text:
Ronald McDonald is a clown character used as the primary mascot of the McDonald's fast-food restaurant chain.
Willard Scott Joe Camel Burger King John Wayne Gacy Gordon Ramsey
DigiToolbox has chosen The Ronald Mcdonald House to help and support raise money
This Saturday, 2/6 NC will be volunteering at the Ronald McDonald house in Winfield. We will make brunch for the families.
Seventh Graders making Valentines for guests staying at the Ronald McDonald House!
ok Ronald McDonald see you in the gymð
Rochester Freemasons' raising $ NOW till Feb 14 for The Ronald McDonald House of Rochester...again! htâ¦
Ronald McDonald is called "Tim Horton" up in the Great White North, i guess... weird.
Ronald McDonald would never do this to me. Neither would Max Brenner or Charlie Brown.. I need some of their fatty/sugary goodness.
Ronald McDonald and Fritz are hitting up the black diamonds after ski lessons with kids at â·
Little skiers learning before hitting the bunny slopes with Ronald McDonald at
Also, Willard Scott made the creepiest Ronald McDonald of all time.
study to see if it is wise to possibly seek the presidency. Willard Scott is a possible running mate along with Ronald McDonald.
Weatherman Willard Scott was the first original Ronald McDonald.
It's an old source but not as old as Ronald McDonald. Terry Cruise is starting to get tiring too tbh
Ah, Bisto! Robbie Williams criticised the notion of marriage between platypuss Ronald McDonald.
more chance of signing Ronald McDonald pal
Adam James' inspiration is Ronald McDonald. He is the only person in the world with more chips then Matt Norman.
The golden arches of McDonald's was a happy sight when I was a kid. Now, it makes me wanna fight Ronald McDonald.
Hoekstra Driver, Arnold Gandy, On Giving Tuesday last week he donated $50 to the Ronald McDonald House.
I liked a video Awkward Sex Ed with Ronald McDonald
We had so much fun at the Ronald McDonald assembly this morning learning about reading with EXCITEMENT!!!
The Ronald McDonald Houses in Albany are decorated for the holidays, thanks to
Just a reminder-we are collecting for Riley's Children's Hospital-Ronald McDonald House-ask your child about it
NEW INVENTION! 'The Gangsta Ronald McDonald' is a goal net mouse for $600
Ronald McDonald House opened. 46 families accommodated when they most need help. Royalties for Regions assisting! httpâ¦
NY: Volunteer abled spa provides comfort to caregivers
Low Country Dermatology holding holiday donation drive to collect supplies for the Ronald McDonald House.
Baby A was less than 1 pound when she was born.
Celebrating the end of our first marking period with a guest speaker- Ronald McDonald! Keep up your hard work!
I'm not saying I'm attracted to Ronald McDonald, but he does have great hair and endless McNuggets, so I might let himâ¦
Oh yeah, that's right, I forgot. We're on some quest to find Ronald McDonald or something like that.
Thanks to for Breakfast this morning! Check out the cookies that care program that benefits Ronald McDonald House
having a great time decorating cookies & making crafts w/ the families at Ronald McDonald house
Thanks to our team members that spent time baking treats for The Ronald McDonald House of Central Ohio this weekend!
what a lovely gift! Thank you Zipsters for supporting families staying at a Ronald McDonald House this season.
53 Division is partnering with along with Ronald McDonald House to have a Toy Drive for the Holidâ¦
Looking to give back during the holidays? Join us this Sunday at the Ronald McDonald House and cook dinner with LSP!
Ronald McDonald House makes the holidays special for residents
wasn't it Ronald McDonald that said that? Or McDonnell? Or McTwat?
Come back Ronald McDonald, all is forgiven!
Actual quote from Oh, that Las Vegas thing is on tonight, Ronald McDonald in Las Vegas. Think you mean Trevor...
So excited for our team in Aukland -- over $25,000 raised for the McDonald House Auckland.
PC as DPRK in Health discussing the march of Ronald McDonald throughout the world!
After another year of successful fund raising, we today donated £2300 to the Ronald McDonald House at St.Georges...
Houston employees supporting the Ronald McDonald House. ..over $3k raised!
We are in the holiday spirit! Volunteered at the Ronald McDonald house of Orlando today.
If I eat anymore McDonalds I will literally wake up one morning as Ronald McDonald himself burger in hand ðâ
Today in Calgary Jazz operates a special flight "searching for Santa" in cooperation with Ronald McDonald House...
Please help me raise money for the Ronald McDonald Charities.
someone once said that I look like ronald mcdonald. they dont talk much anymore â¤
even Ronald McDonald needs his christmas chlo x
Thanks to everyone who came out yesterday to the Max's Teddy Bear Brunch to support the Ronald McDonald House in Springfield!
While on a stopover in Singapore Kurt Cobain took some time-out to hang with Ronald McDonald (1992)
NEW INVENTION! 'The Nice Ronald McDonald' is a mouse socks for $700
Lovely early morning charity run in support of the Ronald Mcdonald House charity! ðð» https:/â¦
Architectural with a and by The Ronald in
NEW INVENTION! 'The Chubby Ronald McDonald' is an asylum ball for $14
New $27m Ronald McDonald House provides home away from home to families of seriously ill kids receiving treatment https:/â¦
I added a video to a playlist Ronald McDonald Tastes Burger King
Girl lemme draw your brow. Dang you'd be looking like Ronald McDonald with that ratchet brows ððð
Sigmas giving back during this holiday season by volunteering at the Ronald McDonald House! ð
Ronald McDonald house fundraiser socks got me feelin a lil cute!
Rev. Jesse Jackson, marchers call for justice for McDonald, Johnson:
Hanging out with Adrian Brody in his weird Bono / Ronald McDonald outfit at his debut art â¦
Ronald McDonald & Murphy helping 2 Light the House So can u 720.382.7242 be a Ray of Hope for $20/month
Ronald McDonald got money but he still a clown!ð¹
Allowing banks to teach financial literacy is "equivalent of having Ronald McDonald teaching kids about nutrition"
My attempt at red lipstick had me feeling like Ronald McDonald today. ð
Thank you Cyril, Thank you Ronald McDonald, Thank you ANC, Thank you bae Hellen Zille.. We have
Made it to Ronald McDonald house just fine. Craig Rookstool Paul J Long John Stoner. checked in at 4:45 made it...
Willard Scott was the first Ronald McDonald - he was fired for being too fat even though McDonald's is the reason why 20 milâ¦
Help us raise funds for Monroe Carell Jr. Children's Hospital at Vanderbilt at Vanderbilt and Ronald McDonald...
Long-banned chapters of Judge Dredd battling Ronald McDonald to be published
there's some Chucky/Ronald McDonald stuff going on there, too.
Ironically, the original Ronald McDonald, Jeff Juliano, is now a vegetarian
Ya girl Fragile will be performing LIVE with Trevor Turner aka "That Boi Vegas" to support Ronald McDonald House.
If you want to help people, itâs simple. Donate to Ronald McDonald House of Charities here:
That moment when you think Ronald McDonald followed you but it was actually just a weird old man...
At the Ronald McDonald House helping these wonderful children carve some pumpkins
Louis dresses up as Ronald McDonald for Harry. - (summary)
Ronald McDonald and Malfoy plotting to kill Harry Potter
Tonight Mariposa partners with the Ronald McDonald House for our annual "Trunk or Treat". We decorate our cars...
All of our YLH boys look like mini Ronald McDonald's ð
Ronald McDonald is going to eat you
HLHS students volunteering in the community cooking a home cook meal for children and families at Ronald McDonald...
We are proud to be working with the Ronald McDonald House for 36 years â¤ï¸ðð
NEW INVENTION! 'The Smelly Ronald McDonald' is a goal net ipad for $100
Ruth helped us write a cheque for the Ronald McDonald House Vancouver today as well.
Ok so today at school we could dress up & this guy was Ronald McDonald and he was running around and..
We are very proud to be in an organization that has been partnered with Ronald McDonald Houseâ¦
Today (10/30/15) we made our annual donation to the Ronald McDonald Houseâ¦
Less than an hour to go and every bit helps. CALL 1 800 230 KIDS. @ Ronald McDonaldâ¦
Glad to be part of 1st annual Halloween Masquerade Ball-Albany. Benefits Ronald McDonald House Charities Cap. Region
NEW INVENTION! 'The Thug Ronald McDonald' is a goal net wristband for $100
that's pretty impressive ðð I'm going as Ronald McDonald tomorrow - not quite as sexy.
9/9 people would rather have a dog as president than Ronald McDonald Trump
Final hour to donate to the Ronald McDonald House Radiothon. Help give our families a "home-away-from-home."
Ronald McDonald House trick or treat party! Cute kids!
on a next video you should react to Ronald McDonald slaughter
*** !ð³ð¬I really thought he was actually ronald mcdonaldð¡ð¿ Thisð is why you take them swimmingð on the first dateðð¤
Hey Eagle Nation! ClubStJude just dropped off PopTab donation at the Ronald McDonald House~~342 lbs.! WOW
Oregon Blaze Gold off and running at tourney. READ >
Just saw Ronald McDonald and he was waving as he drove by. I don't like Halloween anymore.
So true. No need to drag Ronald McDonald into that mess in Ames.
should've came to Ronald McDonald today then you lick
.donate $63,484 to the Ronald McDonald House!. -
Today we celebrate 36 years of endless love provided by the Ronald McDonald House. We love supporting â£ðâ£
never mind a one night stand with Ronald Mcdonald id be like that anywaysðð
is that John Wayne Gacy jr beside Ronald McDonald
how did you get Ronald McDonald to pose with a bazooka? (bottom left)
Ronald McDonald statue found decapitated, burned, with his feet cut off - by Heather Dockray
Happy birthday to my beautiful mama aka... Angrykidd, sideshow bob and Ronald McDonald ððð
Why clowns are the most terrifying mofos around:. Pennywise. Ronald McDonald. John Wayne Gacy. Donald Trump. That should get my point across.
