On the Exact Hazard and Survival Functions of the MVK Stochastic Carcinogenesis Model

The MVK two-stage carcinogenesis model is one of the most widely accepted mechanistic models in carcinogenesis modeling. However, due to a perceived difficulty in obtaining analytic solutions for the hazard and survival functions, approximations and numerical methods have been used to calculate these two fundamental quantities. This paper focuses on a special case of the homogeneous MVK model where the number of normal cells is constant. The probability generating function (pgf) for the number of tumor cells is derived, and the exact analytic solutions to the hazard and survival functions are obtained from the pgf.     

On the MVK Stochastic Carcinogenesis Model with Erlang Distributed Cell Life Lengths

This paper proposes extending the MVK carcinogenesis model by adopting the Erlang distribution for the life length of the intermediate cells. The investigation concentrates on the survival function and the mean value functions. The approach is basically numerical, making use of the Mathematica software system. The paper also provides a closed form expression for the survival function for a variation of the original MVK model, where all the model parameters are piecewise constants.     

Biological Models of Carcinogenesis and Quantitative Cancer Risk Assessment

Biologically-based models of carcinogenesis were originally developed to explain certain quanti-tative phenomena associated with carcinogenesis, and to provide a framework within which questions regarding the process could be addressed. Some limitations in the use of these models for quantitative cancer risk assessment are discussed.     

基于阶梯型衰退效用函数的竞争选址问题

研究了连锁型企业新设施选址的2个重要因素：市场份额的划分和设施的服务半径。依照效用函数为竞争环境下设施市场份额分配的重要依据,结合消费者的空间选择行为提出了阶梯型效用函数,并应用此效用函数建立了一个竞争环境下连锁型企业新设施选址的新模型,此模型既考虑了服务设施覆盖衰退又考虑了设施的服务半径。最后,给出了求解模型的遗传算法和具体案例。结果表明,该模型和算法可以用于连锁型企业新设施选址决策中,并能够有效地得到问题的近似解。     

Uncertainty Importance Analysis Using Parametric Moment Ratio Functions

This article presents a new importance analysis framework, called parametric moment ratio function, for measuring the reduction of model output uncertainty when the distribution parameters of inputs are changed, and the emphasis is put on the mean and variance ratio functions with respect to the variances of model inputs. The proposed concepts efficiently guide the analyst to achieve a targeted reduction on the model output mean and variance by operating on the variances of model inputs. The unbiased and progressive unbiased Monte Carlo estimators are also derived for the parametric mean and variance ratio functions, respectively. Only a set of samples is needed for implementing the proposed importance analysis by the proposed estimators, thus the computational cost is free of input dimensionality. An analytical test example with highly nonlinear behavior is introduced for illustrating the engineering significance of the proposed importance analysis technique and verifying the efficiency and convergence of the derived Monte Carlo estimators. Finally, the moment ratio function is applied to a planar 10‐bar structure for achieving a targeted 50% reduction of the model output variance.     

A genetic algorithm for assembly line balancing

Assembly line balancing is a very important aspect in any mass production setup. However, finding the optimal balance is a very difficult proposition because of the computational complexity involved. Hence sub-optimal solutions are preferred over optimal solutions. In this work, a genetic algorithm (GA) is presented for obtaining good quality solutions for assembly line balancing problems. A major feature of GA is the ability to take care of a variety of objective functions. A modified GA working with two populations, one of which allows infeasible solutions, and exchange of specimens at regular intervals is proposed for handling irregular search spaces. The experimental results obtained with a single population, as well as two populations are encouraging.     

