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The Malone Family Foundation was founded in 1997 by Dr. John C. Malone, a well-known communications and media executive and investor, and his family, with one principal objective: to improve access to quality education, particularly at the secondary school level, for gifted students who lack the financial resources to best develop their talents.
In 2008, Brownell Talbot was selected as the recipient of a $2 million grant from the Malone Family Foundation to provide scholarships for gifted students with financial need. Brownell Talbot is one of only 50 independent schools in the country given the opportunity to partner with the Malone Family Foundation.
"Our goal is to provide an outstanding education to every young student who is among the top five percent of his or her class and who displays the keen desire and motivation to learn, yet lacks the resources to finance such an education," said Cathie Wlaschin, Executive Director of the Malone Family Foundation based in Englewood, Colorado.
Malone Scholars are selected by Brownell Talbot on the basis of merit and financial need alone without regard to race, creed, or any demographic characteristics.
Malone Scholars Program Application
Malone Scholar Requirements
Each student selected as a Malone Scholar by Brownell Talbot must:
Be a U.S. citizen.
Be a new student to BT.
Be a rising seventh through twelfth grader in the top five percent of his/her class as identified by school records, standardized test scores, and other recognized assessment methods.
Show evidence of enthusiasm for and motivation toward maximizing his/her educational opportunities.
Qualify for funding of at least 30 percent of his/her tuition through the school's financial aid qualification process.
Display leadership potential and high character standards in accordance with BT's Points of Pride.


For me, the only thing better than having a good time with family and friends is knowing that I'm getting the most for the money I spend while we're out and about. That's why I've enjoyed using the Groupon app so far, and why the shopping and coupon app has earned a permanent place on my iPhone. Whether I'm looking for discounts at restaurants, money-saving deals on a hotel room or other travel expenses, or even experiences like couples massage or indoor playground tickets for the kids, the Groupon app always seems to have a coupon or rebate to help keep costs down. Best of all, the Groupon mobile app is free, and there are constantly new businesses and merchants offering some of the best coupons and discounts I've found anywhere online or in print. Let's get started learning about the Groupon app for iPhone and iPad, so you can start saving money, too!


Mothers and Fathers covers everything from finance to health to personal issues. Louis Sapi, CA, tackles the financial component, with advice on pensions, RRSPs and taxation, and areas that could be overlooked, such as tax-planning strategies that conflict with probate planning. Peter Zawadzki, a licensed pharmacist, writes compassionately about health issues facing seniors – which, with government cutbacks to healthcare, are increasingly interconnected with financial issues. In addition to purchasing extended healthcare insurance, Mothers and Fathers suggests attaining two powers of attorney – one for property and another for personal care. The book also highlights the CICA's new ElderCare Practice program, in which CAs take additional training to better assess the financial and medical needs of this growing demographic.
Finally, and perhaps most important, the book provides tips on how to work with parents on emotional subjects, such as if or when to sell the family home and planning for possible disability.


as i groomed and was groomed.
My stepmother gave me an amethyst necklace when I was five years old, right when she was diagnosed with breast cancer. I hardly knew her then. She's still alive and has now been with me most of my life. This souvenir is my favorite because when I touch it, I don't have to miss anything.
Simone Wolff is an MFA student at Vanderbilt, Head Poetry Editor for the Nashville Review, social media intern for Coconut Magazine, and publications intern for Kit Yan Productions. Their work can be found in Split Lip, Finery, Inpatient Press, WE'RE HERE WE'RE QUEER zine, Coldfront, and is forthcoming in The Subterranean Quarterly.


Department of Fashion & Design celebrated teacher's day on 5th September 2018. The students organized cultural programs for the teachers. They welcomed the teachers with "Tilak Ceremony" and various activities. The program was an eventful day where the teachers and the students bonded together and performed various task-based programs. All the teachers shared their experiences which were inspirational for the students. The program ended with a vote of thanks by the Dean, where he appreciated the students for organizing such a wonderful event.


Here's a page I came up with in my repurposed book. Lots of layers here, which means I should be cutting out more pages than I am to keep it from becoming too bulkly to close. I could put some sort of closing method on it – and I might – after it's finished.
This caused me more than a bit of angst. Why? Because I love this orange ink. Love, love, lOVE it! And it came from the only art store around (that I know of – I know the internet tells me there are two more but both are a bit father away and in/near downtown Milwaukee and that is a p.i.t.a. to get to, but I digress).
And while this store isn't hard to get to, they are iffy when it comes to having things stocked. When I found this fabulous orange ink, I was really looking for yellow – I have yet to find yellow. The shelf has a spot for it, but it's always empty – as are most shelves.
I know it may be due to kids coming in and shoplifting. But really – I can never find help until I wander by the Golden Acrylics section where I am promptly pounced on by employees kindly saying how Golden is for "professional" artists in a tone that indicates that they would believe that pigs could fly before I could possibly be an artist.
Not all of them are like that. Just a few. There is one woman that works there that has the most fab frames on her glasses and almost seems like a work of art herself. She's always VERY good at listening and helping me find things that I need. Too bad I run into the others more often. But again, I'm off the path. The point is, I'll go back to the store, look for the ink, then stand in the Golden aisle until I'm approached and pray that they have a bottle in the back.
In the meantime, I have my orange pages floating around and I swear one of them told me that I should grab the forest green ink and add a few dribbles – or maybe stamp a few things….
I don't mind accidents like these too much – not when the end result gives me more opportunities to create!


If you already have access to the Nevada Department of Employment, Training & Rehabilitation (DETR) website, and have a withholding tax ID number, please STOP, and simply provide us with the data requested in the "Give us the Info" section of the Nevada tax document. If you have access to the Nevada DETR website but do not have a withholding tax ID, please log into your Nevada DETR account and apply for access to a withholding ID. If you have any questions, please call the Nevada DETR directly at 1-(775)-684-6310.
The DETR will The Nevada DETR will issue you a Modified Business Tax account number.
The rate will be issued by the DETR as well and ranges from 0.47%–6.29% with a wage base of $29,500.
It can be found on your Notice of Employer's Contribution Rates.
Please follow the steps below to register your business with the Nevada Department of Employment, Training & Rehabilitation (DETR). Unless these steps are followed in their entirety, OnPay will be unable to file and pay your Nevada DETR taxes.
Register with the DETR online.
Click the "Create a new online user account".
You will receive your Unemployment ID Number Immediately once the online registration is completed, in 30 days if registering by mail.
The Nevada Bond Factor Tax is a new tax that was introduced in 2014. All new employers' rate will be 0.29%.
Businesses subject to Nevada Unemployment tax are also subject to the Modified Business Tax.
when you register for Unemployment you will also be automatically registered with the Nevada Department of Taxation for the Modified Business Tax (MBT).
You will then receive your MBT account number with your "New Nevada Employer Welcome Package."


Olympic rowing medallist Cath Bishop joined children from Sancton Wood Prep School at Goldie Boathouse in Cambridge, thanks to appliance brand Beko and its Eat Like A Pro campaign.
The campaign comes in response to the World Health Organisation announcing that 70 million children will be obese by 2025. Responding to the global need to reduce child obesity, Beko is hoping to inspire families to take action, by working with nutritionists from FC Barcelona to access the eating habits of professional footballers through its new Eat Like A Pro website. The site encourages parents, children and their families to partake in a range of fun activities, view healthy eating tips, as well as allowing them access to over 100 recipes, ranging from smoothies to family favourites such as cottage pie.
Sancton Wood Prep School children from Year 2, 3 and 4 took part in a mixture of rowing related fitness activities led by Cath Bishop and members of the rowing club. Talking about the success of the day, Cath said: "I love rowing, so it was great to see the passion and enthusiasm shown by the children today. I've had so much fun seeing the children get involved and hear them talk about the foods they do and don't like.
Beko plc research and design manager Dr Natasha Conway added: "We've had a brilliant day at Goldie Boathouse with Cath and Sancton Wood Prep School. Our Beko R&D centre is based in Cambridge, so it's important to us that we give back to the community. It was wonderful to see the children inspired by Cath and our Eat Like A Pro initiative. A quarter of 2-10-year olds in the UK are overweight or obese which is a frightening but real figure. We hope that through activities like today we can make more people aware of the issue of childhood obesity in the UK and as a brand, make a difference.
Next Post Budget 2018: where is the desire to reform?