Best news! Ip Man 3 is coming out. I have no clue as why people say I look like Donnie Yen. To be fair, my hair looks like Ronald McDonald.
Me: This diet is easy. Mayor McCheese: We miss you!. Ronald McDonald: Come back!. Hamburglar: We have your *** pics. Me: On mâ¦
Symphony Victoria here with DeKalb Chamber meeting Ronald McDonald for the first time! Love the redâ¦
I liked a video The Wacky Adventures of Ronald McDonald: Scared Silly (1/4)
Today our members volunteered & ran at the Ronald McDonald House 5k.Thanks to all who came & congrats to our winners hâ¦
That video was right on time, close to October. I never trusted Ronald McDonald lol
Video: Ronald McDonald Playground Slaughter! (Skit) via LMFAO bro this has me DEAD.
Building an inclusive strategy to better serve families and kids
Another Sunday, another visit to Riley's Ronald McDonald House to make a home cooked meal.
Ronald stepped it up! This new McDonald's concept is a step up from the Big Mac
Today 12-5pm in at the annual grape stomp! Partial proceeds donated to Ronald McDonald House
I liked a video from HIS TONGUE! - Reacting to Ronald McDonald Playground Massacre!
I just got really scared that Ronald McDonald fanfic probably exists
leave the put downs to Gordon Ramsey and the cooking to Ronald McDonald
Me gustó un video de Ronald McDonald Playground Slaughter!
Ronald McDonald cheap as *** ð I got a 10 piece nugget what Ima go with 1 ranch pack ð
Having fun with Ronald McDonald after the Zoo Run! @ Kansas City Zoo Run
Alden Richards & Maine Mendoza with Ronald McDonald for the second TVC.
Help the Ronald McDonald house charities. By ordering from
and we have to watch stone footed Ronald McDonald fkn Fellaini come on. Sickening
Come to room 227 tomorrow after school to take part in FCCLA's 1st service project of the year! We're making snackbags for Ronald McDonald!
Jack in the Box as Moe. The Burger King King as Larry. Ronald McDonald as Curly, no Shemp, he strikes me more of a Shemp
My flight has overhead bins decorated by kids from the Ronald McDonald house charities!
"Micheal Jackson... the animatronic lovechild of Ronald McDonald and An American Werewolf In London" - Bob Stanley, Yeah Yeah Yeah
Watching Mack Brown and Mark May talk football is like watching Ronald McDonald and Hamburgler talk about prime rib.
serving all-day breakfast descends into talk about the ugly original Ronald McDonald on The 10 At10.
what worries me is who is coming the other way? Mayor mccheese or Ronald McDonald. Would prefer hamburglar
Nah my home boy Ronald McDonald will take care of youð
Still haunted by the memory of Ronald McDonald roaming our halls when we were the fox8 cool school
Chicago Jazz takes time off from training to prepare dinner for families at the Ronald McDonald house
Why yo eyebrows look like Ronald McDonald though?
And to think, all this time I've been afraid of Ronald McDonald.
Bill Burr to be Ronald McDonald. Jim Gaffigan to be Jack. Brian Regan to be Burger King. Louis C. K. to be Wendy.
You listen to Ronald McDonald. You yell with a bear. You stay at the Roger Moore Lodge. Good night.
Thought Ronald McDonald was transport cabinet member gcc as the traffic planning in high street is a joke ...
Yet another year and still no Ronald McDonald birthday party.Thanks, timehop
They mix it in with the blood of the Ronald McDonald house children
We may have to head home today because every hotel seems to be full along with Ronald McDonald house
Ronald McDonald House Charities of San Diego's Table For Tots event is happening this month. Check out the...
HEADY: Ronald McDonald decapitated by Museum of Broadcast Communication. Head rescued by
Ronald McDonald House has a charity golf tournament on Mon. August 31 and needs a photograâ¦
I stopped eating at Mcd's when I tried to donate money to the Ronald McDonald House but the employee didn't speak English.
The amount of fast food trash I clean out of my car would make Ronald McDonald embarrassed, but I like to see it as an achievement instead.
Got to see Ronald McDonald well getting a coffee today
Miss Tina is hosting a Pasta Fundraiser in order to give back to her home away from home, The Ronald McDonald...
UHY donates to Ronald McDonald House by 'socking' co-workers
News flash: the Ronald McDonald Care Mobile will be at Gemini on 8/20! Open to all D63 students. Find out more.
*** matt is that Ronald McDonald behind you?
HMHS graduate receives scholarship from Ronald McDonald House Charities
Happy birthday Ronald McDonald I love you ðð wishing you many, many more!
DuPont Pioneer golf tournament raises more than $3K for Ronald McDonald House.
Thankful for Rady Children's Hospital and The Ronald McDonald House San Diego for making aâ¦
Before and after shots of Ronald McDonald House Charities Hamilton's new website designed by
Ever wonder what Ronald McDonald Houses do? Watch this:
Got called in early for treatmentð© maybe I'll get into Ronald McDonald House today
You never know what can happen at a NoFX show. Ronald McDonald had no idea what was in store forâ¦
thought bringing back the colonel was cute. Just like the adult Ronald McDonald ads years ago.
Those Ronald McDonald commercials are a lie. Like *** I would let my child sit outside and eat with a man in a clown outfit!
And and two of her friends, Ronald McDonald and coffee.
Earlier this Summer, UHY's Michigan office donated to via their "Ronald Sock Challenge":
3 cents from every Happy Meal sold goes to Ronald McDonald House & helps fund grants like the one that built this new playground equipment.
Getting breakfast at a fast food restaurant is quite the gamble. You put the outcome of your entire day in the hands of Ronald McDonald
I just saw that you can go to online school to work at a weed dispensary. Is that the same as going to Ronald McDonald college?
oh cool, sounds similar to the Ronald McDonald thing we had to use when Grace was rushed to St.Thomas' in London ð
Vandalism could not damper the spirit of the new ADA compliant playground equipment here at Wesselman Park thanks to Ronald McDonald House!
Thank you to all our members & staff for helping raise funds for our local Ronald McDonald House
Giving Back to our Community - The Story of the Ronald McDonald House "Juice with Love" Program - Glow Juicery
Assist w/check-out & other duties as a volunteer for Ronald McDonald House
Brooms and bad language used to chase rat from McDonald's
If Rob Ryan is suing some people because his house is sinking Burger King, Ronald McDonald, Wendy and Colonel Sanders should retain counsel
Just for the fun of using the Ronald McDonald phone. Mind you, phoning Wimpy would be more ironic.
Today's moment of zen... at Ronald McDonald House.
Come on down to support the Ronald McDonald House NY today- 405 East 73rd St, NY -- sidewalk sale!!
Fun team visit to the Ronald McDonald House in Bakersfield today.
QSI donated necessities to the Kansas City Ronald McDonald House last month and enjoyed personally delivering them. httpâ¦
Kyle,it's Ronald McDonald get it right
I came here for Ronald McDonald guro, and I leave disappointed
That clown Trump getting any votes at all is a complete disgrace to our Democracy. Might as well elect Ronald McDonald.
the Ronald McDonald kids call our games "Texas games" since they've never heard of them up here. :-D
Norm McDonald as Colonel Sanders? I wonder what his twin brother Ronald has to say about that.
cant be a paedo your mum is over 18. An atleast you acknowledge I have a "lass" somethin u clearly struggle with Ronald McDonald
Old McDonald had a farm. He also had a redheaded goth son named Ronald who did acid and talked to hamburgers and purple blobby things.
So Grace Jones and Ronald Mcdonald had a 'love child'?
If Matt Jones wins a major before Jason day. It's like Ronald McDonald being the chosen party clown only to have the Hamburgler turn up.
Eat this, Ronald McDonald has helped bring into the world a Thames estuary
Fantastic night tonight! Looking forward to annual Ronald McDonald 5ks and even more frequent Cooks for Kids!!
no next is Bozo, then Twisty, Ronald Mcdonald, then Joe the plumber.
Why not run as Ronald McDonald since he is basically a banking and corporate shill at our expense.
Participating in the 2015 Glow Run 5K tonight benefitting the Ronald McDonald's homes in Arkansas. First time experience for me.
Happy Birthday to Ronald McDonald, 1 of greatest men in and my favorite client
People want to retire Ronald McDonald? Further proof that society is against redheads. Are you paying attention, Weasleâ¦
Alpha Delta Pi foundation has just announced that we've now contributed over {$10 Million} to Ronald McDonald...
We don't mind waiting in traffic so Ronald McDonald can scoot past us, right?
Ray Martin from ACA conducting a review into is like having Ronald McDonald hand out Michelin Stars.
Ronald McDonald kills millions of cows and he's the world's most beloved clown, but I butcher one and I "ruined your son's birthday party"?
Ronald McDonald Visits Main Library @ 64 East 1st St Mesa. 2-245pm on June 16th. Ronald McDonald and his big red...
Come clean growin up in Harlem thou all I seen was Jordan/Nas/Martin Luther King Jr/Jesus Christ/ & Ronald McDonald. Childhood top 5s.
you dressed my cat up as Ronald Mcdonald.
Andy Townsend critiquing these players, it's like Ronald McDonald telling Gordon Ramsey how to cook.
DYK: McDonald's first Ronald McDonald was played by none other than TV personality Willard Scott?
Marreese Speights (giant purple slob whose clumsy antics provide comic foil to Ronald McDonald) will not play in Game 3 on Saturday
Fact: French fries were discovered on accident after Ronald McDonald shot the Burger King over a fryer using a potato as aâ¦
Ronald McDonald lookin Jason is still swinging from tunas *** ! What a ***
Annual Halifax moose heads teddy bear toss for the Ronald McDonald house!
