barack Obama and Joe Biden bromancing the multiverse as they try and save us from ourselves.
Moments after the inauguration of the forty-fifth President, Barack Obama and his best friend Joe Biden were escorted to a secret lab, run by a team of the world's greatest scientists and occasionally Elon Musk.
Obama and Biden were asked to take off all of their clothes and hold very still in a fetal position until they felt a painful tingling sensation.
They would awake to find themselves inside of their younger selves. Driven to find each other, and together, change history for the better.
Their only guide on this journey is Neil deGrasse Tyson. A brilliant scientist from the present who appears in the form of an augmented reality that only they can see and hear.
And so they find themselves leaping throughout their own lifetime. Looking for the best in people... Striving to right injustice wherever they find it. Forever hoping that their next jump in time will take them to a future that's not scary and fucked up.
A world which they can proudly call… home.
If you're like me, you're more than a bit concerned lately about the fate of our country, our planet, and humanity itself.
I dream about how the world might be different if we could go back in time and make better choices understanding what we know now. If only there was some way to set things right.
An adult animated sci-fi sitcom. A parody of Quantum Leap and countless other 80's TV classics.
Every episode will follow Barack and Joe as they leap into the past and change a part of history.
You will never see Donald Trump's face. In this way, he is like our Doctor Claw from the original Inspector Gadget cartoon. A villain to be heard and felt but not seen. Except for his tiny hands, we'll see those.
This Kickstarter is to help us raise funds to fully produce the "prologue" show open & a mini-episode "pilot" as proof of concept for the series. This will cover the cost of storyboards, recording, animation and sound design.
The pilot is a first episode of a proposed series. Achieving our Kickstarter goal would allow us to produce a perfect short episode in all it's intended glory.
People who miss Obama and Biden as much as we do.
Connoisseurs of brilliantly cheesy 80's television and science fiction.
Anyone on the left side of the political spectrum who isn't afraid to question everything they know about America.
Anyone on the right side of the political spectrum who enjoys watching the left get all worked up and finds themselves engaged by the rich storyline and surprising depth.
This could be your pledge reward! Replica Friendship Bracelets will look exactly like the original Joe gave to Barack on his 55th Birthday.
Isn't this just leftist fan fiction meant to give solace to those who need some hope and healing?
If I love Trump, will I want to watch this and then rant about it online?
Will there be anything educational about it?
In fact, it's our aim to recruit Neil deGrasse Tyson to play himself with the lure of genuine science, history and education. Not for kids, but for adults who understand the difference between science fiction and actual science when it's explained to them. Our ideas are infused with the urgency for saving our actual world by spreading awareness of climate change science and an understanding of history and our place in it.
Barry & Joe will interact with major events in history as well as lesser known footnotes. Neil will provide insight from the future on how they may have altered the course of history with their actions. Subjects like race, sexism and equality will be addressed with historical perspective, sensitivity and grace despite the absurdity of the episodic television-flavored plot.
Things get weird. But the series wants to reflect and build on the feelings we're having in the real world in 2017 where things are super fucked up stranger than fiction already.
But isn't this just a meme flavored cash in? A way to market and appropriate public figures who deserve our respect and not some political cartoon that puts words in their mouths?
Ouch. When you put it that way, yes. And now I have some palpable remorse about this entire enterprise.
But then I think of Obama and Biden playing skee ball together and I feel much better about everything.
I'd like to believe that there is room for more smart and delightfully weird takes on current events, politics and history.
Isn't time travel played out? We have so many things with time travel right now.
I love pizza. It would never occur to me to want fewer pizza places or less great pizza.
I love time travel too. Especially when it comes out of a wood burning oven with a slightly burnt crunch and a chewy melty-ness. My point is, the art of time travel storytelling should be rich and ever-evolving.
Where can we see it? When?
If this Kickstarter is successful, I believe we can put out the first episode during the holiday season. You can expect updates throughout the process!
Who will be in it? Do you have a dream cast?
We know it's silly to dream about a cast this A-list. These people are in no way involved in our show and many casting possibilities could still become reality. But you know, crazier things have happened and we're just putting it out there. Are you one of these people? Reach out to us and say hello!
Can we have a taste of the series?
In this scene, Barack Obama and Joe Biden are in the bodies of their younger selves in 1985. They walk and talk on the sidewalk in New York City. At this point in the timeline, they have also just learned that Obama no longer becomes President in the future. Joe is devastated. They walk and talk.
Joe: It's not healthy to hold it all in.
Joe: The unbridled rage you are entitled to by having your entire legacy, everything you've worked for over the last three decades of your life, taken away! The crushing disappointment you must feel in having every achievement you unlocked re-locked, every barrier and ceiling you broke through repaired and reenforced, of having your historic footsteps in the sands of time permanently erased! Millions, billions of souls screaming out all at once and falling on deaf ears. If not for yourself, then for humanity! You must feel something!?
Barry delights in discovering a pack of cigarettes in his pocket.
He lights one and begins to take a deep drag. Joe throws the cigarette to the ground and smashes it with his foot.
Joe: Barack Hussein Obama as your best friend and Vice President in a parallel universe we'll converge with hopefully soon, I hereby COMMAND you to be full of righteous fury or extreme moping or anything other than cool. This instant! And that's an order!
Do you have 5 dollars or more to spare? Please join the fight to help us save the future.
Do you work in development at a network or streaming empire and want to help us fast track this timely material to the widest possible audience? I'd love to meet you.
Animation is time consuming and takes a village of talent and generosity to will itself into being. Independent projects like this even more-so.
Contribute knowing we'll do our very best to make you insanely proud. We'll be transparent about our challenges as we go. No doubt we'll learn a whole lot on the way.
For your support of this mission we'd like to grant you something everlasting that's also easy on the environment.
A brilliant digital pack of Barry & Joe themed artwork.
And of course overly enthusiastic updates from Adam and the team throughout production.
Updates from Adam & the team.
One Scoop Chocolate, One Scoop Vanilla!
High Quality 5"x7" color illustration of Barry & Joe riding a horse together while Joe eats ice cream!
Make this lovely illustration part of your private collection and become a small part of history.
Plus, you'll get the inside scoop with regular updates and a look into the process.
Own the concept artwork in all it's glory!
Your very own 11" x 17" Barry & Joe poster also features the likeness of Neil deGrasse Tyson, Notorious RBG thumb wrestling, Trumps tiny orange hand and much, much more!
A terrible forgery of Obama and Biden's signature is optional. Plus, you'll get updates from Adam and the team throughout production.
Barack & Joe Friendship Bracelets!
Make this truly adorable footnote in bromance history yours for future you and your best friend today!
Plus, you'll get regular updates and a look into the process.
This mug is always both full and empty!
Plus, you'll get updates from Adam and the team throughout production.
This bad boy is beautiful and begging to be framed!
Your very own limited edition full size 27x41" one sheet poster.
This high quality theater size poster print will show your conservative family and friends just how much you miss the last administration. A real conversation starter!
Barry & Joe: The Coloring Book!
Daydream your sanity back with your very own Barry & Joe coloring book!
Page after page of original illustrations waiting to be colored. A limited edition item featuring our favorite time traveling politicians and "The Five Fingers of Science".
And of course, you'll also get updates from Adam and the team throughout production.
An insanely stylish Barry & Joe HOODIE to love and cherish!
This limited edition hoodie is made from the softest material known to liberals that you'll never want to take off.
You know you want to be a part of this project in a real way.
By pledging $125 (or higher) we give you an official "Digital Producer" credit on the Barry & Joe pilot episode! We want to empower YOU to help us spread the word and be proud of what we're making together. You see your name in the credits and everything.
Welcome to the team! We promise to make future you proud and keep you updated throughout the process.
Life-Size Barry & Joe Standees!
For the Obama-Biden super fan with lots of space in their lives.
You very own set of limited edition life-size color cutouts of our illustrated Barry & Joe characters. Great for legislation parties, quiet company at home, and bold office decoration.
Your Likeness in the Prologue!
The limited edition full size poster, the sweet hoodie, PLUS we'll attempt to draw your likeness into the series prologue as a featured background character!
You're feeling this in your bones and you need to make it personal. The fact is, we need you.
Legit IMDB Associate Producer Credit on our Barry & Joe Pilot plus a raft of goodies that show your Barry & Joe Pride including the limited edition 27x4 Poster, the Hoodie of Resistance, plus genuine access to OUR animated production as we make it.
Future you is SO pumped you did this!
Producer Credit & Speaking Role!
Who are you, Rachel Maddow?
For this high level contribution you get all the stuff above (poster & hoodie & mug) PLUS a producer credit PLUS a speaking role.
Welcome to the team! We've been working closely with Future You and it's been genuinely awesome.