If you have ever found yourself feeling as though you're going crazy trying to simultaneously navigate yourself and your business, feeling like you're manifesting some weird version of Jim Carrey in Me, Myself, and Irene.. Don't worry, this is perfectly normal and there is a reason why!
The reality is that each of us must embody these three personas if we are going to have a successful and thriving business. Unfortunately, most of us are battling within ourselves over which personality is in the drivers seat. What are these personality types, you ask? They are the Entrepreneur, the Manager, and the Technician.
I was introduced to this concept when reading Michael E. Gerber's book, The E-Myth Revisited, where he does an excellent job breaking down the common mistakes small businesses often make, how to avoid them, and how to build a strategic business model. This book is a MUST READ for any business owner out there, no matter how experienced you are.
Gerber opens the book by first defining these personalities and how they are interrelated and interdependent; each playing an essential role in establishing and sustaining a successful business. He also explains how most people usually have one dominant personality that tends to take over, and that lacking awareness of this could quite possibly be the reason why you and your business are struggling.
Upon learning more about the three personality types, I was instantly able to identify each them within myself, as well as which one of them was typically the one in charge. As I go over them here, try to determine for yourself which one is your dominant personality type, and I'll explain the impact that will have on you and your business as each personality plays out in your work— but before I do that, take a guess on which one is your dominant type. Is it the Entrepreneur, the Manager, or the Technician?
Let myself and the readers know what your guess was in the comments below. And if your initial guess was wrong, let us know which one was, in fact, the dominant one. Personally, while I certainly find myself playing into all three, I tend to oscillate most between being Entrepreneur dominant and Technician dominant a majority of the time.
So lets get into the personalities and perspectives of each type, shall we? Starting off with the Technician.
Believe it or not, its our Technician personality type that often sparks the desire within us to go into business for ourselves. The Technician experiences what Gerber calls the Entrepreneurial Seizure, where we start saying things to ourselves like, "I am really good at the thing that I do, I know the craft better than anyone, and I am exceptionally skilled in it. In fact, I am better than anyone else at this! Why am I making money for my boss, who is clearly less skilled than I am, when I could be running this for myself and making MYSELF the money??" This entrepreneurial seizure is essentially the itch that each Technician has when they decide to to take the thing that they love to do, and strike out to make a business out of it.
The barber opens a barber shop, the baker a bakery, the fitness instructor a fitness studio, the cook a restaurant. The lawyer leaves the firm to start his own; the doctor leaves the medical group for private practice. Every single one of these examples are skilled "technicians" who see's a business not AS a business but as a place to work for themselves.
The Technician is a doer, by default. Their motto is "if you want to get something done right, do it yourself!" They are fully immersed in the present moment, and firmly focussed on the task at hand. They don't worry themselves with anything besides the work itself. While others consume themselves with thinking about doing things, the Technician gets. things. done.
"The Technician is a resolute individualist, standing his ground, producing todays bread to eat at tonights dinner. He's the backbone of every cultural tradition.. if the technician didn't do it, it wouldn't get done," Gerber explains. For the Technician, there is nothing more important than the work itself. They hate being bothered by systems and structure, thats what the managers are for. And they hate obsessing over problems and trying to create solutions, thats what the entrepreneur is for. The Technician does what needs to be done as they have always been done, and doesn't like being interrupted by new approaches, ideas, opportunities, or external demands. They are the personality type that is most resistant to change.
Gerber argues that each Technician believes "that by understanding the technical work of the business they are immediately and eminently qualified to run a business that does THAT kind of work," meaning that they see the business as being an extension of their skill set, and THIS is where they typically get themselves in trouble.
A Technician goes into business and focuses solely on the doing the work and the delivery of the product or service, so much so that they don't nurture the development and growth of the business itself. They don't recognize just how essential that component is to the success of the business, nor do they want to have anything to do with it. The nuts and bolts of the business itself are a part of the job that they are most resistant to, and would rather avoid. And so in large part it gets neglected all together, which leads their business straight into danger.
The Technician loves to work. But not just any work, they LOVE to work in the business on their skill, product, or service; they hate, however, working on the business. The Technician is passionate about the skill, and focusses on getting the work done. At least initially this is how it starts.
Upon building the business, the technician is thrilled, loving their carte blanche opportunity to do things the way THEY want to, for themselves. However, very soon they become inundated with the demand of the work, stressed out and terrified of the responsibility that they have, yet don't know how to cope with. They are soon after exhausted from having to carry the burden of everything on their own, and are finally filled with despair.
Not only have they lost the passion for the skill, but they have lost themselves along the way, feeling overwhelmed by a process that demands everything of them. They are their own boss, yet they resent themselves and the work now as much as they did when they did it for someone else. The only difference is they HAVE to show up now if the business is going to stay open.
The Technician is an essential personality within each business, because work certainly needs to get done! But, if the Technician is ultimately in charge of the business, with no integration of the other two personality types, too often the business itself starts to suffer from lack of strategy, development, and neglect of they very things the business needs to survive in the long term. A Technician in charge for too long will not only lead to an exhausted and overworked business owner, but a business that will stagnate and eventually die.
Which is why the Manager is such an important persona within the business owner. The Manager not only loves everything the Technician hates, they excel in it. They love systems, order, organization, structure, and planning!
They are the neurotic type-A personalities who like things color coded, filed, and tidy at all times. They want everything to work exactly as it is designed to work, in timely fashion, without skipping a beat. And they fret and fuss over the details of how things get done, and become stressed when anything shifts the balance of things.
The Manager craves order above everything. They want everything to work like a well-oiled machine, effectively and consistently. They see problems and strive to return everything back to the status quo. The Manager is essential for any business to succeed. There would be no business, no society, with out managers. Its the Managers pragmatism that ensure stability in the chaotic world of the entrepreneur, and productivity and momentum in the world of the task-oriented Technician.
The Manager handles the operation and implementation of things. They thrive in predicability, they will always clean up the mess left in the wake of the Entrepreneur, and they see work as being a system of results, always to be maintained and controlled. But a Manager who goes unchecked will never test the limits of the business to grow and expand beyond the status quo. If a business wants to play the long game, the Entrepreneur personality has to have to take the stage from time to time.
When it come to the Entrepreneur, I think its safe to say that we are all familiar with these personality types. They are the innovators, creators, and risk takers in the group. They see chaos as an opportunity for discovering potentials and opportunities. They are the visionary in each of us.
"The Entrepreneur," Gerber explains, " is our creative personality— always at its best dealing with the unknown, prodding the future, creating probabilities out of possibilities, engineering chaos into harmony." The Entrepreneur likes change and thus create havoc around themselves so they can find projects to enlist themselves in.
The Entrepreneur always lives in the future and is vary rarely concerned with the present. Although they don't concern themselves with the order of things as much as the manager might, the Entrepreneur does in fact like control; they like to control people, events, outcomes etc… the more control they have the more they can pursue their dreams. But as they are usually miles ahead of others, control is difficult for them because most people have a hard time keeping up.
So which one of these personalities is your dominant one? Are you a more balanced business owner or one that has one overly dominant type at the helm?
Gerber writes that it is uncommon for most of us to be blessed with a balance of the three of them, and that most small business owners are actually seventy percent Technician, twenty percent manager, and only ten percept entrepreneur.
No matter what combination you are of the three, or whichever your dominant type is, it is important that you try to cultivate each personality type within you, with foresight enough to know that your dominant one will always try to take control. And to ensure that you don't get blind-sighted by your weaker persona's inability to keep up, create a team that enables you to stay in your area of strength and genius, while partnering with others who compliment you in areas where you are deficient.
These different personalities are interdependent upon one another, and must work together for your business to succeed. If you are experiencing struggles in your business, perhaps by identifying which personality is behind the steering wheel and which one needs to take over, you can course correct, and create solutions for growth.
The question for you, as a business owner, is, how can you create more balance by giving each personality within you more life? Can you learn to identify which personality is functioning at various times? And how can you create a team around you that supports you in the personality type/characteristics where you are weak and need greater support in?
Let us know your answers to these questions, I am eager to see where you land among the personalities!


In addition to "traditional" shelling with 120-mm mortars as well as 122-mm and 152-mm artillery, Russian-terrorist forces in Donbas have stepped up the use of armored vehicles and air reconnaissance (at least 10 UAV flights recorded) during the past twenty-four hours. Active operations by "small groups" of militants in the "greenery" have not ceased, while terrorist sabotage and reconnaissance groups and raiding parties are active across the whole of the Luhansk sector (especially along the Severskyi Donets river).
The situation has intensified the most in the Donetsk and Horlivka areas, where the bulk of the shelling and armed provocations by militants occurred in the past day. In addition to the sector from Mar'inka to the northwestern outskirts of Horlivka, another area of especially heightened enemy activity consisted of the settlements of Svitlodarsk, Luhanske and Mironovskyi.
So, in the past twenty-four hours, militants repeatedly carried out fire strikes using 122 mm and 152 mm artillery in the Shyroka Balka – Novhorodske area. The enemy opened fire with 82 mm and 120 mm mortars on the advanced positions of Ukrainian troops from Ozeryanivka and the eastern shore of the Horlivske reservoir, at the same time as terrorists made active use of AGS-17 automatic grenade launchers along the demarcation line close to Leninske – Shumy.
Near the Donetsk airport and the settlement of Opytne, militants used several armored groups (each with 5-6 AFVs–armored fighting vehicles – IFVs–infantry fighting vehicles or APCs–armored personnel carriers). These armored groups opened intensive fire from their on-board weapons on the advanced positions of Ukrainian troops. The militants used 122 mm artillery to provide cover fire for their armored vehicles as the latter took firing positions. Firing was by two batteries of D-30 howitzers – one from the vicinity of Spartak, the other – from beyond the settlement of Vesele, and south of Stratonavtiv Street (Donetsk city).
Militants shelled the southern suburbs of Avdiivka, Opytne and Pisky using 120 mm mortars.
In the area of Mar'inka, Krasnohorivka and Lozove, the movements of small terrorist infantry groups, under cover of the "greenery," were recorded. In particular, the enemy tried to approach the ATO forces' positions in order to scout out the front edge of the Ukrainian troops. These groups opened small arms fire randomly to provoke retaliatory fire from ATO forces and in this way identify their firing positions.
Shelling from 82 mm mortars was recorded near the settlement of Luhanske. An enemy armored group was also operating in this area – fire strikes from tank guns were directed at the advanced ATO forces' positions.
In the direction of Alchevsk, a militants' mortar group (six 82 mm mortars and three 120 mm mortars) kept shelling the positions of ATO forces near the settlement of Krymske.
Armed clashes among the "greenery" were recorded in the Zolote, Orikhove, Vesela Hora and Shchastya sector and near the settlement of Stanytsia Luhanska. Near the settlement of Shchastya, the enemy used AGS-17 grenade launchers several times.
In the coastal direction (near Shyrokyne and east of Hnutove), militants operating as infantry groups opened fire several times using small arms.
The number of militant troops and armored vehicles continue to grow south of Donetsk and towards the coast. A manoeuvring of part of the Russian-terrorist troops and their materiel was recorded towards the Kulykove–Shevchenko–Kozatske sector from the Komsomolske–Starobesheve district. At least two additional units of "motorized rifle-company" strength (totaling 160-180 men) accompanied by eight tanks and 16-18 AFV–armored fighting vehicles (mainly IFV-1 and IFV-2 armoured fighting vehicles and 1 MT-LB multipurpose light-armoured transporter) have been observed moving to the front line. Both units arrived from the north through Telmanove. Some arriving forces are in the process of deploying to the east of this sector as a tactical reserve (in particular, another subunit of a combat tank company of up to 8 tanks and a company of infantry troops unaccompanied by armored vehicles on Kamaz\Ural trucks).
Another tactical terrorist group has been spotted in the Bezimenne – Patriotychne –Samsonove area. It consists of 10 tanks, 25-26 AFV–armored fighting vehicles and up to 30 trucks and other transport vehicles.
To the east of Highway T0508, several militant artillery units (two 4-gun batteries of 122 mm D-30 howitzers, as well as six SAU 2S1 "Gvozdika" [self-propelled guns] have been identified. A terrorist two-battery BM-21 "Grad" MLRS division is being deployed near the settlement of Huselshchykove.
North of Luhansk (in the area of Vesela Hora – Khristovo – Pankivka) a new militant armored group has been spotted (10 tanks and 9 APCs–armored personnel carriers, including four of the latest Russian APC-82A model). The armored vehicles are being camouflaged and dug in.
The IR group concludes, based on operational information, that the terrorists are currently forming two large tactical strike forces: the first in the Volnovakha direction (south of Donetsk) in the section from Olenivka to Hranitne and Staromarivka. And the second, directly in the coastal area itself from slightly north of Bezimenne to Pavlopil and Chermalyk.


