On Some Application of Non-Homogeneous Semi-Markov Processes

In this paper a non-homogeneous semi-Markov process is applied to a study of the behaviour of a cell after irradiation. The definition and main properties of the non-homogeneous semi-Markov process are reminded. Moreover one assumes that the cell may stay in one of four states namely, normal state, damaged state 1, damaged state 2, state of death, which are defined. Using the results of the theory of non-homogeneous semi-Markov processes and Markov renewal theory the characteristics of interest pertaining to the cell behaviour are studied.     

Some techniques in building and validating stochastic models of human reproduction

Stochastic models of human reproduction are beginning to play significant roles in the evaluation of family planning programs. A class of stochastic processes called absorbing, agedependent, semi-Markov processes frequently arises in the construction of such models. The paper begins with a discussion of some technicalities regarding absorbing, age-dependent, semi-Markov processes. Then, an algorithm due to Littman, which makes possible the computerization of this class of stochastic processes, is presented. Briefly, Littman’s algorithm provides an efficient method for numerically solving systems of renewal type integral equations, provided the system does not contain a large number of equations. After setting down a concrete model for a large clinical trial of intrauterine devices conducted in Taiwan, the paper concludes with a discussion of a method for validating the model based on the data collected in the clinical trial. Presented at the Society for Mathematical Biology Meeting, University of Pennsylvania, Philadelphia, August 19–21, 1976.     

Mathematical models of eye movements in reading: a possible role for autonomous saccades

 An efficient method for the exact numerical simulation of semi-Markov processes is used to study minimal models of the control of eye movements in reading. When we read a text, typical sequences of fixations form a rather complicated trajectory – almost like a random walk. Mathematical models of eye movement control can account for this behavior using stochastic transition rules between few discrete internal states, which represent combinations of certain stages of lexical access and saccade programs. We show that experimentally observed fixation durations can be explained by residence-time-dependent transition probabilities. Stochastic processes with this property are known as semi-Markov processes. For our numerical simulations we use the minimal process method (Gillespie algorithm), which is an exact and efficient simulation algorithm for this class of stochastic processes. Within this mathematical framework, we study different forms of coupling between eye movements and shifts of covert attention in reading. Our model lends support to the existence of autonomous saccades, i.e., the hypothesis that initiations of saccades are not completely determined by lexical access processes. Received: 21 March 2000 / Accepted in revised form: 10 January 2001     

An approach to the residence time distribution for stochastic multi-compartment models

Stochastic compartmental models are widely used in modeling processes such as drug kinetics in biological systems. This paper considers the distribution of the residence times for stochastic multi-compartment models, especially systems with non-exponential lifetime distributions. The paper first derives the moment generating function of the bivariate residence time distribution for the two-compartment model with general lifetimes and approximates the density of the residence time using the saddlepoint approximation. Then, it extends the distributional approach to the residence time for multi-compartment semi-Markov models combining the cofactor rule for a single destination and the analytic approach to the two-compartment model. This approach provides a complete specification of the residence time distribution based on the moment generating function and thus facilitates an easier calculation of high-order moments than the approach using the coefficient matrix. Applications to drug kinetics demonstrate the simplicity and usefulness of this approach.     

On some formulas in a partnership model from the perspective of a semi-Markov process

Many deterministic models of sexually transmitted diseases, as well as population models in general, contain elements of stochastic or statistical reasoning. An example of such a model is that of Dietz and Hadeler (1988) concerning sexually transmitted diseases in which there is partnership formation and dissolution. Among the interesting formulas in this paper, which enter into the analysis of the model, are those for the expected number of partners a male or female has during a lifetime. To a probabilist such formulas suggest the possibility that some stochastic process may be constructed so as to yield these formulas as well as others that may be of interest. The principal purpose of this paper is to demonstrate that such a stochastic process does indeed exist in the form of a three state semi-Markov process in continuous time with stationary laws of evolution and with a one-step density matrix determined by four parameters which were interpreted as constant latent risk functions in the classical theory of competing risks. This construction of a semi-Markov process not only provides a framework for the systematic derivation of the formulas of Dietz and Hadeler but also suggests pathways,for extensions to the age-dependent case.This research was partially supported by NATO Grant D.890350     

A class of general stochastic compartmental systems

In this paper a general class of semi-Markov compartmental systems is studied. Two models for different input processes are analysed. Attention has been paid to the recurrence times associated with each compartment and to the distribution of the number of particles in each compartment. As an example, a three-compartment system is discussed to study the movement between three health states of patients with chronic diseases.     