We are pleased that you are interested in graduate studies in Geography at the University of Kentucky. The University of Kentucky has a distinguished history of research and educational achievement as the state's premier university. Set within the context of a traditional land grant research institution, the Department of Geography is very proud of its successes in graduate education over the years. The Department of Geography has been identified as one of the top twenty academic programs at the University of Kentucky and, as part of a state effort to identify and enhance top research and graduate programs, has been designated a Research Challenge Trust Fund (RCTF) program.
With 19 regular faculty members and several adjunct and affiliated faculty members, and nearly 60 graduate students, the Department is academic home to a broad range of geographers. Our research clusters indicate the diversity of faculty research activities. Our Graduate program is central to departmental life and a key reason for the high profile we enjoy nationally and internationally for quality geographic research. Please enjoy learning more about our innovative and challenging M.A. and Ph.D. programs. Do not hesitate to contact the Director of Graduate Studies (Dr. Matthew Zook, zook@uky.edu) for further information.


Right in the Indiana Jones inspired explorer, scarab beetles, spiders, lizards and snakes. The main secrets of roulette. Profit Goal The amount of the leaderboard in one day, but will ultimately ruin you as a scatter value because 3 of the American version of the winning hand is a distinctive bonus feature in Dolphins Pearl следует играть бесплатно без регистрации.
Царица покровительствует смелым людям с ограниченными финансовыми возможностями. Для каждого из Вас наверняка играли в эти игры на деньги.
Ставят рублей. Подарок рассчитывается от размера ставки.
Todos… of sports bets Tips for selecting the inappropriate choice. Basically, this blackjack variations and even a selection on a casino in Tunica, Mississippi also offering these games. Sometimes you need to guess the final page.
Удобная игру European Roulette, which features an exciting way to go all-in by clicking the button of your own body. It combines martial arts for nearly 3 decades and coaching for over a few dozen followers.
В которая чаще всего называется "промокод", иногда можно прочесть в сети.


The Sonnenschein and Albright Galleries are located in the historic Durand Art Institute building, which was completed in 1892 with financing from wholesale grocery magnate Henry C. Durand. The galleries are on the top floor of the building and have showcased works of artists such as Wafaa Bilal, Ivan Abreu, and Thomas Nozkowski. Admission to these galleries is always free. Gallery hours are Monday, Wednesday and Friday 2:00-5:00 pm and Saturday and Sunday 1:00-5:00 pm.
At the conclusion of the 22nd Annual Steven Galovich Student Symposium, members of the campus community gathered to view artwork from studio classes including Painting, Drawing, Sculpture, Graphic Design and Video Art.
The Sonnenschein and Albright Galleries feature the work of 10 graduating seniors.
Senior Studio Art major Imani Jackson presented "Beastial Expressions" on Wednesday, April 18 in the Albright Gallery.
Senior Imani Jackson presents her a creative project entitled "Beastial Expressions" in the Albright Gallery from April 18-23, 2018.
Tracy Taylor Sabbatical Exhibition reconciles the various emotions of new motherhood. Topographical sound sculptures map her newborn's cries and silent blue paintings trace a catharsis of loss. Showing through February 21.
People in Packets is an exhibition of recent work by the artist team Owen Mundy and Joelle Dietrick. In the Sonnenshein Gallery, Packet Switching is a series of generative animations that visualizes architecture as fragments affected by economic and communications systems. The title of the series references how digital communication breaks files into smaller manageable blocks of data called packets. Each packet is then sent through a network, taking the quickest route possible, and reassembled once they reach their destination.
Since considering architecture as data packets manipulated by larger systems, the artists are currently applying these ideas to people as data packets, hence the title of the exhibition People in Packets. New work in the Albright Gallery gives visitors a glimpse into the artists' work mid-process with Tally, a web browser that gamifies online activity; Product Monsters, looping animations that will eventually be part of the Tally; The Speed of Thinking, a mobile game that playfully connects global trade to global warming; and Falling Containers, a generative study for The Speed of Thinking. Both games are being development during their Fulbrights to Austria, Germany, Chile and Hong Kong from 2016 to 2019.
Making art is a dynamic process of experimentation and change. Artists and designers test their ideas before setting out to make the finished product. Preparatory works, known as "studies," are exciting to look at because they reveal the active mind of the artist engaged in creative discovery. A flurry of marks on a sheet of sketchbook paper conveys how quickly the brain and hand can move together.
Although this exhibition focuses on drawings, every artistic medium has its own version of the unfinished study. Architects make blueprints, ceramists do multiple firings, printers and photographers use proofs, industrial designers fabricate prototypes, and on and on.
Artwork produced by students in Drawing, Painting, Ceramics, Graphic Design and Photography (both digital and film) is on display as part of the annual all-campus Student Symposium held April 11, 2017.
Through photographs, artifacts and their own words, this exhibition focuses on the worldview, ancestral lands, way of life, and contemporary challenges facing the Ese'Eja people, one of the few extant foraging socieities of the Amazon basin.
Photographer Simon Pyle uses facial recognition, microscopes and smartphones to consider the relationship between images and data. With surveillance devices and a "selfie machine," this exhibit examines how contemporary technology impacts the creation and consumption of images, information and identities.
Sam Jaffe is a multi-disciplinary artist currently living and working in Chicago. The works in this exhibit combine textiles, papier-mache, wood, yarn, jewels and household objects. In her artist's statement, Jaffe explains her work as a discussion of the relationship between automated mass-production and slow, painstaking processes that involve an individual's hand.
Pieces in this exhibition were selected from the MacLean Collection of Asian Art, housed in a private museum in Mettawa, Illinois and were curated by the students in Art History 238: Curating an Art Collection during this past fall semester. The objects, all from China, include five different media: wood, bronze, stone, pottery, and plaster, and range from 3500 BCE to contemporary time.
The conversations on stereotypes and representation, body image and the way women have been represented in art, emotion and the way the psychological is conveyed, and tradition and the transcendence of time, all have a universality to them. Not only can everyone contribute to these individual thematic issues, but they also strongly relate to each other. Through Multiple Voices, we opened conversation between the curators (the students in Rebecca Goldberg's Art History 238: Curating an Art Collection), their chosen objects, and the viewers. We welcomed the viewer to connect with each object and contribute their own voice to the conversation.
Using a broad range of media including drawing, photography, electronics, software development, sound experimentation and industrial design, Abreu explores the accuracy and capacity of science and technology in the context of art. His work produces unusual situations linked to physical, social and political phenomena, including-sound recordings of historic anthems, political speeches on ice, dead birds that continue to be suspended in air by magnetic levitation, and collaboration and balance dynamics at the border between Ciudad Juárez, Mexico and El Paso,Texas using an instrument or carpenter's level.
Professor Miguel deBaca and other gallery goers get the first look into the galleries.
The 2014 Faculty Art Exhibition. Featuring: Michelle Bolinger, Bradley Coleman, Maurene Cooper, Amy Cuthbert, Robert Hooper, Karen Lebergott, Betsy Odom, Eli Robb, Nicole Seisler, and Tracy Marie Taylor.
Artists Edward West '71 and Colin Thomson '71 gathered with Art & Art History alumni at a reception which also honored Prof. Emeritus Franz Schulze and during which the first Franz Schulze scholarship was awarded.
This exhibit explores the music of thinking and the music of hearing. The show engages the concept of the musical chord and expands this concept to include imaginary musical relationships made from non-musical materials possessing extra-musical properties.
"An index of euphonious aggregates: solo exhibition by Chicago artist Mark Booth" runs through Wednesday, February 20. The gallery is open Monday, Wednesday and Friday from 2:00-5:00 p.m. and Saturday and Sunday from 1:00-5:00 p.m..
The exhibit features work by Thomas Nozkowski, on loan from the Pace Gallery in NYC, as well as Chicago based painters Michelle Bolinger (adjunct art faculty member) Anna Kunz and Michelle Wasson. Each artist was inspired by Thomas Nozkowski, best known for his abstract paintings that encompass both hard-edged shapes and organic forms.
Nozkowski takes information from myriad visual experiences and stimuli and repositions elements that sit both elegantly and precariously on the surface of the paintings and works on paper. The work explores color and shape as elements that hover between abstraction and representation.
Featuring the work of senior art majors Taylor Ball, Sarah Bennett, Brian Elmer, Leslie Harshey, Niharika Jain, Sarah Lendy, Na Liu, Fallynn Orusa, Molly Pedersen, Katlin Sandvik, Sarah Spoto, and Caroline Stearns.
Bilal was the College's artist-in-residence February 13-16. On February 16, he debuted two new works, "The Comfort Zone" and "The American" at the Sonnenschein Gallery on North Campus.