"You look like a *** cat dressed up like Ronald McDonald". Oh college humor... You always make me laugh...
Willard Scott as Ronald McDonald! "Watch for me on TV. We'll have lots of fun."
I hear Gove as Justice Secretary a "tough call" for Cameron - with strong claims from Joe Pasquale, Ronald McDonald and the Chuckle Brothers
How many of you knew that Ronald McDonald was 1st portrayed by Willard Scott?
that is Willard Scott who was on the Today Show for many years just never saw his pic as Ronald McDonald
That's Willard Scott as Ronald McDonald. He was also Bozo the Clown in DC. There are many more clowns in DC now.
Willard Scott was the original Ronald McDonald who was fired from McDonald's for being overweight.
Not all negative with this draft: RB Melvin Gordon hosted a charity event Tuesday night to benefit Ronald McDonald house.â¦
your mate Ronald McDonald is back in the news!
she can't go out with you Ronald McDonald. I thought you knew Mickey Ds was open 24/7
John Wayne Gacy and Ronald Mcdonald in a buddy comedy.
Art night again at the Ronald McDonald house. This Brennig asked if I would paint Morning Glories.â¦
What's fair about using schools to market fast food to kids? . Ronald McDonald is the Joe Camel of fast food.
Ronald McDonald is not Ronald belisario. Therefore, Ronald Reagan is not Ronald McDonald
Joe Camel was ousted from ads because of his appeal to kids. Yet we let Ronald McDonald cater to them.
Sweat Shop Brew Kitchen cooked up a good honest feed to provide dinner at the Ronald McDonald house last week.
Jamie has Ronald McDonald hair when he's spanking Claire.
the Senators may have the Hamburglar, but Capitals have Ronald McDonald in their corner:
Champagne flutes, set and ready for the Ronald McDonald gala tonight! @ The Pavilions at the Angus Barn
He may as well have said "I'd be happy with Heinrich Himmler in drag, or a coked up, cry wanking, Ronald McDonald , or, Boris Johnson !!"
When my mom calls Ronald McDonald the president instead of Ronald Reagan
WARNING: Ronald McDonald has a censored button, so don't curse @ American Legion Post 854
I was voted most likely to be a teacher . Was Brian Williams? No. He was Ronald McDonald
Willard Scottâs Ronald McDonald: Forefather of Nightmare Fuel: When the idea to write something about Willard ...
Happy birthday to the first Ronald McDonald, Willard Scott, the forefather of nightmare fuel. by
Fun fact: Willard Scott was the original Ronald McDonald, between 1963 and 1966.
Born this date in 1934, Today Show weatherman Willard Scott who was also the 1st Ronald McDonald.
Aye && then can we take a picture with Ronald McDonald ???
so that's why Ronald McDonald wasn't in Supersize Me.
La-Z-Boy with Ronald McDonald House partnership exhibits how corporations help advance the cause of non-profits.
in the words of Ronald McDonald... I'm lovin' it!
Why are there no photoshops of Will Ferrell as Ronald McDonald, I want to see this!
lololol nope I got the Ronald McDonald semen special
Have fun with Ronald McDonald and his gang when you celebrate your baby's birthday in McDonalds! Get a party...
Ronald McDonald wouldn't treat me like thisð©.
What from all ten American's present! "Awesome" Most Americans think Ronald McDonald is "Awesome"!
Popped hella tabs for Julie and the Ronald McDonald House tonight
The Shamrock Shake is making its annual return! Did you know that is started as a means to fund the first Ronald McDonald hâ¦
My dad is the original Ronald McDonald Can you imagine how many women he had at the height of his fame ?
Ronald McDonald house brings families together but never a story like this
Ronald McDonald may have a bone to pick with LeBron James after this one. While talking to the media on Tuesday, James opened up about how
Use to have a Ronald McDonald made out of leggos, but my smart *** took it apart thinking I can put that *** together.
My bike got the Ronald McDonald deluxe paint job.
I wish URL would get a pretty darkskin girl to be on stage instead of Ronald McDonald.
"Ronald McDonald ain't chillin in tears ð
maybe..but that's like my girl tears out my heart and leaves me for Ronald McDonald and then I wanna wear his clown shoes lol
Spent the day painting at Ronald McDonald house with the crew and presented them with a $1,000 donation
wait is mac's real name really... Ronald McDonald?
I can never get tired of Ronald McDonald being turnt up. ð ð.
another one i got is ronald mcdonald. I NEVER SEEN GREASE
Ronald McDonald was the creepiest clown ever and that's before being forced to sit on his lap.
Go on Instagram and like this picture of my smokin hot sister to help us donate ðµ to the Ronald McDonald house!!
Our working bee at Ronald McDonald House Parkville was a great success. We look forward to volunteering again in...
. Check out Ronald McDonald rare print destroying the earth
Rochester's Ronald McDonald House celebrating 25 years - they tell us how next on
Key club is doing a pop tab drive for the Ronald McDonald House so if you want to donate some bring them to me :)
Uhhh"this is what ronald mcdonald would want
Reverse raffle to benefit Ronald McDonald House: HUNTINGTON - There will be a Reverse Raffle t...
"Let's McFreakin' Lose it! Ronald Mcdonald after hearing the Rocket Ship song to much.
I like the Ronald McDonald before he sold out to the big sirloin business
I wanna keep my futures so bad but they make my feet look big af like Ronald McDonald big ðð
Make a lil money leave a little on the dresser-Ronald McDonald
Great day volunteering at Ronald McDonald House with my family! MB is lucky to have a facility like that!
Paint n Sip :) we painted canvas's for the Ronald McDonald house. ðð°
Ronald McDonald House in Orange is just weeks away from welcoming their first families. Tonight
Talking about Politics. "...Bill McDonald...". Katie "wait did he say Ronald McDonald. Like the clown ?"
Kate Kirchen don't give a fuq what color the dress is, she just shares lipstick with Ronald McDonald instead âï¸ð
her: the manager of the McDonalds down the street called today... him: [sitting on couch next to Ronald McDonald statue] Diâ¦
and being Panhellenic for our mock sip and paint! Loved painting canvases for the Ronald McDonald House!ðð¨
those the Ronald McDonald ones I was talking about. Terrible nickname at that point, but MJ wore it in a McD's commercial
is Ronald McDonald the CEO of McDonald's? No. He is a spokesman, a face of the company. Same as Potus.
When Ronald McDonald finds out you like Burger King more
SigEp takes over the Ronald McDonald House Kitchen! Great job boys, keep up the good work!
Tennessee Tuxedo! Bought the complete set for $20. So I think Chumley & "Ronald McDonald's Autistic friend Grimace" would get along. :D
he lives in Kentucky in a big house with colonel sanders, Ronald McDonald and papa john & mr nando
delta beta sigma is selling these for $18! all the money goes to the Ronald McDonald house in littleâ¦
is what happens when Steve Zahn and Ronald McDonald mate.
Please help my son raise some money for Ronald McDonald House Charities.
Makeup has some of these women thinking they look like Beyonce but they look like Ronald McDonald. Less is more.
Robert Durst Chris Borland Hillary Clinton Prince Harry Top Gear White House March Madness St Patrick San Francisco Don Quixote Jeremy Clarkson Champions League Kendrick Lamar United Airlines Middle East Kanye West New Orleans Justin Bieber Los Angeles Loretta Lynch Twin Peaks Apple Watch Benjamin Netanyahu Prime Minister Benjamin Netanyahu Islamic State Mitt Romney Pete Rose Jeb Bush Manchester City Saint Patrick Rand Paul Best Photo Internet Explorer 8 Comedy Central Stefano Gabbana Vladimir Putin Secret Service Saudi Arabia Paul Walker Premier League Jimmy Savile James Bond Evander Holyfield Will Ferrell Michelle Obama David Cameron Las Vegas Man City Tony Blair Internet Explorer World Cup Whole Foods Jessica Lange Vin Diesel Howard Schultz Kim Kardashian Dulles International Airport Long Island Ellen Pao Good Reason South Pacific Ray McDonald Robin Thicke White Americans Notre Dame Mad Max North Carolina Molly Ringwald Mariah Carey Marvin Gaye Miles Teller Scott Disick Taylor Swift Wayne Rooney Zlatan Ibrahimovic Grand Slam Nigel Farage Six Nations Hong Kong Century Fox Chris Christie Natalia Kills Mars One Gareth Bale Cyril Smith George Osborne Home Page Manchester United Loch Ness Jeremy Forrest New Zealand Pernod Ricard Prime Minister Benjamin Nou Camp Mutual Fund Marie Slaughter Kappa Delta Rho Kleiner Perkins Jimmy Kimmel Miley Cyrus
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text:
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subset: commoncrawl


text:
David Gibson Jr.March 10,2013David Gibson Jr.
BRANDON David Gibson Jr., 88, of Brandon, died Friday, March 8, 2013, at the Helen Porter Health & Rehabilitation Center in Middlebury.
A full obituary and funeral arrangements will be published in a later edition of the Rutland Herald.
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text:
Linear Partial Differential Equations for Scientists and Engineers / Edition 4by Tyn Myint-U, Lokenath Debnath
Pub. Date: 12/15/2006
Publisher: Birkhauser Verlag
One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena. PDEs have a wide range of interesting and important applications in every branch of applied mathematics, physics, and engineering, including fluid dynamics, elasticity, and optics.
This significantly
One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena. PDEs have a wide range of interesting and important applications in every branch of applied mathematics, physics, and engineering, including fluid dynamics, elasticity, and optics.
This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books, including conservation laws, the spherical wave equation, the cylindrical wave equation, higher-dimensional boundary-value problems, the finite element method, fractional partial differential equations, and nonlinear partial differential equations with applications.
