Super-paramagnetic clustering of yeast gene expression profiles

High-density DNA arrays, used to monitor gene expression at a genomic scale, have produced vast amounts of information which require the development of efficient computational methods to analyze them. The important first step is to extract the fundamental patterns of gene expression inherent in the data. This paper describes the application of a novel clustering algorithm, Super-Paramagnetic Clustering (SPC) to analysis of gene expression profiles that were generated recently during a study of the yeast cell cycle. SPC was used to organize genes into biologically relevant clusters that are suggestive for their co-regulation. Some of the advantages of SPC are its robustness against noise and initialization, a clear signature of cluster formation and splitting, and an unsupervised self-organized determination of the number of clusters at each resolution. Our analysis revealed interesting correlated behavior of several groups of genes which has not been previously identified

Combining chromosomal arm status and significantly aberrant genomic locations reveals new cancer subtypes

Many types of tumors exhibit chromosomal losses or gains, as well as local amplifications and deletions. Within any given tumor type, sample specific amplifications and deletionsare also observed. Typically, a region that is aberrant in more tumors,or whose copy number change is stronger, would be considered as a more promising candidate to be biologically relevant to cancer. We sought for an intuitive method to define such aberrations and prioritize them. We define V, the volume associated with an aberration, as the product of three factors: a. fraction of patients with the aberration, b. the aberrations length and c. its amplitude. Our algorithm compares the values of V derived from real data to a null distribution obtained by permutations, and yields the statistical significance, p value, of the measured value of V. We detected genetic locations that were significantly aberrant and combined them with chromosomal arm status to create a succint fingerprint of the tumor genome. This genomic fingerprint is used to visualize the tumors, highlighting events that are co ocurring or mutually exclusive. We allpy the method on three different public array CGH datasets of Medulloblastoma and Neuroblastoma, and demonstrate its ability to detect chromosomal regions that were known to be altered in the tested cancer types, as well as to suggest new genomic locations to be tested. We identified a potential new subtype of Medulloblastoma, which is analogous to Neuroblastoma type 1.Comment: 34 pages, 3 figures; to appear in Cancer Informatic

The influence of risk perception in epidemics: a cellular agent model

Our work stems from the consideration that the spreading of a disease is modulated by the individual's perception of the infected neighborhood and his/her strategy to avoid being infected as well. We introduced a general ``cellular agent'' model that accounts for a hetereogeneous and variable network of connections. The probability of infection is assumed to depend on the perception that an individual has about the spreading of the disease in her local neighborhood and on broadcasting media. In the one-dimensional homogeneous case the model reduces to the DK one, while for long-range coupling the dynamics exhibits large fluctuations that may lead to the complete extinction of the disease

Derivation of Hebb's rule

On the basis of the general form for the energy needed to adapt the connection strengths of a network in which learning takes place, a local learning rule is found for the changes of the weights. This biologically realizable learning rule turns out to comply with Hebb's neuro-physiological postulate, but is not of the form of any of the learning rules proposed in the literature. It is shown that, if a finite set of the same patterns is presented over and over again to the network, the weights of the synapses converge to finite values. Furthermore, it is proved that the final values found in this biologically realizable limit are the same as those found via a mathematical approach to the problem of finding the weights of a partially connected neural network that can store a collection of patterns. The mathematical solution is obtained via a modified version of the so-called method of the pseudo-inverse, and has the inverse of a reduced correlation matrix, rather than the usual correlation matrix, as its basic ingredient. Thus, a biological network might realize the final results of the mathematician by the energetically economic rule for the adaption of the synapses found in this article.Comment: 29 pages, LaTeX, 3 figure

Coupled Two-Way Clustering Analysis of Gene Microarray Data

We present a novel coupled two-way clustering approach to gene microarray data analysis. The main idea is to identify subsets of the genes and samples, such that when one of these is used to cluster the other, stable and significant partitions emerge. The search for such subsets is a computationally complex task: we present an algorithm, based on iterative clustering, which performs such a search. This analysis is especially suitable for gene microarray data, where the contributions of a variety of biological mechanisms to the gene expression levels are entangled in a large body of experimental data. The method was applied to two gene microarray data sets, on colon cancer and leukemia. By identifying relevant subsets of the data and focusing on them we were able to discover partitions and correlations that were masked and hidden when the full dataset was used in the analysis. Some of these partitions have clear biological interpretation; others can serve to identify possible directions for future research

Thresholds in layered neural networks with variable activity

The inclusion of a threshold in the dynamics of layered neural networks with variable activity is studied at arbitrary temperature. In particular, the effects on the retrieval quality of a self-controlled threshold obtained by forcing the neural activity to stay equal to the activity of the stored paterns during the whole retrieval process, are compared with those of a threshold chosen externally for every loading and every temperature through optimisation of the mutual information content of the network. Numerical results, mostly concerning low activity networks are discussed.Comment: 15 pages, Latex2e, 6 eps figure

Three-phase point in a binary hard-core lattice model?

Using Monte Carlo simulation, Van Duijneveldt and Lekkerkerker [Phys. Rev. Lett. 71, 4264 (1993)] found gas-liquid-solid behaviour in a simple two-dimensional lattice model with two types of hard particles. The same model is studied here by means of numerical transfer matrix calculations, focusing on the finite size scaling of the gaps between the largest few eigenvalues. No evidence for a gas-liquid transition is found. We discuss the relation of the model with a solvable RSOS model of which the states obey the same exclusion rules. Finally, a detailed analysis of the relation with the dilute three-state Potts model strongly supports the tricritical point rather than a three-phase point.Comment: 17 pages, LaTeX2e, 13 EPS figure