Semi-Markov graph dynamics

In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs.     

On the Chemical Nature and Origin of Teleonomy

The physico-chemical characterization of a teleonomic event and the nature of the physico-chemical process by which teleonomic systems could emerge from non-teleonomic systems are addressed in this paper. It is proposed that teleonomic events are those whose primary directive is discerned to be non-thermodynamic, while regular (non-teleonomic) events are those whose primary directive is the traditional thermodynamic one. For the archetypal teleonomic event, cell multiplication, the non-thermodynamic directive can be identified as being a kinetic directive. It is concluded, therefore, that the process of emergence, whereby non-teleonomic replicating chemical systems were transformed into teleonomic ones, involved a switch in the primacy of thermodynamic and kinetic directives. It is proposed that the step where that transformation took place was the one in which some pre-metabolic replicating system acquired an energy-gathering capability, thereby becoming metabolic. Such a transformation was itself kinetically directed given that metabolic replicators tend to be kinetically more stable than non-metabolic ones. The analysis builds on our previous work that considers living systems to be a kinetic state of matteras opposed to the traditional thermodynamic states that dominate the inanimate world     

桃树修剪分枝模式的模拟

在不同修剪手法下,对栽培桃树(Prunuspersica(L.)Batsch)不同母枝上的分枝模式进行了比较研究.从分枝模式来看:修剪后的母枝基本由3个不同的区域组成,基部是不萌发的潜伏芽形成的未分枝区域;中部是延迟分枝和多次分枝组成的分枝区域(主要的枝条类型有短枝、长枝和多次枝);顶部是被剪除的部分.我们通过隐式半马尔可夫模型来模拟这一分枝模式,主要是定量描述1次枝和多次枝在母枝上的数量及其分布状况.在上述模型中,未分枝区、延迟分枝区和多次分枝区称为瞬时态,被剪除的部分称为吸收态.模拟的结果与观察的结果进行对比后发现,两者具有很好的一致性.这说明隐式半马尔可夫模型是模拟植物分枝过程的一种有效方法,尽管隐式半马尔可夫链模型只是一个描述性的模型,但仍能对其所描述的生物现象进行解释,在预测修剪手法对母枝分枝模式影响方面比传统的方法具有明显的优势.本研究结果是建立三维虚拟桃树树冠分枝结构的基础.     

Effect of caffeine on the recombination process of Bacillus subtilis

Summary The effect of caffeine on the recombination process was studied by using transformation and transfection of Bacillus subtilis as genetic systems. Data were obtained showing that caffeine reduces strongly both transformation and transfection. The inhibitory effect seems ascribable to an interference of caffeine with the process of recombination.     

桃树修剪分枝模式的模拟

在不同修剪手法下,对栽培桃树(Prunuspersica(L.)Batsch)不同母枝上的分枝模式进行了比较研究。从分枝模式来看修剪后的母枝基本由3个不同的区域组成,基部是不萌发的潜伏芽形成的未分枝区域;中部是延迟分枝和多次分枝组成的分枝区域(主要的枝条类型有短枝、长枝和多次枝);顶部是被剪除的部分。我们通过隐式半马尔可夫模型来模拟这一分枝模式,主要是定量描述1次枝和多次枝在母枝上的数量及其分布状况。在上述模型中,未分枝区、延迟分枝区和多次分枝区称为瞬时态,被剪除的部分称为吸收态。模拟的结果与观察的结果进行对比后发现,两者具有很好的一致性。这说明隐式半马尔可夫模型是模拟植物分枝过程的一种有效方法,尽管隐式半马尔可夫链模型只是一个描述性的模型,但仍能对其所描述的生物现象进行解释,在预测修剪手法对母枝分枝模式影响方面比传统的方法具有明显的优势。本研究结果是建立三维虚拟桃树树冠分枝结构的基础。     

