Related papers: Zipf's Law in Importance of Genes for Cancer Class…
Cancer is fundamentally a genetic disease characterized by genetic and epigenetic alterations that disrupt normal gene expression, leading to uncontrolled cell growth and metastasis. High-dimensional microarray datasets pose challenges for…
The expression levels of many thousands of genes can be measured simultaneously by DNA microarrays (chips). This novel experimental tool has revolutionized research in molecular biology and generated considerable excitement. A typical…
Several populational networks present complex topologies when implemented in evolutionary algorithms. A common feature of these topologies is the emergence of a power law. Power law behavior with different scaling factors can also be…
Over the past few years, there has been a considerable spread of microarray technology in many biological patterns, particularly in those pertaining to cancer diseases like leukemia, prostate, colon cancer, etc. The primary bottleneck that…
Predicting the response of cancer cells to drugs is an important problem in pharmacogenomics. Recent efforts in generation of large scale datasets profiling gene expression and drug sensitivity in cell lines have provided a unique…
Many biomedical experiments are carried out by pooling individual biological samples. However, pooling samples can potentially hide biological variance and give false confidence concerning the data significance. In the context of microarray…
An Atlas model is a rank-based system of continuous semimartingales for which the steady-state values of the processes follow a power law, or Pareto distribution. For a power law, the log-log plot of these steady-state values versus rank is…
We have previously reported that a 'universal' growth law with fixed scaling exponent p, as proposed by West and collaborators for all living organisms, appears to be able to describe also the growth of tumors in vivo. Here, we investigate…
We calculate measures of hierarchy in gene and tissue networks of breast cancer patients. We find that the likelihood of metastasis in the future is correlated with increased values of network hierarchy for expression networks of…
We discuss the meaning of Zipf's law in nuclear multifragmentation. We remark that Zipf's law is a consequence of a power law fragment size distribution with exponent $\tau \simeq 2$. We also recall why the presence of such distribution is…
Zipf's law states that if words of language are ranked in the order of decreasing frequency in texts, the frequency of a word is inversely proportional to its rank. It is very robust as an experimental observation, but to date it escaped…
Throughout history most young adults have chosen to live where their parents did while a smaller number moved away. This is sufficient, by proof and simulation, to account for the well-known power law distributions of city sizes. The model…
Since the sequencing of large genomes, many statistical features of their sequences have been found. One intriguing feature is that certain subsequences are much more abundant than others. In fact, abundances of subsequences of a given…
Microarray is one of the essential technologies used by the biologist to measure genome-wide expression levels of genes in a particular organism under some particular conditions or stimuli. As microarrays technologies have become more…
We describe the link between the Zipf law and statistical distributions for the Fortuin-Kasteleyn clusters in Ising as well as Potts models. From these results it is seen that Zipf's law can be a criterion of a phase transition, but it does…
Over the past decades, statisticians and machine-learning researchers have developed literally thousands of new tools for the reduction of high-dimensional data in order to identify the variables most responsible for a particular trait.…
In this work we suggest a statistical mechanics approach to the classification of high-dimensional data according to a binary label. We propose an algorithm whose aim is twofold: First it learns a classifier from a relatively small number…
The probability distribution P(k) of the sizes k of critical trees (branching ratio m=1) is well known to show a power-law behavior k^(-3/2). Such behavior corresponds to the mean-field approximation for many critical and self-organized…
Apparently random events in nature often reveal hidden patterns when analysed using diverse and robust statistical tools. Power-law distributions, for example, project diverse natural phenomenon, ranging from earthquakes1 to heartbeat…
Current-day genomes bear the mark of the evolutionary processes. One of the strongest indications is the sequence homology among families of proteins that perform similar biological functions in different species. The number of proteins in…