Intermediate ternary code: a redundancy-reducing runlength code for digital facsimile transmission

AbstractGiven the ever-increasing amount of high-dimensional and complex omics data becoming available, it is increasingly important to discover simple but effective methods of analysis. Divergence analysis transforms each entry of a high-dimensional omics profile into a digitized (binary or ternary) code based on the deviation of the entry from a given baseline population. This is a novel framework that is significantly different from existing omics data analysis methods: it allows digitization of continuous omics data at the univariate or multivariate level, facilitates sample level analysis, and is applicable on many different omics platforms. The divergence package, available on the R platform through the Bioconductor repository collection, provides easy-to-use functions for carrying out this transformation. Here we demonstrate how to use the package with sample high throughput sequencing data from the Cancer Genome Atlas.

Download Full-text

An R package for divergence analysis of omics data

PLoS ONE ◽

10.1371/journal.pone.0249002 ◽

2021 ◽

Vol 16 (4) ◽

pp. e0249002

Author(s):

Wikum Dinalankara ◽

Qian Ke ◽

Donald Geman ◽

Luigi Marchionni

Keyword(s):

R Package ◽

The Cancer Genome Atlas ◽

High Dimensional ◽

Omics Data ◽

Ternary Code ◽

Cancer Genome Atlas ◽

Level Analysis ◽

Data Analysis Methods ◽

Genome Atlas ◽

Omics Data Analysis

Given the ever-increasing amount of high-dimensional and complex omics data becoming available, it is increasingly important to discover simple but effective methods of analysis. Divergence analysis transforms each entry of a high-dimensional omics profile into a digitized (binary or ternary) code based on the deviation of the entry from a given baseline population. This is a novel framework that is significantly different from existing omics data analysis methods: it allows digitization of continuous omics data at the univariate or multivariate level, facilitates sample level analysis, and is applicable on many different omics platforms. The divergence package, available on the R platform through the Bioconductor repository collection, provides easy-to-use functions for carrying out this transformation. Here we demonstrate how to use the package with data from the Cancer Genome Atlas.

Download Full-text

Lower Bounds for the Football Pool Problem for 7 and 8 Matches

The Electronic Journal of Combinatorics ◽

10.37236/945 ◽

2007 ◽

Vol 14 (1) ◽

Author(s):

Wolfgang Haas

Keyword(s):

Lower Bounds ◽

Covering Radius ◽

Linear Inequalities ◽

Minimal Cardinality ◽

Covering Code ◽

Ternary Code ◽

Systems Of Linear Inequalities

Let $k_3(n)$ denote the minimal cardinality of a ternary code of length $n$ and covering radius one. In this paper we show $k_3(7)\ge 156$ and $k_3(8)\ge 402$ improving on the best previously known bounds $k_3(7)\ge 153$ and $k_3(8)\ge 398$. The proofs are founded on a recent technique of the author for dealing with systems of linear inequalities satisfied by the number of elements of a covering code, that lie in $k$-dimensional subspaces of F${}_3^n$.

Download Full-text