Evaluation of criteria for bioreactor comparison and operation standardization for mammalian cell culture

Development of bioprocesses with mammalian cell culture deals with different bioreactor types and scales. The bioreactors might be intended for generation of cell inoculum and production, research, process development, validation, or transfer purposes. During these activities, not only the difficulty of up and downscaling might lead to failure of consistency in cell growth, but also the use of different bioreactor geometries and operation conditions. In such cases, criteria for bioreactor design and process transfer should be carefully evaluated in order to select appropriate cultivation parameters. In this work, power input, mixing time, impeller tip speed, and Reynolds number have been compared systematically for the cultivation of the human cell line AGE1.HN within three partner laboratories using five different bioreactor systems. Proper operation ranges for the bioreactors were identified using the maximal cell‐specific growth rate (μ_max) as indicator. Common optimum values for process transfer criteria were found in these geometrically different bioreactors, in which deviations of μ_max between cultivation systems can be importantly reduced. The data obtained in this work are used for process standardization and comparability of results obtained in different bioreactor systems, i.e. to guarantee lab‐to‐lab consistency for systems biology approaches using mammalian cells.     

Semi-Markov Model and Its Application

In this paper, a numerical procedure based on the theory of semi-Markov process is presented to study the prognosis of the cancer of cervix. Data is used to illustrate the predictive ability of the model.     

Quantitative analysis of directional strengths in jointly stationary linear multivariate processes

Identification and analysis of directed influences in multivariate systems is an important problem in many scientific areas. Recent studies in neuroscience have provided measures to determine the network structure of the process and to quantify the total effect in terms of energy transfer. These measures are based on joint stationary representations of a multivariate process using vector auto-regressive (VAR) models. A few important issues remain unaddressed though. The primary outcomes of this study are (i) a theoretical proof that the total coupling strength consists of three components, namely, the direct, indirect, and the interference produced by the direct and indirect effects, (ii) expressions to estimate/calculate these effects, and (iii) a result which shows that the well-known directed measure for linear systems, partial directed coherence (PDC) only aids in structure determination but does not provide a normalized measure of the direct energy transfer. Simulation case studies are shown to illustrate the theoretical results.     

A queueing model for chronic recurrent conditions under panel observation

In many chronic conditions, subjects alternate between an active and an inactive state, and sojourns into the active state may involve multiple lesions, infections, or other recurrences with different times of onset and resolution. We present a biologically interpretable model of such chronic recurrent conditions based on a queueing process. The model has a birth-death process describing recurrences and a semi-Markov process describing the alternation between active and inactive states, and can be fit to panel data that provide only a binary assessment of the active or inactive state at a series of discrete time points using a hidden Markov approach. We accommodate individual heterogeneity and covariates using a random effects model, and simulate the posterior distribution of unknowns using a Markov chain Monte Carlo algorithm. Application to a clinical trial of genital herpes shows how the method can characterize the biology of the disease and estimate treatment efficacy.     

On the study of two interacting populations one of which acts independently of the other

Many ecological and biological systems can be studied in terms of a bivariate stochastic branching process, {X ₁ (t), X ₂ (t)}, each of whose components (or populations) varies in magnitude according to the laws of a generalized birth-death process. Of particular interest is such a model in which the birth and death rates of the first population,X ₁, are constant while those of the second population,X ₂, exhibit a functional dependence upon the magnitude of the first. It is shown, first, that the existence of the stochastic mean of a birth death process implies the existence of all higher moments. The values of all the factorial moments of such a process are then determined. The moments of the dependent population of the bivariate process are given in terms of its expectation and the joint probability density function of the process is determined. It is possible, therefore, to use Bayesian techniques to infer conclusions about the independent population, given information about the variation of the dependent one.     

