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2 Warps to Neptune
Surveying the Gen X landscape and the origins of geek
We Are the Mutants is Here!
Published August 30, 2016	Announcements 2 Comments
We Are the Mutants, my new online magazine, is alive! It focuses on many of the things I wrote about on 2 Warps to Neptune—Cold War-era sci-fi, fantasy, genre, pulp, proto-geek, and occult media. Please check it out and share if it fires your synapses. We're 100% DIY, fueled by word of mouth. You can also follow us on Facebook and Twitter.
Robert Adragna Cover Art for the Three Investigators Series (Random House, 1979 – 1985)
Published June 29, 2016	Books , Cover Art 4 Comments
Yes, many of you will remember these wonderful books. If you held onto them, good for you. They're costly today. It's one of many series we plan to review at We Are the Mutants (launch still scheduled for late August or early September).
The Three Investigators debuted in 1964 and went through several editions. Pictured here are a few of the "Hitchcock" and "Keyhole" editions (the ones I read), published between 1979 and 1987, with cover art by Robert Adragna. Read more about Adragna, and see more of his fantastic covers, here.
Buck Rogers Night Light (General Electric, 1980)
Published June 24, 2016	Buck Rogers in the 25th Century 1 Comment
(Via eBay)
The Black Hole Wallpaper (Borden, 1979)
Published June 1, 2016	'70s Decor/Design/Fashion , Black Hole, The 2 Comments
Strangely aseptic design, isn't it? Via eBay.
Starcruiser UFO Ad (Cox, 1979)
Published May 25, 2016	Space Toys/Playsets , UFOs 2 Comments
They're waving because that damn thing's never coming back. See the actual product here.
Marc Bolan with Man-Wolf, Circa 1975
Published May 19, 2016	'70s Music , Big Kids Reading Comics , Comic Books , Make Mine Marvel , Stan "The Man" 1 Comment
The magazine behind Creatures on the Loose #33, identified by Richard McKenna, is Modern Screen (November 1974). Bolan was a huge Marvel fan who interviewed Stan Lee on the BBC's Today show in 1975, where Lee revealed that Angie Bowie was interested in doing a Black Widow TV series—which would have been so much more entertaining than whatever morbidly expensive glob of superhero goo that came out last week (or the week before, or the week before, or the week before…). Bolan himself was interviewed about comics in 1975 by soon-to-be Pet Shop Boy Neil Tennant (credit to McKenna once again). You can read the transcript here, and there's a picture of the article below.
Bonus: here's Bolan with Stan Lee and Roy Wood (ELO, Wizzard) at London's Institute of Contemporary Arts in 1975. The Marvel exhibit ran from October 18 through November 2. Bolan died in a car wreck two years later, on September 16, 1977.
(Photos via @jackellyreed and everything second-hand)
ON TV Subscription Box, Circa 1980
Published May 9, 2016	Cable/Subscription TV , Commercials 6 Comments
One switch. Two choices. As I said way back here, where you can see the box in the wild, ON TV (1977-1983) was a subscription service that would unscramble UHF channels in participating markets. Los Angeles was one of those markets, and it was the first pay-for-TV service my parents got, probably around 1982. That same year, ON TV secured the rights to Star Wars and aired the film on a pay-per-view basis in September. My parents and a number of other neighborhood parents chipped in, and a whole mess of ecstatic kids joined me in our tiny living room for the occasion. Our TV was 19″ at most.
Here's the intro to ON TV's "opening night" in 1980, featuring 10, Norma Rae, and Slap Shot. Not exactly a kid's dream line-up. I dig how the logo mimics the straightening out of the scrambled UHF signal.
2 Warps to Neptune Going on Hiatus; 'We Are the Mutants' Coming Soon
Published May 2, 2016	Announcements 37 Comments
I started 2 Warps to Neptune at the beginning of 2012. I was about to turn 40, my first daughter was about to be born, and I was feeling old and out of touch with the 21st century. In short, I was getting nostalgic. I wanted to carve out a space where I could look back on my youth and relate my growing fondness for the uniquely lavish, uniquely tangible "kid culture" of the 1970s and early 1980s. Although I'll never get tired of the emotional comfort an old toy or an old iron-on can evoke, I soon became more critical of the backwards glance. I realized that I didn't want to relive the past; I wanted to study it. I became much more interested in the foundations, innovations, and recurring themes of the era, especially as they related to the generation growing up under the spell of Dungeons & Dragons, Atari, and Star Wars.
Now I want to go further. I want to seriously and objectively explore the popular culture of the entire Cold War era, especially the more underappreciated and esoteric artifacts, artists, and attitudes: everything from EC horror comics and first wave ufology to post-apocalyptic cinema and space disco. I can't do that alone, and I don't want to. So, with the help of a number of excellent writers (and more to come, I hope), I'm starting an online magazine called We Are the Mutants. (The title of the magazine is taken from graffiti seen at the University of California at Berkeley in the late 1960s: "The bomb has already dropped, and we are the mutants.") The magazine will focus on the period from the late 1960s to the early 1980s, but anything from the end of World War II to the fall of the Berlin Wall is fair game.
2 Warps to Neptune has been a labor of love, and occasional frustration (for reasons still unclear to me, people will take your words, images, and ideas and pass them off as their own, or simply not give credit where credit is due; such is the internet) for almost five years. That's not long in blogging years, I know, but it's a long time for me. I've done my best to offer something original, and I sure as hell refused to serve swill (clickbait lists, "retro" idolatry and "good old days" propaganda, man-child birthday cakes in the shape of Atari 2600s, etc.). I always understood that 2W2N would appeal to a relatively small group, and I'm proud of that. I'm also happy that so many of you got something out of the blog, and I've appreciated every single positive comment and email. A geek or a nerd, to me, is not someone who dresses up like a superhero, rolls d20s, owns a complete set of Kenner's Star Wars figures from 1978, or is a "fan" of one or more fictional franchises; a geek or a nerd is simply an intellectual who explores serious ideas and speculative notions within the context of fantasy. That's the definition I'm bringing to We Are the Mutants, anyway.
Launch is currently scheduled for August 29, 2016. Follow We Are the Mutants on Facebook and Twitter for updates. I'll be posting at 2 Warps to Neptune for a few more weeks at a reduced rate, although I'm taking this week off. If you're interested in contributing to We Are the Mutants, please email Kelly at watm@wearethemutants.com.
Hope to see you on the other side.
The Lord of the Rings Comic Book Adaptation, 1979 – 1981
Published April 29, 2016	Comic Books , Lord of the Rings, The 3 Comments
There was no American or English comic book adaptation of The Lord of the Rings following Ralph Bakshi's animated movie of 1978—the closest we got was the Warren Special Edition magazine—but there was a beautiful three volume adaptation that appeared throughout Europe, licensed by Tolkien Enterprises in California. The lack of an English adaptation is attributed to "copyright issues," which probably means that it was prohibitively expensive.
The artist is Luis Bermejo Rojo, a Spanish illustrator best known to American audiences for his work on Warren's Creepy from 1974 to 1983. The covers above, all by Bermejo, are the Icelandic editions, and the pages are from the Spanish editions. The series was released between 1979 and 1981. Bermejo passed away in 2015.
(Images via Tumba Abierta and Tolkien Library)
Erol Otus Illustration for the Advanced D&D Dungeon Masters Adventure Log (TSR, 1980)
Published April 28, 2016	D&D , Erol Otus 5 Comments
The product is absolute nonsense, a flagrant money-grab; the illustration, however, is a definitive representation of the dungeon crawl. The main figures prepare to battle in three dimensions, while the bordering monsters, pitched in darkness, await the survivors in two (torches first, heroes; you can't fight if you can't see). Otus distills, in a single monochrome image, the suspense, danger, and otherworldliness of the fantasy RPG. See more early illustrations of role-playing here.
The Adventure Log is billed as the second "playing aid" produced by TSR for AD&D. The first was the AD&D Rogues Gallery (below), also from 1980, also illustrated by Otus.
Disco Snoopy Colorforms Set (Colorforms, 1978)
Star Wars Bedding, 1977/1978
Products of Your (Sexist) Imagination: TSR's Heart Quest Books, 1983 – 1984
A Portrait of Young Geeks Playing Dungeons & Dragons, 1984
Kid Art: Star Wars (1977)
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EduTECH 2020
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Prof Genevieve Bell, Anthropologist, Senior Fellow At Intel, Director Of The 3A Institute (3Ai), The Australian National University
Genevieve established the 3A Institute (3Ai) in September 2017 at the ANU in collaboration with CSIRO's Data61 with the mission of building a new applied science to effectively and ethically manage the impact of artificial intelligence (AI) on humanity through better design and management of...
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Richard Gerver, World Renowned Speaker And Author, Coach to the worlds elite
Richard Gerver has been described as one of the most inspirational leaders of his generation. He is an award-winning speaker, bestselling author and world-renowned thinker.Richard began his career in education, most notably as headmaster of the failing Grange Primary School. In just two years, he...
Maggie Macdonnell, Global Teacher Prize Winner 2017, The million dollar teacher
Maggie MacDonnell, aka "The Million Dollar Teacher" is the winner of the Global Teacher Prize, a $1 Million US award considered to be the Nobel Prize of Education. Maggie was chosen from over 20,000 nominated teachers from 179 countries. Her work has spanned diverse communities and populations –...
Pasi Sahlberg, Deputy Director - Research, Gonski Institute For Education, University of New South Wales
Pasi Sahlberg is a Finnish educator and author who has worked as schoolteacher, teacher educator, researcher, and policy advisor in Finland and has studied education systems, analysed education policies, and advised education reforms around the world. He has written and spoken widely about these...
Ken Shelton, Chief Executive Officer, Elevate Education
Ken currently holds an M.A. in Education with a specialization in Educational Technology as well as New Media Design and Production. He has worked as an Educator for over 14 years and most recently taught technology at the Middle School level. As a part of his active involvement within the...
Anita Collins, Founder, Muse Consulting & Bigger Better Brains
Dr Anita Collins is an award-winning educator, researcher and writer in the field of brain development and music learning. Anita is best known for her role as on-screen expert and campaign lead for the Don't Stop the Music documentary that aired on the ABC in late 2018. She is internationally...
Marc Prensky, Founder And Executive Director, The Global Future Education Foundation and Institute
arc Prensky—coiner of the term "Digital Native" —is an award-winning, internationally acclaimed speaker, author, and "practical visionary" in the field of education. Today he champions an emerging new "Empowered to Better Their World" education paradigm that more directly benefits all students and...
Sharon Mullins, Executive Director, Queensland Department of Education
In her recent role as Executive Director, Youth Engagement, Dr Sharon Mullins has led the Department of Education's mission to develop and implement key policy directions and initiatives to support all young Queenslanders to remain engaged in study or work, particularly those who are disengaged and ...
Paul Consentino, , Australia's no1 Illusionist
Cosentino's personal story is astounding and inspiring. Learn how Cosentino, a boy with learning difficulties, overcame adversity, beat the odds to reach his dreams and turn a boyhood hobby into an international success story and pioneer a dying art-form in the process. Newscorp's Stellar...
Charles Fadel, Chair And Founder, Center for Curriculum Redesign
Charles Fadel is a global education thought leader and futurist, author and inventor, with several active affiliations; his work spans the continuum of Schools, Higher Education, and Workforce Development/Lifelong Learning. Through his 25-year high-tech career, he has witnessed firsthand the...
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Tamsyn Rose has over 15years experience in performance coaching and Leadership facilitation. Founder and CEO of two of Australia's leading Mental Wellbeing organisations, Get Real International and Alive Project, she not only has mastered the skills required for successful leadership she is on the ...
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redpajama_set_name: RedPajamaCommonCrawl