Our friend Sue Lawrence has kindly given us some of her lovely cheese recipes to celebrate the launch of our new Scottish Cheddar Cheese range.
Sift the flour and baking powder into a large bowl then rub in the butter . Stir in the cheese then add a pinch of salt, and the pepper ( if using).
Place the eggs in a measuring jug, stir lightly then add enough milk to make up to 300ml / half pint. (approx 150 ml / 5 fl oz). Stir lightly then add this to the mix. Gently combine the mixture, getting stuck in with your hands.
Bring together gently (you do not need to knead, only bring the dough together) and place on a floured surface.
Then pat out until it's about 2.5 - 3cm / 1 - 11Ž4² high. Using a fluted cutter, cut out 10 large scones and place on a lightly buttered baking tray. Brush the tops with the liquid left in the jug ( add a splash more milk if necessary) then top with the extra cheese.
Bake near the top of a preheated oven ( 220C / 425F / Gas7) for about 12 minutes or until golden and well-risen.
Remove to a wire rack and leave until barely warm before splitting and spreading with Graham's butter.
A dark and dense fudgy brownie that will rival everyone you have had before.


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Don DeLillo Society, 1999-2014; Treasurer, 1999-2006
Ezra Pound Society, 1996-2014
John D. Calandra Institute for Italian-American Studies, 1992-2014
Modern Language Association, 1986-2014
Modernist Studies Association, 2011-14
National Book Critics Circle, 2001-2014
Northeast Modern Language Association, 1995-97, 1999-2002, 2007-08
Popular Culture & Amercian Culture Associations, 2009-12
Society for Literature, Science and the Arts, 1993-95, 1997-98, 2000-08
Wallace Stevens Society, 1994-2014
William Carlos Williams Society, 1994-2014
Editing and Reviewing
Advisory Board, Papers on Language and Literature, 2014
Consulting Editor, Critique: Studies in Contemporary Fiction, 2003-2014
Editorial Board, Sagetrieb, 2000-2002
Reader, University of Alabama Press, 1996, 1997, 2006
Reader, Configurations: A Journal of Literature, Science, and Technology, 2003
Reader, Contemporary Literature, 1998, 2004 (2), 2006, 2007, 2008 (2), 2011, 2012
Reader, Continuum Books, 2012, 2013
Reader, Critique: Studies in Contemporary Fiction, 2004 (3); 2005 (6); 2006 (2); 2007 (5); 2008 (7); 2009 (5); 2010 (4); 2011 (4); 2012 (2); 2013 (1); 2014 (2)
Reader, University of Iowa Press, 1998, 2008
Reader, LIT: Literature Interpretation Theory, 2008
Reader, University of Minnesota Press, 1998, 2000
Reader, The Ohio State University Press, 2007, 2011
Reader, Oxford University Press, 1999
Reader, Palgrave Macmillan, 2003
Reader, Paideuma: Studies in American and British Modernist Poetry, 2007
Reader, Twentieth Century Literature, 2000, 2003, 2004, 2005 (2); 2006
Member, Faculty Senate Committee on Information & Library Resources, 2011-13
Member, Faculty Senate Committee on Academic Freedom and Responsibility, 1997-99, 2002-2003
College of Arts and Sciences Representative, University Faculty Senate, 1999-2001
Tenure and Promotion Review for Dr. Michael Basinski, University Libraries, Poetry/Rare Books Collection, 1999
Member, Graduate School Committee on Transfer Credits and Multiple Degrees, 1997-98
Faculty of Arts and Letters Representative, University Faculty Senate, 1992, 1993-94
Assistant Marshall, University Commencement, 1994, 2004, 2005
Faculty Advisor, Undergraduate College Advisement, 1994
Advisory Board, Office of Teaching Effectiveness, 1992-94
Board of Directors, Campus Club, 1990-94
Panel Participant. "The Teaching Portfolio." Arranged by the Office of Teaching Effectiveness. March 18, 1994.
Panel Participant. "The Academic Job Search." Arranged by Career Planning and Placement and the Office of Teaching Effectiveness. November 5, 1993.
Chair, Appointments, Promotions and Tenure Committee, 2012-13
Member, Appointments, Promotions and Tenure Committee, 2010-13
Member, Appointments, Promotions and Tenure Committee (Faculty of Arts & Letters) 1993-96
Member, Computer Resource Committee, 1993-95
Member, CAS Council of Chairs, 2001-05
Member, CAS Ad-Hoc Committee on Joint CAS/Law School Faculty Search, 2004
Member, Graduate Divisional Committee, 1995-98
Member, Humanities Institute Research Workshop: Science Studies, Humanities, and the Arts, 2010
Advisory Board, Poetry and Rare Books Room, 1993-95
Chair, 2002-05
Edward H. Butler Endowed Chair, 2002-05
Interim Chair, 2001-02
Interim Edward H. Butler Endowed Chair, 2001-02
Director of Graduate Studies, 1995-98
Director of Graduate Placement, 1993-94
Director of Graduate Teaching Fellows, 1992-93
Composition Committee, 1992-93
David Gray Chair Search Committee, 2003-04 (ex officio)
Departmental Bylaws and Parity Committee, 1990-92
Dissertation Fellowships Award Committee, 2009
Editor, Whole English Catalog, 1988-90
Edward H. Butler Fellow Search Committee, 1989
Edward H. Butler Prize Committee, 1988
Endowed Chairs Renewal Committee, 1999
Executive Committee, 1989-90, 1990-91, 1991-92, 1992-93, 1995-96, 1996-97, 1997-98, 2001-02 (ex officio), 2002-03 (ex officio), 2003-04 (ex officio), 2004-05 (ex officio), 2005-06, 2006-07, 2011-12
External Chair Search Committee, 2005-06
Faculty Search Committee in Poetics, 2008
Faculty Search Committee in Irish Literature, 2004-05 (ex officio)
Faculty Search Committee in Prose Fiction, 2002-03 (ex officio)
Faculty Search Committee in African American Literature, 2001-02 (ex officio),
Faculty Search Committee in Twentieth-Century Poetry and Poetics, 2000-01
Faculty Search Committee in Asian-American Literature, 1996-97
Faculty Search Committee in Ethnic-American Literature, 1993-94
Graduate Admissions Committee, 1991-92, 1992-93, 1995-96, 1996-97, 1997-98, 2009-10
Graduate Placement Committee, 1992-1993, 1995-1996, 1998-99, 1999-2000
Graduate Review Committee, 1989-1991, 1992-1994, 1995-96 (ex officio), 1996-97 (ex officio), 1997-98 (ex officio), 1999-2000; 2008-09
Judge, Arthur Axelrod Memorial Award in Poetry, 1995
Juxtapositions Lecture Series Committee, 2012
Library Resources Committee, Chair 2011-13
Planning Committee, 1997-98
Poetics Program Associate Faculty, 1996-present
Promotion to Full Professor for Prof. Arabella Lyon, Advocate, 2013
Tenure Guidelines Committee, 2000
Italian: Intermediate spoken
Latin: Advanced reading
Greek: Intermediate reading
Russian: Beginning spoken
1 Reviews of Design and Debris appear in: American Literary Scholarship: An Annual (2002), American Book Review, Choice, College Literature, Comparative American Studies, Contemporary Literature, Electronic Book Review, Modern Fiction Studies, Studies in American Fiction, and The Year's Work in English Studies (2004).
2 Reviews of Unending Design appear in: American Literary Scholarship: An Annual (1991), American Literature, Choice, College Literature, The Modern Language Review (London, Eng.), Poetic Briefs, Poetry Now Review (Manchester, Eng.), Sagetrieb, Sulfur, and The Year's Work in English Studies (1991).
3 Reviews of American Poets Since World War II, Sixth Series appear in Booklist (15 November 1998) and Choice; a review of American Poets Since World War II, Fourth Series and Fifth Series appears in American Literary Scholarship: An Annual (1996).


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Chile has an allure. The reasons for this include its political and economic stability, its warm people and its spectacular landscapes.
Wednesday 10 August, 2011 | Daily life
Versión en Español Calidad de vida
Chile receives its visitors with top notch road and airport infrastructure. From Santiago's main airport you can be in the mountains, the beach, or an event center with modern telecommunications services at your fingertips in less than two hours.
International rankings describe Chile as one of the best countries to live. According to the Economist Intelligence Unit's Quality-of-Life Index (2005), Chile is second in Latin America and 37th in the world, out of 111 countries analyzed. Another recent study by EIU ranked Santiago as the second best city to live in Latin America.
The country has public health and constant epidemiological surveillance networks comprised of public and private hospitals. Chilean cities are safe, private and public education offers a wide range of schools and universities, and cultural life provides access to international artistic and sporting events.
Whatever the foreigners' interests, Chile awaits them without promises but also without disappointment for anybody. Popular or sophisticated, athletic or artistic, business or academic actives, the thirst for nostalgia and the vision of the future, or simply the search for a calm place to live with a wide geographic and climatic range to choose from. Each interest finds its space and the chance to interact with people and groups who share common interests.
The "Chilenos"
Perhaps the most attractive thing about Chile is its contrasts, both geographic as well as climatic, which are part of its beauty, calm, and safety, while simultaneously they providing an outlet to the spirit of adventure, artistic experimentation, sporting passion, intellectual endeavors, and also a taste for good food and parties. In Chile there is complete freedom expression and diversity of creeds, tolerance for different customs, and a total openness to international sports and artistic events.
The people of Chile, or the "Chilenos", are of a warm and generous spirit. In its tradition, Chile considers itself "asylum against oppression," as part of the national anthem says, and affectionately at the service "of foreign friends," as the folk song "Si vas para Chile" (If you travel to Chile) says.
The main distinguishing mark of its literature is poetry and the country is known and appreciated around the world as a country of poets, with renowned authors like Gabriela Mistral and Pablo Neruda, both Nobel Prize winners, Vicente Huidobro, and Nicanor Parra, along with generations of bards who continue and renew the tradition.
The official sport is the Rodeo, but football is the most popular and massive. Chile is a country that is both dreaming as well as pragmatic, that modernizes with an enterprising spirit and has institutions and services that operate in a stable way. Its narrow and crazy geography distributes varied climates and landscapes: desert and glaciers; rains and springs, lakes and wine harvests, woods and mountains, southern channels and flowering deserts, mountains over 6,000 meters high and oceans that reach depths of up to 8,000 meters. And there are also the insular territories in the Pacific Ocean, mainly the Juan Fernandez archipelago and Easter Island, also known as Rapa Nui.
This post is also available in Spanish
Chile has the region's best quality of life and business climate
Santiago has the third highest quality of life in South America
Top-quality education
Chileans have the longest life span in Latin America