Key features include:
* Applications to a wide variety of physical problems in numerous interdisciplinary areas
* Over 900 worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry
* Historical comments on partial differential equations
* Solutions and hints to selected exercises
* A comprehensive bibliography—comprised of many standard texts and reference books, as well as a set of selected classic and recent papers—for readers interested in learning more about the modern treatment of the subject
Linear Partial Differential Equations for Scientists and Engineers, Fourth Edition will primarily serve as a textbook for the first two courses in PDEs, or in a course on advanced engineering mathematics. The book may also be used as a reference for graduate students, researchers, and professionals in modern applied mathematics, mathematical physics, and engineering. Readers will gain a solid mathematical background in PDEs, sufficient to start interdisciplinary collaborative research in a variety of fields.
Also by L. Debnath: Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition, ISBN 0-8176-4323-0.
Product Details
- 9780817643935
- Publisher:
- Birkhauser Verlag
- Publication date:
- 12/15/2006
- Edition description:
- 4th ed. 2007
- Pages:
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Table of Contents
Preface to the Fourth Edition Preface to the Third Edition Introduction First-Order, Quasi-Linear Equations and Method of Characteristics Mathematical Models Classification of Second-Order Linear Equations The Cauchy Problem and Wave Equations Fourier Series and Integrals with Applications Method of Separation of Variables Eigenvalue Problems and Special Functions Boundary-Value Problems and Applications Higher-Dimensional Boundary-Value Problems Green's Functions and Boundary-Value Problems Integral Transform Methods with Applications Nonlinear Partial Differential Equations with Applications Numerical and Approximation Methods Tables of Integral Transforms Answers and Hints to Selected Exercises Appendix: Some Special Functions and Their Properties Bibliography Index
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Gene-expression profiling of tumors may soon become a routine part of how an oncologist decides on the best way to treat an expanding number of malignancies. While many technologies are in early stages of clinical validation, few have made it to the market. As in the early days of 2-D electrophoresis, though, finding meaningful predictive differences in a sea of data remains elusive.
Increasing progress in validating multiple-gene signatures has reduced the firehose effect. In February 2007, the FDA okayed Agendia's (www.agendia.com) MammaPrint for the prediction of breast cancer returning within 5 to 10 years from initial diagnosis. It became the first multivariate in vitro diagnostic assay to be approved by the agency.
Fifteen percent of stage 1 breast cancers recur, and among those patients with recurrences, chemotherapy will benefit a minority. Since oncologists can't predict who will respond the most to chemo, standard practice is to prescribe it to all patients. Treatment regimens cost between $15,000 and $30,000 per patient and have serious side effects.
Companies are thus developing gene-signature tests that aid in identifying patients most likely to benefit from treatment for various types of cancers. Thus far insurance providers have been willing to pay for tests because they potentially save on chemotherapy costs.
Patricia F. Dimond, Ph.D. ([email protected]), is a principal at BioInsight Consulting.
Patricia F. Dimond, Ph.D. ([email protected]), is a principal at BioInsight Consulting.
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Pyridoxal-5'-phosphate (PLP) is an obligatory cofactor for the homodimeric mitochondrial enzyme 5-aminolevulinate synthase (ALAS), which controls metabolic flux into the porphyrin biosynthetic pathway in animals, fungi, and the α-subclass of proteobacteria. Recent work has provided an explanation for how this enzyme can utilize PLP to catalyze the mechanistically unusual cleavage of not one but two substrate amino acid α-carbon bonds, without violating the theory of stereoelectronic control of PLP reaction-type specificity. Ironically, the complex chemistry is kinetically insignificant, and it is the movement of an active site loop that defines kcat and ultimately, the rate of porphyrin biosynthesis. The kinetic behavior of the enzyme is consistent with an equilibrium ordered induced-fit mechanism wherein glycine must bind first and a portion of the intrinsic binding energy with succinyl-Coenzyme A is then utilized to perturb the enzyme conformational equilibrium towards a closed state wherein catalysis occurs. Return to the open conformation, coincident with ALA dissociation, is the slowest step of the reaction cycle. A diverse variety of loop mutations have been associated with hyperactivity, suggesting the enzyme has evolved to be purposefully slow, perhaps as a means to allow for rapid up-regulation of activity in response to an as yet undiscovered allosteric type effector. Recently it was discovered that human erythroid ALAS mutations can be associated with two very different diseases. Mutations that down-regulate activity can lead to X-linked sideroblastic anemia, which is characterized by abnormally high iron levels in mitochondria, while mutations that up-regulate activity are associated with X-linked dominant protoporphyria, which in contrast is phenotypically identified by abnormally high porphyrin levels. This article is part of a Special Issue entitled: Pyridoxal Phosphate Enzymology.
ALAS1 (EC 184.108.40.206) catalyzes the PLP-dependent reaction of glycine with succinyl-Coenzyme A to produce Coenzyme A, carbon dioxide, and ALA, the latter of which is the common committed precursor of all biological tetrapyrroles, including hemes, chlorophylls, and cobalamins [1,2]. ALAS is found exclusively in non-plant eucaryotes and the α-subclass of proteobacteria. Plants and other bacteria do not code for an ALAS and in these organisms ALA is instead produced by the evolutionarily related PLP-dependent enzyme glutamate-1-semialdehyde 2,1-aminomutase, which catalyzes the single substrate intramolecular transamination of glutamate-1-semialdehyde to ALA [3,4].
ALAS activity couples heme and cytochrome production to aerobic respiration via common utilization of succinyl-Coenzyme A, as illustrated in Fig. 1. This reaction is both the key regulatory and rate-determining step of porphyrin biosynthesis [2]. Consequently, alterations in ALAS activity have marked effects on porphyrin production. In animals two chromosomally distinct and differentially regulated ALAS genes are present, one of which is devoted to hemoglobin biosynthesis in developing erythrocytes (ALAS-2), and the other of which is expressed in all tissues for production of cytochromes and other hemoproteins (ALAS-1) [2]. Excluding the mitochondrial import sequences, the two human ALAS gene products share 74% identity at the amino acid level.
The differential production of ALA in plants and animals provides a very interesting area for speculation on the key evolutionary branch points between these kingdoms of organisms. Whereas animals utilize ALA to produce hemoglobin and other hemoproteins primarily for aerobic respiration, plants preferentially employ this metabolite in the biosynthesis of chlorophylls for photosynthesis. In both cases PLP-dependent ALA formation plays a central role in energy acquisition and utilization by the host organism [5,6]. ALAS is nuclear encoded and targeted to mitochondria, which are most closely related to α-proteobacteria, the only procaryotes known to code for ALAS [7]. This suggests that ALAS may have been an important factor in the natural selection of these particular bacteria as mitochondrial progenitors. In plants glutamate-1-semialdehyde 2,1-aminomutase is also nuclear encoded but is instead targeted to chloroplasts [5]. These organelles are evolutionarily derived from cyanobacteria, which obtain their energy via photosynthesis [7]. The structurally based finding that ALAS likely evolved from glutamate-1-semialdehyde 2,1-aminomutase would arguably identify a primary feature of the momentous divergence in eucaryotic metabolism away from utilizing metalloporphyrins to harvest photon energy, and instead focusing on stepwise reduction of molecular oxygen to water [8].
ALAS has been classified as a member of the α-family of PLP-dependent enzymes [9], which catalyze transformations of amino acids wherein the bonding rearrangements occur at the substrate α-carbon atom [10]. ALAS was initially categorized as part of the aminotransferase fold-type I subfamily branch of the α-family tree, based on sequence alignments [11], but recent analyses based on crystallographic data indicate that it is more appropriately considered to be part of the fold-type II subfamily branch [8]. Similar to the related l-amino acid transaminases, ALAS is a homodimer wherein the active sites reside at the subunit interface (Fig. 2) [12].
Currently the only crystal structures of ALAS available are for the enzyme from Rhodobacter capsulatus, but with 49% sequence identity and 70% similarity to the catalytic core of human ALAS there is little doubt that these structures provide excellent models for the catalytic cores of all ALASs [13]. Not only has the holoenzyme structure been solved, but also the structures with either glycine or succinyl-CoA bound [13]. Alignment of these substrate-bound structures permits construction of an excellent model for the Michaelis complex, and the open active site loop in the holoenzyme structure allows visualization of just how this loop enforces an induced-fit type mechanism and must move away from the active site cleft in order to allow ALA dissociation [14]. The R. capsulatus ALAS crystal structures have proven to be invaluable aids to robust interpretation of kinetic and spectroscopic data obtained with the purified recombinant murine ALAS-2 enzyme.
The PLP cofactors delineate the area of the active site where the bonding rearrangements occur, and are very near the center of the three-dimensional structure. Although the adenine ring of succinyl-Coenzyme A binds near the enzyme surface, the pantothenate portion of the molecule extends down a cleft towards the cofactor, over 20 from the surface. This solvent excluded active site environment appears exquisitely evolved to ensure highly specific molecular recognition of succinyl-Coenzyme A, while the area where glycine binds is so spatially constrained that even l-or d-alanine will not substitute as alternative substrates. At the apex of the active site loop T4302 forms a strong 2.4-2.5 low barrier hydrogen bond with the carboxylate tail of succinyl-Coenzyme A upon adoption of the closed conformation (Fig. 5) [15]. T430 is in turn held rigidly in place by bracketing proline residues at positions 429 and 432, and despite being approximately 10 away from the center of the PLP cofactor this residue is clearly essential for effective catalysis, as even the conservative T430S mutation has been found to be associated with X-linked sideroblastic anemia [16,17].