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Home / ... / hidden europe 14 / travel for the millions: Thomas Cook
Travel for the millions: Thomas Cook
A look at the man who brought travel to the millions: the Victorian temperance campaigner, Thomas Cook.
In the summer of 1891, William Gladstone was holed up at Hawarden Castle, his country estate in North Wales, nursing his health and planning yet another comeback as prime minister of Great Britain and Ireland. A letter arrived at Hawarden, soliciting Gladstone's presence at a London dinner in honour of a company then celebrating fifty years in business. Gladstone's doctor was not inclined to make an exception to the strict rule that prohibited the statesman, already prime minister on three separate occasions, from attending public banquets, so Gladstone never did make it to London's Guildhall to celebrate the achievements of Thomas Cook & Son. Nor, as it happens, did Thomas Cook himself.
It had been a dozen years since Thomas Cook had taken any active part in the company that bore his name, and by the time of the half-centennial dinner in 1891, Thomas' only son, John Mason Cook, was firmly at the helm. Thomas, living in retirement in Leicestershire, had his mind on other matters: past journeys, the temperance movement and an ambitious plan to endow the Derbyshire village of Melbourne with a handsome set of cottages, a bakery, laundry and - most importantly - a mission hall.
Strangely, there is no evidence that Thomas Cook ever really had the travel bug.
source: https://hiddeneurope.eu/travel-for-the-millions-thomas-cook
Thomas Cook: March 1873
By the end of February 1873, Thomas Cook had encircled most of the northern hemisphere. Cook and his party of circumnavigators had sailed from Liverpool in September 1872. The travellers discovered iced water, Pullman cars and Sioux warriors in the ...
The other Germany
My brief was to take the pulse of eastern Germany on the 21st anniversary of her union (in October 1990) with her bigger neighbour to the west. Thus was a new and larger Germany born. Twenty-first birthdays have symbolic rather than any legal ...
Through Romanian eyes
The Romanian aristocrat, traveller and writer Dinicu Golescu deserves to be better known outside his home region, for he rates as one of the finest travel writers of the early 19th century. His 1826 book 'Account of My Travels' is an important ...
border zone: around Lake Prespa
frozen in time: a border town in Belarus
the soul of Estonia: Saaremaa
thinking about festivals
Marne-la-Vallée: pure fantasy
beckoning rocks: the Elie chain walk
island in the sun
what's in a name: the island of Jan Mayen
what makes a country?
without let or hindrance: passports of yesteryear
mapping routes: some unusual waymarks
peace parks
Estonian links
a European map
Trans-Caucasus rail link

redpajama_set_name: RedPajamaCommonCrawl


And in among them I could swear I saw a shield.
About a group that he called The Society.
Within a dream that has not passed away.
He was a Knight, he said. I asked him how it felt.
Sounded like history -- it echoed in my head.
To make way for the King -- and everybody bowed.
© 1979 by Derek Foster. All rights reserved. Used by Permission.
This is the recognized Web site for the Barony of al-Barran of the Society for Creative Anachronism, Inc. This site may contain electronic versions of the groups governing documents. Any discrepancies between the electronic version of any information on this site and the printed version that is available from the originating office will be decided in favor of the printed version.
Copyright © 2007-2011 al-Barran. The original contributors retain the copyright of certain portions of this site.
For information on using photos, articles, or artwork from this web site please contact the Webminister . They will assist you in contacting the original creator of the piece. Please respect the legal rights of our contributors.


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Burn the Stage: The Movie
Burn the Stage: The Movie is the first movie from BTS, going behind-the-scenes of the BTS WINGS TOUR to reveal the full story of the band's meteoric rise to fame. This unmissable cinema event provides an intimate look at what happens when the most successful global boyband of all time breaks down barriers and invades the mainstream music scene. Exclusive tour footage and brand-new one-on-one interviews with BTS members give fans an unprecedented glimpse into their lives and an opportunity for everyone to celebrate together in movie theaters worldwide.
Director: Jun-Soo Park, Park Jun-Soo
Actors: BTS, J-Hope, Jeong-guk Jeon, Ji-min Park, Nam-joon Kim, Seok-jin Kim, Suga, Tae-Hyung Kim
Keywords:Burn the Stage: The Movie
With the help of more than 10,000 dedicated Zappa fans, this is the long-awaited definitive documentary project of Alex Winter documenting the life and career of enigmatic groundbreaking rock star…
A documentary about the expanding powers of the European Union.
The Black Godfather
Follows the life of Clarence Avant, the ultimate, uncensored mentor and behind-the-scenes rainmaker in music, film, TV and politics.
Hunt vs Lauda: F1's Greatest Racing Rivals
James Hunt has never been equalled. Could swashbuckling Hunt catch the scientific Lauda? Could Niki overcome an appalling crash to come back from the dead and fight James all the…
Beyond Barricades
Beyond Barricades is a documentary on political punk band Anti-Flag, featuring interviews with Tom Morello, Billy Bragg, Tim McIlrath, Brian Baker & More. The film explores the trials and tribulations…
Genre: Biography, Documentary, History, Music
One man's journey to discover the bitter truth about sugar. Damon Gameau embarks on a unique experiment to document the effects of a high sugar diet on a healthy body,…
Every year, thousands of Antarctica's emperor penguins make an astonishing journey to breed their young. They walk, marching day and night in single file 70 miles into the darkest, driest…
Genre: Documentary, Family
Ai Weiwei: Never Sorry
Ai Weiwei is known for many things – great architecture, subversive in-your-face art, and political activism. He has also called for greater transparency on the part of the Chinese state….
The China Hustle
An unsettling and eye-opening Wall Street horror story about Chinese companies, the American stock market, and the opportunistic greed behind the biggest heist you've never heard of.
Geek, and You Shall Find
After attending a local comic book convention, three filmmakers are so moved by the stories shared with them by cosplayers that they decide to investigate geek culture even further. Attending…
Shawn Mendes: In Wonder
A portrait of singer/songwriter Shawn Mendes' life, chronicling the past few years of his rise and journey.
Martial Law 9/11: Rise of the Police State
Evil has spread across the land. Martial Law: 9/11 Rise of the Police State exposes the high-tech control grid that is being set up across America Out of the ashes…
Genre: Documentary, Horror, War


Here are some design predictions for 2017, the first of which is the return of elegant upholstery. Although an L-shaped sofa might be the ideal place for a Saturday-night , they miss the point that well-designed sofas are intended to enhance an interior, rather than simply provide a quasi-bed. Sofas aren't just for vegetating on — for an insight into the infinite possibilities of upholstery, look no further than a Conversation Piece sofa, Secondly, an idea which is more nebulous but potentially even more exciting: the return to a more considered approach to design. This is a move on from the unhinged eclecticism that resulted in people being encouraged to 'mix it up' and accept that 'there are no rules', precipitating some disturbing juxtapositions of pretty much every style under the sun—a bit of Miami here, a bit of Scandinavian there and a light dusting of Vintage. Designers such as Rose Uniacke and Ben Pentreath are the masters of the more disciplined approach. The third source of interest is the return of the four-walled room (as opposed to the open-plan space ).
Interior designers have spoken to Architectural Digest, and they each selected a trend that they definitely do not want to see this year. So, if you want to know which interior design trends you should avoid in 2017, now is the time to keep up.
REPLICATE MID-CENTURY ROOMS LIKE YOU LIVE IN THE 60`S .
Interior designer Anne Hepfer "would love to see Ombré be replaced with beautiful printed fabrics and watercolour paintings, like those from Ferrick Mason.
Designer Wesley Moon stated that the one trend she wants gone is related to "that cheap-looking bright gold metal that is on every piece of new furniture. Old brass is great on antiques, but the trend of having a bright, shiny (yet somehow also matte) version of it on every new piece of furniture (often paired with lacquer, sometimes chevron patterns) is wearing very thin.
Reblogged this on Superior Interiors .


text:
Q: Send data to php file with javascript on submit so basically, when someone clicks the submit input, I want to retrieve values from various inputs and spans using javascript, then send it to php using $post to then send it by email. I have already tried to delete all the javascript code (except the preventdefault and the click function) and replacing it by a alert, and when I click submit, the alert does execute as it should. But now i'm trying to figure out how to make retrieve all this data and send it by email.
I have a live example here, if you want to see what i'm trying to do.
Thanks

<?php
        $PrimaryParentName=$_POST['PostPrimaryParentName'];
        $SecondaryParentName=$_POST['PostSecondaryParentName'];
        $PrimaryEmail=$_POST['PostPrimaryEmail'];
        $SecondaryEmail=$_POST['PostSecondaryEmail'];
        $PrimaryPhone=$_POST['PostPrimaryPhone'];
        $SecondaryPhone=$_POST['PostSecondaryPhone'];
        $Address=$_POST['PostAddress'];
        $ChildName=$_POST['PostChildName'];
        $ChildBirth=$_POST['PostChildBirth'];
        $ChildAllergies=$_POST['PostChildAllergies'];
        $ChildSchool=$_POST['PostChildSchool'];
        $ChildLevel=$_POST['PostChildLevel'];
        $UniformSize=$_POST['PostUniformSize'];
        $PreferedPositions=$_POST['PostPreferedPositions'];

        $to='email@gmail.com';
        $subject= 'Nouvelle inscription pour le CSEO';
        $message="Contact information"."Primary parent's name: ".$PrimaryParentName."\n"."Primary parent's email: ".$PrimaryEmail."\n"."Primary parent's phone number: ".$PrimaryPhone."\n\n"."Secondary parent's name: ".$SecondaryParentName."\n"."Secondary parent's email: ".$SecondaryEmail."\n"."Secondary parent's phone number: ".$SecondaryPhone."\n\n"."Address: ".$Address."\n
 \n"."Child's information"."\n"."Child name: ".$ChildName."\n"."Child's date of birth: ".$ChildBirth."\n"."Allergies: ".$ChildAllergies."\n"."Child's school: ".$ChildSchool."\n"."Child's level of experience: ".$ChildLevel."\n"."Prefered positions: ".$PreferedPositions."\n"."Uniform size: ".$UniformSize;

        mail($to, $subject, $message);
?>

A: Alright I solved it, the problem was with the if in before the $post.
if (document.getElementById("second_phone").value ==
                                    null || document.getElementById("second_phone")
                                    .value == "") {
                                    SecondaryPhone = 'N/A';
                                } else {
                                    SecondaryPhone = document.getElementById(
                                        "second_phone").value;
                                }
I don't know what the exact issue was but it works without it and i'm fine without them.

redpajama_set_name: RedPajamaStackExchange


The new study is a "very significant piece of work," said Alasdair Whittle, an emeritus professor of archaeology at Cardiff University in the U.K. who was not involved in the study.
It's "not surprising" that some of the outsiders hailed from western Britain, given the bluestone movement, Whittle said. Going forward, it would be helpful to learn more about the dates over which this connectivity spread — for instance, "was it concentrated into one or two generations, or a relationship spread over a much longer period, as the paper (perhaps rather loosely) implies?"Whittle told Live Science in an email.


text:
← 2017 Sundance Docs in Focus: DINA
On DVD: HEY BARTENDER →
2017 Sundance Docs in Focus: DOLORES
Peter Bratt celebrates an unheralded pioneer of the modern labor rights movement.
Festival Section:
US Documentary Competition
Sundance Program Description:
History tells us Cesar Chavez transformed the US labor movement by leading the first farm workers' union. But missing from this narrative is his equally influential co-founder, Dolores Huerta, who fought tirelessly alongside Chavez for racial and labor justice and became one of the most defiant feminists of the twentieth century.
Like so many powerful women advocates, Dolores and her sweeping reforms were – and still are – sidelined and diminished. Even as she empowered a generation of immigrants to stand up for their rights, her relentless work ethic was constantly under attack. False accusations, from foes and friends alike, of child neglect and immoral behavior – she married three times and raised 11 children – pushed Dolores out of the very union she helped create.
Peter Bratt's provocative and energizing documentary challenges an incomplete history. Through beautifully woven archival footage and interviews from contemporaries and from Dolores herself, now an octogenarian, the film sets the record straight on one of the most effective and undervalued civil and labor rights leaders in modern US history.
Some Background:
Peter Bratt
This is Bratt's third feature, and first documentary. His two previous films – LA MISSION (2009) and FOLLOW ME HOME (1996) – both also debuted at Sundance.
Brian Benson
Like Bratt, this marks Benson's first documentary credit as producer. He has produced or co-produced several Sundance fiction alums, most recently HOWL (2010), and assistant directed alums DIARY OF A TEENAGE GIRL (2015) and LA MISSION.
Angelica Santana
This is the first producing credit for Santana, daughter of legendary musician Carlos Santana, the film's executive producer.
Consulting Producer:
Actor Benjamin Bratt previously produced and starred in his brother Peter Bratt's LA MISSION.
This marks the first documentary feature project executive produced by the acclaimed multiple Grammy Award winner.
Jessica Congdon
Past Sundance docs:
THE MASK YOU LIVE IN (2015, producer/editor)
MISS REPRESENTATION (2011)
In addition to her previous Sundance nonfiction credits, Congdon also cut Sundance narrative alum DOPAMINE (2003), which was coproduced by Benson.
Why You Should Watch:
Featuring fantastic archival material and candid commentary from Huerta, her family, and other figures involved in her social justice struggles, Bratt's film serves as a necessary corrective to conventional historical accounts that have downplayed the vital roles played by female organizers.
For Sundance screening dates and times, click the film title in the first paragraph.
To experience the festival through the eyes of this year's filmmakers, follow my Sundance 2017 Twitter list.
Filed under Documentary, Film, Film Festivals, Recommendations, Sundance