Deputy Chief Information Technology Officer in Charge of Infrastructure at the University of Ghana Computing Systems Mr. Francis Boakye has debunked speculations of a supposed blockade by his office of some features of online messaging application Whatsapp on the institution's server.
This follows concerns raised by a cross-section of residents on Sunday decrying their inability to access certain basic features on some social media platforms via the school's Wi-Fi connection which is run by the University of Ghana Computing Systems. These restrictions include the inability to download audio files, videos and documents on the message sharing application Whatsapp, a situation some individuals have indicated to have affected their academic activities on campus.
Demystifying the claims, Mr. Boakye told Univers News on Monday that his office is however working around the clock to ensure that the source of this defect is determined and addressed within the shortest possible time.
"There's nothing that the UGCS has actually done to restrict Whatsapp downloads, that is not from us. But I've heard it and asked my colleagues to investigate if anything is the problem", he said.
In a related development, a previous initiative rolled out by the UGCS some months ago which disallowed users from accessing some online portals such video sharing platform Youtube, among others from the university of Ghana servers within a stipulated period of time each day is still underway.
But Mr. Francis Boakye gave the assurance that the UGCS, in collaboration with search engine giant Google, is on the path of finding alternative and effective means to ease the pressure on the University's daily bandwidth.
"We are working with Google, we haven't yet gotten there yet, but we are hoping to find a solution, but we cannot do it in real time when we are all on campus", he added.


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Resolutie 1642 van de Veiligheidsraad van de Verenigde Naties werd op 14 december 2005 unaniem aangenomen door de VN-Veiligheidsraad en verlengde de VN-vredesmissie op Cyprus met een half jaar.

Achtergrond
Nadat in 1964 geweld was uitgebroken tussen de Griekse en Turkse bevolkingsgroep op Cyprus stationeerden de VN de UNFICYP-vredesmacht op het eiland. Die macht wordt sindsdien om het half jaar verlengd. In 1974 bezette Turkije het noorden van Cyprus na een Griekse poging tot staatsgreep. In 1983 werd dat noordelijke deel met Turkse steun van Cyprus afgescheurd. Midden 1990 begon het toetredingsproces van (Grieks-)Cyprus tot de Europese Unie maar de EU erkent de Turkse Republiek Noord-Cyprus niet.

Inhoud

Waarnemingen
Volgens de secretaris-generaal bleef de situatie rond de Groene Lijn in Cyprus rustig en bleef het aantal incidenten dalen, al waren enkele van die incidenten onrustwekkend. Op beide partijen werd nu aangedrongen verdere spanningen te vermijden. In die zin was men bezorgd over enkele militaire oefeningen die waren gehouden. Voorts zaten de onderhandelingen over een politieke oplossing nog steeds in het slop.

Handelingen
De Veiligheidsraad besloot het mandaat van UNFICYP te verlengen tot 15 juni 2006.

Bij de Turks-Cyprioten en het Turkse leger werd opnieuw aangedrongen het militaire status quo in Strovilia van voor 30 juni 2000 te herstellen.

Verwante resoluties
 Resolutie 1568 Veiligheidsraad Verenigde Naties (2004)
 Resolutie 1604 Veiligheidsraad Verenigde Naties
 Resolutie 1687 Veiligheidsraad Verenigde Naties (2006)
 Resolutie 1728 Veiligheidsraad Verenigde Naties (2006)

 1642
VR1642

redpajama_set_name: RedPajamaWikipedia


The West Hartford Art League's spring fundraiser will feature a preview of the upcoming CT+6 spring exhibit as well as ARTinis, wine, and food.
The West Hartford Art League will be holding a spring fundraiser Friday, April 27, in its Clubhouse Gallery from 6:30-8:30 p.m.
The ARTini Preview Party will be held in the Clubhouse Gallery at 37 Buena Vista Rd. Guests will be able to preview the CT+6 art exhibit before it opens on Sunday April 29, while they enjoy live music from Goza Latin Jazz Trio, specialty ARTinis, and wine and finger food from Park and Oak Restaurant.
Tickets are $40 each and can be purchased online on the Art League's website. Tickets will not be sold at the door. This event supports the many programs, classes, and exhibits the Art League offers through the year.
CT+6 is the West Hartford Art League's most prestigious juried exhibit and is open to artists in all mediums throughout Connecticut, New York, and New England. Jeffrey Cooley, owner and director of the Cooley Gallery in Old Lyme, CT, is the 2018 juror of selection and awards. The Best of Show winner will receive a $1,000 cash prize as well as the opportunity for a one person exhibit at the West Hartford Art League.
For more information, please call the office at (860) 231-8019 or visit westhartfordart.org.


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Legendary Producer Jerry Wexler Dead at 91
Posted in News on August 15, 2008
Jerry Wexler, a record producer known for his contributions to music through recordings by such greats as Aretha Franklin, Ray Charles, Bob Dylan and Willie Nelson, died August 15 in Sarasota, Florida. He was 91. The cause of death was congenital heart disease.
Wexler was born January 10, 1917 in New York City to Polish immigrants who steered him to pursue a career in journalism, a path he choose after serving in World World II and earning a college degree. During his tenure as a writer for Billboard magazine in the 1940s, Wexler coined the term "rhythm and blues" for the magazine's black music charts. While at Billboard, Wexler met Ahmet Ertegun and forged a friendship that lead to his position as co-director of Atlantic Records, a then small r&b label in New York.
Atlantic Records provided an outlet for African-American performers to release numerous ground-breaking records in the 1950s and '60s, and later became the home for rock icons like Led Zeppelin and The Rolling Stones. Wexler's production credits include Franklin's "Respect" and Wilson Picket's "In the Midnight Hour," among other classic songs. In 1967, Wexler and Ahmet Ertegun sold Atlantic Records but both continued to oversee the company. Jerry's musical tasted broadened, which lead to his work with such artists as Willie Nelson, Delaney & Bonnie, Carlos Santana, Dire Straits, and George Michael.
In 1987, the Rock and Roll Hall of Fame inducted Wexler for his sizeable contribution to the music industry. Known for historical perspective and appreciation of all genres of music, he recognized BMI's role in and impact on the industry.
Wexler stated, "It's hard to imagine what music would be like without BMI. Before World War II there was only one kind of music that seemed to be allowed in America. It was continuation of what had been the European tradition of 32-bar songs, whether they came from shows or popular songwriters. And it was an elite club. The lid was kept on rhythm & blues music, country music, ethnic music, folk. Once the lid was lifted — which happened when BMI entered the picture — the vacuum was filled by all of these archetypical American musics. BMI turned out to be the mechanism that released all those primal American forms of music that fused and became rock & roll."
SOURCENews TAGS R&B R&B / Hip-Hop Rock Ray Charles Aretha Franklin Willie Nelson Carlos Santana Jerry Wexler


NCTCOG and the Criminal Justice Policy Development Committee (CJPDC) recognize the importance of assessing local needs and identifying gaps in services. Criminal Justice strategic planning is encouraged throughout the 16-county service area and NCTCOG staff are available as time permits to provide technical assistance for justice-related planning. Local priorities will be identified by the CJPDC and will be assessed during the application scoring process.
Grant application workshop attendees will be made aware of the importance of justice-related strategic planning. All planning documents will be posted on NCTCOG's website.
In December 2017, a Regional Criminal Justice Strategic Plan Survey was distributed to NCTCOG Criminal Justice contacts. Results of this survey were used to develop the Criminal Justice Regional Strategic Plan. The Regional Strategic Plan will be updated as needed.


