# Ramsey problems

19.10.2020The nerve that controls your facial muscles passes through a narrow corridor of bone on its way to your face. Ramsay Hunt syndrome herpes zoster oticus occurs when a shingles outbreak affects the facial nerve near one of your ears. In addition to the painful shingles rash, Ramsay Hunt syndrome can cause facial paralysis and hearing loss in the affected ear. Ramsay Hunt syndrome is caused by the same virus that causes chickenpox.

After chickenpox clears up, the virus still lives in your nerves. Years later, it may reactivate. When it does, it can affect your facial nerves. Prompt treatment of Ramsay Hunt syndrome can reduce the risk of complications, which can include permanent facial muscle weakness and deafness. Facial weakness or paralysis may cause one corner of your mouth to droop. If you're experiencing facial weakness or paralysis, you may have trouble closing the eye on the affected side of your face.

Usually, the rash and the facial paralysis occur at the same time. Sometimes one can happen before the other. Other times, the rash never occurs. Call your doctor if you experience facial paralysis or a shingles rash on your face.

## Ramsey theory

Treatment that starts within three days of the start of signs and symptoms may help prevent long-term complications. Ramsay Hunt syndrome occurs in people who've had chickenpox.

Once you recover from chickenpox, the virus stays in your body — sometimes reactivating in later years to cause shingles, a painful rash with fluid-filled blisters. Ramsay Hunt syndrome is a shingles outbreak that affects the facial nerve near one of your ears.

It can also causes one-sided facial paralysis and hearing loss. Ramsay Hunt syndrome can occur in anyone who has had chickenpox. It's more common in older adults, typically affecting people older than Ramsay Hunt syndrome is rare in children. Ramsay Hunt syndrome isn't contagious. However, reactivation of the varicella-zoster virus can cause chickenpox in people who haven't previously had chickenpox or been vaccinated for it.

The infection can be serious for people who have immune system problems. Children are now routinely vaccinated against chickenpox, which greatly reduces the chances of becoming infected with the chickenpox virus. A shingles vaccine for people age 50 or older also is recommended. Mayo Clinic does not endorse companies or products. Advertising revenue supports our not-for-profit mission.Gordon Ramsay and controversy have gone hand in hand ever since the potty-mouthed celebrity chef took London's culinary scene by storm back in the s.

Over the years, the tabloids have had a field day chronicling Ramsay's exploits, which have involved lawsuits, allegations of shady dealings in his restaurants, and claims that he's faked his TV shows.

So get ready to take a deep dive into some of the many, many scandals that have plagued Gordon Ramsay over the years. Long before Gordon Ramsay was a household name, he was already getting in trouble for the bad-boy antics that would become his hallmark.

Inan old incident resurfaced that spelled embarrassment for the celebrity chef. As the Daily Mail reported, Ramsay had been arrested back inalong with two other male chefs, caught in "various stages of undress" in a tube station lavatory. While the three were cited for "gross indecency," a spokesperson for Ramsay insisted the incident was just a little booze-fueled tomfoolery. The spokesperson described the boozy hijinks of three men who'd had a bit too much to imbibe and were "horsing around" in a public bathroom after a celebratory evening.

After talking with Ramsay about what transpired all those years ago, the spokesperson explained that "one of them was having a pee in the sink. The other one was running around with his trousers around his ankles and Gordon was actually just at a urinal with his head slumped on the wall.

## Ramsey problem

InGordon Ramsay was accused of infidelity by self-described "professional mistress" Sarah Symonds via HuffPostwho claimed she'd had a seven-year affair with the married chef. He loves the risk and needs that adrenaline rush. Ramsay, however, denied everything, even joking about the allegations while filming a cooking show — with his mother in the audience. I didn't do it, mum, I love you. In an interview with Men's JournalRamsay restated his innocence, and graphically explained why he would never cheat on his wife.

Inseveral of Gordon Ramsay's London gastropubs were found to be serving previously prepared frozen food to oblivious customers. The revelation came about thanks to a sting orchestrated by The Sun tabloid, reported The Guardianwhich revealed that the eateries were supplied with boil-in-the-bag coq au vin supplied by Ramsay-owned kitchen facility GR Logistics.