Mark Thain is Head of Citizenship programming in the Americas and Director of the Barclays Social Innovation Facility, an internal accelerator for the development of commercial solutions to social and environmental challenges. As a professional management accountant, Thain had extensive experience in project finance before joining the Barclays Community Investment team in 2009. Initially taking responsibility for strategy, finance, and impact evaluation across a global portfolio of community partnerships, he later brought together the worlds of business and society to develop and launch the Barclays Social Innovation Facility. After launching the facility with an initial £25 million financial commitment, he now leads the social innovation team, overseeing a portfolio of investments and driving a pipeline of new opportunities that help social innovation and intrapreneurs thrive.


text:
\subsection{Unweighted Robust Budgeted Allocation}
\label{subsec:unweighted}

Our general approach will be to \emph{simulate} the following idea: Suppose we first receive the $f$ stochastic items drawn from $D$. We could allocate these items optimally (assuming they are the entire input). If this uses up most of the budgets of the agents, we automatically have a good solution, even if we do not allocate any of the adversarial items. If some fraction of the budgets remain unused, use this remaining capacity to allocate any adversarial items that arrive. If there is a way to allocate these adversarial items using the remaining capacities, we obtain $1-1/e$ fraction of this value.

Unfortunately, in the real Robust Budgeted Allocation model, we do not know which items are stochastic and which are adversarial, so we cannot perform this clean separation perfectly. Still, we can approximate this separation as follows: Let $A$ be an algorithm for Stochastic Budgeted Allocation. We have two algorithms running simultaneously. The first is a slight variant of $\textit{DeRand}^F_\eps(A)$, and the second is Balance~\cite{kp-balance}. More precisely, we send each item to $\textit{DeRand}^F_\eps(A)$; recall that this algorithm first checks if the input seen so far is $\varepsilon$-close to $D$. If it is, it allocates this item according to $A$; otherwise, it returns false. Now, instead of returning false, we assume that this item must have been sent by the adversary. As such, we erase this item from the history of $\textit{DeRand}^F_\eps(A)$, and try to allocate it using Balance. That is, we `guess' that all items that are matched by $\textit{DeRand}^F_\eps(A)$ are stochastic items and all other items are adversarial.

Note that $\textit{DeRand}^F_\eps(A)$ does not match more than $(1-\varepsilon)f$ items, $(1-\varepsilon)fP_{D=t}$ from each type $t$. From Lemmas~\ref{lm:DisGood} and \ref{lm:DisGood2}, we know that w.h.p., the sequence of stochastic items is $\varepsilon$-close to $D$; by ignoring the case when it is $\varepsilon$-far from $D$, we lose at most $\frac{1}{m}$ in the competitive ratio. Given the long input assumption, $1/m < \varepsilon$, and hence by losing $\varepsilon$ in the competitive ratio, we assume that the stochastic items are always $\varepsilon$-close to $D$. Since the sequence of stochastic items is $\varepsilon$-close to $D$, we have at least $(1-\varepsilon)f P_{D=t}$ items of type $t$. Therefore, the items that $\textit{DeRand}^F_\eps(A)$ leaves unallocated are a superset of all the adversarial items. (More precisely, there may be an adversarial item of type $t$ that we guess is stochastic, but there must be a corresponding stochastic item of type $t$ that we treat as adverarial instead.)

We now complete the description of our combined algorithm: Given an allocation, let $x_j$ denote the fraction of agent $j$'s budget used in this allocation. Let $\textit{Alg}_S$ be a $(1-\varepsilon)$-competitive algorithm for Stochastic Budgeted Allocation with the further property that it minimizes $\sum_{j=1}^n x_j^2$. (In other words, $Alg_S$ reproduces an optimal offline solution such that each item is allocated to an eligible agent with the lowest $x_j$.) We run $\textit{DeRand}^F_\eps(\textit{Alg}_S)$ as the first of our two algorithms. Recall from Remark~\ref{re:DeRand} we know the exact allocation of $\textit{DeRand}^F_\eps(Alg_S)$, which is independent of the random draws. If $x_j$ denotes the fraction of agent $j$'s capacity used by this allocation, for items unallocated by $\textit{DeRand}^F_\eps(Alg_S)$, we run the Balance algorithm on the instance of Budgeted Allocation with the adversarial items, and in which the capacity of agent $j$ is $1-x_j$.

How does this combined algorithm perform? We use $S$ to denote the stochastic items, and $A$ the adversarial items. From Corollary~\ref{cr:R} we know that $\textit{DeRand}^F_\eps(\textit{Alg}_S)$ is $1-O(\varepsilon)$ competitive against $Opt(S)$. We will prove in Lemma \ref{lm:goodAdv} that the optimum solution on the items of $A$ using the remaining capacities $1 - x_j$ is at least $(1-\lambda-O(\varepsilon))(Opt(A\cup S)-Opt(S))$. Since Balance is a $(1 - 1/e)$-competitive algorithm, the value we derive from Balance is at least $(1-\frac 1 e) (1-\lambda-O(\varepsilon)) (Opt(A\cup S)-Opt(S))$. Therefore, the competitive ratio of the combined algorithm is at least:
\begin{align*}
&\frac {(1-O(\varepsilon))Opt(S)+(1-\lambda-O(\varepsilon))(1-\frac 1 e)(Opt(A\cup S)-Opt(S))}{Opt(S\cup A)} \\
& = \frac {\lambda Opt(S\cup A)+(1-\lambda)^2(1-\frac 1 e)Opt(S\cup A)-O(\varepsilon)Opt(S\cup A)}{Opt(S\cup A)} \\
&= \lambda+(1-\lambda)^2(1-\frac 1 e)-O(\varepsilon)
\end{align*}
where the first equality uses the definition of $\lambda$-stochastic to replace $Opt(S)$ with $\lambda Opt(S \cup A)$. This proves the following theorem.

\begin{theorem}
Assuming the long input condition, there exists a $\lambda+(1-\lambda)^2(1-\frac 1 e)-O(\varepsilon)$ competitive algorithm for Robust Budgeted Allocation when the input is $\lambda$-stochastic. This algorithm does not depend on $\lambda$.
\end{theorem}

In order to prove the key Lemma~\ref{lm:goodAdv}, we first write Mathematical Program~\ref{fig:MPunW}, and show in Lemma~\ref{lm:MPisAns} that this lower bounds the ratio of the optimum allocation of the adversarial items on the remaining capacities to the overall optimum. Next, in Lemma~\ref{lm:goodMP}, we show that the solution of this mathematical program is at least $1-\lambda$. Lemma~\ref{lm:goodAdv} is an immediate result of combining these two lemmas.

\begin{figure}
\begin{center}
\fbox{\parbox{.97\columnwidth}{
\parbox{.94\columnwidth}{
\begin{alignat*}{6}
\text{Minimize:}\;\;\;&\mathrlap{\frac{\sum_{j=1}^{n}{(y_j-z_j)}}{\sum_{j=1}^{n}{y_j}}}&
\\
\text{Subject to:}\;\;\
&z_j\leq \max(0,x_j+y_j-1)&\;\;\; \forall 1\leq j\leq n \\
&\sum_{k=j+1}^{n}{(x_k+y_k)}\leq n-j &\;\;\; \forall 1\leq j \leq n-1\text{ s.t. } x_j<x_{j+1}\\
&x_j\leq x_{j+1} &\;\;\; \forall 1\leq j \leq n-1\\
&\lambda(\sum_{j =1}^{n}{x_j}+\sum_{j =1}^{n}{y_j})\geq \sum_{j =1}^{n}{x_j}\\
& 0 \leq x_j,y_j,z_j\leq 1 &\;\;\; \forall 1\leq j \leq n
\end{alignat*}
}}}
\end{center}
\caption{Mathematical Program 2 to bound the optimum allocation of adversarial items on the remaining capacities in uniform weight case.}
\label{fig:MPunW}
\end{figure}

We now show that there exists an optimum allocation of all items such that the contribution of stochastic items in this allocation is exactly $Opt(S)$. We will need this for Lemma~\ref{lm:MPisAns}.

\begin{lemma}\label{lm:goodSinOpt}
  For any disjoint sets of items $A$ and $S$, there exist an optimum allocation of $S\cup A$ such that the contribution of items of $S$ in this allocation is exactly $Opt(S)$.
\end{lemma}

\begin{proof}
	We prove this lemma by contradiction. Assume that in all optimum allocations of $S \cup A$, the contribution of items of $S$ is less than $Opt(S)$. Consider an optimum allocation $Opt'(S\cup A)$ of $S \cup A$ such that the items of $S$ have the maximum contribution to the allocation. Denote the allocation of items of $S$ in $Opt'(S\cup A)$ by $A'(S)$. By definition, $A'(S)$ is not an optimum allocation of $S$. Thus, there exists an augmenting path in $A'(S)$ which can increase the number of assigned items to one of the agents by exactly one, and keep the number of assigned items to all other agents the same. This change increases the number of assigned items in $A'(S)$ by one, and may decrease the number of assigned items from $A$ by at most one. Therefore, it is an optimal solution of $S\cup A$ in which items from $S$ have more contribution, and hence gives a contradiction.
\end{proof}

\begin{lemma}\label{lm:MPisAns}
  The optimum allocation of the adversarial items on the remaining capacities is at least $Opt(S\cup A)-Opt(S)$ times the solution of Mathematical Program~\ref{fig:MPunW}.
\end{lemma}
\begin{proof}
Let $x_j$ be the fraction of the capacity of the agent $j$ which is filled by $\textit{Alg}_S$. Without loss of generality, assume that $x_j$s are in increasing order. That is, for all $1\leq j\leq n-1$, we have $x_j\leq x_{j+1}$, which is the third constraint in Mathematical Program \ref{fig:MPunW}.

Consider the optimum solution of $S\cup A$ from Lemma \ref{lm:goodSinOpt}. Let $y_j$ be the fraction of the capacity of the agent $j$ that is filled by the adversarial items in this solution. One can see that the fourth constraint says that the contribution of the stochastic items is at most $\lambda$ fraction of the total value. (From Lemma~\ref{lm:goodSinOpt}, we could have equality in the fourth constraint, but for simplicity of analysis, we maintain the inequality.)