Bert Leeder has over 30 years experience in the financial services and investment industry. Bert was a partner in national accounting firm BDO Dunwoody and served as a chair of the National Policy Board of BDO Dunwoody. His accounting practice focused on management and tax and estate planning for owner managed business and professional practices. Bert has been an Investment Advisor since 1998 and moved to RBC Dominion Securities in 2004. A Fellow of the Institute of Chartered Accountants of Ontario, Bert is also a Certified Financial Planner. These designations equip him to manage a full spectrum of client needs, including wealth management and financial and estate planning. A firm contributor to his community, he has been involved with the Grey Bruce Regional Health Centre Foundation, including chairing the MRI fundraising campaign, the Owen Sound Golf & Country Club and the local Red Cross among others. He coached minor hockey in the Grey Bruce Highlanders organization for many years.
With over 18 years investment industry experience, Greg served as an Investment Advisor with another major investment firm for seven years prior to joining RBC Dominion Securities in 2004. He obtained his bachelor's degree, majoring in economics, from the University of Western Ontario and received a diploma in Financial Services from Fanshawe College. A strong believer in continuing education, he has completed the Professional Financial Planning (PFP) course and attained the Certified Financial Planner (CFP) designation. Greg has also completed the Options Licensing Course. As a Member of Leeder and Associates of RBC Dominion Securities, Greg works to raise money for the local hospital foundation.
Christie Leeder has over 7 years of experience in the financial services industry. Her passion for helping people lead her to join the Leeder and Associates Wealth Management Group of RBC Dominion Securities in 2015. Prior to joining RBC, Christie was a Manager at National Accounting Firm BDO Canada LLP working out of the Owen Sound office. She obtained her Chartered Accountant Designation in 2009 after having completed her Bachelor of Business Administration degree at Wilfrid Laurier University in Waterloo in 2008. Throughout her employment with BDO, she gained significant knowledge of personal and corporate taxes and spent time working with a wide range of clients from small not for profit entities to large multinational corporations. Christie has sat on the Executive of the Owen Sound and District Chamber of Commerce as Treasurer since 2013 and is a Committee Member for the Canadian Cancer Society "Bears in Blue" and "Pink in the Rink" fundraising events in Owen Sound. She also completed both area "Amazing Race" events in 2015 put on by the Rotary Club of Wiarton and the Bruce Grey Child and Family Services Foundation.
Lisa Gamble has worked in the financial services and investment industry for 27 years with the Royal Bank of Canada. She served in many roles throughout the bank at both local and head office levels. In 1997 Lisa returned to her Bruce County roots to work as the Branch Manager in both Sauble Beach and Owen Sound before turning her focus to Financial Planning. She obtained her Personal Financial Planning designation in 1999 from the Canadian Securities Institute. Lisa's decision to join the Leeder & Associates Wealth Management Group, a full service investment firm, seemed like a natural progression for her career. Her many years of experience providing client service excellence as well as her extensive financial planning knowledge is a great asset to the team. Lisa currently lives in Oliphant and serves on the Board of Directors for the Bruce Peninsula Hospital Services Foundation and has been a past participating member of both the Sauble Beach and Owen Sound & District Chamber of Commerce.
Robyn brings industry experience dating back to 1996 to her role in the team and has worked with Bert since his entry into the business in 1998. Since her son successfully battled Acute Lymphoblastic Leukemia from 2008-2011, she, her family & co-workers have kept very active supporting ChildCan - a non profit organization based in London, Ontario who are there to support those children & their families during their cancer journey. Yearly they participate in The Inside Ride Owen Sound, an event organized by the Coast to Coast Against Cancer Foundation helping support children fighting cancer. On the team, Robyn is a licensed associate who provides day-to-day support and is aware of all the policies and procedures relevant to the office. She is a point of contact for all clients who call or visit.
Jennifer has worked in the investment industry since 1999, joining RBC Dominion Securities in 2004. She has obtained her bachelor's degree in Sociology from the University of Western Ontario and a diploma in Finance from Fanshawe College. Jennifer is a licensed associate who can assist you with your trade orders and requests of an administrative nature. She is proficient in office policies and procedures and is a point-of-contact for our clients that call or visit.


Nominated for a 2009 GRAMMY® award for "Best Latin Jazz Album", Áurea is a groundbreaking recording of folkloric Afro-Peruvian and Argentinian music mixed with jazz, featuring today's hottest players from around the globe. In an effort to give back, we're donating 10% of sales to help impoverished families in Latin America, with gifts of livestock via Heifer International. We've donated three llamas already.


text:
A Stepwise Approach to Nonoperative and Operative Management of the Diabetic Foot Ulceration
Katherine M. Raspovic, Matthew J. Johnson, Dane K. Wukich
Physical Medicine and Rehabilitation Clinics of North America
https://doi.org/10.1016/j.pmr.2022.06.004
Achilles tendon lengthening
Charcot neuroarthropathy
Offloading
Surgical offloading
Total contact cast
10.1016/j.pmr.2022.06.004
Raspovic, K. M., Johnson, M. J., & Wukich, D. K. (Accepted/In press). A Stepwise Approach to Nonoperative and Operative Management of the Diabetic Foot Ulceration. Physical Medicine and Rehabilitation Clinics of North America. https://doi.org/10.1016/j.pmr.2022.06.004
A Stepwise Approach to Nonoperative and Operative Management of the Diabetic Foot Ulceration. / Raspovic, Katherine M.; Johnson, Matthew J.; Wukich, Dane K.
In: Physical Medicine and Rehabilitation Clinics of North America, 2022.
Raspovic, KM, Johnson, MJ & Wukich, DK 2022, 'A Stepwise Approach to Nonoperative and Operative Management of the Diabetic Foot Ulceration', Physical Medicine and Rehabilitation Clinics of North America. https://doi.org/10.1016/j.pmr.2022.06.004
Raspovic KM, Johnson MJ, Wukich DK. A Stepwise Approach to Nonoperative and Operative Management of the Diabetic Foot Ulceration. Physical Medicine and Rehabilitation Clinics of North America. 2022. doi: 10.1016/j.pmr.2022.06.004
Raspovic, Katherine M. ; Johnson, Matthew J. ; Wukich, Dane K. / A Stepwise Approach to Nonoperative and Operative Management of the Diabetic Foot Ulceration. In: Physical Medicine and Rehabilitation Clinics of North America. 2022.
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title = "A Stepwise Approach to Nonoperative and Operative Management of the Diabetic Foot Ulceration",
keywords = "Achilles tendon lengthening, Charcot neuroarthropathy, Diabetic foot ulcer, Offloading, Surgical offloading, Total contact cast",
author = "Raspovic, {Katherine M.} and Johnson, {Matthew J.} and Wukich, {Dane K.}",
note = "Funding Information: D.K. Wukich is a consultant for Orthofix, Stryker Wright and receives royalties from Arthrex. He is also on the executive board of the International Association of Diabetic Foot Surgeons. K.M. Raspovic is a consultant for Orthofix. M.J. Johnson has no disclosures.",
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journal = "Physical Medicine and Rehabilitation Clinics of North America",
T1 - A Stepwise Approach to Nonoperative and Operative Management of the Diabetic Foot Ulceration
AU - Raspovic, Katherine M.
AU - Johnson, Matthew J.
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N1 - Funding Information: D.K. Wukich is a consultant for Orthofix, Stryker Wright and receives royalties from Arthrex. He is also on the executive board of the International Association of Diabetic Foot Surgeons. K.M. Raspovic is a consultant for Orthofix. M.J. Johnson has no disclosures.
KW - Achilles tendon lengthening
KW - Charcot neuroarthropathy
KW - Diabetic foot ulcer
KW - Offloading
KW - Surgical offloading
KW - Total contact cast
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JF - Physical Medicine and Rehabilitation Clinics of North America