Apoptosis and Chemical Carcinogenesis

Long recognized as a normal component of organogenesis during development, apoptosis (programmed cell death) has recently been implicated in alterations of cell growth and differentiation. Tissue homeostasis is normally maintained by a balance between cell division and cell death, with apoptosis often functioning in complement to cell growth. Thus, antithetical parallels in chemical carcinogenesis can be drawn between apoptosis and the proliferative events more commonly addressed. While enhanced cell replication may contribute to an increased frequency of mutation, apoptosis within a tissue may counteract chemical carcinogenesis through loss of mutated cells. Many strong carcinogens act as tumor promoters, selectively expanding an initiated cell population advantageously over surrounding cells. Similarly, chemicals with a selective inhibition of apoptosis within an initiated population would offer a growth advantage. In contrast, chemicals causing selective apoptosis of initiated cells would be expected to have an anticarcinogenic effect. Selective apoptosis, in concert with cell-specific replication, may explain the unique promoting effects of different carcinogens such as the peroxisome-proliferating chemicals, phenobarbital, and 2,3,7,8-tetrachloro-dibenzo- p -dioxin (TCDD). Cell turnover, both cell growth and cell death, is central to the process of chemically induced carcinogenesis in animals and understanding its impact is a critical determinant of the relevance of chemically induced effects to man.     

The Two-Stage Model of Carcinogenesis: Overcoming the Nonidentifiability Dilemma

The two-stage mathematical model of carcinogenesis has been shown to be nonidentifiable whenever tumor incidence data alone is used to fit the model (Hanin and Yakovlev, 1996). This lack of identifiability implies that more than one parameter vector satisfies the optimization criteria for parameter estimation, e.g., maximum likelihood estimation. A question of greater concern to persons using the two-stage model of carcinogenesis is under what conditions can identifiable parameters be obtained from the observed experimental data. We outline how to obtain identifiable parameters for the two-stage model.     

A Cellular Dynamics Model of Experimental Bladder Cancer: Analysis of the Effect of Sodium Saccharin in the Rat

To make the methodology of risk assessment more consistent with the realities of biological processes, a computer-based model of the carcinogenic process may be used. A previously developed probabilistic model, which is based on a two-stage theory of carcinogenesis, represents urinary bladder carcinogenesis at the cellular level with emphasis on quantification of cell dynamics: cell mitotic rates, cell loss and birth rates, and irreversible cellular transitions from normal to initiated to transformed states are explicitly accounted for. Analyses demonstrate the sensitivity of tumor incidence to the timing and magnitude of changes to these cellular variables. It is demonstrated that response in rats following administration of nongenotoxic compounds, such as sodium saccharin, can be explained entirely on the basis of cytotoxicity and consequent hyperplasia alone.     

A Stochastic Two-Stage Model for Cancer Risk Assessment. I. The Hazard Function and the Probability of Tumor

We present a mathematical treatment of a two-mutation model for carcinogenesis with time-dependent parameters. This model has previously been shown to be consistent with epidemiologic and experimental data. An approximate hazard function used in previous papers is critically evaluated.     

A Stochastic Two-Stage Model for Cancer Risk Assessment. II. The Number and Size of Premalignant Clones

Mathematical expressions are derived, under different dosing patterns, for the number and size of premalignant clones within the framework of a two-mutation model for carcinogenesis, which has previously been shown to be consistent with a large body of epidemiologic and experimental data.     

Calculating the Hazard Function and Probability of Tumor for Cancer Risk Assessment When the Parameters Are Time-Dependent

The probability of tumor and hazard function are calculated in a stochastic two-stage model for carcinogenesis when the parameters of the mode are time-dependent. The method used is called the method of characteristics.     

Multistage Models of Carcinogenesis: An Approximation for the Size and Number Distribution of Late-Stage Clones

Multistage models have become the basic paradigm for modeling carcinogenesis. One model, the two-stage model of carcinogenesis, is now routinely used in the analysis of cancer risks from exposure to environmental chemicals. In its most general form, this model has two states, an initiated state and a neoplastic state, which allow for growth of cells via a simple linear birth-death process. In all analyses done with this model, researchers have assumed that tumor incidence is equivalent to the formation of a single neoplastic cell and the growth kinetics in the neoplastic state have been ignored. Some researchers have discussed the impact of this assumption on their analyses, but no formal methods were available for a more rigorous application of the birth-death process. In this paper, an approximation is introduced which allows for the application of growth kinetics in the neoplastic state. The adequacy of the approximation against simulated data is evaluated and methods are developed for implementing the approximation using data on the number and size of neoplastic clones.     