Jencks [18] suggested that God created PLP especially for enzymologists who enjoy pushing electrons, and to the extent this might be true ALAS should provide ample opportunity for entertainment, as the chemical mechanism is not only complex, but also unusual and enlightening. Two-dimensional depictions of the reaction chemistry such as that in Fig. 3 give a good indication of the complexity, yet fail to convey the precise stereoelectronic control that is believed to be involved in substrate recognition and the conversion of substrates to products. In fact, ALAS would probably provide a good model system for examining the seemingly never ending question as to the extent to which an enzyme can "freeze out" torsional motions of the reactants and translate this so called "entropy trap" into rate enhancements [19–21].
The ALAS reaction chemistry is unusual for a PLP-dependent enzyme in that not one, but two substrate amino acid α-carbon bonds are cleaved during the reaction cycle, as if it were both a transaminase and a decarboxylase. This was for many years difficult to reconcile with the generally accepted theory that reaction-type specificity of PLP α-carbon substrate bond-cleavage is under strict stereoelectronic control [22–24]. The stereoelectronic control hypothesis (sometimes referred to as "Dunathan's hypothesis") states that upon formation of an external aldimine the relative lability of the three substrate amino acid α-carbon bonds is crucially dependent upon their orientation relative to the planar and electron withdrawing cofactor π-bonding system. Cleavage only occurs rapidly when a bond is aligned perpendicular to the plane of the PLP-aldimine conjugated system. This three-dimensional stereoelectronic orientation most closely aligns the σ-orbitals of the bond to be cleaved with the π-orbitals of the cofactor, and since these orbitals must overlap and rehybridize for any reaction to occur, the favorable positioning accelerates the rate of cleavage over the out-of-alignment α-carbon bonds, by a factor that has been estimated to be approximately a million-fold [25,26]. Thus, an important function of PLP-dependent enzymes in general is to simply bind the external aldimine complex such that the target bond is oriented perpendicular to the plane of the cofactor, thereby optimally exposing this single bond to the electron sink functionality of the cofactor, while simultaneously providing a means of discriminating against side reactions. Cleavage of more than one bond during a reaction cycle, as in the ALAS or dialkylglycine decarboxylase reactions [27], therefore implies that there must be some intermediate torsion about the α-carbon bond between reaction steps, an alternate reaction pathway that does not utilize the electron sink property of the cofactor, or that the stereoelectronic control hypothesis is flawed or incomplete. In the case of dialkylglycine decarboxylase it is essentially the first of these possibilities, torsion about the α-carbon bond between decarboxylation and transamination half-reactions, that was found to be operative [24]. In the ALAS reaction, however, it is the second possibility, an alternate reaction pathway, which explains how the enzyme catalyzes multiple α-carbon bond rearrangements. Thus the two unusual PLP-dependent enzymes support the theory of stereoelectronic control, but each in a different way.
The overall reaction essentially involves the PLP-dependent replacement of the carboxyl group of glycine with a succinyl group donated from succinyl-CoA, but the mechanistic pathway is far more involved than a PLP chemist might envision, as seen in Fig. 3. The evolutionary relationship to l-amino acid transaminases is mechanistically manifested in utilization of the conserved active site lysine residue, that forms an internal aldimine with PLP in the absence of amino acid substrates, to catalyzes proton transfers following formation of external adimines with glycine or ALA [28,29]. The stereospecific cleavage of the pro-R bond of glycine and ALA carbon-5 by ALAS corresponds to recognition of these achiral stereocenters as it they were in fact the L-isomers. Upon formation of the external aldimine with glycine the binding of succinyl-Coenzyme A triggers accelerated removal of the pro-R proton of glycine by lysine-313, (structures II–III in Fig. 3) [29–31]. Kinetic and structural data converge upon the conclusion that succinyl-Coenzyme A binding promotes an induced fit type mechanism involving movement of the highly conserved active site loop over the active site such that the cofactor, substrates, and key enzyme residues are brought into optimal apposition for catalysis to occur [13,31–33]. Crystallographic data from succinyl-Coenzyme A bound R. capsulatus ALAS indicate that in three out of four monomers the PLP cofactor is released from the active site lysine and is present as the free aldehyde, further suggesting that binding of this substrate facilitates reaction of the cofactor with glycine, as previously demonstrated kinetically [13,31].
During stopped-flow experiments the reaction from structures II to V occur over approximately ten milliseconds at 30 °C, and the quinonoid intermediate (III) forms and decays too rapidly to be directly observed, and can only be detected spectroscopically when glycine is replaced by O-methyl glycine3 [34]. Reaction with succinyl-Coenzyme A yields an unstable tetrahedral intermediate (IV), which rapidly collapses to form an external aldimine with α-amino-β-keto adipate (V). Decarboxylation of this intermediate produces a remarkably stable and pH-titratable quinonoid intermediate (VII) [29,35], but due to the stereoelectronic constraints discussed above the decarboxylation step does not directly utilize the cofactor as an electron sink, and instead proceeds via an enol (VI) formed by β-keto acid decarboxylation. This step is acid catalyzed with an apparent pKa of 7.7 ± 0.1 by H207, which resides almost directly above the cofactor, as depicted in Fig. 4 [32]. The enol is in turn in rapid equilibrium with an unusually stable quinonoid intermediate (VII), as well as the product bound external aldimine formed by protonation of the enol by K313 (VIII) [29]. Ironically, the quinonoid intermediate that has been the key spectroscopic signal used to study the enzyme chemistry is not directly on the reaction pathway! ALA is then released in the slowest step of the reaction to complete the cycle. The remarkable precision of these steps is evidenced by kinetic isotope data with deuteroglycine as substrate, which indicated that the deuteron removed from glycine at the beginning of the reaction cycle is, at least in a significant proportion of turnovers, returned back to the ALA product, and is not exchanged with protons from water or the enzyme during the catalytic cycle [32].
Although the ALAS reaction chemistry may be complex, it is not kinetically significant. Instead it is movement of the active site loop towards the open conformation (Fig. 5) that controls the rate at which ALA dissociates, and therefore the overall catalytic rate [14,31,32,35,36]. This is depicted in Scheme 1, which records the rates and equilibrium constants for the kinetic mechanism, along with the assigned reaction steps and the conformational status of the enzyme at each step. The binding of substrates and formation of the 1-amino-2-ketoadipate intermediate external aldimine are rapid, and in stopped-flow experiments the first positive signal observed is formation of a quinonoid intermediate coincident with the rate of product formation as determined by quench-flow [31,32,35]. This has been interpreted as indicating that the time taken to go from structures I to V in Fig. 3 is no more than approximately five milliseconds, and it is the subsequent steps that dominate the overall kinetics. Thus the kinetic mechanism of ALAS diverges substantially from the chemical mechanism [32].
The slow rate of the conformational change is coincident with kcat [14,16] and presumably confers some important selective advantage, as a surprisingly diverse variety of "hyperactive" ALAS variants can be created and isolated by simply mutagenizing non-conserved loop residues [36]. In some cases the rate of loop opening is increased to the point where it no longer limits the overall reaction rate, in which case decay of the quinonoid intermediate becomes the slowest step [33,36].
As of this writing there is no definitive biochemical explanation as to why a relatively modest conformation change associated with product release should determine the rate of porphyrin biosynthesis in animals, but it seems likely that this situation has evolved to allow for some form of regulation of activity that still awaits discovery. One possibility would be allosteric control of the ALAS conformer equilibrium by a small molecule such as iron or heme. The animal enzyme contains a C-terminal extension with a conspicuously conserved C-X-X-C motif that might form a binding site for a small allosteric effector such as heme or iron. Mutations associated with the disease X-linked dominant protoporphyria, which is characterized by increased ALAS activity and accumulation of porphyrins, have been observed in this region of the enzyme [37]. Another possibility is that functional interaction with one or more other enzymes, such as succinyl-Coenzyme A synthetase [38], modulates loop mobility and therefore enzyme activity. It is even possible that the conformer equilibrium is post-translationally regulated by phosphorylation or nitrosylation, although there is no experimental data to support this possibility at this time. It is important to unravel the mystery behind the deliberately slow conformational control of ALAS activity, because it would represent an important step forward in our understanding of the regulation of heme biosynthesis and aerobic metabolism.
Several conserved active site residues have recently been characterized by site-directed mutagenesis [14,16,39]. These fall into the three broad categories defined here and in Fig. 4, namely: residues forming a hydrogen bonding bridge between the PLP ring nitrogen and the carbonyl derived from succinyl-Coenzyme A; residues donating a hydrogen bond to the PLP phenolate oxygen atom; and residues that bind and orient the carboxylate tail of succinyl-Coenzyme A.
Of the four residues spanning the electron sinks of the cofactor ring nitrogen and the substrate carbonyl, only mutation to murine erythroid ALAS position D279 has produced variants that are not refractory to purification.3 Studies with D279 verified that this residue enhances the electron withdrawing properties of the cofactor, and that a carboxylic amino acid at this position is essential for activity to be observed [40]. Of the other three residues, four different mutations each at positions N184 and S209 resulted in proteins localized in inclusion bodies, none of which were refoldable in amounts necessary for characterization, and three different mutations at H207 resulted in proteins so unstable that overproduction of active enzyme was not possible.4 It therefore seems likely that the integrity of this hydrogen bond network is crucial for proper enzyme folding and stability, in addition to activity.
The functional role of the phenoxy-like anion in PLP biochemistry is, generally speaking, two-fold. It promotes catalysis by stabilizing the electron withdrawing iminium cation, while simultaneously serving as an effective enzyme binding determinant that facilitates stereoelectronic control of amino acid α-carbon activity [41,42]. The phenoxy-like anion of ALAS-bound PLP acts as a hydrogen bond acceptor for the side chains of two residues, H282 and S254, with a subtle but important difference between the two. While H282 donates a hydrogen bond to PLP in both the open and closed enzyme conformations, S254 only comes within hydrogen bonding distance of the cofactor in the closed conformation [14,39]. As one might expect, mutation of H282 to alanine has multiple effects on the enzyme kinetic and cofactor properties, including losses in catalytic efficiencies for substrates ranging from two-to-three orders of magnitude, and alterations in the protonation state and microenvironment about the PLP cofactor as seen in absorbance, fluorescence and circular dichroism spectra. In particular the circular dichroism spectra of the holoenzymes and external aldimines with glycine or ALA indicate that in H282A ALAS the cofactor does not undergo the same ~15° reorientation observed in the wild-type enzyme [13,39].