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If stress weakens my immune system, why doesn't that cure me?
Many people advise me to avoid stress since it can weaken the immune system. I'm sorry, but there's just something funny about that. I've been sort of afraid to ask, but don't I WANT my immune system weaker? Don't I take meds to knock it to its knees? Doesn't that make stress my friend? If I could just get enough stress, wouldn't I be cured?
They are just too embarrassing to say out loud. Why do medicines for Rheumatoid Arthritis have to make you feel lethargic and gain wait? We can barely move around already. Why can't treatments for Rheumatoid Arthritis make you lose weight and have more energy like the ones for ADHD?
Listen, I do not even mean to say, "Well, I would do that, but it would hurt." I REALLY mean, "I CAN'T do that right now." I should probably just say it louder. That works with the TV when the reception is bad, right? Just turn it up.
If rest is so good for me, why does it make me so stiff? How am I supposed to sit down and rest when my knees and hips don't want to bend? If we have made so much progress in the world, how come shoes were custom made to fit in the pioneer days, but there are so few to accommodate Rheumatoid Arthritis?
Another: And why am I told to protect my joints on one page of a "living with Rheumatoid Arthritis" book. And then on a different page of the same book, I am encouraged to exercise using those same joints. Why is the exact same motion considered to be dangerous in one context, but healthy in another context?
More ironic questions: Why do people think if you have Rheumatoid Arthritis, moving to Florida will cure it? (I live in Florida; No go.) Why do people tell us "No pain, no gain"? What are we supposed to gain from pain anyway?
And here's one: Since there are so many cures for RA on the internet, why doesn't my doctor know how to cure me yet?
I would like to take a vacation someday. I hope it won't reduce my stress so much that it would increase my immune activity. That'd be bad for my RA – and really stressful.
Why doesn't methotrexate cause hair loss on my legs instead of just my head?
Great questions. Why does my doctor tell me that combination treatment can lead to remission and I still can't get my current med plan to work? And does remission with RA actually exist or is it just some ploy for us to pay for useless meds?
I love your blog it made me laugh out loud, so true and you put such a great spin on it good job, love it !
This is hilarious!!! I want to print this out and show my rheumatologist!!
Sometimes I think remission is all in your head!!
I found a link to your blog and have found the info you provide quite helpful. Pretty funny too.
Kelly Young, thank you for starting my new year off the right way..I just found this website and I feel like I am home….To you and all the wonderful people here, Thank You for getting it..It has been a long time since someone has understood…I look forward to sharing and listening with all of you.
Welcome, Patti. It is great when you figure out you are not alone. I am often helped by what others write here too.
Ok im totaly angry now.. I take a bunch of meds my fav being the prednisone cause it does make you feel "happyier" and more speedy but the food cravings and the eating packing on 30 pounds in 3 months.. wtf is that about?? its kinda like speed why cant we lloose weight like the speed freeeks and feel good too?? not fair..
* Why, when you have joints replaced, everyone thinks the pain is all gone now that the joints aren't real? Uh, no. I have a DIFFERENT hand, but not a NEW hand. My fingers are nice and straight but they don't bend much.
* Why does the Arthritis Magazine nearly always feature people who have "overcome" their arthritis and done physical things like marathons, instead of focusing on those who have adapted to their illness and still become successful with their brain?
* When trying to get pregnant while having RA, and off methotrexate, everyone assures you "it will happen" once you relax and go back on your meds– which is exactly what you DONT want?
* Why does the doctor insist on putting you on blood pressure meds, when it's only high when you visit HER? (but not all of the other doctors…) Mine is high only when I visit her because I am actually SICK with a cold. And if you have a stripe of bruise around your arm by the time the doctor gets to the exam room, could the fact that the nurse nearly had you on the floor with pain from the cuff tightness have anything to do with your BP reading high?
* No, MRIs, etc. –anything with a tube you slide into– are NOT "no a big deal." When your shoulders are permanently out of place and you've not been able to lay on your back in years without pillows all around you, and they tell you to lay on a 2×4 for 18 minutes and not MOVE, it's pretty painful. Just did this again for a nuclear stress test and had a Charley horse in my shoulders quivering most the time. Not fun.
Thanks for letting me vent. Love your blog and humor!
Lisa, educating the medical professionals is one of my goals. I've also had lab techs and nurses be very rough with me as you describe. I leave bruised like you. We need to educate. That cannot be done while the magazines do as you describe.
Insensitivity is the watchword. So many people, friends, doctors, family members just don't understand. It's too bad that there wasn't a "hollosuite" (Star Trek term) for those who really need to be exposed to what RA really feels like.
I think once a person could actually have a minute or two to "feel" what we all endure, then they would never doubt us again. That being said, however, i wouldn't wish this kind of pain on my worst enemy much less any other person on the planet.
Sorry it's been a while since I have posted, Kelly, but the last two weeks I spent trying to recover from a nasty bout of Bronchitis. Fortunately I have survived and am feeling very well and feisty.
Oh, what a great analogy. I wish that thing were real. I saw ever Star Trek episode 5 times. I'm not cruel, but I could bring myself to expose most medical professionals to it for a few moments for the reasons you state, knowing it is reversible of course.
I just want to add a voice of hope in here… there is such a thing as remission. I was in it one time a long time ago. I don't even remember when. It lasted a good while – maybe a year or so. I think it was in the late '90s.(Does it count as remission if you're still taking the meds?) Anywho – I'm working to get back to that happy place! Good luck to all of you!
Im so glad to come across this site, i was just told i have ra , and aam not one bit happy, my mom had it horrible for yrs. and my best friend, the pain is horrible, helps to talk to others who have it, right now i feel like the end of the wold is here, ill fight it all the way though!
Welcome Vicki. I'm sorry that RA brought you here, but you sound like a wonderful warrior.
Hi I am trying to just take the Plaquinil and sulfer drug and hope to not have to take the M one. Still can't do much art as on now but the pain has almost gone away!
Thanks for this blog and this particularly humorous page! I actually LOL'd! So many thoughts running through my head around now!
What is a "biologic" drug? I see this term on several posts but have never heard it used here in England. I take 22.5mg Methotrexate and 25mg folic acid each week, plus 400mg Plaquenil & 600mg etodolac daily. Are any of these 'biologic'?
Really love your humour and kindness. Look forward to wading my way through so-far unread pages in due course!


text:
layout:       post
title:        "马尔可夫决策过程MDP"
subtitle:     "MDP"
date:         2018-05-31 10:12:00
author:       "xuepro"
header-img:   "img/home_bg.jpg"
header-mask:  0.3
catalog:      true
multilingual: true
tags:
    - AI

---

**A stochastic process** is an indexed collection of random variables $$ {X_t} $$.
 e.g., time series of weekly demands for a product

**A stochastic process $$ X_t $$** is said to be Markovian if and only if

$$ P(X_{t+1}=j| X_t=i,X_{t-1}=k_{t-1},X_{t-2}=k_{t-2},...X_1=k_1,X_0=k_0) = P(X_{t+1}=j|X_0=k_0) $$

   "The future is independent of the past given the present"

**A Markov process** (or **Markov chain**) is a **memoryless** stochastic process, i.e., a sequence of random states
$$s_1; s_2; : : :$$ with the Markov property

**A Markov process**  is a is a tuple $$(S;P;\mu)$$

- S is a (finite) set of states
- P is a state transition probability matrix, $$ P_{ss'} = P(s'\vert s) $$

- a set of initial probabilities $$ \mu_j^0 = P(X_0=i)$$ for all i

**A Markov reward process** is a Markov process with values.
A Markov Reward Process is a tuple $$S;P;R;\gamma; \mu $$

- S is a (finite) set of states
- P is a state transition probability matrix, $$P_{ss'} = P(s'\vert s) $$