Note that we want to compare the optimum solution of the adversarial items on the remaining capacities $1 - x_j$ with the total value  $\sum_{j=1}^{n}{y_j}$ of the adversarial items in the optimum solution of $S \cup A$. For some agent $j$, if we have $y_j+x_j\leq 1$, we can assign the same adversarial items to the agent $j$ as in the optimum allocation. On the other hand, if $y_j+x_j \geq 1$, we can only use $1-x_j$ fraction of the capacity of agent $j$ for the adversarial items. Thus, we can always assign $y_j-max(0,x_j+y_j-1)$ fraction of the capacity of agent $i$ to the adversarial items. This quantity is denoted by $z_j$ in the first constraint.

By assigning adversarial items as in the optimum solution of $S \cup A$ using the remaining capacities, we can obtain at least $\sum_{j=1}^{n}{y_j-z_j}$. The objective function of Mathematical Program \ref{fig:MPunW} compares this to what the optimum solution of $S \cup A$ can get from adversarial items.

Finally, fix an index $j$ such that $x_j<x_{j+1}$ and look at all agents with index greater than $j$. All stochastic items that we match to agents with index greater than $j$ have no edge to the agents with index less than or equal to $j$. (By definition of $\textit{Alg}_S$, which assigns items to the eligible agent with lowest value of $x_j$.) Thus, in any optimum solution of $S$, they cover at least $\sum_{k=j+1}^n x_k$ of the agents with index greater than $j$. Thus, this optimum solution of $S \cup A$ covers $\sum_{k=j+1}^n (x_k+y_k)$ of the agents with index greater than $j$. Consider that we have $n-j$ such agents, we get $\sum_{k=j+1}^n (x_k+y_k)\leq n-j$. This is the second constraint in Mathematical program \ref{fig:MPunW}.
\end{proof}

\begin{lemma}\label{lm:goodMP}
For any small number $\delta$, the solution of the mathematical program \ref{fig:MPunW} is at least $1-\lambda-O(\delta)$.
\end{lemma}

\begin{proof}
	First, we show that given any solution to the Mathematical Program~\ref{fig:MPunW}, we can construct a related solution with a very restricted structure that only increases the objective function by $O(\delta)$. We will lower bound the objective value of this new solution, which will imply a lower bound on the original competitive ratio.

	Our restricted solution will satisfy Properties \ref{pr:MP1}, \ref{pr:MP2}, \ref{pr:MP2.5}, \ref{pr:MP3} ,\ref{pr:MP4}, and \ref{pr:MP5}, which we state below. Finally, we use these properties to bound the value of the objective function by $1-\lambda$. This means that the solution of MP \ref{fig:MPunW} is bounded by $1-\lambda-O(\delta)$.

	\begin{property}\label{pr:MP1}
		Without loss of generality we can assume that for any positive number $\delta$, we have, $\frac{1}{\sum_{j=1}^n y_j}\leq \delta$.
	\end{property}

	To prove this property given an instance of the Mathematical program \ref{fig:MPunW}, we provide another instance that satisfy this property and has a solution equal to the optimum solution of the initial instance.
	Consider a solution $Sol^n=<(x_1,\dots,x_n),(y_1,\dots,y_n),(z_1,\dots,z_n)>$, to the MP \ref{fig:MPunW} with $n$ agents. For any integer $C$, one can construct an equivalent feasible solution, $Sol^{Cn}=<(x'_1,\dots,x'_{Cn}),(y'_1,\dots,y'_{Cn}),(z'_1,\dots,z'_{Cn})>$ to an extended Mathematical Program equivalent to \ref{fig:MPunW} with $Cn$ agents as follow. For all $1\leq j\leq n$ and all $1 \leq k \leq C$, set
	\begin{align*}
		x'_{C(j-1)+k}=x_j,\;\; y'_{C(j-1)+k}=y_j,\;\;
		z'_{C(j-1)+k}=z_j.
	\end{align*}
	One can easily check that if $Sol^n$ is feasible, $Sol^{Cn}$ is feasible as well. The value of the objective functions in both $Sol^n$ and $Sol^{Cn}$ are the same. Thus, if we bound the value of the objective function in $Sol^{Cn}$, this bound holds for $Sol^n$ as well. Moreover, since we have $C$ copies of each variable here, we have $\sum_{j=1}^{Cn}y'_j = C\sum_{j=1}^{n}y_j$. Hence, if we set $C=\frac{1}{\delta\sum_{j=1}^{n}y_j }$, it satisfies Property~\ref{pr:MP1}. In the rest of the proof, we assume that the solution that we are considering has Property \ref{pr:MP1}, and for simplicity we refer to it as a solution with $n$ agents and variables $x_j$s, $y_j$s and $z_j$s.

	Note that Property \ref{pr:MP1} means that if we decrease the value of a constant number of $z_j$s to $0$, we only increase the objective value by $O(\delta)$. We later use this to provide Property \ref{pr:MP2}.

	\begin{definition}
		We say an agent $j$ is \emph{harmful} if we have $z_j>0$. Otherwise, we say the agent is a sink.
	\end{definition}

	If an agent $j$ is harmful, $z_j$ is positive and thus it contributes to reducing the objective value below $1$.

	\begin{property}\label{pr:MP2}
		All $y_j$s are either $0$ or $1$.
	\end{property}
	Let $j$ be the largest index such that the agent $j$ is harmful and $y_j$ is neither $1$ nor $0$. If this is not the only harmful agent with this property, there is some other index $k$ such that agent $k$ is harmful and $y_k$ is neither $1$ nor $0$. We decrease the value of $y_j$ and $z_j$ by some $\varepsilon$ and increase $y_j$ and $z_k$ by $\varepsilon$. This change has no effect on the objective function, or the third and fourth constraints. It increases both sides of the first constraint by $\varepsilon$ for agent $k$ and decreases both sides by $\varepsilon$ for agent $j$, keeping them both feasible.
	One can verify that this change may only decrease the left hand side of the second constraint for indices between $k$ and $j$.

	We can repeat this procedure until there is just one harmful agent $j$ with a fractional $y_j$. We decrease $y_j$ and $z_j$ of this agent to $0$, and by property \ref{pr:MP1}, only increase the objective value by $O(\delta)$. Note that harmful agents with $y_j = 0$ now become sink agents.

	We can use the same procedure to make the $y_j$s of all sink agents either $0$ or $1$.

	\begin{property}\label{pr:MP2.5}
		If agent $j$ is harmful, $z_j=x_j$.
	\end{property}
	For each harmful agent $j$, the value of $z_j$ can be as much as $x_j$ (since $y_j$ for a harmful agent is now $1$). Increasing $z_j$s of harmful agents up to their $x_j$s may only decrease the objective function, and keeps all the constraints feasible.

	From now on, for each harmful agent $j$, we keep $x_j$ and $z_j$ the same, and if we change one of these two, we change the other one as well. This implicit change of $z_j$ keeps the constraints feasible. However, each time we decrease $x_j$ of a harmful agent, we need to guarantee that the objective function does not increase. This guarantee is trivial when we are increasing the value of some other $x_k$ to match.

	\begin{property}\label{pr:MP3}
		If an agent $j>1$ is a sink, we have $x_{j-1}=x_j$.
	\end{property}
	Let $j$ and $h$ be two consecutive harmful agents with $j<h$. For all agents $k$ in the range $[j,h)$ we replace the value of $x_k$ with the average value of $x$s in this range i.e. we set $x_k = \frac{\sum_{k=j}^{h-1}x_k}{h-j}$. This keeps the sum of all $x_k$s the same, and keeps all of the constraints feasible. Moreover, since $x_j$ has the minimum value in the range $[j,h)$, and agent $j$ is the only harmful agent in this range, we are only increasing the $x$ valuess of harmful agents. This only decreases the objective function.

	\medskip
	Let $k$ be the number of different $x_j$ values that we have, and let $\alpha_h$ be the $h$-th smallest value among distinct $x_j$s. For simplicity, we assume we always have some $x_j=0$. Let $\beta_h$ be the number of $x_j$s which are at most $\alpha_h$, and set $\beta_0=0$. Thus, $\beta_{h-1}\leq j<\beta_{h}$ means that $x_j=\alpha_h$.

	\begin{property}\label{pr:MP4}
		For any $1\leq h\leq k$, all harmful agents in the range $(\beta_{-h1},\beta{h}]$, are the first agents in the range.
	\end{property}

	Let $i$ be a sink and let $i+1$ be a harmful agent, such that $x_i=x_{i+1}$. We can replace the value of the variables for these two agents and make $i$ harmful, instead of $i+1$. It is easy to see that this keeps the mathematical program feasible. By repeating this, for each range $(\beta_{j-1},\beta{j}]$, we can move all harmful agents to be the first agents in the range.

	\begin{property}\label{pr:MP5}
		All $x_j$s are either $0$ or the same fixed number $x^*$.
	\end{property}

	We iteratively decrease the number of distinct $x_j$s as follow.

	Let $\xi$ be some small number that we set later. It is easy to see that one of the following two actions decreases the objective function, since the effect of one on the objective function is the negative of the effect of the other one. The action that decreases the objective function is the one that we do.
	\begin{itemize}
		\item For all $\beta_1< j \leq \beta_2$ decrease $x_j$ by $\frac{\xi}{\beta_2-\beta_1}$ and for all $\beta_2< \ell \leq \beta_3$ increase $x_\ell$ by $\frac{\xi}{\beta_3-\beta_2}$

		\item For all $\beta_1< j \leq \beta_2$ increase $x_j$ by $\frac{\xi}{\beta_2-\beta_1}$ and for all $\beta_2< \ell \leq \beta_3$ decrease $x_\ell$ by $\frac{\xi}{\beta_3-\beta_2}$
	\end{itemize}

	We can set $\xi$, such that the mathematical program remains feasible and one of the following situations happen.
	\begin{itemize}
		\item $x_j$s in the range $(\beta_1,\beta_2]$ are all $0$.
		\item $x_j$s in the range $(\beta_2,\beta_3]$ are all $x_{\beta_3+1}$.
		\item The second constraint of the MP is tight for $j=\beta_2$.
	\end{itemize}
	In the first two cases, the number of distinct $x_i$s is reduced by one and we are done in these cases.

	Therefore, we assume that we are in the third case. Now suppose that $k>3$ (that is, there are more than $3$ distinct values of $x_j$); later, we consider the case that $k=3$. Let $\xi'$ be some small number that we set later. For all $\beta_2< j \leq \beta_{k-1}$ we increase $x_j$ by $\frac{\xi'}{\beta_{k-1}-\beta_{2}}$ and for all $\beta_{k-1}< \ell \leq \beta_k$ we decrease $x_\ell$ by $\frac{\xi'}{\beta_{k}-\beta_{k-1}}$. Below, we show that by doing so, the objective function does not increase. We can set $\xi'$ to make the largest and second largest value of $x_j$s become equal. This decreases the number of distinct values of $x_i$s.

	The second constraint in MP \ref{fig:MPunW} for $j=\beta_{k-1}$ says that the fraction of harmful agents in the range $(\beta_{k-1},\beta_k]$ is at most $1-x_n$. This constraint is tight for $j=\beta_2$. Thus, the fraction of harmful agents in the range $(\beta_2,\beta_k]$ is at least $1-x_n$, which means the fraction of harmful agents in the range $(\beta_2,\beta_{k-1}]$ is at least $1-x_n$. Thus, taking some fraction of $x_\ell$s in the range $(\beta_{k-1},\beta_k]$ and distributing it equally over the range $(\beta_2,\beta_{k-1}]$ increases the sum of $z_j$s and thus decreases the objective function.

