A new method for classifying bacteria is presented and applied to a large set of biochemical data for the Enterobacteriaceae. The method minimizes the bits needed to encode the classes and the items or, equivalently, maximizes the information content of the classification. The resulting taxonomy of Enterobacteriaceae corresponds well to the general structure of earlier classifications. Minimization of stochastic complexity can be considered as a useful tool to create bacterial classifications that are optimal from the point of view of information theory.

• Keywords
• Enterobacteriaceae, classification, information theory, stochastic complexity, taxonomy,
• Publication type
• Journal Article MeSH

Cryo Electron Tomography (cryoET) plays an essential role in Structural Biology, as it is the only technique that allows to study the structure of large macromolecular complexes in their close to native environment in situ. The reconstruction methods currently in use, such as Weighted Back Projection (WBP) or Simultaneous Iterative Reconstruction Technique (SIRT), deliver noisy and low-contrast reconstructions, which complicates the application of high-resolution protocols, such as Subtomogram Averaging (SA). We propose a Progressive Stochastic Reconstruction Technique (PSRT) - a novel iterative approach to tomographic reconstruction in cryoET based on Monte Carlo random walks guided by Metropolis-Hastings sampling strategy. We design a progressive reconstruction scheme to suit the conditions present in cryoET and apply it successfully to reconstructions of macromolecular complexes from both synthetic and experimental datasets. We show how to integrate PSRT into SA, where it provides an elegant solution to the region-of-interest problem and delivers high-contrast reconstructions that significantly improve template-based localization without any loss of high-resolution structural information. Furthermore, the locality of SA is exploited to design an importance sampling scheme which significantly speeds up the otherwise slow Monte Carlo approach. Finally, we design a new memory efficient solution for the specimen-level interior problem of cryoET, removing all associated artifacts.

• Keywords
• 3D reconstruction, Cryo electron tomography, Metropolis–Hastings, Monte Carlo, Stochastic reconstruction, Subtomogram averaging,
• MeSH
• Algorithms MeSH
• Cryoelectron Microscopy methods   MeSH
• Macromolecular Substances chemistry   MeSH
• Monte Carlo Method MeSH
• Image Processing, Computer-Assisted methods   MeSH
• Reproducibility of Results MeSH
• Ribosomes chemistry   MeSH
• Stochastic Processes * MeSH
• Electron Microscope Tomography methods   MeSH
• Imaging, Three-Dimensional methods   MeSH
• Publication type
• Journal Article MeSH
• Names of Substances
• Macromolecular Substances MeSH

This article presents a stochastic model of binaural hearing in the medial superior olive (MSO) circuit. This model is a variant of the slope encoding models. First, a general framework is developed describing the elementary neural operations realized on spike trains in individual parts of the circuit and how the neurons converging onto the MSO are connected. Random delay, coincidence detection of spikes, divergence and convergence of spike trains are operations implemented by the following modules: spike generator, jitter generator, and coincidence detector. Subsequent processing of spike trains computes the sound azimuth in the circuit. The circuit parameters that influence efficiency of slope encoding are studied. In order to measure the overall circuit performance the concept of an ideal observer is used instead of a detailed model of higher relays in the auditory pathway. This makes it possible to bridge the gap between psychophysical observations in humans and recordings taken of small rodents. Most of the results are obtained through numerical simulations of the model.

• MeSH
• Action Potentials physiology   MeSH
• Acoustic Stimulation methods   MeSH
• Humans MeSH
• Models, Neurological * MeSH
• Nerve Net * physiology   MeSH
• Olivary Nucleus * physiology   MeSH
• Auditory Pathways * physiology   MeSH
• Stochastic Processes MeSH
• Animals MeSH
• Check Tag
• Humans MeSH
• Animals MeSH
• Publication type
• Journal Article MeSH
• Research Support, Non-U.S. Gov't MeSH

Cell cycle is controlled by the activity of protein family of cyclins and cyclin-dependent kinases that are periodically expressed during cell cycle and that are conserved among different species. Genome-wide location analysis found that cyclins are controlled by a small number of transcription factors that form closed network of genes controlling each other. To investigate gene expression dynamics of this network, we developed a general procedure for stochastic simulation of gene expression process. Using the binding data, we simulated gene expression of all genes of the network for all possible combinations of regulatory interactions and by statistical comparison with experimentally measured time series excluded those interactions that formed gene expression temporal profiles significantly different from the measured ones. These experiments led to a new definition of the cyclins regulatory network coherent with the binding experiments which are kinetically plausible. Level of influence of individual regulators in control of the regulated genes is defined. Simulation results indicate particular mechanism of regulatory activity of protein complexes involved in the control of cyclins.

