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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Combinatorial statistics: a common theme and a few examples
组合统计 霰弹枪组装 随机图匹配
2023/4/13
In this talk, I will overview the general flavor for the topic of “combinatorial statistics”, and I will describe some recent progress on shotgun assembling problems as well as random graph matching p...
We provide a natural interpretation of the secondary Euler characteristic and generalize it to higher Euler characteristics. For a compact oriented manifold of odd dimension, the
secondary Euler char...
Closed Form Summation for Classical Distributions: Variations on Theme of De Moivre
Binomial distribution Stirling's formula his- tory of probability Pearson curves Stein's identity mean absolute deviation.
2015/7/14
De Moivre gave a simple closed form expression for the mean
absolute deviation of the binomial distribution. Later authors showed
that similar closed form expressions hold for many of the other cl...
The Fuglede-Kadison determinant, theme and variations
Determinant Fuglede-Kadison determinant Banach algebra
2011/8/25
Abstract: We review the definition of determinants for finite von Neumann algebras, due to Fuglede and Kadison (1952), and a generalisation for appropriate groups of invertible elements in Banach alge...
Interpretations of the Beurling–Lax–Halmos Theorem on invariant subspaces of the unilateral shift are explored using the language of Hilbert modules. Extensions and consequences are considered in both...