Extensive Monte Carlo simulations on three qualitatively different model supercritical fluids (square-well fluid, Lennard-Jonesium, and primitive water) have been performed to examine percolation threshold parameters for continuum (correlated) models and their relation to general results valid for random lattice models; random-site percolation simple-cubic lattice has therefore been considered as well. Two different bond criteria, the configurational and self-bound ones, defining a cluster have been used. In addition to the percolation threshold occupation probability $p_c$ and the percolation threshold fluid density ${\rho }_c$, the correlation length exponent $\nu$ and the wrapping probability at the percolation threshold $R_{w,c}$ have also been evaluated. It is found that parameters $\nu$ and $R_{w,c}$ exhibit not only strong temperature dependence but also, unlike the case of lattice systems, dependence on the nature of the system considered and the employed definition of the cluster.

We examine different spanning probability functions (wrapping and crossing) near the percolation threshold of a supercritical square-well fluid and determine the threshold values of these probabilities, which may be universal for all fluids. It is shown that for a continuous system, over a wide range of system size, the wrapping probabilities can be described by universal scaling functions, whereas the crossing probabilities do not show such universal behavior over the same range of system size. The obtained universal functions for the wrapping probabilities can be used for an estimation of the percolation threshold in fluids in general. The results for the crossing probabilities allow us then to characterize large clusters in real fluids.

In this paper, we present the results of the research concerning extraction of informative gene expression profiles from high-dimensional array of gene expressions considering the state of patients’ health using clustering method, ML-based binary classifiers and fuzzy inference system. Applying of the proposed stepwise procedure can allow us to extract the most informative genes taking into account both the subtypes of disease or state of the patient’s health for further reconstruction of gene regulatory networks based on the allocated genes and following simulation of the reconstructed models. We used the publicly available gene expressions data as the experimental ones which were obtained using DNA microarray experiments and contained two types of patients’ gene expression profiles—the patients with lung cancer tumor and healthy patients. The stepwise procedure of the data processing assumes the following steps—in the beginning, we reduce the number of genes by removing non-informative genes in terms of statistical criteria and Shannon entropy; then, we perform the stepwise hierarchical clustering of gene expression profiles at hierarchical levels from 1 to 10 using the SOTA (Self-Organizing Tree Algorithm) clustering algorithm with correlation distance metric. The quality of the obtained clustering was evaluated using the complex clustering quality criterion which is considered both the gene expression profiles distribution relative to center of the clusters where these gene expression profiles are allocated and the centers of the clusters distribution. The result of this stage execution was a selection of the optimal cluster at each of the hierarchical levels which corresponded to the minimum value of the quality criterion. At the next step, we have implemented a classification procedure of the examined objects using four well known binary classifiers—logistic regression, support-vector machine, decision trees and random forest classifier. The effectiveness of the appropriate technique was evaluated based on the use of ROC (Receiver Operating Characteristic) analysis using criteria, included as the components, the errors of both the first and the second kinds. The final decision concerning the extraction of the most informative subset of gene expression profiles was taken based on the use of the fuzzy inference system, the inputs of which are the results of the appropriate single classifiers operation and the output is the final solution concerning state of the patient’s health. To our mind, the implementation of the proposed stepwise procedure of the informative gene expression profiles extraction create the conditions for the increasing effectiveness of the further procedure of gene regulatory networks reconstruction and the following simulation of the reconstructed models considering the subtypes of the disease and/or state of the patient’s health.

The paper presents the information technology of gene expression profiles processing in order to reconstruct gene regulatory networks. The information technology is presented as a structural block-chart, which contains all stages of studied data processing. DNA microchips of patients, which were studied on different types of diseases, were used as experimental data. The relative criteria of validation for all reconstructed networks were calculated during simulation process. The obtained results show high efficiency of the proposed technology. High values of the validation criteria indicate a high level of the obtained gene networks objectivity.