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تسجيل مستخدم جديدHMC, an example of Functional Analysis applied to Algorithms in Data Mining. The convergence in $L^p$
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We present a proof of convergence of the Hamiltonian Monte Carlo algorithm in terms of Functional Analysis. We represent the algorithm as an operator on the density functions, and prove the convergence of iterations of this operator in $L^p$, for $1<p<infty$, and strong convergence for $2le p<infty$.
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The main purpose of this paper is to facilitate the communication between the Analytic, Probabilistic and Algorithmic communities. We present a proof of convergence of the Hamiltonian (Hybrid) Monte Carlo algorithm from the point of view of the D
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Using Guths polynomial partitioning method, we obtain $L^p$ estimates for the maximal function associated to the solution of Schrodinger equation in $mathbb R^2$. The $L^p$ estimates can be used to recover the previous best known result that $lim_{t
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Multifractal analysis studies signals, functions, images or fields via the fluctuations of their local regularity along time or space, which capture crucial features of their temporal/spatial dynamics. It has become a standard signal and image proces
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Let $fin L_{2pi}$ be a real-valued even function with its Fourier series $ frac{a_{0}}{2}+sum_{n=1}^{infty}a_{n}cos nx,$ and let $S_{n}(f,x), ngeq 1,$ be the $n$-th partial sum of the Fourier series. It is well-known that if the nonnegative sequence
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