	In the case that $k=3$, we move the harmful agents in the range $(\beta_1,\beta_2]$ to some higher indices, to make the second constraint tight. Then, we can use the above technique and decrease the value of the only two non zero distinct $x_j$s to become equal.

	Now, given the property \ref{pr:MP5} we can easily bound the objective function of the mathematical program as follow. If $x^*\leq \lambda$, all $z_j$s are at most $\lambda$, while $y_j$s are all $1$. This bounds the objective function by $1-\lambda$. On the other hand, if $x^*>\lambda$, the second constraint in MP \ref{fig:MPunW} says that the number of harmful agents is at most $1-x^*$ fraction of the value from the stochastic items. This means that sum of $z_j$s is at most $1-x^*$ fraction of value of the stochastic items. Thus, it is at most $(1-x^*)\frac{\lambda}{1-\lambda}\leq \lambda$ and this bounds the objective function by $1-\lambda$.
\end{proof}

The following lemma is an immediate result of combining Lemma \ref{lm:MPisAns} and Lemma \ref{lm:goodMP}.

\begin{lemma}\label{lm:goodAdv}
  The optimum allocation of adversarial items on the remaining capacities is at least $(1-\lambda-O(\delta))(Opt(S\cup A)-Opt(S))$.
\end{lemma}

\subsection{Weighted Robust Budgeted Allocation}
\label{subsec:weighted}
\input{WeightedAlgorithm.tex}

\subsection{Hardness of Robust Budgeted Allocation}
\label{subsec:hardness}

\begin{theorem}\label{thm:hardness}
  No online algorithm for Robust Budgeted Allocation (even in the unweighted case) has competitive ratio better than $1 - \frac{1-\lambda}{e^{ 1-\lambda}}$ for $\lambda$-stochastic inputs.
\end{theorem}

\begin{proof}
	Consider the following instance: We have $n$ agents each with capacity one and $n$ items. Initially, all of the agents are \emph{unmarked}. Each item is connected to all agents which are unmarked upon its arrival. The first $\lambda n$ items are connected to all agents. After the arrival of the first $\lambda n$ items, we \emph{mark} the $\lambda n$ agents with minimum expected load. Subsequently, after assigning each item we \emph{mark} the agent with the minimum expected load among all unmarked agents.

	Note that all of the first $\lambda n$ items are adjacent to all agents, and there is no uncertainty about them. Thus, one can consider the first $\lambda n$ items as being part of the forecast $F = (D, \lambda n)$, where the distribution $D$ has a single type (items adjacent to all agents). The last $(1-\lambda)n$ vertices as adversarially chosen items. Let $v_j$ denote the $j$th agent that we mark. An optimum algorithm that knows the whole graph in advance can match the $j$th item to the $j$th agent and obtain a matching of size $n$.

	Now consider an arbitrary online algorithm. Let $\ell^i_j$ be the expected load of agent $v_j$ after assigning the $i$th item and let $\ell_j = \ell^n_j$ be its expected load at the end of the algorithm. One can see that $\ell_j=\ell_j^{\max(\lambda n,j)}$. The first $\lambda n$ items put a load of $\lambda n$ on the agents and agents $v_1$ to $v_{\lambda n}$ are the $\lambda n$ agents with lowest expected loads. Thus, we have $$ \sum_{j=1}^{\lambda n} \ell_j \leq \lambda^2 n.$$

	In addition, for each $\lambda n < j \leq n$, the first $j$ items put a load of at most $j$ on the agents, and the expected load on the agents $v_1$ to $v_{j-1}$ is $\sum_{k=1}^{j-1} \ell_k$. Therefore, we can bound the expected load of the $j$th agent as follows: $$ \ell_j \leq \frac {j-\sum_{k=1}^{j-1} \ell_k} {n-j+1}.$$

	Further, the expected load of an agent cannot exceed $1$, and the optimum solution is a matching in which each agent has a load of $1$. Therefore, the competitive ratio of any algorithm for Robust Budgeted Allocation on $\lambda$-stochastic inputs is bounded by Linear program \ref{fig:LPunW}.

	\begin{figure}
		\begin{center}
			\fbox{\parbox{.97\columnwidth}{
					\parbox{.94\columnwidth}{
						\begin{alignat*}{6}
							\text{Maximize:}\;\;\;\;\;&\mathrlap{\frac {\sum_{j=1}^{n} \ell_j}{n}}&
							\\
							\text{Subject to:}\;\;\;\;\
							&\sum_{j=1}^{\lambda n} \ell_j \leq \lambda^2 n \\
							&\ell_j \leq \frac {j-\sum_{k=1}^{j-1} \ell_k} {n-j+1}&\;\;\; \forall \; {\lambda n+1\leq j\leq n}\\
							&0 \leq \ell_j \leq 1 &\;\;\;\;\; \forall \; {1\leq j \leq n}
						\end{alignat*}
					}}}
				\end{center}
				\caption{Linear program to bound the competitive ratio of the best online algorithm.}
				\label{fig:LPunW}
			\end{figure}

			First note that w.l.o.g., we can assume that in any optimal solution to LP~\ref{fig:LPunW}, each $\ell_j$ for $1 \le j \le \lambda n$ has the same value. Consider an optimal solution in which as many constraints as possible are tight. It is easy to see that if the constraint for $\ell_j$ is not tight, we can raise $\ell_j$ by $\varepsilon$ and decrease $\ell_{k}$ by at most $\varepsilon$ (to maintain feasibility) for the first $k > j$ such that $\ell_k > 0$. By repeating this procedure iteratively, we make all of the constraints tight. This solution is correspond to the algorithm that matches items to their eligible agents uniformly. Hence, it allocates all $\lambda n$ stochastic items and at most $\xi n$ adversarial items, for some $\xi$ such that
			$\sum_{i=1}^{\xi n}  \frac {1}{(1-\lambda)n-(i-1)}\geq 1-\lambda$. Notice that we have
			\begin{align*}
				\sum_{i=1}^{\xi n}  \frac {1}{(1-\lambda)n-(i-1)} \geq \int_{(1-\lambda-\xi)n}^{(1-\lambda)n} \frac 1 x dx = \log((1-\lambda)n) - \log((1-\lambda-\xi)n) = \log (\frac {1-\lambda}{1-(\lambda+\xi)}).
			\end{align*}
			By setting $\log (\frac {1-\lambda}{1-(\lambda+\xi)}) = 1-\lambda$ and rearranging the parameters we have  $\lambda+\xi = 1 - \frac{1 - \lambda}{e^{1-\lambda}}$.
\end{proof}

\subsection{Other Related Work}
{\bf \noindent Online Stochastic Allocation.}  Two general techniques have been applied to get improved approximation algorithms for online stochastic allocation problems: {\em primal-based} and {\em dual-based} {techniques}.  The dual-based technique is based on solving a dual linear program on a sample instance, and using this dual solution in the online decisions. This method was pioneered by Devanur and Hayes~\cite{devanur-hayes} for the AdWords problem and extended to more general problems~\cite{FHKMS10, AWY09, VeeVS}.  It gives a $1-\varepsilon$-approximations for the random order model if the number of items $m$ is known to the algorithm in advance, and ${{\sc OPT}\over w_{ij}}\ge O({m\log n \over \varepsilon^3})$, where $n :=|Y|$ is the number of agents.  The primal-based technique is based on solving an offline primal instance, and applying this solution in an online manner.  This method applies the idea of power-of-two choices, and gives improved approximation algorithms for the iid model with known distributions. This technique was initiated by \cite{FMMM09} for the online (unweighted) matching problem and has been improved~\cite{BK10,MOS11,HMZ11,JL13}. All the above algorithms heavily rely on an accurate forecast of the traffic. An alternative technique that has been applied to online stochastic allocation problems is based on optimizing a potential function at each stage of the algorithm~\cite{DJSW11, DevanurSA12}. This technique has been analyzed and proved to produce asymptotically optimal results under the i.i.d. model with unknown distributions. Although this technique does not rely on the accurate predictions as much, it does not combine stochastic and adversarial models, and the analysis techniques used are not applicable to our robust online allocation model.  For unweighted graphs, it has been recently observed that the Karp-Vazirani-Vazirani $1-{1\over e}$-competitive algorithm for the adversarial model also achieves an improved approximation ratio of $0.70$ in the random arrival model~\cite{KMT11,MY11}.  This holds even without the assumption of large degrees. It is known that without this assumption, one cannot achieve an approximation factor better than $0.82$ for this problem (even in the case of i.i.d. draws from a known distribution)~\cite{MOS11}.  All the above results rely on stochastic assumptions and apply only to the random-order or the iid stochastic models.

{\bf \noindent Robust stochastic optimization.} Dealing with traffic spikes and inaccuracy in forecasting the traffic patterns is a central issue in operations research and stochastic optimization.  Methods including robust or control-based stochastic optimization~\cite{BN02,BPS04,Wang06,srikant} have been proposed. These techniques either try to deal with a larger family of stochastic models at once~\cite{BN02,BPS04,Wang06}, try to handle a large class of demand matrices at the same time~\cite{Wang06, AC06, AzarCFKR}, or aim to design asymptotically optimal algorithms that react more adaptively to traffic spikes~\cite{srikant}.  These methods have been applied in particular for traffic engineering~\cite{Wang06} and inter-domain routing~\cite{AC06,AzarCFKR}. Although dealing with similar issues, our approach and results are quite different from the approaches taken in these papers. For example, none of these previous models give theoretical guarantees in the adversarial model while preserving an improved approximation ratio for the stochastic model.  Finally, an interesting related model for combining stochastic and online solutions for the Adwords problem is considered in~\cite{MNS07}, however their approach does not give an improved approximation algorithm for the i.i.d. model.

\section{Introduction}
\input{introduction-backup.tex}

\section{Preliminaries and Techniques}
\label{sec:prelims}
\input{prelim.tex}

\section{Robust Online Budgeted Allocation}
\label{sec:robust}
\input{AlmostStochastic.tex}

\section{Approximating Adversarial and Stochastic Budgeted Allocation}
\label{sec:simultaneous}

\input{simultaneous.tex}

\bibliographystyle{ACM-Reference-Format}

\subsection{Model}
\label{subsec:model}

Let $\mathcal{I}$ denote a set of item `types'; in the Internet advertising applications, these represent queries / ad impressions with different properties that are relevant to advertiser targeting and bidding. A \emph{forecast} $F = (D, f)$ has two components: A distribution $D$ over $\mathcal{I}$, together with a number $f$; this is interpreted as a prediction that $f$ items will arrive, each of which is drawn independently from $D$.

In the \emph{Stochastic Budgeted Allocation problem}, the input known to the algorithm in advance is a forecast $F = (D, f)$, and a set of agents $Y$, with a capacity $c_j$ for agent $j$. A sequence of $f$ items is drawn from the distribution $D$ and sent to the algorithm one at a time; the algorithm must allocate these items as they appear online.  The total weight of items allocated to agent $j$ must not exceed $c_j$, and the objective is to maximize the weight of the allocation. As discussed above, there has been considerable work on near-optimal algorithms for Stochastic Budgeted Allocation~\cite{devanur-hayes, FHKMS10, AWY09, VeeVS, AHL-Prophet}.