• MeSH
• Cyclin-Dependent Kinases genetics   MeSH
• Cyclins biosynthesis   genetics   MeSH
• Transcription, Genetic MeSH
• Gene Regulatory Networks * MeSH
• Gene Expression Regulation, Fungal * MeSH
• Saccharomyces cerevisiae genetics   MeSH
• Stochastic Processes MeSH
• Publication type
• Journal Article MeSH
• Research Support, Non-U.S. Gov't MeSH
• Names of Substances
• Cyclin-Dependent Kinases MeSH
• Cyclins MeSH

For further understanding of neural coding, stochastic variability of interspike intervals has been investigated by both experimental and theoretical neuroscientists. In stochastic neuronal models, the interspike interval corresponds to the time period during which the process imitating the membrane potential reaches a threshold for the first time from a reset depolarization. For neurons belonging to complex networks in the brain, stochastic diffusion processes are often used to approximate the time course of the membrane potential. The interspike interval is then viewed as the first passage time for the employed diffusion process. Due to a lack of analytical solution for the related first passage time problem for most diffusion neuronal models, a numerical integration method, which serves to compute first passage time moments on the basis of the Siegert recursive formula, is presented in this paper. For their neurobiological plausibility, the method here is associated with diffusion processes whose state spaces are restricted to finite intervals, but it can also be applied to other diffusion processes and in other (non-neuronal) contexts. The capability of the method is demonstrated in numerical examples and the relation between the integration step, accuracy of calculation and amount of computing time required is discussed.

• MeSH
• Action Potentials MeSH
• Time Factors MeSH
• Models, Neurological * MeSH
• Neurons physiology   MeSH
• Numerical Analysis, Computer-Assisted * MeSH
• Computer Simulation * MeSH
• Reproducibility of Results MeSH
• Software MeSH
• Stochastic Processes * MeSH
• Publication type
• Journal Article MeSH
• Research Support, Non-U.S. Gov't MeSH

PURPOSE: To propose an improved version of RADACK, a stochastic simulation of radiolytic attack on DNA, that takes into account the reactivity of each amino acid of a specifically bound protein with hydroxyl radicals. To apply it to the natural lactose operator-repressor complex taking advantage of recently reported structures. To compare the obtained probabilities of DNA strand break induction with those calculated with the previous versions and with an experimental pattern of strand break probabilities. MATERIALS AND METHODS: Models of complexes close to the natural ones, derived from crystallography- and NMR-based structures recently available in the PDB databank, were used. The specific chemical reactivity of each amino acid was introduced in the new version of RADACK (the reactivity model). The probabilities of strand break induction by the irradiation of the complex were calculated with this new version as well as with previous ones. RESULTS: The patterns of probabilities of strand break induction calculated with the improved version of RADACK were partially different from those obtained with previous versions. The patterns obtained for both, using putative models of natural complexes, were consistent with the experimental results, but some discrepancies were suggestive of slight differences between these structures and the real natural system. The crystallographic structure agreed best with the experimental results. CONCLUSIONS: A new version of RADACK was validated that took into account the reactivity of atoms in both DNA and protein. The putative modelled structures of a natural lactose operator-repressor complex were discussed.

• MeSH
• Amino Acids chemistry   MeSH
• Models, Biological MeSH
• Databases as Topic MeSH
• DNA chemistry   metabolism   MeSH
• Hydroxyl Radical * MeSH
• Radiation, Ionizing MeSH
• Kinetics MeSH
• Crystallography, X-Ray MeSH
• Lactose chemistry   MeSH
• Magnetic Resonance Spectroscopy MeSH
• Models, Molecular MeSH
• Molecular Sequence Data MeSH
• Nucleosomes chemistry   MeSH
• Operon MeSH
• DNA Damage MeSH
• Amino Acid Sequence MeSH
• Base Sequence MeSH
• Software * MeSH
• Stochastic Processes MeSH
• Protein Binding MeSH
• Publication type
• Journal Article MeSH
• Research Support, Non-U.S. Gov't MeSH
• Names of Substances
• Amino Acids MeSH
• DNA MeSH
• Hydroxyl Radical * MeSH
• Lactose MeSH
• Nucleosomes MeSH

We explored the transition of 13 X-linked markers across two separate portions of the house mouse hybrid zone, asking whether such a comparison can distinguish the effects of selection from random factors. A heuristic search in the likelihood landscape revealed more complex likelihood profiles for data sampled in two-dimensional (2D) space relative to data sampled along a linear transect. Randomized resampling of localities analyzed for individual loci showed that deletion of sites away from the zone center can decrease cline width estimates whereas deletion of sites close to the center can significantly increase the width estimates. Deleting localities for all loci resulted in wider clines if the number of samples from the center was limited. The results suggest that, given the great variation in width estimates resulting from inclusion/exclusion of sampling sites, the geographic sampling design is important in hybrid zone studies and that our inferences should take into account measures of uncertainty such as support intervals. The comparison of the two transects indicates cline widths are narrower for loci in the central part of the X chromosome, suggesting selection is stronger in this region and genetic incompatibilities may have at least partly common architecture in the house mouse hybrid zone.