text:
Rome, Florence, Cinque Terre, & Venice - 12 Days
Start your trip in Rome and visit the legendary Colosseum. Admire the Sistine Chapel and stroll through the streets of its buzzing nightlife. See Michelangelo's 'David' sculpture in Florence, meander through piazzas and across the famed Ponte Vecchio bridge before exploring the colorful, seaside villages of Cinque Terre. Finish off in Venice, shopping for carnival masks and handblown art.
Soak in the tradition and culture as you tour Rome's top cultural sites
Discover ancient legends and Rome's darker side at the Colosseum
Tour Florence's beautiful medieval piazzas & cathedrals
Discover the rugged nature and medieval villages of the Cinque Terre
Explore Venice's canals & grand palaces
Day 1 Arrive in Rome Rome
Day 2 Self-Guided Visit of the Colosseum and Forum Rome
Day 3 Early Morning Vatican Experience Rome
Day 4 Rome to Florence, Evening Wine Tasting Experience Florence
Day 5 Florence Self-Guided City Tour Florence
Day 6 Local Cooking Class in Florence Florence
Day 7 From Florence to Cinque Terre Cinque Terre
Day 8 Sunset Cruise on the Cinque Terre Coast Cinque Terre
Day 9 From Cinque Terre to Venice Venice
Day 10 Self-Guided City Tour of Venice Venice
Day 11 Murano & Burano Half Day Excursion Venice
Day 12 Depart Venice
Day 1: Arrive in Rome
Streets of Trastevere, Rome
Welcome to Rome, known as the City of the Seven Hills! According to legend, Rome was founded by brothers Romulus and Remus in 753 BCE atop Palatine Hill. As the long-time center of the powerful Roman Empire, you'll find nearly 3,000 years of architecture, history, and culture throughout the city.
After arriving at one of Rome's airports, you'll transfer to your hotel in the historic center. Settle in and relax, then head out for a stroll and your first look at the Eternal City. The next few days will involve lots of sightseeing, so spend your first few hours enjoying some of the highlights. Suggested activities include:
Visit the Catacombs of Priscilla, which were originally used from the 2nd to 5th centuries as burial grounds for the elite families of Rome. After the entrance was blocked for centuries to protect against grave robbers, the catacombs were rediscovered in the 16th century. Visitors can see the original structures as well as paintings and artifacts from various time periods.
Stroll through the tangle of narrow streets in Centro Storico, one of Rome's most historic districts, to see classical Roman and baroque architecture.
Stop to see the Colonna di Marco Aurelio, a Doric column with a spiral of relief sculptures. It was erected in the 2nd century C.E. to celebrate the victories of the emperor Marcus Aurelius.
Head to the Colle Aventino, one of Rome's famous seven hills. Stroll through the Roseto Comunale, the rose garden which sits on the site of a former Jewish cemetery. Then continue to Parco Savello (Orange Tree Park), where you can find the famous keyhole that gives visitors a direct view of the Vatican. Grab a cappuccino and snack from one of the adjacent cafes.
For an authentic market experience, stop by the Mercato dei Fiori, where locals shop for fresh vegetables, flowers, meats, and cheeses. Browse for authentic Italian pasta and other souvenirs, then take a break with coffee and a pastry at one of the many cafes surrounding the market.
For dinner, head to the Trastevere neighborhood for some of the city's best trattorias.
Day 2: Self-Guided Visit of the Colosseum and Forum
Dive into the history of the Roman Empire with a self-guided visit to the Colosseum, the world's largest amphitheater. Walking through the ancient amphitheater is like taking a trip back in time to the days of the Roman Empire. Learn about some of ancient Rome's most famous and illustrious citizens, such as Julius Caesar, Emperors Augustus and Nero, and the Flavian Emperors who built the Colosseum.
As you approach the Colosseum, you will see the Outer Wall with 3 levels of arches. Near the Colosseum, stands the Arch of Constantine which was constructed to honor Emperor Constantine's victory in the battle of Milvian Bridge in 312 AD. The Colosseum, the Roman Forum, and the Palatine Hill are all located very close to each other in the same archaeological area.
Best to start early in the morning! Give yourself 2-3 hours to visit the Colosseum- with a little extra time to go through security- and around 1 -2 hours to explore the Roman Forum & Palatine Hill.
While many rush to visit the Colosseum first, the Palatine Hill is typically the least crowded of these three sites and offers an entrance with shorter lines. As it's not the typical order to visit- it might a good idea then to start your visit bright and early here. As you walk through Palatine Hill, make your way to the directly connected and incredible Roman Forum. Your entrance ticket serves for all three sites, so after making your way through the Roman Forum to see the impressive monuments, the exit will lead you right next to the entrance of the Colosseum.
After all this exploring, venture to the nearby Monti neighborhood- less than a 10-minute walk- to tuck into a well-deserved meal.
Day 3: Early Morning Vatican Experience
St. Peter's Square and the Vatican
Today you will visit the Vatican City museums and Sistine Chapel, as well as other top sights in a 3-hour guided tour of the city's incredible art and history. The tour will start early at the Vatican, entering the Museums at 8 am and giving you a one-hour head start on the rest of the crowds. See the Pio Clementio Museum, Gallery of the Candelabra, Gallery of Tapestries, and Gallery of the Geographical Maps.
Continue on to the magnificent Raphael Rooms, ending in the breathtaking Sistine Chapel to see Michelangelo's Genesis ceiling frescoes and his Last Judgement altar fresco. Finally, end the tour at St. Peter's Basilica and Square and experience the magic of Renaissance art as you learn about the secret details and untold stories of the masterpieces.
The rest of the day is free for you to explore on your own. The rest of the day is free for you to explore on your own. Stroll through the Centro Storico, the historic center, of Rome wander past iconic monuments and architecture such as the Spanish Steps and Trevi Fountain. Head over to Piazza Navona and admire the Fountain of the Four Rivers, designed by the iconic Italian sculptor, Bernini. Finish your evening with a stroll through the piazza, stopping for some pizza, gelato, and people-watching.
Day 4: Rome to Florence, Evening Wine Tasting Experience
Ponte Vecchio across Arno at night
Take the morning to say your goodbyes to Rome and head to the city of Florence.
Florence is home to many masterpieces of Renaissance art and architecture, including the iconic Duomo, a terracotta-tiled dome, and the Galleria dell'Accademia, which displays Michelangelo's 'David' sculpture. Make the most of your time at some of these spots:
Take a walk through the peaceful Boboli Gardens to see the oval-shaped Isolotto, a small island surrounded by various sculptures and lots of greenery
Visit the Chiesa e Museo di Orsanmichele, which served as the granary for the Sisters of San Michele in previous years
In the evening, head to a local family-run wine bar, where you'll be guided through a tasting of the wines Tuscany is so known for. You'll learn about the culture and tradition behind each glass and the best way to pair and taste them. Enjoy an accompanying meal with your tasting in this intimate setting, all without leaving the city center of Florence.
Plan your trip to Italy
Day 5: Florence Self-Guided City Tour
Piazza della Signoria, a UNESCO site
Spend the day strolling the streets of Florence and exploring this incredible city with this suggested self-guided route. All together, the route is just a couple of miles, but take your time to enjoy the sites along the way for a full-day experience.
Start your day at the iconic Duomo, the earlier the better! Also known as the Cathedral of Santa Maria del Fiore, Florence's Duomo is the third-largest church in the world. Entrance into the main sanctuary is free - but keep in mind a modest dress code. As there is often a line to get in, give yourself an hour to properly visit this iconic spot.
From there, make the 5-minute walk over to the Mercato Centrale, on the second floor of the San Lorenzo market, where you'll be able to stroll through the stalls of local goods and grab a morning coffee to start your day. Give yourself an hour or two to soak in the sights and smells, and to buy some traditional leather goods as souvenirs. After, the nearby Piazza della Republica is the perfect place to soak in the atmosphere of Florence's city center and the incredible architecture that embodies it.
Take a moment to pass through Piazza della Signoria, where replicas of famous statues, including that of Michelangelo's David, line the square and give it an incomparable air of elegance before stopping for lunch nearby.
Across this same piazza, you'll find the entrance to the Uffizi museum. Even if you decide not to make a stop to peruse the expansive art collection, you can cross through its courtyard, Piazzale degli Uffizi, to make your way to the Ponte Vecchio. This famed bridge is now dotted with jewelry shops and is an iconic sight in the Florence cityscape. Cross the bridge, stopping to admire the views along the Arno River that passes underneath.
End your day with a visit to Piazzale Michelangelo. It's a bit of an uphill climb or a quick taxi ride away. This spectacular viewpoint offers an incredible view of all of Florence and is the perfect place to watch the sunset before you head over to Piazza Santo Spirito for some pre-dinner aperitivos.
Day 6: Local Cooking Class in Florence
Learn How to Make Traditional Italian Pasta
Enjoy a leisurely morning in Florence, with breakfast at your hotel and a few slow strolls through the historic center. Popular highlights include the sprawling 15th-century Pitti Palace and the world-famous Uffizi Gallery, which houses works by artists like Michelangelo and Leonardo de Vinci.
In the afternoon, you'll meet your host near the center of Florence for a traditional Italian cooking class. They'll welcome you with a glass of prosecco. Enjoy the venue as you begin the experience with an appetizer of Italian cheeses and other local products.
Next you'll roll up your sleeves and learn to cook regional Italian pasta from recipes passed down through generations. Your hands-on Italian cooking class will last about three hours. You'll learn to cook four dishes from scratch, including a side or dessert. Observe the chef's different tricks and techniques involved in cooking Italian family recipes. In the summer months, you might be able to use the small vegetable and herb garden in the courtyard where zucchini, tomatoes, and herbs are grown.
The best part of the class is at the end, where you'll enjoy your freshly-made dinner in a traditional Italian style, shared with your hosts.
Day 7: From Florence to Cinque Terre
Cinque Terre houses
Today, head by train or private transport to La Spezia, where the local train that connects to all five villages of Cinque Terre begins.
Cinque Terre is a rugged strip of the Liguria coastline made up of five old fishing villages—Monterosso al Mare, Vernazza, Corniglia, Manarola, and Riomaggiore. The coast, villages, and surrounding hillsides are all part of the Cinque Terre National Park and are a UNESCO World Heritage Site.
The region is renowned for its beautiful nature and by the abundance of Mediterranean plants that cover the scrubby hillsides that tumble down to the turquoise water. The historic villages and breathtaking beauty of the region make it a popular choice for travelers. The historic towns prohibit vehicles to preserve the traditional charm, so most travelers arrive by train that runs along the coast or by tour boat.
The area's coastline hiking trails are some of the world's best, linking the small villages together on a beautiful footpath. The path from Riomaggiore to Manarola is called the Via Dell'Amore (Italian for Lover's Walk), and its midpoint—The Lover's Lock, a statue of two people kissing—is a favorite place for couples to copy the gesture for a photo. Bring a small lock to attach to one of the gates or rails on the way to seal your eternal love.
Day 8: Sunset Cruise on the Cinque Terre Coast
The coastline of Cinque Terre
Take the morning to explore Cinque Terre on your own. Whether it's soaking in the sunshine on a beach, hiking through its breathtaking trails, or wandering around the colorful villages, be enchanted by this incredibly unique area.
We recommend some of these activities to make the most of your day:
The Cinque Terre has no shortage of churches—visit a few of them, including the Santuario di Nostra Signora di Montenero in Riomaggiore and the Church of San Giovanni Battista in Corniglia
Explore the 13th-century Castello Di Riomaggiore, which dominates the Cinque Terre coastline. Built to protect the town from seafaring pirates, the castle is now simply a throwback to a different time, as well as a great place for photographs. Head inside the castle to see the museum exhibit of the centuries of town history
Walk up to the Torre Aurora, a medieval castle that stands on the intersection of Monterosso's Old Town and New Town
Pay a visit to Cantina 5 Terre in Riomaggiore, the Cinque Terre's only major winery, to learn about how ancient traditions mix with modern-day production techniques to produce a unique and flavorful wine. Sample the wines, especially the local white, and enjoy a relaxing afternoon
In the evening, head out onto the water to enjoy a small group sunset boat tour. Sit back and admire the views of the charming Cinque Terre fishing villages on a 2.5-hour route from Vernazza. You'll pass by grottos tucked into cliffsides, and admire the villages of Corniglia, Manarola, and Riomaggiore from the sea.
Go for a dip in the water off the deck of the boat and toast your time on the Cinque Terre coast with a drink in hand as you watch the sunset.
Day 9: From Cinque Terre to Venice
Photo taken by Mick R
Time to say goodbye to the Ligurian Coast of Cinque Terre. Head to the La Spezia train station and from there, you'll make your way to the other side of Italy, to the city of Venice. Settle in for about a 5-hour journey, with usually two train changes along the way.
Venice in northern Italy is famous for both industry and tourism. With nicknames like "Queen of the Adriatic", "City of Water", and "The Floating City", it's clear that the city's myriad canals are its main draw. Stretching across 117 small islands in the marshy Venetian Lagoon along the Adriatic Sea, the city has long been a commercial and cultural hub thanks to its strategic placement. Silk, grains, spices, and art were traded through the Middle Ages, making Venice very wealthy.
Venice is well known for several artistic movements, particularly from the Renaissance period. The city's many musicians, like Antonio Vivaldi and others, played important roles in the shaping of symphonic and operatic music. Numerous artists have called Venice home, and their work continues to draw visitors worldwide.
The city is also famous for its many beautiful historic attractions, such as the Piazza San Marco and San Marco Basilica, the Grand Canal, and the ornate Doge's Palace. The Lido de Venezia is a popular luxury destination that attracts actors, critics, and other cinema industry celebrities.
Take the evening to explore the Cannaregio district. This area of Venice, known for holding the Jewish Quarter is the perfect place to simply walk through admiring the unique, iconic architecture. Cannaregio has plenty of artisanal shops to explore and not to mention a plethora of delicious restaurants and lively bars to stop in for dinner and drinks.
Day 10: Self-Guided City Tour of Venice
Traditional Venetian carnival masks
We'd recommend starting at the center of it all in St. Mark's Square, or Piazza San Marco. Take a moment to breathe in the sights and sounds of this famed square before getting a deeper look inside the impressive buildings and architecture that surround it.
Admire the impressive Basilica San Marco from outside before venturing in. While admission is free, there is a skip-the-line fee that can be purchased online to avoid lining up in busy months. Be sure to wear appropriate clothing entering inside. Marvel at the incredible mosaics that adorn the inside of the building. If you're up for it, you can climb the campanile, the bell tower of the Basilica that offers incredible views! Here, we'd recommend buying tickets ahead of time online.
From here, turn your attention to Doge's Palace, also located in St. Mark's Square. This almost 600-year-old building has served many purposes over the course of time but always continued to remain an impressive symbol of Venetian history. Most notably, it was the home to the Doge, the ruler of Venice, and the center of government during the Venetian Republic. Before entering for a visit of the incredibly lavish interior of the palace (buy your admission tickets online to save yourself time!), walk over to the Grand Canal side of the palace for a look at another iconic spot in Venice- the Bridge of Sighs. This ornate Baroque-style bridge connected the palace with its first-floor prison and was used to transfer its prisoners.
Having seen the highlights of St. Mark's Square, it's time to make the 10-minute walk to Rialto Bridge. As you explore Venice on foot, you'll surely cross one of the four bridges that span the Grand Canal. The Rialto Bridge is the oldest and arguably most well-known. Linking the districts of San Marco with San Polo, the bridge gives amazing views of both sides of the canal.
A little further down along the Grand Canal you'll find the Rialto Market. This iconic food market is buzzing with local life and flavors. Overlooking the canal, you can stroll around this lively epicenter of daily Venetian life and culture seeing and tasting the local products that make up its incomparable cuisine. Note that the market shuts down around midday and is closed on Sundays and Mondays.
To round out your day, head to another of the four iconic bridges crossing the Grand Canal, the Ponte dell'Accademia. The vantage point from this bridge offers an incredible view of Venice and the canal it spans. Take a moment to admire this picture-perfect setting before heading to a nearby bar to finish off your day with a glass of wine and Cicchetti- the Venetian version of tapas.
Day 11: Murano & Burano Half Day Excursion
Glassmaker on Murano
When in Venice, a visit to its lagoon and neighboring islands is a must! These picturesque villages offer a getaway from the city of Venice and a unique look into the local life and culture nearby. This morning, head out for a half-day tour of Venice's famous neighbors—the islands of Murano and Burano.
Board your motorboat in the center of Venice and make your way first to Burano, about 45 minutes away. Along the way, your guide will offer insights about the spectacular Venetian lagoon and the various islands it contains. Arrive first at Burano and have free time to explore the island. Traditionally a quiet fishing village, it's known for its exquisite lacemaking and the colorful houses that adorn its canals. You'll be sure to leave with a camera roll full of photos, as this charming island is incredibly postcard-worthy.
From there, return to your boat and head over to the island of Murano. Murano is famous for its colorful glass-making. Visit a glassblower to see a demonstration and learn about the history of glass-making on Murano and the process behind it. Marvel at the intricate pieces, and peruse Murano's many local shops to see the many forms of this delicate craft for yourself.
After spending the better part of your morning enjoying the sights and sounds of the unique islands, return to Venice by boat in time for lunch at one of its many delicious local eateries.
In the afternoon, explore Venice on your own with one of these options to make the most of your time:
Discover art at the Peggy Guggenheim Collection Modern Art Museum, and La Biennale di Venezia Art Museum
See an opera show at the Teatro La Fenice
Browse textiles, craft shops, unique boutiques, and galleries in the bohemian San Samuele district
Day 12: Depart Venice
Farewell, Venice!
Your exploration of Italy will end after breakfast, with a transfer to the airport to catch your flight home or to your next destination.
Map of Rome, Florence, Cinque Terre, & Venice - 12 Days
Written by Lisa Calabrese, updated May 21, 2020
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text:
\section{Introduction}
\label{sec:introduction}

