Related papers: Zipf's Law in Importance of Genes for Cancer Class…
Using data from gene expression databases on various organisms and tissues, including yeast, nematodes, human normal and cancer tissues, and embryonic stem cells, we found that the abundances of expressed genes exhibit a power-law…
In the last years, researchers have realized the difficulties of fitting power-law distributions properly. These difficulties are higher in Zipf's systems, due to the discreteness of the variables and to the existence of two representations…
Motivation: Microarray data has been recently been shown to be efficacious in distinguishing closely related cell types that often appear in the diagnosis of cancer. It is useful to determine the minimum number of genes needed to do such a…
DNA microarray gene-expression data has been widely used to identify cancerous gene signatures. Microarray can increase the accuracy of cancer diagnosis and prognosis. However, analyzing the large amount of gene expression data from…
The joint probability distribution of many degrees of freedom in biological systems, such as firing patterns in neural networks or antibody sequence composition in zebrafish, often follow Zipf's law, where a power law is observed on a…
Most of various large-size complex systems in nature and society can be well described as complex networks (graphs) to better understand the evolutional mechanisms and dynamical functions behind themselves. Of some part follow scale-free…
Although Zipf's law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the…
It is shown that the distribution of low variability periods in the activity of human heart rate typically follows a multi-scaling Zipf's law. The presence or failure of a power law, as well as the values of the scaling exponents, are…
Zipf's law, which states that the probability of an observation is inversely proportional to its rank, has been observed in many domains. While there are models that explain Zipf's law in each of them, those explanations are typically…
Microarray data are often used to determine which genes are differentially expressed between groups, for example, between treatment and control groups. There are methods of determining which genes have a high probability of differential…
Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…
It turns out that some empirical facts in Big Data are the effects of properties of large numbers. Zipf's law 'noise' is an example of such an artefact. We expose several properties of the power law distributions and of similar distribution…
Gene expression data is widely used in disease analysis and cancer diagnosis. However, since gene expression data could contain thousands of genes simultaneously, successful microarray classification is rather difficult. Feature selection…
n-tuple power law widely exists in language, computer program code, DNA and music. After a vast amount of Zipf analyses of n-tuple power law from empirical data, we propose a model to explain the n-tuple power law feature existed in these…
We introduce a non-growth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary…
Cancer is a term that denotes a group of diseases caused by abnormal growth of cells that can spread in different parts of the body. According to the World Health Organization (WHO), cancer is the second major cause of death after…
The DNA microarray technology has modernized the approach of biology research in such a way that scientists can now measure the expression levels of thousands of genes simultaneously in a single experiment. Gene expression profiles, which…
Many machine learning models have been proposed to classify phenotypes from gene expression data. In addition to their good performance, these models can potentially provide some understanding of phenotypes by extracting explanations for…
Why does Zipf's law give a good description of data from seemingly completely unrelated phenomena? Here it is argued that the reason is that they can all be described as outcomes of a ubiquitous random group division: the elements can be…
When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear…