George Takei 
🏳️🌈🖖🏽The rule is that only dead people can appear on our currency, so…
Pait
@pait
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@georgetakei One of the good guys, standing up for our country, our people, our laws.
Brent Toderian“Helsinki hasn’t registered a single traffic-related fatality in the past year…Citing data that shows the risk of pedestrian fatality is cut in half by reducing a car’s speed from 40 to 30km/hr, city officials imposed the lower limit in most of Helsinki’s residential areas and city center in 2021.”
Helsinki just went a full year...
Helsinki just went a full year...
@villares Cheguei a perder 5 minutos, um transeunte passou e informou, mudei minha rota, senão teria perdido avião.
Em 2027 a Universidade de São Paulo faz 200 anos - o Curso de sciencias jurídicas, e sociaes, na cidade de S. Paulo foi criado por decreto imperial em 1827.
A USP não pode perder a oportunidade de marketing, reconhecendo oficialmente sua tradição.
@everton137 I can pull cash out of an ATM, you pay me later, let me know if you're nearby.
Paul Balduf#paperOfTheDay is "Correlation functions and zeros of a Gaussian power series and Pfaffians" from 2013.
This paper is a generalisation of the study of random polynomials: They consider random power series, i.e. polynomials with infinitely many terms. These have (almost always) a radius of convergence of unity, so that it only makes sense to study them in the domain (-1,1). There is an accumulation of zeros (=roots) close to the boundaries of this interval.
Given that the coefficients of the power series are random, so are the locations of zeros. The positive locations form an infinite sequence of random numbers, a point process. As such, one can ask about the mean, variance, and all other correlation functions. The main result of the article is that these quantities are given by a Pfaffian (which is an algebraic object similar to a determinant) of some explicitly known matrices.
I got interested in this observation because Pfaffians also show up in #quantumFieldTheory . For example, Isserlis theorem (sometimes called Wicks theorem by physicists) says that the expectation of a product of Gaussian variables is the Pfaffian of their covariances. Or, Pfaffians show up as the integrands in #FeynmanIntegral s in topological field theories.
#mathematics #probabilityTheory
https://projecteuclid.org/journals/electronic-journal-of-probability/volume-18/issue-none/Correlation-functions-for-zeros-of-a-Gaussian-power-series-and/10.1214/EJP.v18-2545.full
This paper is a generalisation of the study of random polynomials: They consider random power series, i.e. polynomials with infinitely many terms. These have (almost always) a radius of convergence of unity, so that it only makes sense to study them in the domain (-1,1). There is an accumulation of zeros (=roots) close to the boundaries of this interval.
Given that the coefficients of the power series are random, so are the locations of zeros. The positive locations form an infinite sequence of random numbers, a point process. As such, one can ask about the mean, variance, and all other correlation functions. The main result of the article is that these quantities are given by a Pfaffian (which is an algebraic object similar to a determinant) of some explicitly known matrices.
I got interested in this observation because Pfaffians also show up in #quantumFieldTheory . For example, Isserlis theorem (sometimes called Wicks theorem by physicists) says that the expectation of a product of Gaussian variables is the Pfaffian of their covariances. Or, Pfaffians show up as the integrands in #FeynmanIntegral s in topological field theories.
#mathematics #probabilityTheory
https://projecteuclid.org/journals/electronic-journal-of-probability/volume-18/issue-none/Correlation-functions-for-zeros-of-a-Gaussian-power-series-and/10.1214/EJP.v18-2545.full
@johncarlosbaez That of the heat the human body loses, 50% is by radiation.
Then 30% by convection, and 20% by evaporation of sweat, the latter being highly variable. Very little by conduction, unless the person is immersed in water.
I did not think radiation would amount to that much.
@escrevoemportugues.wordpress.com Também é a 3a língua mais falada em Massachusetts!