Estimation of Parameters in Mixtures of Distributions Arising in Cultivation Problems

In many processes one has to describe events in which given particles or elements divide themselves so that these elements are to observe only after the division. In biological problems one meets such a situation i.e. in the cultivation of bacteria. In this paper we investigate a mathematical model which describes such a phenomenon. We give estimators for the expectation μ and the variance σ² of the distribution of the undivided particles. Therefore we give a best linear unbiased estimator for μ and an estimator μ where a clustering of the observation is essentially. In an example for the judgment of a cultivation method we demonstrate the given estimation procedures.     

Estimation of Covariance Matrices in Unbalanced Random and Mixed Multivariate Models

Three HENDERSON'S Methods of estimating the variance components are generalized from one to p variables using a compact matrix notation. These results are obtained using a generalized Kronecker product of matrices, generalized trace of order p and a generalized quadratic form.     

Measures of Imbalance for Higher Order Designs

In this paper we consider a generalization of the measures of imbalance given by AHRENS and PINCUS (1981) considering the cases: m-fold hierarchical model and m-way classification model in order to quantify the degree of imbalance in an unbalanced design. These measures of imbalance satisfy the same properties as those for the one-way classification model.     

Solvable models of neighbor-dependent substitution processes

We prove that a wide class of Markov models of neighbor-dependent substitution processes on the integer line is solvable. This class contains some models of nucleotidic substitutions recently introduced and studied empirically by molecular biologists. We show that the polynucleotidic frequencies at equilibrium solve some finite-size linear systems. This provides, for the first time up to our knowledge, explicit and algebraic formulas for the stationary frequencies of non-degenerate neighbor-dependent models of DNA substitutions. Furthermore, we show that the dynamics of these stochastic processes and their distribution at equilibrium exhibit some stringent, rather unexpected, independence properties. For example, nucleotidic sites at distance at least three evolve independently, and all the sites, when encoded as purines and pyrimidines, evolve independently.     

Mathematical models of mycelium growth and ergosterol synthesis in stationary mould culture

Aims:  To develop mathematical models for mycelium growth and ergosterol formation in conditions of periodic stationary culture; to verify possibilities of applying a model describing the relationship between ergosterol content and mycelium quantity.
Methods and Results:  The mould growth and ergosterol formation models covering all phases of mould growth are described using a modified logistic equation with the addition of an exponential function. The correlation between ergosterol and mycelium biomass depended on the growth phase of mould. Meaningful relation was obtained for initial two phases, when both parameters were growing equally. The quadratic function for estimation of the biomass based on ergosterol content was formulated. The error resulting from the application of this function in initial phases of moulds growth was small at 5–7%, in the following phases it was at 11–31%.
Conclusions:  Mycelium biomass can be precisely determined basing on the ergosterol content, when we know the moulds growth phase. In natural environments, without the information about growth phases, it will be possible, but with the higher error.
Significance and Impact of the Study:  Presented model based on the ergosterol content making possible to estimate the quantity of mycelium in moulds cultures and natural environments.     

The Polynomial Model in the Multivariate Analysis of Variance

Assuming that the independent variables (factors) are quantitative, there exist besides the coding schemes generally used for the multivariate analysis of variance (dummy-coded or effect-coded design matrices) the so-called polynomial models. The advantage of these polynomial models are the full rank design matrices, which allow a more comprehensible analysis, i.e. the unambiguous interpretation of tested hypotheses and simultaneous confidence intervals.     

Statistical Modeling of Observational Data With Spatial Dependencies

Abstract I provide a brief introduction to the concept of spatial autocorrelation and its incorporation into regression-type models. Spatial autocorrelation occurs when the response variable is correlated with itself at other locations in the region of interest. The autocorrelation usually takes a specific form where observations close in space are more correlated than those farther apart, and the rate of decay of the correlation is a function of the distance separating 2 locations. I present 2 commonly used models: 1) geostatistical modeling in which data are collected at points in the study region and 2) conditional autoregression (lattice) models in which data are aggregated over small nonoverlapping sub-areas of the study region. I also describe incorporation of explanatory covariates, such as habitat or physico-chemical attributes. I emphasize frequentist methods, but I briefly describe Bayesian approaches. I also provide some advantages, such as obtaining correct standard errors for estimators, and disadvantages, such as requirements for larger sample sizes, of incorporating spatial autocorrelation into the modeling effort. This information can aid researchers in designing and analyzing models of the relationships between species distributions and habitat. As a result, more informative models can be developed which further aid in management of wildlife.     

Fuzzy knowledge- and data-based models of damage to reeds by grazing of Greylag Geese

This paper describes a fuzzy and neuro-fuzzy approach to modelling feeding intensity of Greylag Geese on reed. As a consequence of the presence of some non-measurable or random factors and the heterogeneity of reed and goose behaviour, the relationships between the model variables are often not well known and the data collected have a high degree of uncertainty. A fuzzy approach was selected which can be applied with vague knowledge and data of high uncertainty. Fuzzy logic can be used to handle inexact reasoning in knowledge-based models with fuzzy rules and fuzzy sets to handle uncertainty in data. The neural network technique was applied to develop the fuzzy data-based models. For training, several dataset combinations of three lakes in North Germany were used. The generalisation capability of these models was checked for other lakes. The performance of these models was compared with the results of the fuzzy knowledge-based model developed in the next step. The knowledge base of this model contains the Mamdani-type rules formulated by a domain expert. All models were implemented using the Fuzzy Logic Toolbox of MATLAB^®.     