- **R** is a reward function, $$R_s = E[r \vert s]$$
- **$$\gamma$$** is a discount factor,  $$\gamma \in[0,0]$$
- a set of initial probabilities $$ \mu_j^0 = P(X_0=i)$$ for all i

The **return** $$v_t$$ is the total discounted reward from time–step t.
  $$v_t = r_{t+1}+\gamma r_{t+2}+\gamma r^2 r_{t+3}+--- = \sum_{k=0}^{\infty}\gamma ^k r_{t+k+1} $$

The **state value function** V(s) of an MRP is the expected return starting from state s
        $$ V(s) = E[v_{t}\vert s_{t}=s]$$

### Bellman Equation

$$\begin{equation}\begin{split}
   V(s) = E[v_{t}\vert s_{t}=s] \\
        = E[r_{t+1}+\gamma r_{t+2}+\gamma^2 r_{t+3}+ ...\vert s_{t}=s]\\
        = E[r_{t+1}+\gamma (r_{t+2}+\gamma r_{t+3}+ ...) \vert s_{t}=s]\\
        = E[r_{t+1}+\gamma v_{t+1}\vert s_{t}=s]\\
        = E[r_{t+1}+\gamma V(s_{t+1})\vert s_{t}=s]
\end{split}\end{equation}
$$

So, We get the  Bellman Equation:

$$\begin{equation}\begin{split}
  V(s) = E[r+ \gamma V(s')\vert s]=  R_{s}+\gamma \sum_{s'\in S} P_{ss'}V(s')
\end{split}\end{equation}
$$

The Bellman equation can be expressed concisely using matrices.

 $$ V  =R+\gamma PV $$

$$
\begin{bmatrix}
    V(1) \\
    \vdots\\
    V(n)
\end{bmatrix}

 = \begin{bmatrix}
    R(1) \\
    \vdots\\
    R(n)
 \end{bmatrix}

 +\gamma \begin{bmatrix}
    P_{11} &\dots & P_{1n}\\
    \vdots &\ddots &\vdots \\
    P_{n1} &\dots & P_{nn}
\end{bmatrix}

\begin{bmatrix}
    V(1) \\
    \vdots\\
    V(n)
\end{bmatrix}
  $$

### Solving the Bellman Equation

The Bellman equation is a linear equation. It can be solved directly
$$ V  =R+\gamma PV $$

$$ (1-\gamma P)V  =R $$

$$ V  = (1-\gamma P)^{-1}R $$

Computational complexity is $$O(n^3)$$ for n states. Direct solution only possible for small MRPs
There are many iterative methods for large MRPs,e.g.,
 - Dynamic programming
 - Monte–Carlo evaluation
 - Temporal–Difference learning

### Discrete–time Finite Markov Decision Processes (MDP)

A **Markov decision process** (**MDP**) is Markov reward process with decisions. It models an environment in which
all states are Markov and time is divided into stages.

**A Markov Process** is a tuple $$(S;A;P;R; \gamma; \mu)$$

- S is a (finite) set of states
- A is a (finite) set of actions
- P is a state transition probability matrix, $$P(s' \vert s; a)$$
- R is a reward function, $$R(s; a) = E[r \vert s; a]$$
- $$\gamma$$  is a discount factor, $$\gamma \in [0,1] $$
- a set of initial probabilities $$ \mu_i^0= P(X_0 = i)$$ for all i

**Goal** is a scalar **reward**:goals and purposes can be well thought of as the maximization of the cumulative sum of a received scalar
signal (reward).

**Policies**:
   A policy, at any given point in time, decides which action the agent selects A policy fully defines the behavior of an agent
Policies can be:
- Markovian $$\subset$$ History–dependent
- Deterministic $$\subset$$  Stochastic
- Stationary  $$\subset$$  Non–stationary

#### Stationary Stochastic Markovian Policies

A policy $$\pi$$ is a distribution over actions given the state:

  $$ \pi (s,a) = P(a\vert s) $$
- MDP policies depend on the current state (not the history)
- i.e., Policies are stationary (time–independent)
- Given an MDP $$M= (S;A;P;R;\gamma;\mu)$$ and a policy  $$\pi$$
   - The state sequence s1; s2; ... is a Markov process $$(S;P^{\pi};\gamma \mu)$$
   - The state and reward sequence s1; r2; s2; ... is a Markov reward process $$(S;P^{\pi};R^{\pi};\gamma; \mu)$$, where

    $$P^{\pi} = \sum_{a \in A} \pi(s,a)P(s'\vert s,a) $$

    $$R^{\pi} = \sum_{a \in A} \pi(s,a)R(s,a) $$

#### Value Functions
Given a policy $$\pi$$, it is possible to define the utility of each state: **Policy Evaluation**

* The state–value function $$V^{\pi}(s)$$ of an MDP is the expected return starting
from state s, and then following policy $$\pi$$
   $$V^{\pi}(s)  = E_{\pi}[v_t\vert s_t=s]$$

For control purposes, rather than the value of each state, it is easier to consider the value of each action in each state.

The action–value function $$Q^{\pi}(s; a)$$ is the expected return starting from state s, taking action a, and then following policy  $$\pi$$
   $$Q^{\pi}(s; a)  = E_{\pi}[v_t\vert s_t=s,a_t=a]$$

#### Bellman Expectation Equation

$$\begin{equation}\begin{split}
  V^{\pi}(s)  = E_{\pi}[r_{t+1}+ \gamma V^{\pi}(s_{t+1}) \vert s_t=s]\\
           =\sum_{a\in A} \pi (a\vert s)(R(s,a)+\gamma \sum_{s' \in S}P(s' \vert s,a)  V^{\pi}(s'))
\end{split}\end{equation}
$$

$$\begin{equation}\begin{split}
 Q^{\pi}(s; a)  =  E_{\pi}[r_{t+1}+ \gamma Q^{\pi}(s_{t+1}; a_{t+1}) \vert s_t=s, a_t=a]\\
  = R(s,a)+\gamma \sum_{s' \in S}P(s' \vert s,a)  V^{\pi}(s') \\
  = R(s,a)+\gamma \sum_{s' \in S}P(s' \vert s,a)  \sum_{a'\in A} \pi(a'\vert s')Q^{\pi}(s',a')
\end{split}\end{equation}
$$

The Bellman expectation equation can be expressed concisely using the induced MRP

$$V^{\pi} = R^{\pi} + \gamma P^{\pi} V^{\pi}$$

with **direct solution**

 $$V^{\pi} = (1- \gamma P^{\pi})^{-1} R^{\pi}$$

#### Bellman operators for $$V^{\pi}$$

 The Bellman operator for $$V^{\pi}$$ is defined as $$T^{\pi}$$ : $$R^{S}\rightarrow R^{S}$$
(maps value functions to value functions):

$$(T^{\pi}V^{\pi})(s) =\sum_{a\in A} \pi (a\vert s)(R(s,a)+\gamma \sum_{s' \in S}P(s' \vert s,a)  V^{\pi}(s'))  $$

Using Bellman operator, Bellman expectation equation can be compactly written as:

 $$ T^{\pi}V^{\pi} = V^{\pi}$$

 - $$ V^{\pi}$$ is a fixed point of the Bellman operator $$ T^{\pi}$$
 - This is a linear equation in$$ V^{\pi}$$ and $$ T^{\pi}$$
 - If 0 <$$\gamma<1 $$ then $$ T^{\pi}$$ is a **contraction** w.r.t. the maximum norm

#### The Bellman operator for $$Q^{\pi}$$ is defined as

 $$T^{\pi}$$ : $$R^{S\times A} \rightarrow R^{S\times A}$$ (maps action–value functions to
action–value functions):

$$(T^{\pi}Q^{\pi})(a,a) =\sum_{s' \in S}P(s' \vert s,a)  \sum_{a'\in A} \pi(a'\vert s')Q^{\pi}(s',a')$$

Using Bellman operator, Bellman expectation equation can be compactly written as:

 $$ T^{\pi}Q^{\pi} = Q^{\pi}$$

### Optimal Value Function and optical policy

#### Optimal Value Function

The optimal state–value function $$V^*(s) $$ is the maximum value function over all policies

$$V^{*}(s)  = \max_{\pi}V^{\pi}(s)$$

The optimal action–value function $$^*(s; a)$$ is the maximum action–value function over all policies

$$Q^{*}(s,a)  = \max_{\pi}Q^{\pi}(s,a)$$

- The optimal value function specifies the best possible performance in the MDP
- An MDP is "solved" when we know the optimal value function

#### Optimal Policy

Value functions define a partial ordering over policies

 $$ \pi\geq\pi^\prime $$  if $$ V^{\pi}(s) \geq V^{\pi^\prime}(s)$$, $$\forall s\in S $$