Effect of correlated adjacent interspike interval sequences of the input on the output response in the computer-simulated neuromuscular system

A digital-computer simulated model, which consisted of the neuromuscular synapse and the muscle with external loads, was formulated for the neuromuscular system of the claw opener muscle of the crayfish. By using this model, the relationship between stimuli with correlated adjacent interval sequences and responses was investigated. The imposed correlated sequences generated by the three-state semi-Markov process, with the mean rate, interval distribution and variance held constant, were the following three types: Type I, a positive correlated sequence; Type II, a first order negative correlated sequence; Type III, an independent sequence of the above two. As a result of the model study, it was found that the evoked response by a Type I sequence is maximum among them, which agrees very well with the experimental result obtained from the claw opener muscle in the previous paper. In addition, the response by Type II sequence fluctuates least about its moving average or ensemble mean value at a time although the response is of small magnitude, which also coincides with the experimental results and in part with Birk's model study. The fluctuations about ensemble mean value were evaluated by using the average mutual information for various mean values of stimuli.     

Pichia pastoris: A highly successful expression system for optimal synthesis of heterologous proteins

One of the most important branches of genetic engineering is the expression of recombinant proteins using biological expression systems. Nowadays, different expression systems are used for the production of recombinant proteins including bacteria, yeasts, molds, mammals, plants, and insects. Yeast expression systems such as Saccharomyces cerevisiae (S. cerevisiae) and Pichia pastoris (P. pastoris) are more popular. P. pastoris expression system is one of the most popular and standard tools for the production of recombinant protein in molecular biology. Overall, the benefits of protein production by P. pastoris system include appropriate folding (in the endoplasmic reticulum) and secretion (by Kex2 as signal peptidase) of recombinant proteins to the external environment of the cell. Moreover, in the P. pastoris expression system due to its limited production of endogenous secretory proteins, the purification of recombinant protein is easy. It is also considered a unique host for the expression of subunit vaccines which could significantly affect the growing market of medical biotechnology. Although P. pastoris expression systems are impressive and easy to use with well-defined process protocols, some degree of process optimization is required to achieve maximum production of the target proteins. Methanol and sorbitol concentration, Mut forms, temperature and incubation time have to be adjusted to obtain optimal conditions, which might vary among different strains and externally expressed protein. Eventually, optimal conditions for the production of a recombinant protein in P. pastoris expression system differ according to the target protein.     

Homeostatic dysregulation proceeds in parallel in multiple physiological systems

An increasing number of aging researchers believes that multi‐system physiological dysregulation may be a key biological mechanism of aging, but evidence of this has been sparse. Here, we used biomarker data on nearly 33 000 individuals from four large datasets to test for the presence of multi‐system dysregulation. We grouped 37 biomarkers into six a priori groupings representing physiological systems (lipids, immune, oxygen transport, liver function, vitamins, and electrolytes), then calculated dysregulation scores for each system in each individual using statistical distance. Correlations among dysregulation levels across systems were generally weak but significant. Comparison of these results to dysregulation in arbitrary ‘systems’ generated by random grouping of biomarkers showed that a priori knowledge effectively distinguished the true systems in which dysregulation proceeds most independently. In other words, correlations among dysregulation levels were higher using arbitrary systems, indicating that only a priori systems identified distinct dysregulation processes. Additionally, dysregulation of most systems increased with age and significantly predicted multiple health outcomes including mortality, frailty, diabetes, heart disease, and number of chronic diseases. The six systems differed in how well their dysregulation scores predicted health outcomes and age. These findings present the first unequivocal demonstration of integrated multi‐system physiological dysregulation during aging, demonstrating that physiological dysregulation proceeds neither as a single global process nor as a completely independent process in different systems, but rather as a set of system‐specific processes likely linked through weak feedback effects. These processes – probably many more than the six measured here – are implicated in aging.     

Biochemical systematics of Japanese fireflies of the subfamily Luciolinae and their flash communication systems

Japanese fireflies of the subfamily Luciolinae are biochemically analyzed using 13 allozymes, and the phylogenetic relationships obtained from this analysis are compared with their flash communication systems. As a result, the Japanese Luciolinae can be divided into three groups.Hotaria parvula andH. tsushimana together withLuciola yayeyamana andL. kuroiwae from the first group, and they use the same communication system.L. lateralis, Curtos okinawana, andC. costipennis make up the second group, and their communication systems are also the same.L. cruciata makes up the last one, and its communication system is different from the other fireflies of Luciolinae. Therefore, their taxonomical arrangement and communication systems are not congruent. However, the genetic similarity deduced by allozymic analysis of the members of the Japanese Luciolinae is highly consistent with their flash communication systems.