How long can inflation last? From the observational point of view, the total number of $e$-folds\xspace, $N$, must be larger than $\sim 50$--$60$, which
weakly depends on the inflation scale and thermal history after inflation. On the other hand, an extremely long duration of inflation is often required in certain scenarios. For instance, the relaxion model~\cite{Graham:2015cka}, the stochastic axion
scenario~\cite{Graham:2018jyp,Guth:2018hsa,Ho:2019ayl,Takahashi:2019pqf}, a quintessence model~\cite{Ringeval:2010hf,Ringeval:2019bob} demand the $e$-folding\xspace number of $\log_{10}N\sim\mathcal{O}(10)$, depending on model parameters.\footnote{
If the $e$-folding\xspace number is extremely large, those scenarios that involve scalars with fine-tuned initial conditions
might be significantly modified. For example, such a problem in the curvaton paradigm is reported in Ref.~\cite{Torrado:2017qtr}.
Also, rare events such as the Higgs tunneling to large-field values could take place somewhere in the entire universe
(see e.g. Ref.~\cite{Enqvist:2014bua}).}
The purpose of this Letter is to provide a simple single-field, slow-roll inflation model whose {\it typical} number of $e$-folds\xspace is extremely large.

There is a variety of inflation models which last very long. In the string/axion
landscape~\cite{Bousso:2000xa,Susskind:2003kw,Freivogel:2005vv,Higaki:2014pja,Higaki:2014mwa,Wang:2015rel,Masoumi:2016eqo,Bachlechner:2019vcb}, there are many local minima where the old inflation takes place and continues until the inflaton tunnels toward one of the adjacent local minima with a lower energy
through bubble formation.
In this case, the typical $e$-folding\xspace number can be exponentially large. However, one needs slow-roll inflation after the bubble formation to explain the observed cosmic microwave background (CMB) temperature/polarization anisotropies. For this, one may need  another light scalar, in which case
the two inflation scales are not related to each other, in general.

