In this paper we revisit an open problem posed by Aldous on the max-entropy win-probability martingale: given two players of equal strength, such that the win-probability is a martingale diffusion, which of these processes has maximum entropy and hence gives the most excitement for the spectators?
As such, it does not seem that this theorem can be proven by purely finitary means. However, one can view this result as the conjunction of an infinite number of statements, each of which is a finitary density Ramsey theory statement. To see this, we need some more notation. Observe ...
I have just uploaded to the arXiv my paper “Monotone non-decreasing sequences of the Euler totient function“. This paper concerns the quantity , defined as the length of the longest subsequence of the numbers from to for which the Euler totient function is non-decreasing. The first few va...
Initially she planned on using singing as a means of getting into acting, but the musical bug bit her hard. She was actually discovered by a cameraman from KOLR10 who was filming at Cider Days, a two-day festival in Springfield. After expressing an interest in shooting music videos for ...
You also should vary the pitch and tone of your voice when appropriate to avoid speaking in a monotone and keep students’ attention. Like in a traditional classroom, you want to make eye contact to maintain student engagement, so it is essential to look at the camera and not yourself – ...
Yesterday I was quite disappointed on the “monotoneous” tone of Rick starting keynote. Today, Rohit delivered a completely different show. Very good topics presented in a vivid atmosphere and rhetoric. The talk nicely presented through clear examples the links from business challenges to the tech...
If we say that a sequence converges, it means that the limit of the sequence exists as n →∞ n\to\infty n→∞. If the limit of the sequence asn →∞ n\to\infty n→∞does not exist, we say that the sequence diverges. A sequence always either converges or diverges, there is no ...
The main problem with living autistic in today's society is that the world just isn't built for us. There's so many ways that we can get overwhelmed. For example, the thing that makes me overwhelmed all the time is loud noises, which means I never crank up my music really loud and...
So How Does This Apply to me? This means that the artwork you produce either has to be spot color artwork or CMYK artwork. Never, never NEVER produce RGB artwork. There is no such thing in the world of print. RGB (Red, Green, Blue) is a screen color mode and should only ever be...
A number ofdifferentiation theorems, which assert for instance that monotone, Lipschitz, or bounded variation functions in one dimension are almost everywhere differentiable; and The second fundamental theorem of calculus forabsolutely continuousfunctions. ...