The side chain of S254 oscillates between hydrogen bonding to the amide linkage with M255 in the open conformation, and the cofactor phenoxy-like anion in the closed conformation [13,14]. This is with the interesting caveat that the two oxygen atoms in question are each slightly closer to the succinyl-Coenzyme A sulfur atom than to each other. These structural features suggest that S254 might couple the enzyme conformational change with cofactor and substrate binding and orientation. This supposition is validated by kinetic assays with the S254A mutant, in which both the and kcat are increased, by 32- and 3-fold, respectively [14]. These and other supporting kinetic and spectroscopic data were interpreted as reflecting a loss in succinyl-Coenzyme A binding affinity and optimal orientation relative to the cofactor, along with lessened stability of the closed conformation, the latter resulting in a 3-fold increase in kcat due to faster opening of the active site loop following catalysis.
ALAS forms multiple hydrogen bonds to the carboxyl tail of succinyl-Coenzyme A, the most prominent of which are donated by R85 and T430 (Fig. 6). As noted previously, T430 is located at the apex of the active site loop and forms an unusually strong hydrogen bond with the substrate carboxyl, wherein the hydrogen atom moves freely between the two oxygen atoms. This strong interaction is further enhanced by R85, which donates hydrogen bonds to each of the oxygen atoms involved in the low barrier hydrogen bond.
Acetyl-Coenzyme A is not a substrate for ALAS, and alternative four carbon Coenzyme A esters are very poor substrates, suggesting that selective alteration of R85 or T430 might lead to enzymes with altered Coenzyme A substrate specificities [16,43]. This was recently shown to be the case, although the double mutant R85L/T430V resulted in a reduction of wild-type activity by approximately 99%. Remarkably, the conservative R85K mutation resulted in an enzyme that switched specificity from succinyl-Coenzyme A to butyryl-Coenzyme A, without loss of activity.
Screening a bacterial library of ALAS variants for hyperactivity is facilitated by the observation that porphyrin fluorescence is proportional to ALAS activity [36]. By targeting non-conserved residues in the active site loop for directed-evolution based mutagenesis nine hyperactive ALAS variants were generated, isolated, and characterized. In general, catalytic efficiencies for succinyl-Coenzyme A were increased by about two orders of magnitude, while those for glycine were increased by approximately one. In three of the variants the rate of opening of the active site loop to release products was specifically accelerated to the point where it no longer limited the overall reaction rate. It was also noteworthy that all of the other observable reaction steps were also accelerated, albeit to lesser extents. This generality suggests that active site loop movements may be an integral component of multiple reaction steps, including decarboxylation and protonation of the enol-quinonoid intermediate. In other words individual reaction steps may occur while the loop is in motion, rather than occurring only once the "closed" conformation is fully realized.
In at least some Streptomyces species, including S. nodosus and S. aizunenesis NRRL-B-11277, a novel ALAS has been recently discovered that generates ALA specifically for use in biosynthesis of the 2-amino-3-hydroxycyclopent-2-enone moiety of a variety of structurally related antimicrobial compounds, such as asukamycin and manumycin [44–46]. This latter compound also inhibits Ras farnesyltransferase, and is commonly used in anticancer research [47].
The prominence of ALAS in day-to-day metabolism translates into a relatively low tolerance for genetic alterations, but a variety of mutations have been associated with human disease [13,37,48,49]. Interestingly, these cause one of two very different diseases, depending upon whether ALAS activity is decreased or increased. Decreases in activity are associated with X-linked sideroblastic anemia, which is characterized by pathological accumulation of iron in the mitochondria of erythroid precursors [49]. On the other hand, mutations at the C-terminus of ALAS can result in enhanced activity and X-linked dominant protoporphyra, which is characterized by accumulation of protoporphyrin in plasma and red blood cells [37]. These very different diseases emphasize the cellular requirement for tight coupling of ALAS controlled protoporphyrin synthesis with iron transport during heme biosynthesis.
The current model for ALAS catalysis is summarized as follows. The holoenzyme is in conformational equilibrium between "open" and "closed" states, as seen in the crystal structures and depicted in Fig. 5. Collision complex binding of glycine is rapid but weak, and has little effect on the conformer equilibrium. Subsequent binding of succinyl-Coenzyme A leads to a dramatic shift in conformer equilibrium favoring the closed state. The primary succinyl-Coenzyme A binding determinants leading to the collapse of the enzyme around the Michaelis complex are clustered about the adenine ring and the succinyl carboxyl. The linkage between these determinants is cleaved during the reaction chemistry, which is relatively rapid, facilitating a slow, rate-determining return to the open conformation wherein the reactions products are rapidly released.
One interesting and outstanding question is the extent to which the ALAS enzyme-substrate complex reacts as if it were a unimolecular complex. Obviously, it is assumed to be unimolecular when analyzed using Michaelis–Menten kinetics, but what we really mean here is the extent to which protein dynamics might be inseparable from active site chemistry [50]. For instance, are the observable chemical steps coincident with observable motions of the active site loop? A fluorescence tag approach similar to that taken for DNA polymerase [51,52] might shed further light on this possibility, as well as helping to better understand the translation of succinyl-Coenzyme A binding energy into a change in conformational distribution.
Hyperactive ALAS variants similar to those generated in vitro [36] or in vivo [37] may find utility in producing local accumulation of protoporphyrin IX during photodynamic therapies [53,54]. This approach may find particular utility in conjunction with tumor immunological approaches, potentially leading to anti-tumor immunity [55,56].
This work was supported by grants from the National Institutes of Health (#GM080270 and #DK63191) to G.C.F.
This article is part of a Special Issue entitled: Pyridoxal Phospate Enzymology.
1The abbreviations used are: ALAS, 5-aminolevulinate synthase; ALA, 5-aminolevulinate; PLP, pyridoxal-5'-phosphate.
2Ferreira, G.C., Zhang, J., Lendrihas, T., Gong, J., and Hunter, G. A., unpublished observations.
3Lendrihas, Hunter, and Ferreira, unpublished observations.
4Lendrihas, Zhang, and Ferreira, unpublished observations.
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Wrong on saying no on taking fracking waste. If you treat in-state waste as you treat out-of-state waste there is no conflict with the interstate commerce clause.


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This invention relates to methods and apparatus for distributing funds among a set of investments.
Suppose one has some capital to invest in the stock market. How does one go about investing it? One can try picking "good" stocks at low prices and selling them later at higher prices. That age old strategy although quite simple conceptually, is very difficult to implement. Stocks are inherently risky since they move up and down in a seemingly haphazard fashion on a variety of inputs and the common wisdom says that one should not keep "all eggs in one basket", but rather spread out the investment so as to minimize the risk.
In the 1950s Harry Markowitz, then a graduate student at the University of Chicago, fine-tuned this idea, laying the foundations of the modern portfolio theory. Markowitz's idea is easy to understand. Let us concentrate on picking stocks. The strategy is to pick the right mix of stocks that minimizes the overall risk in terms of losing money that is invariantly caused by the stock values moving below their purchased prices. Stocks move up and down, sometimes violently, causing great volatility in term of the total portfolio value. Markowitz's basic idea was to keep this volatility low by picking the right mix of stocks. One would like to keep the total portfolio value fluctuations to a minimum at all times, i.e. no big variations, and if there are any variations they should amount to small jitters. Actual stock variations are of course beyond one's control, but what is controllable is which specific stocks to add to the overall portfolio from the total pool, and how much of each stock. The idea is to use the right mix of right stocks to minimize the overall volatility. After all the basic goal of a fund manager is to protect the portfolios under his management from losing their values and hopefully increase their return values or the overall gain. The specific stock holdings and their relative importance within the portfolio are unimportant both to the fund manager and to the investor, so long as the portfolio "makes money", or performs well.
Thus two quantities play a role in portfolio selection—the overall risk, and the overall return or gain. Obviously, the overall risk needs to be minimized, and the overall return or gain should be maximized at the same time. Various strategies can be designed using these conflicting goals.
For a random variable, the variance is a good measure of the spread of the random variable around a mean value, and hence volatility minimization for stocks or investments, can be achieved in terms of portfolio variance minimization.
To quantify these ideas, let P represent an overall portfolio consisting of m stocks where si(n) represents the ith stock price at time index n and ai>0 the weight factor associated with the ith stock. Note that the unit of time can be hours, days, months or years depending on the investment duration. Clearly
and the ais are unknown to start with.
If Co represents the total capital, then Coai represents the capital invested in the ith stock so that Coai/si(0)=ki represents the actual number of the ith stock in the portfolio. Hence the portfolio value at time index n equals to
and hence the portfolio return over duration (0, n) equals
represents the ith stock return over the duration (0, n). Thus for portfolio return analysis, the important variable is the stock return value ri(n) rather than the actual stock value si(n) itself.
μi=E{ri(n)} (4)
represent the mean value (expected value) of the ith stock return (see, in "Probability, Random Variables and Stochastic Processes," Fourth Edition, A. Papoulis, and S. U. Pillai, McGraw-Hill Companies, New York, USA, 2001). The mean value μi can also be a good indicator about the future trend, where one hopes the stock will be based on company performance and other related parameters. One may need to predict μi based on all available data. The stock return values move around their mean values, the individual variations depending on the individual variance and related cross-correlations among other stocks.