It is also well known that a large class of inflation models can be eternal~\cite{Linde:1982ur,Steinhardt:1982kg,Vilenkin:1983xq,Linde:1986fc,Linde:1986fd,Goncharov:1987ir} (see also \cite{Guth:2000ka,Guth:2007ng,Linde:2015edk}).
The stochastic dynamics of the inflaton plays a crucial role in eternal inflation: quantum fluctuations of the inflaton drive it upward or downward
compared to the classical motion. In particular, upward quantum fluctuations keep the inflaton from rolling
down the potential, leading to eternal inflation.\footnote{
We note that the downward fluctuations help the inflaton to escape from the eternal inflation regime.}
In eternal chaotic inflation~\cite{Linde:1986fc,Linde:1986fd}, quantum fluctuations overcome the classical motion at
sufficiently large fields values, typically much larger than the Planck scale.
Eternal inflation also occurs  in the new or hilltop inflation~\cite{Linde:1982ur,Steinhardt:1982kg,Vilenkin:1983xq}. This is because the inflaton dynamics becomes stochastic in the vicinity of the potential maximum where the classical motion is suppressed.
In both cases, once the universe enters the stochastic regime,
the inflation continues and never ends in some regions.
The volume of the universe is dominated by such regions where the inflation continues. In this sense the inflation is eternal.

It is worth noting that the eternal inflation is based on the idea that the inflating region expands and dominates the volume at later times.
In fact, if one randomly picks up a point in space where the inflaton dynamics is in the stochastic regime,
the expected $e$-folds\xspace there is not infinite but finite~\cite{Barenboim:2016mmw} (see also Ref.~\cite{Assadullahi:2016gkk}).
In other words, one needs to
choose a specific point in space to have a sufficiently long inflation. Such a special
choice or fine-tuning can be compensated by large physical volume due to the prolonged inflation. Thus, the eternity of the eternal inflation relies
on the volume measure.

The purpose of this Letter is to show that one can make the {\it typical} number of $e$-folds\xspace extremely large
in a context of a simple single-field, slow-roll inflation. In particular, it does not rely on the volume measure.
In Sec.~\ref{sec:stochastic} we address our scenario after a brief review on the stochastic formalism.
In Sec.~\ref{sec:model} we provide an example model which exhibits an extremely long inflation.
The last section is devoted for discussion and conclusions.

\section{Stochastic inflation with large $N$}
\label{sec:stochastic}

In the simplest setup, the inflationary phase in the early universe can be realized by the potential energy of some scalar field inflaton, $\phi$, homogeneously filling the universe. For a sufficiently long inflationary phase, however,
the inflaton field must be extremely light, in which case its homogeneity beyond the horizon scale is no longer guaranteed.
Specifically, superhorizon inhomogeneities are sourced by subhorizon fluctuations which continuously exit the horizon during inflation.
Even though the subhorizon fluctuations originate from the quantum zero-point oscillation, they are well approximated
to be classical ones after the horizon exit due to the gravitational decoherence.
Accordingly the evolution of the local inflaton field value can be described by a diffusion process. This is known as the stochastic approach~\cite{Starobinsky:1986fx,Starobinsky:1994bd}, in which the probability distribution function $P(\phi)$ follows the Fokker-Planck (FP) equation,
\bee{
    \pdif{P}{N}=\mathcal{L}_\mathrm{FP}(\phi)\cdot P, \quad \mathcal{L}_\mathrm{FP}=-\pdif{}{\phi}h(\phi)+\frac{1}{2}\pdif{^2}{\phi^2}D(\phi).
}
Here $N$ is the $e$-folding\xspace number used as a time variable, and it is related to the  Hubble parameter $H$ and the cosmic time $t$
by $\mathrm{d} N=H\mathrm{d} t$.
For single-field and slow-roll inflation, the drift and diffusion coefficients are given by $h=-M_{\rm P}^2V^\prime/V$ and $D=V/12\pi^2M_{\rm P}^2$
in terms of the inflaton potential $V(\phi)$, respectively.
Due to such a random walk behavior, the $e$-folds\xspace $\mathcal{N}(\phi)$ elapsed for the first passage from an initial field value $\phi$
to $\phi_\mathrm{f}$ at the end of inflation also becomes a random parameter.
Its generating function $\chi_\mathcal{N}(\phi;J)=\braket{\mathrm{e}^{i J\mathcal{N}(\phi)}}$ is known to follow
the adjoint FP equation~\cite{Vennin:2015hra,Pattison:2017mbe},
\bee{
    \mathcal{L}_\mathrm{FP}^\dagger\cdot\chi_\mathcal{N}=-iJ\chi_\mathcal{N}, \quad \mathcal{L}_\mathrm{FP}^\dagger=h(\phi)\pdif{}{\phi}+\frac{1}{2}D(\phi)\pdif{^2}{\phi^2},
}
with the boundary condition $\chi_\mathcal{N}=1$ at the end of inflation.
The bracket represents an average over realizations.
An arbitary moment of $\mathcal{N}$ is obtained from this generating function by $\braket{\mathcal{N}^n}=\left.\left(\frac{1}{i}\pdif{}{J}\right)^n\chi_\mathcal{N}\right|_{J=0}$.
Thus, one can estimate the \emph{typical} $e$-folding\xspace number of inflation by calculating
the average of the elapsed $e$-folds\xspace, $\braket{\mathcal{N}}$.

For the single-field slow-roll inflation, these FP equations are reduced to the ordinary differential equations, for which
the moments of $\mathcal{N}$ have recursive analytic solutions. For example, the expectation value of $\mathcal{N}$ is given by
\bee{\label{eq: calN}
    \braket{\mathcal{N}}(\phi)=\int^\phi_{\phi_\mathrm{f}}\frac{\mathrm{d} x}{M_{\rm P}}\int^{\bar{\phi}}_x\frac{\mathrm{d} y}{M_{\rm P}}\frac{1}{v(y)}\exp\left[\frac{1}{v(y)}-\frac{1}{v(x)}\right],
}
where $v=\frac{V}{24\pi^2M_{\rm P}^4}$ is the normalized potential in the Planck unit, and $\bar{\phi}$ represents a constant of integration
at which the first derivative vanishes $\partial_\phi\braket{\mathcal{N}}|_{\bar{\phi}}=0$. For a $Z_2$-symmetric hilltop model we consider later,
$\bar{\phi}=0$ is obviously suitable for this boundary condition.
As shown in Ref.~\cite{Vennin:2015hra},
when the following conditions are satisfied,
\bee{\label{eq: classicality condition}
    v\ll1 \quad \mathrm{and} \quad \eta_\mathrm{cl}=\left|\frac{v^{\prime\prime}v^2}{{v^\prime}^2}\right|\ll1,
}
one can use the saddle-point approximation to simplify
this analytic solution (\ref{eq: calN})
 to the well-known formula for the classical drift-dominated case,
\bee{\label{eq: Ncl}
    \braket{\mathcal{N}}(\phi)\simeq N_\mathrm{cl}(\phi)=\int^\phi_{\phi_\mathrm{f}}\frac{\mathrm{d} x}{M_{\rm P}^2}\frac{v(x)}{v^\prime(x)}.
}
Note that this formula is valid as long as the conditions (\ref{eq: classicality condition})
are satisfied everywhere between $\phi$ and $\phi_\mathrm{f}$.
Since the first condition in Eq.~(\ref{eq: classicality condition}) is trivially satisfied in our context,
it is the classicality parameter $\eta_\mathrm{cl}$ that controls the stochastic effect on the averaged $e$-folding\xspace number.

For a better understanding of the second condition in Eq.~(\ref{eq: classicality condition}), let us consider the change of the inflaton potential value due to the inflaton dynamics in one Hubble time: $\delta v \simeq v' \delta\phi + \frac{1}{2}v'' \delta\phi^2$, where $\delta\phi$ is the sum of the classical motion $\delta\phi_\mathrm{cl} \sim h = -M_{\rm P}^2 v'/v$ and the quantum jump $\delta\phi_\mathrm{sto} \sim \sqrt{D} = \sqrt{2v}M_{\rm P}$. Note that the ensemble average and the variance of $\delta\phi$ are respectively given by $\langle \delta \phi\rangle = \delta\phi_\mathrm{cl}$ and $\langle \delta\phi^2 \rangle = \delta\phi_\mathrm{cl}^2 + \delta\phi_\mathrm{sto}^2$, and hence one obtains $\langle \delta v \rangle \approx v' \delta\phi_\mathrm{cl} + \frac{1}{2}v''(\delta\phi_\mathrm{cl}^2+\delta\phi_\mathrm{sto}^2)$. Thus, the second condition in Eq.~(\ref{eq: classicality condition}) requires that the averaged-change of the inflaton potential value is dominated by the linear term of the classical motion, i.e. $|v' \delta\phi_{\mathrm{cl}}| \gg |v''\delta\phi_\mathrm{sto}^2|$.
Note that $v'\delta\phi_\mathrm{cl} \gg v''\delta\phi_\mathrm{cl}^2$ is satisfied under the second slow-roll condition: $\eta_V \ll 1$ with the second slow-roll parameter $\eta_V=M_{\rm P}^2v^{\prime\prime}/v$.