In this paper, we define the new \emph{Robust Budgeted Allocation problem}, for which our input model is the following: The adversary can create in advance an arbitrary forecast $F = (D, f)$, and a collection of agents $Y$. Further, at each time step, the adversary can either create a new arbitrary item (together with its incident edges and weights) and send it to the algorithm, or choose to send an item drawn from $D$. After at least $f$ items have been drawn from $D$, the adversary can either send additional (arbitrary) items, or choose to terminate the input. The online algorithm knows in advance only the forecast $F$ and the agents $Y$, and so it knows that it will receive $f$ items corresponding to i.i.d. draws from $D$; it does not know anything about the items created by the adversary, where in the sequence they arrive, or the total number $m$ of items that will arrive. As usual, the competitive ratio of the algorithm is measured by the worst-case ratio (over all inputs) of the value of its allocation to the value of the optimal allocation on the sequence that arrives.

With the preceding description of the model, no algorithm can have a competitive ratio better than $1 - 1/e$, for the simple reason that we could set $f = 0$, allowing the adversary to control the entire input. (Or even for larger $f$, the edge weights for the adversarial items could be considerably larger than the weights for the forecast items in $\mathcal{I}$.) We have not quantified the accuracy of the forecast, or meaningfully limited the power of the adversary. Our goal is to design algorithms with a competitive ratio that improves with the accuracy of the forecast. We quantify this accuracy as follows:

\begin{definition}
For an instance $I$ of the Robust Budgeted Allocation problem with forecast $(D, f)$, let $S(I)$ denote the set of $f$
`stochastic' items drawn from distribution $D$. Let $A(I)$ denote the set of $n-f$ `adversarial' items. When $I$ is
clear from context, we simply use $S$ and $A$ to denote the stochastic and adversarial items respectively. We mildly
abuse notation and, when clear from context, also use $I$ to refer to the sequence of items in an instance.
For a solution $Sol$ to an instance $I$, let $\textrm{Val}_S(Sol)$ denote the value obtained by $Sol$ from allocating the items of $S$ to agents, and $\textrm{Val}_A(Sol)$ denote the value obtained by $Sol$ from allocating the items of $A$.
\end{definition}

\begin{definition}
An instance $I$ of the Robust Budgeted Allocation problem is said to be $\lambda$-stochastic if $\lambda=\max_{Sol\in OPT(I)}\{\frac{E[\textrm{Val}_S(Sol)]}{E[\textrm{Val}_S(Sol) + \textrm{Val}_A(Sol)]}\}$, where $OPT(I)$ is the set of all optimal solutions of $I$.
\end{definition}

Note that when the forecast is completely accurate (there are no adversarial items), the instance is $1$-stochastic, and when $f = 0$ (all items are adversarial), the input is $0$-stochastic. Though $\lambda$ is unknown to the algorithm, our goal is to design algorithms which, when restricted to $\lambda$-stochastic instances, have good competitive ratio (ideally, increasing in $\lambda$).

\subsection{Algorithms for Working with Forecasts}

In this section, we consider how to solve the Stochastic Budgeted Allocation problem. Similar problems have been applied
before (see e.g. \cite{AHL-Prophet}), but we describe a specific approach below that will be a useful tool for the
Robust Budgeted Allocation problem. Further, our argument implies that this approach performs well even for an
\emph{adversarial} input sequence if it is sufficiently `close' to the forecast.

Roughly speaking, given a forecast $F = (D, f)$, if the number of items $f$ is sufficiently large, then we can work with
an `expected instance'. In the expected instance, the set of items is created by assuming each type $t \in \mathcal{I}$ arrives
in proportion to $P_{D=t}$. We then run any (offline) algorithm $\textit{Alg}$ on the expected instance; when an item arrives in
the real online instance, we assign it according to the allocation given by $\textit{Alg}$ on the expected instance. If the
number of items $f$ is sufficiently large, then only a small error is induced because we assign according to the
expected instance instead of the random realization of the forecast.

\smallskip
We begin by defining the notion of a sequence being \emph{$\varepsilon$-close} to a distribution. Indeed, we show that with high probability a `long' sequence of draws from a distribution is $\varepsilon$-close to that distribution, where $\varepsilon$ is an arbitrary small constant. We next prove that if we ignore inputs which are not $\varepsilon$-close to the input distribution, we lose only $\frac 1 m$ in the competitive ratio.  Finally, we show that we can modify any online stochastic algorithm, or more strongly any offline algorithm for Budgeted Allocation to work for online adversarial input sequences which are guaranteed to be $\varepsilon$-close to a known distribution. Interestingly, this reduction loses only $4\varepsilon$ on the competitive ratio.

\begin{definition}
Let $S= \langle s_1,s_2,...,s_m \rangle$ be a sequence of items and let $D$ be a distribution over a set of item types $\mathcal{I}$. For a type $t \in \mathcal{I}$, let $P_{D=t}$ be the probability that a draw from $D$ is $t$. We say $S$ is $\varepsilon$-close to distribution $D$, if for any continuous sub-sequence $S_{i,k}=s_i,s_{i+1},\dots,s_k \subset S$ and any type $t$, the number of items of type $t$ in $S_{i,k}$ is within the range $(k-i+1\pm \varepsilon m)P_{D=t}$. If $S$ is not $\varepsilon$-close to distribution $D$ we say it is $\varepsilon$-far from the distribution.
\end{definition}

Consider that $(k-i+1)P_{D=t}$ is the expected number of items of type $t$ in a set of $k-i+1$ draws from $D$. When $k-i+1$ is large, using the Chernoff bound we can show that the number of items of type $t$ is close to the expectation. On the other hand, when $k-i+1$ is small, the term $\varepsilon m$ dominates $k-i+1$, and thus the number of items of type $t$ is in the range $(k-i+1\pm \varepsilon m)P_{D=t}$. Lemma ~\ref{lm:DisGood} formalizes this intuition, showing that with high probability a [long enough] sequence of items drawn from a distribution $D$ is $\varepsilon$-close to $D$.

\begin{definition}
  Given a distribution $D$, a sequence of $f$ items is said to satisfy the \emph{long input condition} for $D$ if $\frac {f} {\log(f)} \ge \frac {15}{\varepsilon^2 min_{t \in D}(P_{D=t})}$.
\end{definition}

We use the following version of the Chernoff bound in Lemma ~\ref{lm:DisGood}.

\begin{proposition}
	Let $x_1,x_2,\dots,x_m$ be a set of independent boolean random variables. For $X=\sum_{i=1}^m x_i$ and $\mu = E[X]$ we have: $Pr(|X-\mu| \geq \delta ) \leq 2\exp(\frac {-\delta^2}{3\mu})$
\end{proposition}

\begin{lemma} \label{lm:DisGood}
  Let $S$ be a sequence of $m$ items drawn from a distribution $D$.
  Assuming the long input condition, the probability that $S$ is
  $\varepsilon$-far from $D$ is at most $\frac 1 {m^2}$.
\end{lemma}
\begin{proof}
	$S$ contains $\frac {m(m-1)}{2}$ subsequences. In addition, the long input condition gives us $P_{D=t}\geq \frac
	{15\log(m)}{\varepsilon^2 m}$. This means that there are at most $\frac {\varepsilon^2m} {15 \log(m)}$ different types. Thus, we have
	fewer than $\frac {m^3} 2$ combinations of a type and a subsequence. We next argue that the probability that
	the number of items of a fixed type $t$ in a fixed sub sequence $S_{i,k}$ is out of the range $(k-i+1\pm \varepsilon
	m)P_{D=t}$ is at most $\frac 2 {m^5}$. Applying the union bound, the probability that $S$ is
	$\varepsilon$-far from $D$ is at most $\frac 2 {m^5}\frac {m^3} 2 = \frac 1 {m^2}$, as desired.

	For a type $t$ and an index $1\leq \ell \leq m$, let $x_\ell^t$ be a random variable which is $1$ if the $\ell$-th item in
	sequence $S$ is of type $t$ and is $0$ otherwise. The variables $x^t_k$ are independent for a fixed
	type $t$ and different indices. Let $X_{i,k}^t$ be $\sum_{\ell=i}^{k} x_\ell^t$, which is the number of items of type
	$t$ in the sub sequence $S_{i,k}$. The expected value of $X_{i,k}^t$ is $(k-i+1)P_{D=t}$, and by applying
	the Chernoff bound we have:
	\begin{align*}
		Pr(|X_{i,j}^t-(j-i+1)P_{D=t}|\geq \varepsilon m ) &\leq 2 \exp(\frac {-\varepsilon^2m^2}{3(j-i+1)P_{t=D}})\\
		&\leq 2\exp(\frac {-\varepsilon^2m^2}{3n\frac {m\varepsilon^2} {15 \log(m)}})\\
		&=2\exp(- 5\log(m))  =\frac 2 {m^5}.
	\end{align*}
	This completes the proof of the lemma.
\end{proof}

In the rest of this section, we use the monotonicity and subadditivity properties of Budgeted Allocation, stated in Lemma \ref{Monoton} and Lemma \ref{Subadditive} respectively.

\begin{lemma}[Monotonicity]\label{Monoton}
  Budgeted Allocation is monotone: Fixing the set of agents and their capacities, for any sequence of items $S$ and
  any sequence $T\subseteq S$, we have $Opt(T)\leq Opt(S)$ where $Opt(S)$ and $Opt(T)$ are the values of the optimum
  solutions when the items that arrive are $S$ and $T$ respectively.
\end{lemma}
\begin{proof}
	Any feasible allocation of items of $T$ is a feasible allocation of items of $S$ as well. This immediately means $Opt(T)\leq Opt(S)$ as desired.
\end{proof}

\begin{lemma}[subadditivity]\label{Subadditive}
  Budgeted Allocation is subadditive: Fixing the set of agents and their capacities, for any sequence of items $S$
  and any sequence of items $T$, we have $Opt(S\cup T)\leq Opt(S)+Opt(T)$ where $Opt(X)$ indicates the size of the
  optimum solution when the sequence of items that arrive is X.
\end{lemma}
\begin{proof}
Fix an optimum solution $Opt(S\cup T)$. The allocation of items of $S$ in $Opt(S\cup T)$ is a feasible allocation for $S$. Similarly the allocation of items of $T$ in $Opt(S\cup T)$ is a feasible allocation for $T$. Therefore we have $Opt(S\cup T)\leq Opt(S)+Opt(T)$.
\end{proof}

Lemma \ref{lm:DisGood} says that w.h.p, a sequence of items drawn from a distribution $D$ is $\varepsilon$-close to $D$. That
is, inputs which are $\varepsilon$-far from the input distribution are rare, but this does not immediately imply that the total
value of such rare $\varepsilon$-far inputs is small as well. Lemma \ref{lm:DisGood2} says that we may ignore all inputs which
are $\varepsilon$-far from the input distribution and only lose a small fraction in the competitive ratio.

\begin{lemma} \label{lm:DisGood2}
  Let $S$ be a sequence of $m$ items drawn from a distribution $D$, satisfying the long input condition. Let $\textit{Alg}$ be
  an $\alpha$-competitive algorithm for Stochastic Budgeted Allocation with forecast $(D, m)$. Let $\textit{Alg}_{\textrm{close}}$
  be an algorithm that has the same outcome as $\textit{Alg}$ when the input is $\varepsilon$-close to $D$ and $0$ otherwise.
  $\textit{Alg}_{\textrm{close}}$ is $(\alpha-\frac {1}{ m} )$-competitive.
\end{lemma}

\begin{proof}
	Let $\textit{Alg}_{\textrm{far}}$ be an algorithm that has the same outcome as $\textit{Alg}$ when the input is $\varepsilon$-far from $D$ and $0$
	otherwise. We slightly abuse notation and use $\textit{Alg}, \textit{Alg}_{\textrm{close}}, \textit{Alg}_{\textrm{far}}$ to refer both to the algorithms and the expected
	values of their outcomes. By definition we have $\textit{Alg}=\textit{Alg}_{\textrm{close}}+\textit{Alg}_{\textrm{far}}$. Let $Opt$ denote the expected value of an optimal
	solution on the sequence drawn from the distribution. We bound the expected outcome of $\textit{Alg}_{\textrm{far}}$ to compare
	the competitive ratio of $\textit{Alg}$ and $\textit{Alg}_{\textrm{close}}$.

