Efficient sampling of random permutations

Gustedt, Jens

doi:10.1016/j.jda.2006.11.002

Cited by 8 publications

(5 citation statements)

References 18 publications

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“…The expected ratio in whole human genome is 0.019 (total number of SNVs in coding and non-coding region divided by total number of bases in the human genome). To evaluate the expected ratio in the whole genome, random sampling of permutation [69] was performed in R (http://www.R-project.org/) for comparing the observed ratio in random fragments and calculating the number of SNVs in each fragment (1000 bases in one fragment). (S3 Table)…”

Section: Methodsmentioning

confidence: 99%

Investigation of somatic single nucleotide variations in human endogenous retrovirus elements and their potential association with cancer

et al. 2019

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Human endogenous retroviruses (HERVs) have been investigated for potential links with human cancer. However, the distribution of somatic nucleotide variations in HERV elements has not been explored in detail. This study aims to identify HERV elements with an over-representation of somatic mutations (hot spots) in cancer patients. Four HERV elements with mutation hotspots were identified that overlap with exons of four human protein coding genes. These hotspots were identified based on the significant over-representation (p<8.62e-4) of non-synonymous single-nucleotide variations (nsSNVs). These genes are TNN (HERV-9/LTR12), OR4K15 (HERV-IP10F/LTR10F), ZNF99 (HERV-W/HERV17/LTR17), and KIR2DL1 (MST/MaLR). In an effort to identify mutations that effect survival, all nsSNVs were further evaluated and it was found that kidney cancer patients with mutation C2270G in ZNF99 have a significantly lower survival rate (hazard ratio = 2.6) compared to those without it. Among HERV elements in the human non-protein coding regions, we found 788 HERVs with significantly elevated numbers of somatic single-nucleotide variations (SNVs) (p<1.60e-5). From this category the top three HERV elements with significantly over-represented SNVs are HERV-H/LTR7, HERV-9/LTR12 and HERV-L/MLT2. Majority of the SNVs in these 788 HERV elements are located in three DNA functional groups: long non-coding RNAs (lncRNAs) (60%), introns (22.2%) and transcriptional factor binding sites (TFBS) (14.8%). This study provides a list of mutational hotspots in HERVs, which could potentially be used as biomarkers and therapeutic targets.

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Section: Methodsmentioning

confidence: 99%

Investigation of somatic single nucleotide variations in human endogenous retrovirus elements and their potential association with cancer

et al. 2019

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“…By Theorem 4, doing so to all the 2 l child nodes requires O(2 l + (2 l B/B) log M/B (n/B)) = O(2 l log M/B (n/B)) amortized I/Os in total. Finally, we generate a random permutation of the 2 l B samples in O(2 l log M/B (n/B)) I/Os [7], and store the permutation as the newly computed Su(l). All these samples are marked as clean.…”

Section: A One-sided Structurementioning

confidence: 99%

“…This is nearly a factor of B higher than the Θ(t/B) cost needed to write t samples. Going back to the baseline solution, one can always retrieve the entire P (q) = P ∩ q, and then sample t elements from P (q) using a standard algorithm [7,15]. Assuming t ≤ k, the query cost is O(log B n + (k/B) log M/B (k/B)), where k = |P (q)|.…”

Section: Introductionmentioning

confidence: 99%

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Independent range sampling

Qiao

Tao

2014

Proceedings of the 33rd ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems

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This paper studies the independent range sampling problem. The input is a set P of n points in R. Given an interval q = [x, y] and an integer t ≥ 1, a query returns t elements uniformly sampled (with/without replacement) from P ∩ q. The sampling result must be independent from those returned by the previous queries. The objective is to store P in a structure for answering all queries efficiently.If P fits in memory, the problem is interesting when P is dynamic (i.e., allowing insertions and deletions). The state of the art is a structure of O(n) space that answers a query in O(t log n) time, and supports an update in O(log n) time. We describe a new structure of O(n) space that answers a query in O(log n + t) expected time, and supports an update in O(log n) time.If P does not fit in memory, the problem is challenging even when P is static. The best known structure incurs O(log B n + t) I/Os per query, where B is the block size. We develop a new structure of O(n/B) space that answers a query in O(log ⋆ (n/B)+log B n+(t/B) log M/B (n/B)) amortized expected I/Os, where M is the memory size, and log ⋆ (n/B) is the number of iterative log 2 (.) operations we need to perform on n/B before going below a constant. We also give a lower bound argument showing that this is nearly optimal-in particular, the multiplicative term log M/B (n/B) is necessary.

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“…They employed two secret keys to protect the watermark against possible attacks. Besides, their methods also embed binary watermark into the cover image by used random permutations [5] and XOR operations. Meanwhile, they claimed that their scheme is not only secure and fast but also can detect and localize the modification position.…”

Section: Introductionmentioning

confidence: 99%

A Robust-Fragile Watermarking Scheme for Image Authentication

Kao

Kuo

et al. 2008

2008 3rd International Conference on Innovative Computing Information and Control

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In 2003, Lu et al. developed a novel fragile watermarking scheme for image authentication to against the quantization attack. Unfortunately, their scheme is not secure enough. In 2006, Liao et al. proposed two types of attack on Lu et al.'s scheme. They pointed out that Lu et al.'s scheme is still impractical. To achieve both the copyright protection and tamper detection of stego-image, a robust-fragile watermarking algorithm is proposed in this paper. Our proposed scheme is not only to against the quantization attack ("Modification attack" and "Counterfeit attack"), but also to achieve both the copyright protection and tamper detection of stegoimage. From experimental result, we can show that the performance of our proposed scheme is better than Lu et al.'s method.

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Efficient sampling of random permutations

Cited by 8 publications

References 18 publications

Investigation of somatic single nucleotide variations in human endogenous retrovirus elements and their potential association with cancer

Investigation of somatic single nucleotide variations in human endogenous retrovirus elements and their potential association with cancer

Independent range sampling

A Robust-Fragile Watermarking Scheme for Image Authentication

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