The expected value of the portfolio return represents the net gain G of the portfolio. Thus the overall gain of the portfolio in (2) is given by (Co=1)
a=[a1, a2, a3, . . . am]T (6)
r (n)=[r 1(n), r 2(n), r 3(n), . . . r m(n)]T (7)
μ=E{r (n)}=[μ1, μ2, μ3, . . . μm]T. (8)
Here E{.} stands for the expected or ensemble averaging operation as in (4). The overall risk of the portfolio is given by the variance of the portfolio return that equals
where (see, in "Probability, Random Variables and Stochastic Processes," Fourth Edition, A. Papoulis, and S. U. Pillai, McGraw-Hill Companies, New York, USA, 2001).
R=E{[r (n)−μ][ r (n)−μ]T}>0 (10)
represents the covariance matrix (positive definite matrix) of the stock return vector r(n). Notice that
R ii =E{(r i(n)−μi)2}=var{r i(n)}=σi 2>0 (11)
represents the variance of the ith stock return, and
R ij =E{(r i(n)−μi)(r j(n)−μj)}=cov{r i(n), r j(n)}=ρijσiσj (12)
represents the covariance between returns ri(n) and rj(n), where ρij is defined as the correlation coefficient between ri(n) and rj(n).
The above equations are well known in the prior art. In addition, the above equations have been used to formulate the following portfolio optimization strategy, which can be called "Prior Art: Minimize Portfolio Risk".
Prior Art: Minimize Portfolio Risk:
Find the right max of stocks that minimizes the overall portfolio risk. Take whatever profit you get.
In the "Minimize Portfolio Risk" approach, the Portfolio risk is minimized by minimizing the portfolio variance σP 2 in equation (9) subject to the constraints in equation (1). This gives the well-known constrained optimization problem referred to in "Mean-Variance Analysis in Portfolio Choice and Capital Markets", H. M. Markowitz, et. al., John Willy, New York, 2000:
min a TR asubject to a T e=1 (13)
where e represents the "all ones" column vector
e=[1, 1, 1, . . . , . . . 1]T (14)
Notice that the nonnegative constraint for a needs to be incorporated as well. One approach of the prior art is to use the simplex type optimization methods to incorporate the positivity constraint for the weight vector a as referred to in "Mean-Variance Analysis in Portfolio Choice and Capital Markets", H. M. Markowitz, et. al. Another approach is to put additional constraints on stock selection to realize this goal.
Eq. (13) leads to the modified Lagrangian function
min Λ= a T Ra +λ( a T e−1) (15)
and its minimization yields
which gives
and the normalization condition
Observe that (18) must turn out to be a positive vector. This is clearly satisfied if R−1 is a positive (Perron) matrix as specified in the prior art in "Matrix Algebra and Its Applications for Statistics and Econometrics", C. R. Rao, M. B. Rao, Singapore,: World Scientific, 1998. Thus if R−1 is a positive definite matrix, then the optimum vector a turns out to be positive since the denominator e TR−1 e>0.
In other words, to start with one may select only those stocks to be in the portfolio for which R−1 satisfies the Perron property (positive matrix). In that case, the minimum volatility is given by:
where Rij represents the (i,j)-th entry of the matrix R−1.
Also, the net gain in that case is given by
For example, in a two-stock portfolio, the Perron property that R−1 contain only positive entries is satisfied by any two negatively correlated stocks since in that case
has all positive entries. Observe that equation (21) represents the covariance matrix of two stock returns with "opposing trends" and they are negatively correlated. Hence when one "goes up", the tendency of the other one is to "go down" thus minimizing the risk of loss. For large m, realizing this nonnegativity condition may be too restrictive. From equation (18), a more relaxed condition is that the row sums of R−1 must be all positive.
From time-to-time, the portfolio manager should recompute R and update the portfolio mix vector a by buying/selling stocks to keep the overall portfolio volatility low.
At least one embodiment of the present invention provides a method and an apparatus for investing a fixed amount of capital optimally by distributing it among a set of stocks and securities so as to maximize the return while minimizing the overall risk. In at least one embodiment a gain to risk ratio is maximized rather than minimizing the risk alone, to determine the fraction of capital that must go to each stock. If short selling stocks and securities is not allowed in a portfolio, then stock selection becomes important so as to maintain the desired fractions to be positive. An optimum gain versus variance plot can be used to determine the type of stocks to be selected in addition to their relative quantity for maximum yield over the duration of interest. By modifying the definition of risk to include some function of the covariance matrix of secondary stocks that are sympathetic to the primary stocks of interest, an alternate investment strategy is also developed here.
At least one embodiment of the present invention includes a method comprising determining a first and second return values for a first stock, and determining a mean return value for the first stock based on the first and second return values. The method further includes determining a first and second return values for a second stock, and determining a mean return value for the second stock based on the first and second return values for the second stock. The method may further include determining an inverse co-variance matrix based on the first and second return values for the first stock, the mean return value for the first stock, the first and second return values for the second stock, and the mean return value for the second stock. The method may also include determining weighting factors for the first and second stocks, respectively, by multiplying the inverse co-variance matrix times the mean return values for the first and second stocks, and normalizing the result by dividing it with their sum. The method may also include specifying an amount of the first stock for purchasing based on the first factor of the weight factor and specifying an amount of the second stock for purchasing based on the second factor of the weight factor.
The method may further be comprised of determining a vector of a plurality of weight factors a opt including the first and second weight factors, and determining a vector μ of a plurality of mean return values including the mean return values for the first and second stocks. The plurality of weight factors may be given by a opt=kR−1 μ, wherein k is a normalization constant so that the entries of the optimum vector add up to unity, and R−1 is the inverse co-variance matrix. The quantity k may be given by
and e T is an all ones row vector.
The present invention, in one or more embodiments also includes a method for investing a given capital sum by distributing it among a set of investments. The method may include determining a plurality of weight factors, one for each investment in the set of investments by which the capital sum will be partitioned so as to determine an actual amount to be invested in each investment. The plurality of weight factors may be determined by maximizing a total gain to overall risk ratio. Alternatively, the plurality of weight factors may be determined by maximizing a square of a total gain to overall risk ratio. A first numerical filter may be used to un-correlate a primary or first set of investments and a second numerical filter may be used to maximally combine the primary or first set of investments.
In at least one embodiment of the present invention a vector of weighting factors a opt for the primary set of investments is determined from the below fraction:
wherein R−1 is the inverse of the covariance matrix for the primary set of investments, μ is the expected mean returns vector for the primary set of investments, and e T is an all ones row vector.
The present invention in one or more embodiments may include maximizing the ratio of the square of an expected investment portfolio gain of a primary or first set of investments to a modified risk. The modified risk may be defined as the sum of the portfolio risk based on the primary set of investments and a function of a covariance matrix of a secondary set of stocks that are sympathetic to the set of primary investments.
The present invention, in one or more embodiments may include a method comprising selecting a primary set of investments, and selecting a secondary set of investments, which are related to the primary set of investments. The method may also include determining returns for the primary set of investments, determining returns for the secondary set of investments, and determining an expected mean returns vector for the primary set of investments. The method may further include determining a covariance matrix for the primary set of investments, and modifying the covariance matrix for the primary set of investments by adding a diagonal matrix generated from a covariance matrix for the secondary set of investments. The method may also include determining weighting factors a for investing in the primary set of investments iteratively from the below fraction:
wherein R is the covariance matrix for the primary set of investments, μ is the expected mean returns vector for the primary set of investments, e T is an all ones row vector; σo 2 is the sum of the variances of the secondary stocks that influence the primary stocks that is obtained by summing the diagonal entries of the covariance matrix of the secondary set of investments. Here ∥a k∥2=a k T a k>0 represents the square of the norm of the vector a k, and I represents the m�m identity matrix (with ones along the main diagonal and zeros elsewhere). In at least one embodiment of the present invention, the constant term σo 2 above may also be treated as a free positive variable and increased in numerical value until the vector of weighting factors for the primary set of investments turns out to be positive.
The primary or first set of investments may include any investment, such as a stock, security, mutual fund, hedge fund, or index following fund, and they may be selected so that the above weight factor vector turns out to be positive.
One embodiment of the present invention makes use of matched filtering concepts for the purpose of picking stocks. These matched filtering concepts were previously used in the field of electrical engineering but were not previously used for the purpose of picking the right mix of stocks in a portfolio.
At least one embodiment of the present invention provides a method for picking stocks, which maximizes gain and simultaneously minimizes risk. This is achieved by maximizing the ratio of gain to risk. The right mix of stocks are selected so as to maximize the gain G while simultaneously minimizing the overall risk σP 2. In at least one embodiment the following ratio is maximized:
Equation (25) represents the gain over the portfolio risk. However, in one embodiment of the present invention, instead of maximizing (25), the following ratio is maximized:
subject to the normalization constraint a T e=1.
Strategy-1 (in Accordance with an Embodiment of the Present Invention):
Clearly, equation (26) represents a more aggressive strategy in term of maximizing gain, but more interestingly, the ratio in equation (26) is the same as the familiar SNR (Signal to Noise Ratio) maximization strategy used in classical receiver design in Communication theory, in Electrical Engineering, where a signal corrupted by interference and noise is presented to a receiver to minimize the effect of output interference plus noise while maximizing the output signal component at the decision instant as referred to in "Signals Analysis", A. Papoulis, McGraw-Hill Companies, New York, USA, 1977, and also "Digital Communications", Fourth edition, J. Proakis, McGraw-Hill Companies, New York, USA, 2001. The solution to the SNR maximization problem leads to well known matched filter (MF) solution as referred to in "Signals Analysis", A. Papoulis.