When heated and served, the food was sold to unsuspecting diners at a markup of around percent. As Daily Mail reported, a spokesperson admitted that GR Logistics did indeed "prepare components of dishes devised and produced to the highest Gordon Ramsay standards. Helen Hokin, food editor for Food and Travel Magazinedidn't buy that explanation. I think he's going to lose the trust of his adoring public. InRamsay opened London's Lucky Cat, described in its press materials as an "authentic Asian eating house" that was "inspired by the drinking dens of s Tokyo and the Far East.

After Hui's scathing critique and her accompanying social media posts called out Ramsay for cultural appropriation, Ramsay issued a statement on Instagram. Acknowledging that critics shouldn't be prevented from providing their honest opinions, Ramsay insisted Hui was biased against him and his restaurants, pointing to "the slew of derogatory and offensive social media posts" she had written about him.

Ramsay concluded by stating if a reviewer is "going to be critical, then I expect them to be professional and have some integrity. Hui wasn't the only one to criticize Lucky Cat. Martin Hyde was manager of Manhattan eatery Dillons, until being fired during an episode in which Ramsay called him out for such infractions as rat droppings on the floor and rotten hamburger meat in the fridge.

A judge subsequently tossed the lawsuitand ordered both sides to enter arbitration. Back inGordon Ramsay purchased an oceanfront five-bedroom home in the English seaside resort of Cornwall.

He then demolished the property and began construction on two new structures — a mansion and a garden house — and that's when problems began. According to the Daily Mailthe new homes boast modern, box-like architecture that Ramsay's ticked-off neighbors have described as "a monstrosity" resembling "a stack of containers.

Ramsay's next-door neighbor, Andrew Nisbet, told Cornwall Live that the chef made no effort to meet with neighbors about their concerns. In fact, Nisbet said he attempted to contact Ramsay but never received a response.

Another neighbor, Gerard Manley, shared his concerns about Ramsay's garden house. During a live appearance in Melbourne, Australia, Ramsay displayed a Photoshopped image of a naked woman on all fours with multiple breasts and a pig's face, declaring, "That's Tracy Grimshaw. I had an interview with her yesterday, holy crap. She needs to see Simon Cowell's Botox doctor.

For the record, I don't.The mathematical study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large. Ramsey theory is named after Frank Plumpton Ramsey, who did seminal work in this area before his untimely death at age 26 in The classical problem in Ramsey theory is the party problemwhich asks the minimum number of guests that must be invited so that at least will know each other i.

Here, is called a Ramsey number. A typical result in Ramsey theory states that if some mathematical object is partitioned into finitely many parts, then one of the parts must contain a subobject of an interesting kind. For example, it is known that if is large enough and is an -dimensional vector space over the field of integers modthen however is partitioned into pieces, one of the pieces contains an affine subspace of dimension. Burr, S. Bari and F.

New York: Springer-Verlag, pp. Graham, R. Graham and J. Heidelberg, Germany: Springer-Verlag, Hoffman, P. New York: Hyperion, pp. Weisstein, Eric W. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.

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MathWorld Book. Terms of Use. Contact the MathWorld Team.Ramsey theorynamed after the British mathematician and philosopher Frank P. Ramseyis a branch of mathematics that studies the conditions under which order must appear in relation to disorder. Problems in Ramsey theory typically ask a question of the form: "how many elements of some structure must there be to guarantee that a particular property will hold?

A typical result in Ramsey theory starts with some mathematical structure that is then cut into pieces. How big must the original structure be in order to ensure that at least one of the pieces has a given interesting property? This idea can be defined as partition regularity. For example, consider a complete graph of order n ; that is, there are n vertices and each vertex is connected to every other vertex by an edge. A complete graph of order 3 is called a triangle.

Now colour each edge either red or blue. How large must n be in order to ensure that there is either a blue triangle or a red triangle? It turns out that the answer is 6. See the article on Ramsey's theorem for a rigorous proof. Another way to express this result is as follows: at any party with at least six people, there are three people who are all either mutual acquaintances each one knows the other two or mutual strangers each one does not know either of the other two.

See theorem on friends and strangers. This also is a special case of Ramsey's theoremwhich says that for any given integer cany given integers n 1A theorem similar to van der Waerden's theorem is Schur's theorem : for any given c there is a number N such that if the numbers 1, 2, Many generalizations of this theorem exist, including Rado's theoremRado—Folkman—Sanders theoremHindman's theoremand the Milliken—Taylor theorem.

A classic reference for these and many other results in Ramsey theory is Graham, Rothschild, Spencer and Solymosi, updated and expanded in to its first new edition in 25 years.

Results in Ramsey theory typically have two primary characteristics. Firstly, they are non-constructive : they may show that some structure exists, but they give no process for finding this structure other than brute-force search. For instance, the pigeonhole principle is of this form. Secondly, while Ramsey theory results do say that sufficiently large objects must necessarily contain a given structure, often the proof of these results requires these objects to be enormously large — bounds that grow exponentiallyor even as fast as the Ackermann function are not uncommon.

In some small niche cases, upper and lower bounds are improved, but not in general. In many cases these bounds are artifacts of the proof, and it is not known whether they can be substantially improved. In other cases it is known that any bound must be extraordinarily large, sometimes even greater than any primitive recursive function; see the Paris—Harrington theorem for an example.

Graham's numberone of the largest numbers ever used in serious mathematical proof, is an upper bound for a problem related to Ramsey theory.

**How Dave Ramsey Is Keeping You Poor (Investing Advice Exposed!)**

Another large example is the Boolean Pythagorean triples problem. Theorems in Ramsey theory are generally one of the following two types.The Ramsey problemor Ramsey pricingor Ramsey—Boiteux pricingis a second-best policy problem concerning what prices a public monopoly should charge for the various products it sells in order to maximize social welfare the sum of producer and consumer surplus while earning enough revenue to cover its fixed costs.

Under Ramsey pricing, the price markup over marginal cost is inverse to the price elasticity of demand : the more elastic the product's demand, the smaller the markup. Frank P. Ramsey found this in the context of Optimal taxation : the more elastic the demand, the smaller the optimal tax. A natural monopoly earns negative profits if it sets price equals to marginal cost, so it must set prices for some or all of the products it sells to above marginal cost if it is to be viable without government subsidies.

Ramsey pricing says to mark up most the goods with the least elastic that is, least price-sensitive demand.

In a first-best world, without the need to earn enough revenue to cover fixed costs, the optimal solution would be to set the price for each product equal to its marginal cost. If the average cost curve is declining where the demand curve crosses it however, as happens when the fixed cost is large, this would result in a price less than average cost, and the firm could not survive without subsidy.

The Ramsey problem is to decide exactly how much to raise each product's price above its marginal cost so the firm's revenue equals its total cost. If there is just one product, the problem is simple: raise the price to where it equals average cost. If there are two firms, there is leeway to raise one product's price more and the other's less, so long as the firm can break even overall.

The principle is applicable to pricing of goods that the government is the sole supplier of public utilities or regulation of natural monopolies, such as telecommunications firms, where it is efficient for only one firm to operate but the government regulates its prices so it does not earn above-market profits. In practice, government regulators are concerned with more than maximizing the sum of producer and consumer surplus. They may wish to put more weight on the surplus of politically powerful consumers, or they may wish to help the poor by putting more weight on their surplus.

Moreover, many people will see Ramsey pricing as unfair, especially if they do not understand why it maximizes total surplus. In some contexts, Ramsey pricing is a form of price discrimination because the two products with different elasticities of demand are one physically identical product sold to two different groups of customers, e.

Ramsey pricing says to charge whichever group has less elastic demand a higher price in order to maximize overall social welfare.

Customers sometimes object to it on that basis, since they care about their own individual welfare, not social welfare. Customers who are charged more may consider unfair, especially they, with less elastic demand, would say they "need" the good more.

Typically, the fixed value is zero, which is to say that the regulator wants to maximize welfare subject to the constraint that the firm not lose money. The constraint can be stated generally as:. This problem may be solved using the Lagrange multiplier technique to yield the optimal output values, and backing out the optimal prices.

The Ramsey-price setting monopoly is in a second-best equilibrium, between ordinary monopoly and perfect competition. An easier way to solve this problem in a two-output context is the Ramsey condition. According to Ramsey, as to minimize deadweight lossesone must increase prices to rigid and elastic demands in the same proportion, in relation to the prices that would be charged at the first-best solution price equal to marginal cost.

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### The biggest scandals to ever plague Gordon Ramsay

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### Ramsey Theory

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