The Exact Formula for Tumor Incidence in the Two-Stage Model

An exact formula for the tumor incidence rate in the usual two-stage model of carcinogenesis is presented. This formula is simple and easily implemented on calculators and computers.     

Stochastic Analysis of Intermediate Lesions in Carcinogenesis Experiments

In many animal model systems for carcinogenesis, well characterized putative premalignant lesions are observed. A much studied example is provided by the enzyme altered foci in rodent hepatocarcinogenesis experiments. In a recent paper, we proposed a method for the quantitative analysis of such premalignant lesions. The model used in that paper assumed that the mean growth of premalignant clones is exponential. However, it has been suggested that such a model is oversimplified. In this paper, we relax the assumption of exponential mean growth. The new model contains one extra parameter that measures departures from exponentiality. Use of the model is illustrated by analysis of ATPase deficient foci in the liver of rats given NNM (N-nitrosomorpholine) in their drinking water. The analysis suggests that the clonal growth of altered cells is significantly accelerated (superexponential) for nontoxic doses of NNM. Finally, the hazard function of the two-mutation model for carcinogenesis is briefly discussed under nonexponential (mean) growth of intermediate cells.     

Horn Clause Computation with DNA Molecules

In this paper, we will propose Horn clause computation as an underlying computational framework of DNA computer. Horn clause program is a subclass of the formulas of first order logic and has close relation to PROLOG language. The computational power of Horn clauses was discussed in (Tärnland, 1977) and it was shown that a finite set of Horn clauses is computationally equivalent to Turing Machine. Furthermore, it should be noted that Horn programs are adequate for representing nondeterministic computation. Thus, its parallel implementation with huge number of molecules might have possibility to overcome the computational power of conventional computers. It should also be noted that the clear logical semantics of Horn programs might enable us to accept it as a higher-level programming language of DNA computer. The aim of this paper is to propose an experimental method for implementing deduction with a subclass of Horn programs, called simple Horn programs. The computational power of this model is theoretically investigated and demonstrated with some applications to NP-complete problems.     

ON PREDICTING COMPUTATIONAL TIME OF A BRANCH AND BOUND ALGORITHM FOR THE ASSIGNMENT OF FACILITIES

Experience with branch and bound algorithms indicates that computational time is a function of not only the size of the problem, but also the nature of the input data. This paper formulates statistically-based variables which describe certain characteristics of the input data and experimentally evaluates their ability to predict computational time for one branch and bound algorithm, the relative location of facilities or “plant layout” problem. Results suggest that the described experimental procedure may be useful for an a priori assessment of the computational difficulty of specific branch and bound problems.     

Piecewise linear approximations for the static–dynamic uncertainty strategy in stochastic lot-sizing

In this paper, we develop a unified mixed integer linear modelling approach to compute near-optimal policy parameters for the non-stationary stochastic lot sizing problem under static–dynamic uncertainty strategy. The proposed approach applies to settings in which unmet demand is backordered or lost; and it can accommodate variants of the problem for which the quality of service is captured by means of backorder penalty costs, non-stockout probabilities, or fill rate constraints. This approach has a number of advantages with respect to existing methods in the literature: it enables seamless modelling of different variants of the stochastic lot sizing problem, some of which have been previously tackled via ad hoc solution methods and some others that have not yet been addressed in the literature; and it produces an accurate estimation of the expected total cost, expressed in terms of upper and lower bounds based on piecewise linearisation of the first order loss function. We illustrate the effectiveness and flexibility of the proposed approach by means of a computational study.