From (26), with
we get
since by Schwarz's inequality
| a T μ|2=|(R 1/2 a )T(R −1/2 μ)|2≦( a T Ra )(μ T R −1 μ), (28)
With equality if
a opt=kR−1 μ. (29)
This gives
In general the entries of the optimum portfolio mix vector shown in equation (29) can be both positive or negative. Negative entries indicate that the corresponding stock is to be shorted. If short sale strategies are prohibited, for example, as in the case of most of mutual funds, then one needs to maintain a>0, and in that case one can perform a constrained optimization strategy of maximizing equation (26) subject to the non-negativity constraint of a. This leads to a suboptimum solution with all positive or non-negative entries for the vector a that requires no short selling. This strategy can be applied to any given set of stocks and securities that the investor has a-priori selected. In that case the capital will be partitioned according to the entries of the suboptimum vector so obtained and invested in the corresponding stocks.
An alternate strategy is to keep the pool of the desired stocks and securities to be selected as potentially open, and select them from a larger pool of stocks and securities in such a way that the inverse of their covariance matrix R−1 turns out to be a positive matrix. If this condition turns out to be too restrictive or severe especially for a portfolio containing a large number of stocks, one can also settle for the less restrictive new condition
R−1 μ>0 (31)
can be easily maintained with the constant k in equation (29) chosen to be
This gives the desired portfolio mixing vector to be
that maximizes the gain and minimizes volatility. In this case,
Equation (33) can be given the whitening followed by matched filtering interpretation as well, as will be shown with reference to
The filter output above is uncorrelated and has unit variance since its covariance matrix equals
and to maximally combine these outputs, the coefficients {bi} in
μ x =E{x (n)}=R −1/2 μ. (39)
From Schwarz's inequality (see (28)), Eq. (38) is maximized if
b=kμx=kR−1/2 μ. (40)
Thus b in (40) is a maximal combiner with respect to μ x. Hence,
G=b T μ x=kμ TR−1/2 μ x=kμ TR−1/2R−1/2 μ=a T μ (41)
a=kR−1 μ (42)
as in equation (29).
Interestingly, Equations (33)-(35) can be used to generate a gain-risk plot by varying over all sustainable μs. Following equation (33), an arbitrary μ is said to be sustainable if R−1 μ is a positive vector. Using a sustainable μ, one can compute the optimum gain and σP using equations (34)-(35).
Notice that although scaling μ does not affect the variance in equation (35), it does affect the gain in equation (34). Hence to avoid duplication by simple scaling, the first entry μ1 in a sustainable μ may be normalized to unity. As an example,
Stock symbols used in FIG. 3.
m = 12
m = 8
m = 6
Interestingly, other variations of the stock picking strategy shown by equations (29) and (33) also lead to the same result.
One may use a less aggressive strategy in terms of returns while maintaining low volatility. Then we may maximize:
instead of equation (26). This leads to
Equality is achieved by solution given by equation (33) and in that case
On the other hand, one can use a much more aggressive strategy such as maximizing
subject to equation (1).
Notice that equation (46) is weighted more towards higher gains.
Once again, equality is obtained in equation (47) by solution given by equation (33).
In summary, for a variety of optimization strategies, the new portfolio mixing vector in equation (33) represents the optimum strategy for building a portfolio. If short selling stocks is allowed, the above strategy can be applied to any set of stocks; if short selling is not permitted, then the selection of stocks and their number that goes into the actual portfolio becomes important and it must be accomplished so as to maintain the desired portfolio mixing vector to be positive, while maintaining a high yield (gain) with minimum fluctuations (risk).
Strategy-2 (in Accordance with Another Embodiment of the Present Invention):
In another embodiment of the present invention, a variation of the maximization of the gain to the risk strategy, to be described below, leads to a somewhat different result in terms of the desired portfolio vector. In the previous method, the risk is defined as the variance of the portfolio under consideration as in equation (9). In a method in accordance with an alternative embodiment of the present invention, this definition is extended as follows:
The actual stocks and securities that go into a portfolio as the primary stocks are identified, and equation (7) represents their returns. In that case the risk defined as in equation (9) represents the variance of the exact combination of the returns of these primary stocks that make up the portfolio. The method next includes identifying through market research and other means another set of stocks as secondary or sympathetic stocks that are correlated to these primary stocks in equation (7). Let R0 represent the covariance matrix of the returns of these secondary stocks that is also defined similar to equation (10). Since the secondary stocks have some influence on the behavior of the primary stocks, the argument here is that their covariance matrix R0 must also contribute to the overall risk of the portfolio. Thus in this approach, a scalar function of R0 is added to the primary risk factor in equation (9). In our case, the trace of R0 (sum of the diagonal entries of the covariance matrix R0) of the secondary returns is used as the scalar function. This gives the modified risk of the portfolio to be
σP 2 =a T Ra+σ o 2 (48)
σo 2 =tr(R 0) (49)
represents the trace of R0. In this case the optimization problem in equation (26) gets modified as
Let the vector a 0 represent the optimum nonnegative vector (constrained optimization using the non-negativity condition) that maximizes the ratio in equation (50) and whose elements add up to unity. In this approach, the capital will be partitioned according to the entries of this new vector a 0 and invested in the primary stocks.
The nonnegative vector a 0 above represents a suboptimum solution, and as in equations (26)-(33) there exists an unconstrained (without the nonnegative condition) optimum vector b opt that maximizes equation (50), and once again the capital can be partitioned according to the entries of the vector b opt and invested in the primary stocks. In this case the strategy can include short sales as well.
The globally optimum vector b opt may be solved by noticing that (50) can be rewritten as
where I represents the m�m identity matrix (with ones along the main diagonal and zeros elsewhere), and
∥ a∥ 2 =a T a >0 (52)
represents the norm (square of the length) of the vector a. In (51), proceeding as in (27) through (29), we obtain the following solution
(where c is a normalization constant) that suggest the iteration
After normalizing (54) as in equations (32)-(33) so that its entries add up to unity, we obtain the desired iteration to be
that can be used to solve for the above optimum vector b opt. The above iteration is seen to converge in a variety of situations.
is determined. At step 310 weighting factors, such as the new vector a k+1 are determined based on the above modified inverse covariance matrix times the means for primary returns vectors divided by the sum of the new vector entries so obtained, such as by equations (54) or (55). At step 314, the difference of the new vector a k+1 and old vector a k is defined as the error vector. At step 316 the error norm is computed as in equation (52) for the error vector, and it is compared with a predetermined threshold value, such as for example 0.001 etc. If the error norm is less than the preset threshold value, the new vector obtained at step 310 is taken as the desired weighing factors at step 318. Otherwise, the old vector is replaced with the contents of the new vector at step 320 and it is fed back to step 310, where the entire cycle is repeated till the desired accuracy is achieved.
Optimum Nonnegative Solution: Interestingly, it is possible to guarantee the solution given by equations (54)-(55) to be nonnegative by treating σo 2 in equations (54)-(55) as a free parameter. Recall that σo 2 represents a measure of the effect of the correlation of the secondary stocks on the primary stocks, and for a given value of σo 2, the optimum vector in (54) can have both positive and negative entries. In such situations, by increasing the value of σo 2 the optimum vector can be made nonnegative there by avoiding short sales. In fact, for any given covariance matrix R and nonnegative vector μ, there exists a minimum positive value for the constant σo 2 in the equation
a =(R+σ 0 2 I)−1 μ (56)
for which the vector a becomes nonnegative. The proof follows by expanding equation (56) and noticing that as the constant σo 2 becomes large, the perturbation terms to the first term μ in the expansion become of decreasing importance, and hence the vector a becomes nonnegative. Using this approach in equations (54)-(55), it follows that there exists a minimum threshold value for the sympathetic stocks' variance term σo 2, above which the optimum vector b opt remains non-negative. Using any value above this threshold value for σo 2 in equations (54)-(55) avoids short sales for the optimum portfolio mixing strategy. To determine this threshold value, one may proceed using the iterative steps in
As an example, consider a portfolio containing three stocks whose 3�3 covariance matrix is give by
and let μ=(0.20 0.50 0.40)T represent their the expected return values vector. In that case the solution in equation (33) that maximizes the overall gain to risk ratio is given by R−1 μ=(−0.237 0.7531 0.310)T and it has one negative entry and hence it involves short sales. However using σo 2=0.034995, the solution in (56) after normalization turns out to be a=(0.0000025 0.683533 0.293664)T. Since the new solution has all nonnegative entries, it avoids short sales. Using any other value above this threshold for σo 2 results in all positive values for the solution and it avoids short sales in the optimum portfolio.
In summary, methods in accordance with embodiments of the present invention for determining the optimization strategies for building a new portfolio mixing vector are disclosed. In at least most if not all of these cases, the ratio of the overall portfolio gain function to the portfolio risk is maximized, where the definition of the portfolio risk is extended in one case to include the influence of stocks that are sympathetic to the primary stocks of interest. If short selling stocks is allowed, the above strategies can be applied to any set of stocks; if short selling is not permitted, then the selection of stocks and their number that goes into the actual portfolio becomes important and it must be accomplished so as to maintain the desired portfolio mixing vector to be positive, while maintaining a high yield (gain) with minimum fluctuations (risk). This can also be accomplished by extending the definition of risk to include a free variable term that denotes the effect of a secondary set of stocks, and by increasing this term the desired portfolio mixing vector can be made positive through an iterative procedure.
Although the invention has been described by reference to particular illustrative embodiments thereof, many changes and modifications of the invention may become apparent to those skilled in the art without departing from the spirit and scope of the invention. It is therefore intended to include within this patent all such changes and modifications as may reasonably and properly be included within the scope of the present invention's contribution to the art.
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|U.S. Classification
|International Classification
|Cooperative Classification
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|Fee payment
Year of fee payment: 4
|May 16, 2016
|Fee payment
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text:
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