Let us  emphasize here that the above classical formula~(\ref{eq: Ncl}) can be valid
even if there is a highly stochastic region between $\phi$ and $\phi_\mathrm{f}$,
as long as the curvature of the potential is sufficiently small.
To see this, let us first define the stochasticity of the inflaton dynamics by $\xi_\mathrm{sto}\equiv\delta\phi_\mathrm{sto}^2/\delta\phi_\mathrm{cl}^2\,(\equiv h^2/D) = 2v^3/{v^\prime}^2M_{\rm P}^2$, which
is nothing but the amplitude of the curvature perturbations in the classical limit. For $\xi_\mathrm{sto} \gtrsim 1$,
the size of the quantum jump is greater than the classical field excursion over one Hubble time, i.e. the inflaton
dynamics is in the stochastic regime (and this is nothing but the necessary condition for eternal inflation).
The stochasticity parameter is related to $\eta_\mathrm{cl}$ by $\eta_\mathrm{cl}=\frac{1}{2}|\eta_V|\xi_\mathrm{sto}$.
Therefore, the conditions (\ref{eq: classicality condition}) can be satisfied in a highly stochastic region $\xi_\mathrm{sto} \gtrsim 1$
if $\eta_V\ll1$, in which case the expected $e$-folds\xspace can be well approximated by the classical formula~(\ref{eq: Ncl}).

As an extreme example,
let us consider a slightly tilted linear potential for which $\xi_\mathrm{sto} \gtrsim 1$ and $\eta_\mathrm{cl}$ vanishes
by definition. Suppose that the inflaton is initially located at some point.
Then, the inflaton distribution spreads out due to the quantum diffusion
because of $\xi_\mathrm{sto} \gtrsim 1$.
However, the quantum diffusion does not change the inflaton potential value on average
because up and downhills occur with the same probability. It is the classical motion that
changes the potential value on average, as it uniformly drifts the whole inflaton distribution.

If $\eta_\mathrm{cl} \gtrsim 1$,
the diffusion dynamics overcomes the uniform drift due to the classical motion. In other words, the evolution of the universe
relies upon the stochastic process, and the classical dynamics is irrelevant. In the usual hilltop model (without a local minimum),
$\eta_\mathrm{cl}$ is large around the potential maximum, and the stochastic diffusion sweeps out the inflaton from the hilltop. This is
the reason why the averaged $e$-folds\xspace are saturated and does not grow as the initial value $\phi$ approaches the hilltop (see Fig.~\ref{fig: Nvsphi}).

In fact, one can slightly modify the hilltop potential to realize an extremely large $e$-folds\xspace.
To this end, we introduce a shallow local minimum surrounded by a region with $\eta_\mathrm{cl} \ll 1$ around the hilltop.
There, the inflaton distribution tends to be pushed back to the local minimum as a whole even in the stochastic regime,
and then the expected $e$-folds\xspace can be significantly enhanced.
In such a case, the escape rate can be analytically estimated by the expansion around the local maximum and minimum for $x$ and $y$ integrals respectively in Eq.~(\ref{eq: calN}), as given by~\cite{Noorbala:2018zlv}
\bee{\label{eq: Nesc}
    \braket{\mathcal{N}}_\mathrm{esc}\simeq\frac{\pi v(\phi_+)}{2M_{\rm P}^2\sqrt{v^{\prime\prime}(0)|v^{\prime\prime}(\phi_+)|}}\mathrm{e}^{\frac{1}{v(0)}-\frac{1}{v(\phi_+)}},
}
for a symmetric potential. Here $\phi_+$ denotes the local maximum and we take the local minimum at the origin $\phi=0$. As suggested by the Hawking-Moss factor $\mathrm{e}^{1/v(0)-1/v(\phi_+)}$~\cite{Hawking:1981fz}, this escape time can be extremely large for a sufficient low scale potential $v\ll1$. In the next section, we concretely provide such a model which generates the primordial density perturbations
consistent with the CMB observations after exiting the local minimum.

\section{Example model}
\label{sec:model}

Let us explicitly show a concrete model of the extreme long inflation. We consider a
 $Z_2$-symmetric hilltop model given by
\bee{
\label{vphi}
    V(\phi)=\frac{1}{2}m^2\phi^2-\frac{1}{4}\lambda\phi^4+\left(\Lambda^2-g\frac{\phi^6}{M_{\rm P}^4}\right)^2,
}
where $\Lambda$ determines the inflation scale, $\lambda$ and $g$ are positive coupling constants, and
$m$ is the mass at the origin.
For a positive mass-squared in the range of $0<m^2 < H^2$, this potential has a shallow local minimum around the origin $\phi=0$,
where the inflaton spends a large number of $e$-folds\xspace. After diffusing out from the shallow local minimum,
the inflaton dynamics is driven by the tilt of the quartic and hexic terms as an ordinary hilltop inflation,
toward the true minimum at $\phi_\mathrm{min}\simeq(\Lambda^2M_{\rm P}^4/g)^{1/6}$.
Some of the parameters are fixed by the CMB data.
For example, the following parameters
\bee{\label{eq: params}
	&&\left(\frac{\Lambda}{M_{\rm P}},\,\lambda,\,\left(\frac{\Lambda^2M_{\rm P}^4}{g}\right)^{1/6}\right) \nonumber \\
	&&\qquad=\left(0.998\times10^{-4},\,3.39\times10^{-14},\,0.1M_{\rm P}\right),
}
result in the curvature perturbations with the amplitude $A_s=2.1\times10^{-9}$ and spectral index $n_{{}_\mathrm{S}}=0.958$
consistent with the recent Planck observation~\cite{Aghanim:2018eyx}.\footnote{
By adding a linear term~\cite{Takahashi:2013cxa} or the Coleman-Weinberg correction~\cite{Nakayama:2012dw},
one can increase $n_s$ to give a better fit to observation.
}
We illustrate the potential form in Fig.~\ref{fig: potential} with these parameters and the typical mass value $m^2/H^2=10^{-7}$.
Here $H=\Lambda^2/\sqrt{3}M_{\rm P}$ is the Hubble parameter around the origin.
For this or larger mass, the local minimum becomes deep enough so that the \emph{classical} region with $\eta_\mathrm{cl} < 1$
appears between the local minimum and maximum. The classical region efficiently pushes the inflaton back to the local minimum
and the expected $e$-folds\xspace will be enhanced significantly as shown below.
The stochasticity itself is high enough as $\xi_\mathrm{sto}>1$ for $\phi\lesssim10^{-4}M_{\rm P}$ enclosing the whole local minimum and maximum.

\bfe{width=\hsize}{potential_combined.pdf}{The potential~(\ref{vphi}) with the parameter values~(\ref{eq: params}) and the typical mass $m^2/H^2=10^{-7}$.
The potential has a shallow local minimum surrounded by the local maximum as
shown in the magnification. The shaded region corresponds with $\eta_\mathrm{cl}>1$. The \emph{classical} region with $\eta_\mathrm{cl}<1$ appears
between the local minimum and maximum that will increase the expected $e$-folds\xspace for $m^2/H^2 \gtrsim 10^{-7}$, because the inflaton is pushed
back to the local minimum by the classical dynamics.}{fig: potential}

Fig.~\ref{fig: Nvsphi} shows the results of the numerical integration of $\braket{\mathcal{N}}(\phi)$ in Eq.~(\ref{eq: calN})
for different masses. One can see that, at sufficiently small $\phi$,
the expected $e$-folds\xspace is saturated due to the stochastic effects, which sweep out the inflaton from the hilltop, $\phi\lesssim10^{-5}M_{\rm P}$.
For $\phi\gtrsim10^{-5}M_{\rm P}$, the inflaton already passes to the right of the local maximum (in the case of $m^2 > 0$),
and  $\braket{\mathcal{N}}$ is reduced to the classical formula $N_\mathrm{cl}$ in Eq.~(\ref{eq: Ncl}) even though
the stochasticity $\xi_\mathrm{sto}$ itself is large until around $\phi\lesssim10^{-4}M_{\rm P}$.
The usual standard slow-roll inflation will take place afterwards, generating the primordial density perturbations consistent with the CMB observation.
There is a slight wiggling around $\phi\sim10^{-2}M_{\rm P}$, which, however, is caused by the numerical error, and not due to any physical effect.
The expected $e$-folds\xspace become enhanced for $m^2/H^2\gtrsim10^{-7}$ as mentioned.