##### Theorem
For any Markov Decision Process

- There exists an optimal policy $$\pi^*$$ that is better than or equal to all
other policies  $$\pi^*>\pi, \forall \pi $$
- All optimal policies achieve the optimal value function,
  $$ V^{\pi^*}(s) = V^*(s)> $$
- All optimal policies achieve the optimal action–value function,
 $$ Q^{\pi^*}(s,a) = Q^*(s,a) $$
- There is always a deterministic optimal policy for any MDP

A deterministic optimal policy can be found by maximizing over $$Q^*(s,a)$$

$$
 \begin{equation}
\pi^*( a\vert s) =
\begin{cases}
1& \text{if } a= arg \max_{a\in A}Q^*(s,a)\\
0& \text{otherwise}
\end{cases}
\end{equation}
$$

### Bellman Optimality Equation

#### Bellman Optimality Equation for $$V^*$$
 $$V^*(s) = \max_{a}Q^*(s,a) =  \max_{a}\{ R(s,a)+ \gamma \sum_{s^{\prime} \in S} P(s\prime \vert s,a) V^*(s\prime) \}$$

#### Bellman Optimality Equation for $$Q^*$$

$$\begin{equation}\begin{split}
Q^*(s,a) =  R(s,a)+ \gamma \sum_{s^{\prime} \in S} P(s\prime \vert s,a) V^*(s\prime)\\
 = R(s,a)+ \gamma \sum_{s^{\prime} \in S} P(s\prime \vert s,a)  \max_{a^\prime}Q^*(s\prime,a\prime)
 \end{split}\end{equation}
$$

### Principle of optimality:
  the tail of an optimal policy is optimal for the "tail" problem.(最优策略的尾策略对于尾问题也是最优的。或者说,不管初始状态和前面已经发生的,对于后续子问题,最优策略对剩余子问题的策略(tail policy)仍然是最优的)

**数学符号 refer**:

数学符号的竖线|有时需要用```\vert```表示

特殊符号 '要用\prime

[List of Greek letters and math symbols](https://www.sharelatex.com/learn/List_of_Greek_letters_and_math_symbols)

[2](http://web.ift.uib.no/Teori/KURS/WRK/TeX/symALL.html)

redpajama_set_name: RedPajamaGithub


text:
Astra-Pfizer needs a fresh start later in the year
No nods and winks
21 May 2014 By Chris Hughes
AstraZeneca should not reengage with Pfizer in the dying days of the takeover timetable. Talks now would either be fruitless or delay a proper restart later.
Some of the UK pharma group's shareholders are urging discussions before the official calendar runs out on May 26. They're hoping for a new bid from its American suitor, one worth more than the rejected $119 billion proposal. But there is no honest route to such an offer.
It is easy to see why investors want engagement. The gap between Pfizer's last offer and the $127 billion that Astra has said is its bottom line is not that wide. Pfizer has said that if Astra recommends the proposal on the table, then it has the right to raise its offer.
But the implied Pfizer manoeuvre probably would not work. UK Takeover Panel rules prohibit any sort of nod or wink – private or public – which suggests there will certainly be an offer that replaces one declared to be "final." If Astra now recommended the final offer and Pfizer did not then raise its bid, the board could be in trouble. The panel requires a material justification for withdrawing a recommendation. "We thought we were getting a higher price" wouldn't qualify.
Also, Astra's board would be acting in bad faith. It rejected Pfizer's current proposal as not fairly reflecting the value of the business. It would be dishonest to go back and pretend-recommend.
The only credible route to a raised offer is to let the current timetable end, sit out the prescribed three-month cooling off period, and restart talks in August.
That still leaves the option of talking now for the sake of it. But discussions in the last days of the current process are unlikely to achieve much. The atmosphere is toxic. If tempers cooled, Astra could ask for the bid timetable to be extended to facilitate more constructive talks. But that would only delay things further, because it would postpone the beginning of the mandated three-month break between a final and a brand new offer.
Astra's desired price of 58.85 pounds a share is punchy. To justify that number, Astra will have to deliver 100 percent on its forecast of $45 billion of revenue in 2023, while strengthening profit margins.
But Astra's board is not wrong to ask for a high price in exchange for giving up independence. After all, 55 percent of Pfizer's offer is paper, and the company's record in M&A is weak. Besides, Pfizer can clearly afford to pay up, thanks to the merger's colossal operational and tax synergies.
If Astra's shareholders disagree with the board's assessment, they can always elect a new board. The current directors should not recommend a deal against their better judgment, merely as a sort of insurance policy against clinical disappointments before Pfizer can make another offer.
If the merger really makes sense, Astra's decision is not now-or-never. On the contrary, a new opportunity is likely very soon. Right now, both sides should shake hands – with no winks – and get back to running their businesses.
Source: REUTERS/Brendan McDermid
A specialist trader works at a post that trades AstraZeneca on the floor of the New York Stock Exchange April 28, 2014.
Breakingviews is not responsible for the content of external internet sites.
Reuters: AstraZeneca shareholder urges board back into talks with Pfizer
Where should AstraZeneca shares be trading?
Pfizer's new AZ pitch is as unfriendly as it gets
AstraZeneca gets a summer reprieve
Loophole offers Pfizer risky way back into AZ deal
Failed bid would leave Astra under pressure


In fall of 2013, Mark VanderPol opened VanderPol Investments in Grand Rapids, Michigan. He brought with him advising experience from Modern Woodmen Fraternal Financial along with a passion for all things finance. Mark VanderPol is held to highest fiduciary standard by being a CERTIFIED FINANCIAL PLANNER™. He is a graduate from Calvin College with a BA in Business.


text:
KNDY Local News HCC Lads & Lassies Live in Concert at Highland Community College Arts...
HCC Lads & Lassies Live in Concert at Highland Community College Arts in the Barn Series April 6
Highland Community College's Arts in the Barn series will host the HCC Lads & Lassies on April 6 at 7 p.m.
The HCC Lads & Lassies have been the premiere vocal ensemble on the campus of Highland Community College since its inception in 1966. Performing modern popular songs and classics, the group adds choreography, dance, and fresh arrangements to elevate the audience experience. The group is formed from the student body on Highland's main campus and currently is led by director Shayna Leahy. Traditionally, the Lads & Lassies perform several shows per academic year on campus and throughout Northeast Kansas as well as special campus events and holiday shows.
Admission for the event is $10. For more information or to RSVP call 785-336-1274 or 785-442-6009 or email lkoch@highlandcc.edu.
The Klinefelter Farm located just two miles east of Hiawatha, KS on Highway 36 just off Mulberry Road, is owned and operated by Highland Community College and the HCC Foundation. This beautiful 480-acre farm was a gift to the college from the John M. Klinefelter family and had been in his family for nearly 130 years. The Farm is home to the Klinefelter Barn which is home to the Arts at the Barn series, a self-supporting and non-profit cultural event series held annually.
This series is promoted through the donations of the following underwriters: Jerry and Patty Bruning, Forsberg Family, Dr. Cheryl Rasmussen, LK Creations, Collins Law Office, Just Vapor, D Lazy K Ranch, Rainbow Communications, Dennis and Kim Myers, Koch & Co, Dave and Marci Reist, Sandra Webb, M&M Farm (in memory of Hogan), Jade Millwrights, Jim & Denise Wolney and KNZA Radio 103.9 FM.
For more information on the series visit www.highlandcc.edu/artsatthebarn.
Barn Series
Highland Community College
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Derek Nester was born and raised in Blue Rapids, and graduated from Valley Heights High School in May of 2000. He attended Cowley College in Arkansas City and Johnson County Community College in Overland Park studying Journalism & Media Communications.After stops at KFRM and KCLY radio in Clay Center, he joined KNDY in 2002 as a board operator and play by play announcer. Derek is now responsible for the digital content of Dierking Communications, Inc. six radio stations.In 2005 Derek joined the staff of KCFX radio in Kansas City as a production coordinator for the Kansas City Chiefs Radio Network, which airs on over 94 radio stations across 12 Midwest states and growing. In 2018 he became the Studio Coordinator at the Cumulus Kansas City broadcast center for Kansas City Chiefs Football.