• MeSH
• Species Specificity MeSH
• Genetic Markers genetics   MeSH
• Genotype MeSH
• Hybridization, Genetic * MeSH
• Mice genetics   MeSH
• Likelihood Functions MeSH
• Reproduction genetics   MeSH
• Selection, Genetic * MeSH
• Stochastic Processes MeSH
• Genetic Speciation * MeSH
• Geography MeSH
• Animals MeSH
• Check Tag
• Mice genetics   MeSH
• Animals MeSH
• Publication type
• Journal Article MeSH
• Research Support, Non-U.S. Gov't MeSH
• Comparative Study MeSH
• Geographicals
• Czech Republic MeSH
• Germany MeSH
• Names of Substances
• Genetic Markers MeSH

The fractional stochastic delay differential equation (FSDDE) is a powerful mathematical tool for modeling complex systems that exhibit both fractional order dynamics and stochasticity with time delays. The purpose of this study is to explore the stability analysis of a system of FSDDEs. Our study emphasizes the interaction between fractional calculus, stochasticity, and time delays in understanding the stability of such systems. Analyzing the moments of the system's solutions, we investigate stochasticity's influence on FSDDS. The article provides practical insight into solving FSDDS efficiently using various numerical techniques. Additionally, this research focuses both on asymptotic as well as Lyapunov stability of FSDDS. The local stability conditions are clearly presented and also the effects of a fractional orders with delay on the stability properties are examine. Through a comprehensive test of a stability criteria, practical examples and numerical simulations we demonstrate the complexity and challenges concern with the analyzing FSDDEs.

• Keywords
• Fractional stochastic delay differential equations, Legendre–Gauss–Lobatto nodes, Spectral method, Stability analysis,
• Publication type
• Journal Article MeSH

Fractals are models of natural processes with many applications in medicine. The recent studies in medicine show that fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Inspired by Sierpinski carpet, we introduce a flexible parametric model of random carpets. Randomization is introduced by usage of binomial random variables. We provide an algorithm for estimation of parameters of the model and illustrate theoretical and practical issues in generation of Sierpinski gaskets and Hausdorff measure calculations. Stochastic geometry models can also serve as models for binary cancer images. Recently, a Boolean model was applied on the 200 images of mammary cancer tissue and 200 images of mastopathic tissue. Here, we describe the Quermass-interaction process, which can handle much more variations in the cancer data, and we apply it to the images. It was found out that mastopathic tissue deviates significantly stronger from Quermass-interaction process, which describes interactions among particles, than mammary cancer tissue does. The Quermass-interaction process serves as a model describing the tissue, which structure is broken to a certain level. However, random fractal model fits well for mastopathic tissue. We provide a novel discrimination method between mastopathic and mammary cancer tissue on the basis of complex wavelet-based self-similarity measure with classification rates more than 80%. Such similarity measure relates to Hurst exponent and fractional Brownian motions. The R package FractalParameterEstimation is developed and introduced in the paper.

• Keywords
• Hausdorff measure, Quermass-interaction process, box-counting dimension, breast cancer, pathology,
• MeSH
• Algorithms MeSH
• Diagnosis, Computer-Assisted methods   MeSH
• Carcinoma, Ductal, Breast MeSH
• Fractals MeSH
• Risk Assessment methods   MeSH
• Humans MeSH
• Breast Neoplasms diagnosis   pathology   MeSH
• Pathology methods   MeSH
• Computer Simulation MeSH
• Stochastic Processes MeSH
• Check Tag
• Humans MeSH
• Female MeSH
• Publication type
• Journal Article MeSH
• Research Support, Non-U.S. Gov't MeSH
• Comparative Study MeSH

The open nature of Wireless Sensor Networks (WSNs) renders them an easy target to malicious code propagation, posing a significant and persistent threat to their security. Various mathematical models have been studied in recent literature for understanding the dynamics and control of the propagation of malicious codes in WSNs. However, due to the inherent randomness and uncertainty present in WSNs, stochastic modeling approach is essential for a comprehensive understanding of the propagation of malicious codes in WSNs. In this paper, we formulate a general stochastic compartmental model for analyzing the dynamics of malicious code distribution in WSNs and suggest its possible control. We incorporate the stochasticity in the classical deterministic model for the inherent unpredictability in code propagation, which results in a more appropriate representation of the dynamics. A basic theoretical analysis including the stability results of the model with randomness is carried out. Moreover, a higher-order spectral collocation technique is applied for the numerical solution of the proposed stochastic model. The accuracy and numerical stability of the model is presented. Finally, a comprehensive simulation is depicted to verify theoretical results and depict the impact of parameters on the model's dynamic behavior. This study incorporates stochasticity in a deterministic model of malicious codes spread in WSNs with the implementation of spectral numerical scheme which helps to capture these networks' inherent uncertainties and complex nature.

• Keywords
• Spectral collocation technique, Stochastic compartmental modeling, Distribution density, Wireless sensor network, Malicious codes propagation, Stability Analysis,
• Publication type
• Journal Article MeSH