Quasi-stationary and ratio of expectations distributions: A comparative study

Many stochastic systems, including biological applications, use Markov chains in which there is a set of absorbing states. It is then needed to consider analogs of the stationary distribution of an irreducible chain. In this context, quasi-stationary distributions play a fundamental role to describe the long-term behavior of the system. The rationale for using quasi-stationary distribution is well established in the abundant existing literature. The aim of this study is to reformulate the ratio of means approach ( [Darroch and Seneta, 1965] and [Darroch and Seneta, 1967]) which provides a simple alternative. We have a two-fold objective. The first objective is viewing quasi-stationarity and ratio of expectations as two different approaches for understanding the dynamics of the system before absorption. At this point, we remark that the quasi-stationary distribution and a ratio of means distribution may give or not give similar information. In this way, we arrive to the second objective; namely, to investigate the possibility of using the ratio of expectations distribution as an approximation to the quasi-stationary distribution. This second objective is explored by comparing both distributions in some selected scenarios, which are mainly inspired in stochastic epidemic models. Previously, the rate of convergence to the quasi-stationary regime is taking into account in order to make meaningful the comparison.     

Longitudinal comparison of virus load parameters and CD8 T-cell suppressive capacity in two SIVcpz-infected chimpanzees

In a longitudinal study we address the hypothesis that resis tance to disease progression in lentivirus-infected chimpanzees is related to potent non-cytotoxic suppression of virus replication. In a long-term follow-up, the viral suppressive capacity in two simian immunodeficiency virus (SIV)cpz-infected chimpanzees was correlated with two polymerase chain reaction (PCR)- and two culture-based virus load measurements. In both animals, quantitative virus isolation (QVI) tended to decline slowly, whereas in vitro virus suppression was sustained or increased over time. In general, plasma virus loads in SIVcpz-infected animals were maintained for extended periods of time. Based on current assays that measure virus suppressive capacity in peripheral blood, it was not possible to conclude that virus suppression played a major role in the maintenance of the disease-free state in lentivirus-infected chimpanzees.     

A coefficient of determination (R2) for generalized linear mixed models

Extensions of linear models are very commonly used in the analysis of biological data. Whereas goodness of fit measures such as the coefficient of determination (R²) or the adjusted R² are well established for linear models, it is not obvious how such measures should be defined for generalized linear and mixed models. There are by now several proposals but no consensus has yet emerged as to the best unified approach in these settings. In particular, it is an open question how to best account for heteroscedasticity and for covariance among observations present in residual error or induced by random effects. This paper proposes a new approach that addresses this issue and is universally applicable for arbitrary variance‐covariance structures including spatial models and repeated measures. It is exemplified using three biological examples.     

Criteria for the determination of the direction of character state changes

Phylogenetic reconstructions cannot be adequately assessed except in terms of probability models which represent the processes of change. An tionary tree model of bifurcating splits, together with a Brownian motion model of genetic drift have been shown to allow successful reconstruction of phylogeny from data relating to gene frequencies of blood groups from human populations. Changes in state cannot be dealt with by the Brownian motion model, and no adequate models have been proposed for character state changes from the many possible sources. So, while the tionary tree model is applicable to these problems too, only heuristic methods of analysis of the state data are available, and these are known to be unsatisfactory under certain conditions. The concepts of homology, polarity and homoplasy have been developed out of the attempt to describe the nature of morphological state data, which is unpredictably related to genetic state data. The experimental study of comparative functional morphology, at any developmental stage of an organism, is considered to be the only valid tool for investigating the resulting character state tree hypothesis. However, the speculative nature of such investigations is admitted.     

Development of evolutionary biomedicine as a novel direction of biological science

This review analyzes the data obtained for the last decade on invertebrate animals (insects, round worms, molluscs) as models of various human diseases. As illustration, there are considered advances in studying of the invertebrate system of insulin-like peptides and signaling mechanisms of their action—evolutionary conservative homologues of the mammalian insulin/IGF-1 system. Results are presented of studies on the nematode Caenorhabditis elegans, Drosophila Drosophila melanogaster, and mollusks, which “model” individual aspects of some human diseases—diabetes, neurodegenerative dysfunction, carcinogenesis, as well as aging. A conclusion is made about the development of a new, synthetic direction combining evolutionary science and molecular biology and medicine, which we call evolutionary biomedicine. The roots of the appearance of this synthetic direction are to be searched for in L.A. Orbeli’s evolutionary ideas, methods, and scientific predictions.     

骨髓间充质干细胞(BMSCs)移植于大鼠肝硬化模型的动物实验研究

目的:探讨骨髓间充质干细胞应用于肝硬化模型的的实验疗效,为临床试验提供数据。方法:制作大鼠肝硬化模型,将肝硬化大鼠随机分为两组,实验组和对照组,每组25只。将骨髓间充质干细胞通过门静脉注射入实验组大鼠肝脏,术后两组大鼠仍然以0.5mL/100g的维持剂量腹腔注射40%CCl4植物油溶液,3周后处死所有实验动物,取其静脉血检测ALT、TBIL、ALB、AFP,并取大鼠肝脏做组织切片观察。结果:实验大鼠肝脏可观察到诱导分化的肝细胞。实验组大鼠死亡3只,对照组死亡2只。对照组与实验组肝功能指标ALT、ALB、TBIL、AFP有显著差异,P<0.05,具有统计学意义,AST差异无统计学意义,P>0.05。结论:BMSCs注入肝硬化大鼠模型中能有效改善肝脏的生理功能,对临床试验有很好的指导作用。     

On the possibility of reduction of dissipative structure models to a simple form

A multicomponent reaction-diffusion system containing two different space scales (contrasting system) is considered. It is shown that if the system answers several conditions enumerated, it can be reduced to a bicomponent system which describes a dissipative structure either of a peak or of a step type. While in the first case the original and the final systems are equivalent only in the neighbourhood of zero, in the second case the equivalence is more general as the solution of these systems does not leave the region for which the procedure of reduction was developed.