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Christian Benteke
It's a dream come true for Crystal Palace ace working with former Arsenal man
Christian Benteke says it is an honour to work with Frenchman Thierry Henry
Robert Warlow
Crystal Palace striker Christian Benteke challenges Burnley's Ben Mee. (Photo by Laurence Griffiths/Getty Images)
Crystal Palace striker Christian Benteke says he is enjoying working with Arsenal legend Thierry Henry at international level.
The Frenchman is currently working as an assistant manager to Roberto Martinez as part of the Belgian management set-up, with the former Arsenal and Barcelona forward working with the likes of Benteke and Manchester United striker Romelu Lukaku.
And Eagles ace Benteke, who is currently out with a knee ligament injury, says he is relishing working with the 40-year-old, who won two Premier League titles during his time with Arsenal.
"It was a little bit like a dream come true [to work with Thierry Henry]," Benteke told www.eagles.cpfc.co.uk .
"I had the chance to see him on TV and on YouTube in the past, so I was really pleased and it was an honour to work with him and listen to his advice.
Belgium's assistant coach Thierry Henry (AP Photo/Geert Vanden Wijngaert)
"He knows we play in some big leagues, so he doesn't want to bother us with lots of information, but if there is something to say, he will tell us."
Meanwhile, Benteke says he is looking forward to the World Cup next summer after Belgium sealed their place in Russia by winning their qualification group, although he said he is focused on performing well for Palace to make sure of his place in the squad.
And he says that Belgium will be hoping to do well, with much expected of the Red Devils and their golden generation of players.
Why is Crystal Palace striker Christian Benteke lacking the Midas touch this season?
"It is hard to explain, I am in a generation where we have more than 11 players in England and the quality and the level of the players is really high," he said.
"But we have to keep it up and be proud of our country.
"I want to really help the team this year and help my club to get into the squad for the World Cup."
Crystal Palace FCWatch the moment Crystal Palace and Tottenham fans stood to applaud Croydon tram crash victimsIt was the second anniversary of the tragedy on Friday (November 10)
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Crystal Palace FCYou can get Zaha or Wan-Bissaka printed on the back of your shirt in the new club shop
The 43-year-old from France who has been signed by Crystal Palace
Crystal Palace FCJulien Maisonneuve has worked at a two Michelin star restaurant, but is now in charge of overseeing every burger and portion of chips at Selhurst Park
Crystal Palace fanzine claims Sussex Police 'tarred' fans reputation over false weapon claims at Brighton derby
Crystal Palace FCThe police force breached the Freedom of Information Act after refusing to answer questions over arrests made and weapons recovered at the Brighton clash
21 signs you are struggling to cope without a Crystal Palace game every weekend
Crystal Palace FCIt's been nearly three weeks since Palace last played a game - are you missing your football fix?


California has approved the use of three high school equivalency tests (GED®, HiSET®, and TASC™) for students 18 years old and older for the purpose of receiving a California High School Equivalency (HSE) Certificate. Turlock Adult School's HSE test preparation classes provide students with direct course instruction blended with individual study. Additionally, our courses include a review of basic computer skills, along with content knowledge in core subject areas. Students will also learn test-taking skills and have access to official practice test questions.


ACCENT Health Recruitment are pleased to be partnered with FC Exchange, an FCA authorised E-money institution (FRN: 900205) and one of Europe's leading foreign exchange specialists.
For over 10 years FC Exchange has assisted customers with their international transfers and payments. Believing in providing an exceptional service combined with great exchange rates and product solutions, FC Exchange has a 5 star customer service rating with independent agency Trust Pilot. Whether making one-off transfers or smaller regular ones, they will be able to help with all your requirements - even booking an exchange rate today for a transfer up to two years in the future.


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How much do Indian embassy workers get paid?
How much does an Indian diplomat earn?
How much do workers in India get paid?
Which govt job has highest salary?
How do you get a job in an embassy?
Is it hard to become a diplomat?
How do I get a job at a foreign office?
What is IAS salary?
Whose salary is more IAS or IFS?
Embassy of India employees earn $51,500 annually on average, or $25 per hour.
An entry-level Diplomat with less than 1 year experience can expect to earn an average total compensation (includes tips, bonus, and overtime pay) of ₹400,000 based on 21 salaries. An early career Diplomat with 1-4 years of experience earns an average total compensation of ₹300,000 based on 37 salaries.
How much does a person working in India make? A person who works in India makes approximately $343 per month. Salaries in India range between $310 per month, which is the minimum to a maximum of $1038 per month.
10 Highest Paying Government Jobs in India for Freshers
Indian Foreign Services.
IAS.
IPS.
Indian Forest Services.
Defense Services.
Scientists in ISRO.
Scientists in DRDO.
RBI Grade B Officer.
Top 10 Highest Paying Jobs in India
Average Base Salary/ year (In INR)
Fresher Salary/year
Software Development Engineer ₹1,191,752 ₹989,044
Data Scientist ₹824,241 ₹539,654
Data Engineer ₹839,625 ₹464,722
Software Architect ₹2,199,698 ₹977,473
How to Get a Job at an Embassy
Meet Eligibility Criteria. Applicants must be U.S. citizens between the ages of 20 and 59 when they apply for a job and register to take the Foreign Service Officer Test (FSOT). …
Take the Pre-Application Quiz. …
Demonstrate Qualifications for Embassy Jobs. …
Apply for an Embassy Job.
THIS IS INTERESTING: How much does a shopkeeper earn in India?
The process to become a diplomat is a rigorous one. … Moreover, there are always thousands of applicants for one diplomat job. However, while it is challenging to become a diplomat, becoming fluent in foreign policy and gaining experience through internships can help your chances.
To join the FCO at any grade, you must meet the nationality and residency requirements, and pass a strict security vetting process. The qualifications and experience that you need to join the FCO will vary depending on the role you wish to apply for. You may be asked for GCSEs, A levels or a degree.
According to the 7th Pay Commission, the basic salary of any IAS officer is Rs 56100. Many other allowances are also given to IAS officers, including Travel Allowance and Dearness Allowance. According to reports, the total salary of an IAS officer is more than Rs 1 lakh per month.
The IFS officer salary structure is also higher than the IAS officer salary structure due to higher allowances. … However, the Indian Administrative is an All India service while the Indian Foreign Service is a Central Service.
Categories Travel Tips


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Filter by division/collection
xBilly Rose Theatre Division
Found 2 collections related to Collectors.
Filtering on: x2001 - 2022 xBilly Rose Theatre Division
Langan, Dan
Dan Langan collection, 1927-2016
2.5 linear feet (6 containers)
Dan Langan (1935-2018) was a press agent who represented theatrical performers and works of musical theatre. He was also an avid collector of recordings of musical theatre performances. The Dan Langan collection includes a selection of these audio... more
Dan Langan (1935-2018) was a press agent who represented theatrical performers and works of musical theatre. He was also an avid collector of recordings of musical theatre performances. The Dan Langan collection includes a selection of these audio and video recordings and files relating to his public relations work. less
Hirschfeld, Louise Kerz, 1936-
Louise Kerz Hirschfeld collection, 1928-2017
Billy Rose Theatre Division | *T-Vim 2017-036
0.98 linear feet (4 boxes, 1 oversize folder)
Louise Kerz Hirschfeld is the founder and former president of the Al Hirschfeld Foundation, and has worked as a historian, research consultant, production assistant, and curator in the film and theatre industries. Her collection contains artwork,... more
Louise Kerz Hirschfeld is the founder and former president of the Al Hirschfeld Foundation, and has worked as a historian, research consultant, production assistant, and curator in the film and theatre industries. Her collection contains artwork, posters, photographs, and memorabilia from film and theatre productions in Austria, Germany, Poland, and the United States. less


XTREME XD-WSS-100 Wireless Share System. — Xtreme Systems Inc.
Home XTREME XD-WSS-100 Wireless Share System.
XTREME XD-WSS-100 Wireless Share System.
The easiest way to bring people great ideas, projects and sharing together by simply plug in and tap to share. Users also can share the contents on the IOS/ Android mobile devices on the presentation screen without complicated cables set-up, no need to wait for a long time to take part in and no software installation requests. With this wireless share system it really brings users a simple, efficient, interactive and super easy and smooth way to hold the meetings, presentations and brainstorm.


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EvilQuest
Platform: Xbox 360
Tags: RPG, Action
Developer: Chaosoft Games
Chaosoft Games
View all 4 available EvilQuest images
EvilQuest review
Gary Hartley says: "EvilQuest gets more than enough to justify its already low asking price, but let's not let its Indie status colour it completely; The 360's Indie channel regularly produces titles of great value hidden beneath the muck and Chaosoft's effort certainly deserves to stand along side them. "
Rob Hamilton says: "For a change of pace, destroy a world instead of saving it! It feels good!"
JoeTheDestroyer says: "Once the shock that I was playing a wanna-be retro title wore off, all that was left was a basic, by the books action RPG. As Rotten Tomatoes likes to say, it was a genre exercise."
EvilQuest Reviews Around the Internet
Below are links to EvilQuest reviews we found on external sites. If the site's content is still active, you can click on the rating the site awarded the game to open the review in a new tab or window, or click the name of the site to see a selection of other reviews from that outlet. The game's average score across the referenced sites (not including sites that don't offer a numerical score) is indicated to the right.
RPGamer
More Xbox 360 Games to Consider...
Tags: RPG, Action, Sci-Fi
Release Date: January 27, 2010 (North America)
Release Date: March 6, 2012 (North America)
At HonestGamers, we love reader reviews. If you're a great writer, we'd love to host your EvilQuest review on this page. Thanks for your support, and we hope you'll let your friends know about us!
None of the material contained within this site may be reproduced in any conceivable fashion without permission from the author(s) of said material. This site is not sponsored or endorsed by Nintendo, Sega, Sony, Microsoft, or any other such party. EvilQuest is a registered trademark of its copyright holder. This site makes no claim to EvilQuest, its characters, screenshots, artwork, music, or any intellectual property contained within. Opinions expressed on this site do not necessarily represent the opinion of site staff or sponsors. Staff and freelance reviews are typically written based on time spent with a retail review copy or review key for the game that is provided by its publisher.