\bfe{width=\hsize}{Nvsphi_revised.pdf}{The averaged $e$-folds\xspace $\braket{\mathcal{N}}(\phi)$ given by Eq.~(\ref{eq: calN})
for different masses, $m^2/H^2=(2\times10^{-7},\,10^{-7},\,0,\,-10^{-4})$, where $H=\Lambda^2/\sqrt{3}M_{\rm P}$ is the Hubble parameter around the origin. The other parameters are fixed by the CMB data as Eq.~(\ref{eq: params}). The shaded region and the orange line represent $\eta_\mathrm{cl}>1$ and $N_\mathrm{cl}(\phi)$ given by Eq.~(\ref{eq: Ncl}), respectively,
for $m^2/H^2=10^{-7}$.
For $\phi\gtrsim10^{-5}M_{\rm P}$, the inflaton is to the right of the local maximum, and $\braket{\mathcal{N}}$ is reduced to the classical formula $N_\mathrm{cl}$ without the diffusion.  Then, a sufficiently long standard slow-roll inflation follows.
For $m^2/H^2\gtrsim10^{-7}$ the expected $e$-folds\xspace are enhanced due to the \emph{classical} region with $\eta_\mathrm{cl}<1$ between the local minimum and maximum.}{fig: Nvsphi}

We show in Fig.~\ref{fig: meanN}  the $m^2$-dependence of the $e$-folds\xspace from the origin $\phi=0$. We have confirmed that the analytic estimate of the escape time~(\ref{eq: Nesc}) agrees well with our numerical result.
One can see that an extremely large number of $e$-folds\xspace as $\braket{\mathcal{N}}\sim10^{10^{10}}$ can be realized with a deep enough local minimum.
Even in such a case, the inflaton mass-squared itself is still smaller than the Hubble scale, so that the slow-roll stochastic approach remains valid.
The typical $e$-folds\xspace in this model is large enough for various light scalars such the QCD axion to reach the Bunch-Davies distribution~\cite{Bunch:1978yq}.
For instance, the required $e$-folds\xspace
for the axion to reach the so-called Bunch-Davies distribution
is $N \gtrsim 10^{26} (H_{\rm inf}/100 {\rm MeV})^2/(m_a/10^{-5}{\rm eV})^2$~\cite{Graham:2018jyp,Guth:2018hsa}.\footnote{
The typical $e$-folds\xspace can be even larger if one considers a lower inflation scale.
}
For comparison,
we also show the result for the usual case with the negative mass-squared, where
the averaged $e$-folding\xspace number decreases as expected.

\bfe{width=\hsize}{meanN_revised.pdf}{The dependence of $\braket{\mathcal{N}}(\phi=0)$ on $m^2$. Again the other parameters are given by Eq.~(\ref{eq: params}).
For sufficiently large and positive mass squared (solid line)
(but still smaller than $H^2$), extremely long inflation is realized. Typical $e$-folds\xspace
can be as large as $\braket{\mathcal{N}}\sim10^{10^{10}}$.
The numerical result is consistent with the analytic estimate~(\ref{eq: Nesc}).
The case of the negative mass squared (dashed line) is also shown for comparison.
}{fig: meanN}

\section{Discussion and Conclusions}
\label{sec:conculsion}

So far we have studied a simple hilltop inflation with a shallow local minimum at the origin. One can realize a hilltop inflation
in terms of an axion field which enjoys discrete symmetry~\cite{Czerny:2014wza,Czerny:2014xja}. In this case
a small modulation(s) can be introduced, which may induce multiple local minima around the hilltop. See Refs.~\cite{Flauger:2009ab,Kobayashi:2010pz,Takahashi:2013tj} for cosmological implications of such small modulations on the inflaton potential.
More comprehensive study for wider classes of the inflaton potential is left for future work.

If $m^2$ is taken to be larger than $H^2$ in the inflation model (\ref{vphi}), the local minimum becomes deeper, and
the stochastic formalism breaks down.
The inflaton trapped in the local minimum may tunnel to the right of the potential barrier by the bubble formation, followed by
slow-roll inflation as in the case of the original new inflation~\cite{Linde:1981mu,Albrecht:1982wi}. For even larger $m^2$, the situation
will be similar to the old inflation~\cite{Guth:1980zm,Starobinsky:1980te,Sato:1980yn}. In this sense, our scenario corresponds to
a limit of the shallow local minimum for which the stochastic formalism can be applied. Interestingly, our scenario inherits
the advantages of the old and new inflation: the typical $e$-folds\xspace can be extremely large as in the old inflation, and slow-roll inflation
naturally follows afterward as in the new inflation.

In this Letter, we have studied a possibility to realize extremely long inflation in the simple single-field slow-roll framework.
In particular we work on a small-field inflation, which can be well described by an effective field theory.
In the usual eternal inflation picture,  the quantum diffusion dominates over the classical dynamics,
and it keeps the inflaton from rolling down the potential in some spatial regions. The inflation continues in such regions,
which subsequently dominate the volume of the universe even if the probability to continue inflation is small.
On the other hand, we have explored a possibility to realize  an extremely large number of \emph{typical} $e$-folds\xspace
$\braket{\mathcal{N}}$, i.e. the expected $e$-folding\xspace number without resort to the volume measure. We have shown that this is
indeed possible by introducing a shallow local minimum around the hilltop, which was numerically confirmed using a
simple toy model: see Fig.~\ref{fig: meanN} showing the dependence of $\braket{\mathcal{N}}$ on the curvature of the local minimum, which
can be understood as the Hawking-Moss decay rate~(\ref{eq: Nesc})~\cite{Hawking:1981fz,Noorbala:2018zlv}.
It is the classical region with $\eta_\mathrm{cl}<1$ to the left of the local maximum that pushes back the inflaton to the local minimum,
and forces the inflaton to stay there for an extremely long time. Although extremely unlikely, it is possible for the inflaton to
move to the right of the local maximum due to the accumulated quantum diffusion. Then,
after moving to the right of the local maximum, standard slow-roll inflation follows as shown in Fig.~\ref{fig: Nvsphi} and
generates the primordial density perturbation consistent with observation.

We emphasize that our scenario does not rely on the volume measure and thus does not need any fine-tuning of the spatial position to
realize extremely long inflation.
Moreover, the eternal inflation and the slow-roll inflation phases are smoothly connected in a single-field regime, without any processes of
tunneling and bubble nucleation.
Therefore, it provides an alternative possibility to naturally realize extremely large number of $e$-folds\xspace, which is often necessary in
some cosmological scenarios.

\section*{Acknowledgments}
F.T. thanks Wen Yin for discussion on the eternal inflation.
This work is supported by JSPS KAKENHI Grant Numbers
JP15H05889 (F.T.), JP15K21733 (F.T.),  JP17H02875 (F.T.),
JP17H02878 (F.T.), JP18J01992 (Y.T.), JP19K14707 (Y.T.), JP18H01243 (N.K.), JP19K14708 (N.K.), JP19H01894 (N.K.), and by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan.

\nocite{}
\bibliographystyle{elsarticle-num}

redpajama_set_name: RedPajamaArXiv


text:
Home'Yank!' — A different kind of bravery
'Yank!' — A different kind of bravery
March 5, 2019 April 10, 2020 PWJW_Indy Reviews, StageBryant Mehay, D. Scott Robinson, David Zellnik, District Theatre, Dominic Piedmonte, drama, gay, historical, IndyFringe, Isaac Becker, Jerry Beasley, Jessica Crum Hawkins, John, Jonathan Krouse, Joseph Zellnik, Joshua Cox, Keven Bell, Lance Gray, lgbtq, musical, review, Scott Fleshood, Tanner Brunson, Tim Spradlin, World War II, Yank!
Emotions run high during war — excitement, anger, patriotic fervor, devotion, and love. For some soldiers thrown into the crucible that was World War II, the ones they wanted to embrace with all their might weren't the pin-up girls.
This is the world of "Yank!" the musical making its Indianapolis premiere at the District Theatre.
Stuart (Jonathan Krouse) answered the call to join the fight against Hitler and Tojo, but first he has to fit in with Charlie Company. He can barely hold a rifle, and he's not sure about his feelings towards his fellow soldiers, especially Mitch (Tanner Brunson), the only one to treat him with kindness. The others suspect he's different, and even call him "Light-Loafers," but they come to accept him, because "your squad is your squad."
On the way to the front, two things happen: Stuart and Mitch start to explore their feelings for each other, and Stuart meets Artie (D. Scott Robinson), a photographer for Yank! magazine, wise to and willing part of the gay underground just outside the U.S. Army's notice. While Charlie Company goes to combat, Stuart — an aspiring writer, keeping a detailed journal — joins Artie as reporters behind the lines.
Stu is doing well out of harm's way, but he still has feelings for Mitch. Then he gets the assignment to write about his old unit, and how war has changed them. More changes are coming for Stu, and he will discover how war is especially hell for a gay soldier — facing danger from his own people as well as the enemy.
The cast includes Isaac Becker, Dominic Piedmonte, Scott Fleshood, Joshua Cox and Bryant Mehay as fellow soldiers. Jerry Beasley, Lance Gray and Kevin Bell play hardened officers and NCOs, as well as somewhat softer characters. Jessica Hawkins wonderfully portrays "every woman," from radio entertainers to a lesbian WAC working for Gen. MacArthur.
Krouse and Brunson turn in wonderful performances, one constantly feeling deeply, the other deeply conflicted. The supporting cast is solid; Beasley earns his stripes. And with us usually seeing Robinson these days behind the scenes as producer or director, it's good to see him show his excellence as an actor.
This is a different kind of love story, but still touching — love is love, after all — and an eye-opening look at a hidden part of our history. While the characters are fictional, there was a Yank! Magazine, and playwright David Zellnik thoroughly researched the secret lives of gay soldiers and sailors of the era.
The songs, by David and his brother Joseph Zellnik, are snappy and sentimental in a style befitting the 1940s setting, including some interesting harmony.
Had this been a boy-meets-girl rather than boy-meets-boy, "Yank!" would look like the cinema hit of 1945. But it's 2019, and LGBTQ GIs are only now living out of the closet. Thus, this show is equal parts entertaining and important. Director Tim Spradlin deserves praise for bringing this gem to downtown Indy, as well as IndyFringe for hosting it at the District (former site of Theatre on the Square), 627 Massachusetts Ave.
This production runs through March 24; get info and tickets at indyfringe.org.
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