Poisson Numbers and Poisson Distributions in Subset Surprisology

Dress, Andreas; Lokot, Tatjana; Pustyl'nikov, L D; Schubert, Walter

doi:10.1007/s00026-004-0234-2

Cited by 18 publications

(13 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Theorem 2.1 allows us to recover Theorem 4.1 and Corollary 4.4 of Dress et al [5] as an immediate consequence of the bound (11) and Remark 2.1. the sizes a 0,n , .…”

Section: Total Variation Boundsupporting

confidence: 57%

“…Below is an extract of the table in [5], comparing the actual values P (W = a) to their Poisson approximants P (Z = a), for various choices of the parameters of the problem, and a. We have augmented the table by including the bound (9) on the total variation distance between W and Z, denoted by Bound, and, for n ≤ 10000, the actual total variation distance, denoted by TV.…”

Section: Numerical Comparisonmentioning

confidence: 99%

“…We have augmented the table by including the bound (9) on the total variation distance between W and Z, denoted by Bound, and, for n ≤ 10000, the actual total variation distance, denoted by TV. The probabilities P (W = a) are calculated using the exact formula in [5], n − a a i − a .…”

Section: Numerical Comparisonmentioning

confidence: 99%

“…A Poisson approximation to W , and an asymptotic result, was proved in Dress et al [5] using the inclusion-exclusion principle and some intricate calculations involving the complex form of the exact distribution of W . Using Poisson approximation, one replaces the exact but difficult to compute probabilities P (W = a) by P (Z = a), where Z has a Poisson distribution with the same mean, λ, as W .…”

Section: Introductionmentioning

confidence: 96%

“…The technique in [5] which justifies the Poisson approximation asymptotically through calculations involving the exact distribution does not give a bound on the error one incurs when approximating W by the Poisson. Here we provide an error bound which holds for all finite n, from which the asymptotic results of [5] follow. We also avoid working directly with the cumbersome form of A n|a 0 ,...,a k (a).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Total Variation Distance for Poisson Subset Numbers

Goldstein

Reinert

2006

Ann. Comb.

View full text Add to dashboard Cite

Let n be an integer and A 0 , . . . , A k random subsets of {1, . . . , n} of fixed sizes a 0 , . . . , a k , respectively chosen independently and uniformly. We provide an explicit and easily computable total variation bound between the distance from the random variable W = |∩ k j=0 A j |, the size of the intersection of the random sets, to a Poisson random variable Z with intensity λ = EW . In particular, the bound tends to zero when λ converges and a j → ∞ for all j = 0, . . . , k, showing that W has a asymptotic Poisson distribution in this regime.

show abstract

“…Theorem 2.1 allows us to recover Theorem 4.1 and Corollary 4.4 of Dress et al [5] as an immediate consequence of the bound (11) and Remark 2.1. the sizes a 0,n , .…”

Section: Total Variation Boundsupporting

confidence: 57%

Section: Numerical Comparisonmentioning

confidence: 99%

Section: Numerical Comparisonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Total Variation Distance for Poisson Subset Numbers

Goldstein

Reinert

2006

Ann. Comb.

View full text Add to dashboard Cite

show abstract

Cytomics in characterizing Toponomes: Towards the biological code of the cell

Schubert

2006

Cytometry Pt A

View full text Add to dashboard Cite

Lysosomal storage disorders (LSD) present great clinical variability. Included in this group are sialic acid metabolism disorders (SAMD). In the present study, we describe the application of a 3‐step protocol for the diagnosis of SAMD, including (1) oligosaccharide and sialyloligosaccharide chromatography; (2) quantitative determination of sialic acid; and (3) measurement of neuraminidase activity. Application of our protocol to 124 individuals at risk for SAMD led to the diagnosis of five affected patients, two with type I sialidosis, one with type II sialidosis, and two with galactosialidosis. Due to its simplicity and efficiency, we propose the use of this protocol for the diagnostic evaluation of patients with suspected SAMD, which could be specially useful to non‐specialized laboratories and to services located in developing countries. © 2003 Wiley‐Liss, Inc.

show abstract

A three‐symbol code for organized proteomes based on cyclical imaging of protein locations

Schubert

2007

Cytometry Pt A

View full text Add to dashboard Cite

Background: A major challenge in the post genomic era is to map and decipher the functional molecular networks of proteins directly in a cell or a tissue. This task requires technologies for the colocalization of random numbers of different molecular components (e.g. proteins) in one sample in one experiment. Methods: Multi‐epitope‐ligand‐“kartographie” (MELK) was developed as a microscopic imaging technology running cycles of iterative fluorescence tagging, imaging, and bleaching, to colocalize a large number of proteins in one sample (morphologically intact routinely fixed cells or tissue). Results: In the present study, 18 different cell surface proteins were colocalized by MELK in cells and tissue sections in different compartments of the human immune system. From the resulting sets of multidimensional binary vectors the most prominent groups of protein–epitope arrangements were extracted and imaged as protein “toponome” maps providing direct insight in the higher order topological organization of immune compartments uncovering new tissue domains. The data sets suggest that protein networks, topologically organized in proteomes in situ, obey a unique protein‐colocation and ‐anticolocation code describable by three symbols. Conclusion: The technology has the potential to colocalize hundreds of proteins and other molecular components in one sample and may offer many applications in biology and medicine. © 2007 International Society for Analytical Cytology.

show abstract

Poisson Numbers and Poisson Distributions in Subset Surprisology

Cited by 18 publications

References 3 publications

Total Variation Distance for Poisson Subset Numbers

Total Variation Distance for Poisson Subset Numbers

Cytomics in characterizing Toponomes: Towards the biological code of the cell

A three‐symbol code for organized proteomes based on cyclical imaging of protein locations

Contact Info

Product

Resources

About