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fabricebaudoin.blog | ||
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inquiryintoinquiry.com
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| | | | | Re: R.J. Lipton and K.W. Regan ? Proving Cook's Theorem Synchronicity Rules? I just started reworking an old exposition of mine on Cook's Theorem, where I borrowed the Parity Function example from Wilf (1986), Algorithms and Complexity, and translated it into the cactus graph syntax for propositional calculus I developed as an extension of Peirce's... | |
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almostsuremath.com
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| | | | | I start these notes on stochastic calculus with the definition of a continuous time stochastic process. Very simply, a stochastic process is a collection of random variables $latex {\{X_t\}_{t\ge 0}}&fg=000000$ defined on a probability space $latex {(\Omega,\mathcal{F},{\mathbb P})}&fg=000000$. That is, for each time $latex {t\ge 0}&fg=000000$, $latex {\omega\mapsto X_t(\omega)}&fg=000000$ is a measurable function from $latex... | |
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djalil.chafai.net
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| | | | | This post is mainly devoted to a probabilistic proof of a famous theorem due to Schoenberg on radial positive definite functions. Let us begin with a general notion: we say that \( {K:\mathbb{R}^d\times\mathbb{R}^d\rightarrow\mathbb{R}} \) is a positive definite kernel when \[ \forall n\geq1, \forall x_1,\ldots,x_n\in\mathbb{R}^d, \forall c\in\mathbb{C}^n, \quad\sum_{i=1}^n\sum_{j=1}^nc_iK(x_i,x_j)\bar{c}_j\geq0. \] When \( {K} \) is symmetric, i.e. \( {K(x,y)=K(y,x)} \) for... | |
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singularityhub.com
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| | | New research says that quantifying progress in AI must account for the fact that the humans AI is measured against are actually a variable, noisy benchmark. | ||