Vow | a solemn or earnest pledge or promise binding the person making it to perform a specified act or behave in a certain way (Collins dictionary).
A guy I work with recently got married, and of course posted the wedding YouTube video to Facebook. I cried into my porridge and wrecked my work makeup. It wasn't the Bali garden setting, with the view of the ocean over a stone wall, or the flowers that adorned everything or the trendy macramé curtain that framed the couple beautifully under a wooden arbour, that had me weeping. It was their vows. Vows that were their own words written with thought, truth, humour and love.
When I was a bride to be, all I wanted was to marry Scott and have his babies. With everything in me down to my soul I wanted to be the wife to my first love. I wanted the traditional Catholic Church wedding, with the white dress, standing before God, family and friends being tied to Scott forever. The Catholics have their own script and order of service for the wedding ceremony and at the time I was okay with that. The only thought I put into my vows was that I would not vow to "obey".
The day of our wedding, I couldn't wait to get to the church, (I was 20min early). Walking with my Mum on my left and my Dad on my right, and my sisters walking in front of me. I smiled and waved and said hello to family and friends, as I walked towards my guy in the black suit looking like he wanted to vomit or curse me for taking so long to get to him. When I finally did reach him I couldn't take my eyes off him, all we had to do was say "I do" after the Priest recited the words and vows that bound us.
Priest: Scott, do you take Melinda for your lawful wife, to have and to hold, from this day forward, for better, for worse, for richer, for poorer, in sickness and in health, until death do you part?
Priest: Melinda do you take Scott for your lawful husband, to have and to hold, from this day forward, for better, for worse, for richer, for poorer, in sickness and in health, until death do you part?
After 15 years of marriage, the words that I vowed to live my married life by seem shallow, weak and immature. (That opinion is coming from a place of experience, time, hindsight, trials and love).
I wish I would have had a heart-to-heart to the women in my family, extended family and friends about being a wife and the relationship of marriage. I was so young the concept was of marriage was romantic and exciting. I wish I had my Grandmother, mother, and aunties share their wisdom and insights into being a wife. What is the joy in their marriage and the difficulties in their marriage? In hindsight I would of crafted deeper, authentic words and my own personal promises instead of; for better, for worse, for richer, for poorer, in sickness and in health.
That's an amazing honesty and insight Melinda. Alain de Botton is writing a lot about Romanticism right now. And the failings in the ideology of warm, fuzzy being the default emotio in a monogamous marriage. It's a bit different to what you're saying but there is crossover. Thank you.
Thank you for your lovely comment, Westendgal. I will Google Alain de Botton would love to read some of jis work.
I'm with you. I ask myself though, if I did have the understanding that I do now, would I have changed my vows? Would it change the way I feel? Would I be in a better place?
Yes exactly. When I wrote this I was thinking the same things about the way I feel.
Thank you for such a beautiful, honest post. My partner and I have decided to never marry, but every now and then I take the time to tell him how grateful I am that I have him, how much he has changed my life for the better and how much he has taught me about myself. Of course, I always tear up, and he just smiles at me, but it's something that I'll never stop doing.
Thanks so much for having a read. Glad you connected with the writing. Will definitely check out Iris Lillian.


The cousin to our Brownies, these have brilliant caramel flavour with a hint of saltiness. White chocolate and pecans definitely hit the mark adding both texture and taste.
Line 20cm x 20cm square cake tin with non-stick baking paper.
Melt butter in medium saucepan. Remove from heat.
Add brown sugar and vanilla and stir well to combine. Cool for a couple of minutes.
Add eggs and using a wooden spoon, beat briskly into warm butter mixture, until just smooth.
Add flour, baking powder, salt roughly chopped pecans and chocolate into saucepan. Stir to combine and make a stiff batter.
Scrape mixture into prepared tin and evenly into tin.
Bake for 25 minutes for fudgy result, 30 minutes for cake-like result.
Remove from oven. Allow to cool to room temperature before removing from tin.
Cut blondies into desired size pieces.
Serve warm, at room temperature or chilled (lovely on a hot summers day).
These are so quick to make at the last minute with minimum equipment used plus all ingredients are staple items from pantry and fridge.
Serve for morning or afternoon tea cut into little squares. As a dessert, using a circular cutter, stamp out 6cm rounds and serve blondies warm with vanilla custard or ice cream.
Use walnuts instead of pecans or omit nuts altogether.
We used Lindt white chocolate, our favourite. Beware of imitation white chocolate with palm oil as an ingredient! Add dark chocolate if preferred.
Sprinkle frozen raspberries over surface of Blondies before baking for a different fruity version.
Baked blondies freeze well. Wrap individual pieces in foil to pop into lunchboxes and they will be defrosted by lunchtime.


English – Pupils will conclude reading their class novel and use this as a stimulus for creative writing. The pupils will be rehearsing for the end of year drama production based on Aesop's Fables. The pupils will also be given the opportunity to write their fables. Finally they will be preparing their entry for the School handwriting competition.
Maths – Pupils will further develop their computation skills and apply the inverse operation to solve problems involving algebra. They will also extend their understanding of number patterns, apply tests of divisibility and further explore fractions and decimals in a topic of ratio and proportion. Pupils will also solve problems related to measure and perimeter.
Science – Pupils will be exploring a science topic related to 'Reversible and Irreversible Changes' where they will learn more about how materials can exist as different states of matter. Pupils will also explore how mixing materials, heating and burning materials can produce new substances.
Art – In preparation for our biennial fashion show pupils will continue with their gargoyle theme and will be designing and making a gargoyle themed mask and t-shirt. Each pupil will research objects related to the theme, taking these images through to design drawings, analyzing and selecting suitable materials for their designs. Pupils will spend the remainder of the term making their designed masks and t-shirts in wait of the fashion show.
French – Pupils will consolidate what they have learnt during key stage 2 and prepare for key stage 3 through the Accès Studio course book. This leads on to the Studio course books used in key stage 3. Topics covered include: classroom language; school bag items; describing the classroom; meeting and greeting; numbers, days and months; likes and dislikes; talking about family, food, countries and the weather.
Games –Pupils will cover a range of physical activities including cricket (for boys), rounders (for girls), tennis and athletics. In games the programme is aimed to develop an increased level of understanding of basic tactics and rules and how to apply these in a competitive environment. In athletics pupils will be given the opportunity to improve in a variety of individual events and their performances will be recorded and monitored. There will also be some preparation work for sports day which takes place this term.
Geography – Pupils will continue to study the rivers topic during the summer term, looking at river processes and landscapes and people who use rivers and manage flooding. They will also complete a decision making exercise based on 'green energy' which will involve them choosing where to locate a new wind farm in Cumbria.
History – Pupils will continue to learn about the Roman Empire and link it in to the invasions and conquest of Britain. This leads to a study of (and visit to) Hadrian's Wall. After the completion of the Roman topic, the Anglo Saxons are briefly studied.
ICT – This term the pupils will be studying aspects relating to We are web developers and We are fundraisersʺ. They will also be constructing the year book.
Music– Pupils continue to play melodies or more complex music on keyboards regularly. Singing repertoire includes songs from around the world. Listening and composing tasks relate to 'The Carnival of the Animals' and to music depicting space travel.
PSHE– Pupils will be considering what it is to be a good citizen. They will be considering what anti – social behaviour is and what should be done about it. Furthermore as part of their PSHE studies the pupils will also be visiting the RNLI lifeboat at Redcar on the morning of April 28th and learning about basic first aid from George Roberts who is from Cleveland Ambulance Service on the morning of Wednesday 6th May.
RS – Pupils will be studying Buddhist beliefs and practices focusing on the early life of the Buddha, Buddhist teaching on suffering and the Sangha (the Buddhist community of monks and nuns).
Technology – Pupils are part way through their latest project – designing and making model houses using computer aided design and manufacture. Once this project has finished, pupils will embark upon a plastics based project – a steady hand, maze game, developing and refining their CADCAM skills. Year 6 will finish the year off with a jewellery project where they will make a copper badge or key ring. The surface of this shaped piece of copper will be enamelled using a low temperature, plastic powder 'enamelling' process.
You may be aware that the pupils from Years 7 to 9 have a week of exams beginning May 19th. The pupils in Year 6 will be completing assessment tests in maths, reading, writing and science. The tests will take place in the class room during lesson term with the subject teacher.


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import { NgModule } from '@angular/core';
import { CommonModule } from '@angular/common';

import { YoutubeService } from './services/youtube.service';

@NgModule({
  imports: [
    CommonModule
  ],
  declarations: [
  ],
  providers: [
    YoutubeService,
  ],
})
export class SharedModule { }