	Let $S_{k}$ be an input that contains $k$ items of each type. The monotonicity of Budgeted Allocation implies that for
	any sequence $S$ of size $m$, $Opt(S_m)$ is greater than $Opt(S)$. Moreover, by subadditivity, $Opt(S_m)$ is at most
	$\frac m 2$ times $Opt(S_2)$. Together, these imply that, for any sequence $S$ of size $m$, we have $Opt(S)\leq \frac
	m 2 Opt(S_2)$.
	%
	 On the other hand, the number of items of type $t$ in any sequence $S$ of size $m$ which is $\varepsilon$-close to $D$ is at least
	 \begin{align*}
	 	(1 - \varepsilon)fP_{D=t} \geq
	 	 (1 - \varepsilon)\frac {15}{\varepsilon^2 min_{t \in D}(P_{D=t})}P_{D=t}\geq
	 	 (1 - \varepsilon)\frac {15}{\varepsilon^2}\geq 2.
	 \end{align*}
	%
	Thus by monotonicity we have $\frac 1 {Pr(S\text{ is } \varepsilon \text{ close to }D)} Opt_{close} \geq
	Opt(S_2)$. Therefore, for \emph{any} sequence $S$ of size $m$ we have

	\begin{align*}
		Opt(S)\leq \frac m 2 Opt(S_2)\leq \frac m 2 \frac 1 {(1-\frac 1 {m^2})} Opt_{close}  \leq m Opt
	\end{align*}
	This together with Lemma \ref{lm:DisGood} gives us
	\begin{align*}
		\textit{Alg}_{\textrm{close}} = \textit{Alg} - \textit{Alg}_{\textrm{far}} \geq \textit{Alg} - m Opt\frac 1 {m^2} \geq \alpha Opt - \frac 1 m Opt = (\alpha-\frac 1 m) Opt
	\end{align*}
	as desired.
\end{proof}

Note that any algorithm $\textit{Alg}$ for Budgeted Allocation has a random outcome when the items are drawn from a forecast,
simply due to the randomness in the sequence of items. We now define a derandomization of such algorithms: Given an
algorithm $\textit{Alg}$, a forecast $F = (D, f)$ and a constant $\varepsilon$, algorithm $\textit{DeRand}^F_\eps(\textit{Alg})$ is defined as follows:

Let $S'$ be a sequence of $(1-\varepsilon)f$ impressions, with $(1-\varepsilon)f P_{D=t}$ impressions of type $t$, for each type
$t$. Run algorithm $\textit{Alg}$ on sequence $S'$. Let $\textit{Alg}(S',t,i)$ be the agent to which $\textit{Alg}$ assigns the $i$th impression of
type $t$ in $S'$. Note that any sequence of $f$ items which is $\varepsilon$-close to $D$ contains at least $(1-\varepsilon)f
P_{D=t} $ impressions of each type $t$. We can now describe how $\textit{DeRand}^F_\eps(\textit{Alg})$ allocates items of a sequence $S$. For each
type $t$, Algorithm $\textit{DeRand}^F_\eps(\textit{Alg})$ allocates the first $(1-\varepsilon) f \cdot P_{D=t}$ impressions of type $t$ in $S$ in the same
manner as $\textit{Alg}$ allocated $S'$. That is, we assign the $i$th impression of type $t$ in $S$ to $\textit{Alg}(S',t,i)$. After the
first $(1 - \varepsilon) f P_{D=t}$ impressions of type $t$ have been allocated, we do not allocate any more items of this type.
Finally, if at any time during the algorithm, we observe that the input sequence (so far) is not $\varepsilon$-close to
distribution $D$, the algorithm stops and returns false. Otherwise, it returns true.

When it is clear from the context, we drop $F$ and $\varepsilon$ from the notation of $\textit{DeRand}^F_\eps(\textit{Alg})$.

\begin{remark} \label{re:DeRand}
  Note that for any forecast $F = (D, f)$ and constant $\varepsilon$, the outcome of $\textit{DeRand}^F_\eps(\textit{Alg})$ on any item sequence of
  length $f$ that is $\varepsilon$-close to $D$ is a function purely of $D$ and $\varepsilon$, but not the actual impressions in the
  sequence.
\end{remark}

\begin{theorem}\label{thm:CloseIsGood}
  Let $F = (D, f)$ be a distribution, and let $A$ be an adversarial input with length $f$ such that $A$ satisfies the long
  input condition and $A$ is $\varepsilon$-close to $D$. Let $\textit{Alg}$ be an $\alpha$-competitive algorithm for Stochastic
  Budgeted Allocation. Though $A$ is not explicitly drawn from $D$, $\textit{DeRand}^F_\eps(\textit{Alg})$ is $\alpha-2\varepsilon$ competitive on
  sequence $A$.
\end{theorem}
\begin{proof}
	Since $A$ is $\varepsilon$-close to $D$, $\textit{DeRand}(\textit{Alg})$ will not return false on $S$, and thus, the allocation of $\textit{DeRand}(\textit{Alg})$ on
	$S$ is identical to that of $\textit{Alg}$ on $S'$.

	Let $S''$ be a sequence of $(1+\varepsilon)d$ impressions, $(1+\varepsilon)f P_{D=t} $ from each type $t$.

	Using the subadditivity of Budgeted Allocation, we have $Opt(S') \ge \frac {1 - \varepsilon} {1+\varepsilon}Opt(S'') \geq (1-2\varepsilon)Opt(S'')$.

	On the other hand, using the monotonicity of Budgeted Allocation, $Opt(A)\leq Opt(S'')$. Together, these inequalities
	imply that $Opt(S')\geq (1-2\varepsilon) Opt(A)$, which means that $\textit{DeRand}^F_\eps(\textit{Alg})$ is $(\alpha-2\varepsilon)$-competitive.
\end{proof}

Consider an $\alpha$-competitive online algorithm (or $\alpha$-approximate offline algorithm), $\textit{Alg}$, for Budgeted
Allocation with stochastic input. By Theorem \ref{thm:CloseIsGood}, for inputs which are $\varepsilon$-close to $D$,
$\textit{DeRand}^F_\eps(\textit{Alg})$ has a competitive ratio that is only $2\varepsilon$ worse than that of $\textit{Alg}$. Moreover, Lemma \ref{lm:DisGood2}
says that if we ignore all inputs which are $\varepsilon$-far from the input distribution, we lose only $\frac 1 m$ on the
competitive ratio. Together with the assumption that $\varepsilon \geq \frac 1 m$, we obtain the following corollary.

\begin{corollary}\label{cr:R}
  Let $\textit{Alg}$ be an $\alpha$-competitive algorithm for Stochastic Budgeted Allocation (or
  $\alpha$-approximate offline algorithm for Budgeted Allocation). Assuming the long
  input condition, for any small constant $\varepsilon\geq \frac 1 m$ and any forecast $F$,
  $\textit{DeRand}^F_\eps(\textit{Alg})$ is an $(\alpha-3\varepsilon)$-competitive algorithm for Stochastic Budgeted Allocation.
\end{corollary}

redpajama_set_name: RedPajamaArXiv


text:
"Don't leave Wales's future in hands of Westminster Tories" Leanne urges Labour
Posted on March 14 2017, 1:54 PM
Leanne Wood used First Minister's Questions to challenge the Labour Government to set out a plan for the constitutional and economic future of Wales in light of a potential referendum on Scottish independence.
The Rhondda AM asked the Leader of the House to set out where she saw Wales in two years' time.
Speaking a day after her call for a "national debate on Wales's future", the Plaid Cymru Leader accused the Labour Government's response to the Scottish referendum announcement of "lacking in detail" and "saying almost nothing about the future of Wales".
The First Minister had previously issued a two sentence statement on the Scottish announcement, in contrast to Plaid Cymru's call for all future options for Wales to be put on the table and discussed.
During FMQs, Leanne Wood also pointed out figures showing that Wales had a £2.2bn trade surplus with the EU, growing from £1.5bn in 2015. She said that the Welsh Government should try and influence the Article 50 process, taking advantage of a "window of opportunity."
Leanne Wood commented:
"The Labour Welsh Government issued a tiny, two sentence statement in response to the Scottish referendum announcement. It's not good enough to have statements which lack detail and say almost nothing about the future of Wales. The government needs to be drawing up detailed plans on how to approach this critical question, which will impact the whole of the UK.
"Wales needs its government to have a vision and a plan for where our country will be in two years' time. We need that proper national debate about what will happen to Wales if Scotland does decide to leave the UK.
"The Welsh economy currently generates a £2.2bn trade surplus with the European single market. Around 200,000 jobs in Wales are linked to this trading bloc. We must use every tool in our armoury to prevent a 'hard Brexit' which would put these at risk.
"In the immediate short-term, Plaid Cymru wants the Labour Government to act decisively to influence the Article 50 letter and ensure that Wales's interests are protected. There is a window of opportunity, and a failure to grasp this will leave our future in the hands of Westminster Tories."


text:
Jimmy Mahoney
The Secrets of Little Saints
Jimmy Mahoney was raised in the Bronx, New York, the first of six children born to Irish immigrant parents. While trying to maintain a humorous perspective on life, he has taken his professional responsibilities seriously. He graduated from Catholic schools, Cardinal Hayes High School, and Manhattan College. He became a Certified Public Accountant, hospital administrator, and university professor after earning his MBA degree at Wagner College. He has been president of his local Rotary Club, active in Big Brothers, a member of his church parish council, and the founder of a referrals networking group.
Jimmy and Anne, his wife of 49 years, now have a life and health insurance business in the Shenandoah Valley of Virginia. They have four children and seven grandchildren.
2 thoughts on "About Jimmy"
Bill Scullion
I can't wait to read the book. You look so angelic as a young altar boy.
James P Mahoney
Nice name….Can't wait to get the book…..I went to Catholic Schools and have heard and told the tales…lucky to have had the chance…
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Bronx-Whitestone Bridge photo credit: Metropolitan Transportation Authority / Patrick Cashin