Permutations

Part 1 of the book "The art of computer programming - Volume 3: Sorting and searching" is concerned with sorting into order; this is a large subject that has been divided chiefly into two parts, internal sorting and external sorting. There also are supplementary sections, which develop auxiliary theories about permutations and about optimum techniques for sorting.

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"The art of computer programming - Volume 3: Sorting and searching" comprises Chapters 5 and 6 of the complete series. Part 1 of book included chapter 5 is concerned with sorting into order; this is a large subject that has been divided chiefly into two parts, internal sorting and external sorting. There also are supplementary sections, which develop auxiliary theories about permutations and about optimum techniques for sorting.

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In information theory, especially in storage model, private sharing, encryption, etc. sometimes we want to distribute a given database into many small parts, each of which is stored by a party in such a way that when there are a cooperation of sufficient number of parties, then it is enable to recover the original information.

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Divide and conquer strategy is applicable in a huge number of computational problems. The first example of divide and conquer algorithm we will discuss is a simple and efficient sorting procedure called We are given a sequence of n numbers A, which we will assume are stored in an array A[1..n]. The objective is to output a permutation of this sequence sorted in increasing order. In this lecture, you find clear explanations of merge sort.

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Lecture Methods of Electric power systems analysis - Lesson 9: Sparse systems, advanced power flow provide students with knowledge about Tinney scheme 2; coding Tinney 2; Tinney scheme 3; sparse forward substitution with a permutation vector; sparse vector methods; factorization paths; path table and path graph; computation with complex and blocked matrices;...

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Multiple hypothesis testing is a major issue in genome-wide association studies (GWAS), which often analyze millions of markers. The permutation test is considered to be the gold standard in multiple testing correction as it accurately takes into account the correlation structure of the genome.

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Fish communities are important indicators of the health of riverine ecosystems. Fish monitoring for The Living Murray (TLM) initiative, one of Australia’s most ambitious restoration undertakings for the degraded river-floodplain biota of the River Murray system (south-eastern Australia), was carried out annually from 2005 to 2011 across six ‘Icon Sites’, including the habitats and reaches therein. These spatial and temporal components of variation in fish community abundance and composition must be taken explicitly into account for consistent assessment of riverine ecosystem health.

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Lecture Discrete Mathematics I - Chapter 6: Counting (Tran Vinh Tan) provide students with knowledge about introduction, counting techniques, pigeonhole principle, permutations and combinations, permutations with indistinguishable objects,...

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A promising approach for solving this problem is to compare gene networks built using experimental gene sets with random networks. One of the resources that make such an analysis possible is CrossTalkZ, which uses the FunCoup database. However, existing methods, including CrossTalkZ, do not take into account individual types of interactions, such as protein/protein interactions, expression regulation, transport regulation, catalytic reactions, etc., but rather work with generalized types characterizing the existence of any connection between network members.

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Bài giảng Xác suất thống kê: Tập hợp giải tích tổ hợp cung cấp cho sinh viên những kiến thức về: Khái niệm về tập hợp, biểu diễn tập hợp, quan hệ giữa các tập hợp, các phép toán trên các tập hợp, quy tắc cộng, quy tắc nhân, tính chất của một nhóm, chỉnh hợp (arrangement), hoán vị (permutation),... Mời các bạn cùng tham khảo.

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In mass spectrometry-based proteomics, protein identification is an essential task. Evaluating the statistical significance of the protein identification result is critical to the success of proteomics studies. Controlling the false discovery rate (FDR) is the most common method for assuring the overall quality of the set of identifications.

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Lecture Discrete Structures for Computer Science - Chapter 5: Counting present the content: introduction, counting techniques, pigeonhole principle, permutations & combinations, applications of combinatorics,...

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The random forest (RF) method is a commonly used tool for classification with high dimensional data as well as for ranking candidate predictors based on the so-called random forest variable importance measures (VIMs).

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The cryptographic algorithms Kuznyechik and Magma since 2015 are block cipher standardized in the Russian Federation, formally called GOST R 34.12-2015. Both use fixed functions as a priori selected and differ on the structure, the block length and the bit-level of the processed blocks. In the present paper, we provide a dynamic variant of Kuznyechik and Magma where some of their functions are randomly generated and dependent on pseudorandom sequences.

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CA_C2195 from Clostridium acetobutylicum is a protein of unknown function. Sequence analysis predicted that part of the protein contained a metallopeptidase-related domain. There are over 200 homologs of similar size in large sequence databases such as UniProt, with pairwise sequence identities in the range of ~40-60%.

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Gene set analysis (GSA) of gene expression data can be highly powerful when the biological signal is weak compared to other sources of variability in the data. However, many gene set analysis approaches utilize permutation tests which are not appropriate for complex study designs.

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Local trend (i.e. shape) analysis of time series data reveals co-changing patterns in dynamics of biological systems. However, slow permutation procedures to evaluate the statistical significance of local trend scores have limited its applications to high-throughput time series data analysis, e.g., data from the next generation sequencing technology based studies.

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Permutation-based gene set tests are standard approaches for testing relationships between collections of related genes and an outcome of interest in high throughput expression analyses. Using M random permutations, one can attain p-values as small as 1/(M + 1).

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DNA methylation offers an excellent example for elucidating how epigenetic information affects gene expression. β values and M values are commonly used to quantify DNA methylation. Statistical methods applicable to DNA methylation data analysis span a number of approaches such as Wilcoxon rank sum test, t-test, Kolmogorov–Smirnov test, permutation test, empirical Bayes method, and bump hunting method.

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In genome-wide association studies (GWAS) for complex diseases, the association between a SNP and each phenotype is usually weak. Combining multiple related phenotypic traits can increase the power of gene search and thus is a practically important area that requires methodology work.

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