Poisson Numbers and Poisson Distributions in Subset Surprisology

详细信息    查看全文

• 作者：Andreas W. M. Dress ; T. Lokot ; L. D. Pustyl¡¯nikov and W. Schubert
• 关键词：Subset surprisology ; Poisson numbers ; Poisson distribution ; exclusion ; inclusion principle ; Mö ; bius inversion ; topological proteomics ; Multi ; Epitope Ligand Cartography ; Multi ; Epitop Liganden Kartographie ; MELK
• 刊名：Annals of Combinatorics
• 出版年：2005
• 出版时间：January 2005
• 年：2005
• 卷：8
• 期：4
• 页码：473-485
• 全文大小：226 KB

文摘

Given a family of k + 1 real-valued functionsf₀ , ?,f_kf_0 , \ldots ,f_k defined on the set{ 1, ?,n}\{ 1, \ldots ,n\} and measuring the intensity of certain signals, we want to investigate whether these functions are T₀ , ?,T_k ,T_0 , \ldots ,T_k , the size a of the collection of numbersj ? { 1, ?,n}j \in \{ 1, \ldots ,n\} whose signalsf₀ (j), ?,f_k (j)f_0 (j), \ldots ,f_k (j) exceed the corresponding threshold valuesT₀ , ?,T_kT_0 , \ldots ,T_k simultaneously for all0, ?,k0, \ldots ,k is surprisingly large (or small) in comparison to the family of cardinalities$ a_i : = \# \{ j \in \{ 1, \ldots ,n\} |f_i (j) > T_i \} \;(i = 0, \ldots ,k) $ a_i : = \# \{ j \in \{ 1, \ldots ,n\} |f_i (j) > T_i \} \;(i = 0, \ldots ,k)