Why mathematical models?

Attempts to convey to undergraduate students of psychology some feeling for the processes involved in formulating and testing quantitative theories of behavior. The role of mathematics in psychology is discussed, the advantages of phrasing psychological notions in quantitative terms are outlined, and 2 simple examples of mathematical models are examined. The question of why undergraduates might want to find out something about mathematical and computer models is also considered. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

现代化高炉数学模型

高炉数学模型具有多变量，估计和预报等特点，介绍了当前实用化的几种典型的数学模型，最后提出了建立高炉群控群管和经济模型的初步设想。     

Occupation and the risk of lung cancer in Uruguay

OBJECTIVES: The purpose of this study was to provide more information regarding the risk of lung cancer associated with asbestos, and other exposures in the Uruguayan work force. METHODS: This multisite case-referent study was part of a large project designed for evaluating the role of occupational exposures in cancer risk in Uruguay. According to the design employed, cases were a subset of the data base corresponding to a particular site (in this instance lung cancer), and they were compared with all other sites combined (referents). RESULTS: Significant increases in risk associated with workers in the construction industry were mainly observed for squamous-cell carcinoma. Asbestos, silica dust, and DDT (dichlorodiphenyltrichloroethane) exposure were also associated with increases in the risk of lung cancer. Pipefitters, bakers, and textile workers were also at increased risk of developing lung cancer. CONCLUSIONS: Workers employed in the construction industry, as well as those exposed to DDT may have an excess risk of lung cancer. These findings are particularly important in showing that developing countries like Uruguay display risk patterns of similar magnitude as those observed in developed communities.     

Avian exposure and risk of lung cancer in women in Missouri: population based case-control study

OBJECTIVE: To investigate the association, previously reported in three European studies, between ownership of pet birds and the risk of lung cancer. DESIGN: A population based case-control study with a structured questionnaire administered by telephone. SETTING: Missouri, a midwestern state in the United States with a population of about 5 million. SUBJECTS: All newly diagnosed cases of primary lung cancer in women aged 30-84 years in Missouri from 1 January 1993 to 31 January 1994 reported to the state cancer registry were invited to participate (n = 652); and 629 population based controls. MAIN OUTCOME MEASURES: Odds ratios were computed in relation to whether or not the study subject ever kept pet birds, the type of bird kept, and several measures of intensity or duration of exposure. Odds ratios were adjusted for smoking. RESULTS: The odds ratio (95% confidence interval) for the development of lung cancer associated with keeping pet birds was 0.84 (0.65 to 1.09). The results were similar for the type of pet bird kept, the number of birds kept, the location of the bird in the house, and the duration of ownership. CONCLUSION: The keeping of pet birds carries no excess risk for the development of lung cancer.     

Dietary factors and risk of lung cancer in never-smokers

The primary purpose of this study was to evaluate the effectiveness of cortical anchorage, by comparing two groups of patients with Class II malocclusions that were treated successfully with Class II elastics. One group of 30 previously treated patients had a utility arch used to set up cortical anchorage in the lower arch before Class II elastic wear; the second group was treated with standard edgewise mechanics where anchorage preparation consisted of full appliances, a well-aligned mandibular arch, and a rectangular arch wire. The groups were selected according to age, sex, and the amount of Class II elastic usage. Pretreatment and posttreatment cephalometric radiographs were used to generate 32 variables. A Student's t test was used to evaluate treatment change between the groups and revealed that there were no statistically significant differences. Lower molar teeth extruded and moved mesially equally in both groups. Although cortical anchorage did not retard lower molar movement, it was no less effective in controlling molar movement with a partial appliance than the fully banded standard edgewise appliance.     

Crystalline silica and risk of lung cancer in the potteries

OBJECTIVE: To evaluate crystalline silica as a human carcinogen. METHODS: A cohort of 5115 men, born 1916-45 and employed in the pottery, refractory, and sandstone industries of Stoke-on-Trent was identified from occupations subject to health surveillance by the local Silicosis Medical Board (now the Department of Social Security). Detailed occupational and smoking histories, and records of small parenchymal opacities on periodic radiographs were extracted from medical records. An exposure matrix was derived from some 1400 personal or static dust samples and tested against the presence of small parenchymal opacities in a subcohort of 1080 men employed for at least 10 years, who had started working in the industry before 1960. RESULTS: Standardised mortality ratios (SMRs) calculated against mortalities for Stoke-on-Trent, with 95% confidence intervals (95% CIs), were raised for all causes (1.15 (1.05 to 1.26)), lung cancer (1.28 (0.99 to 1.62)) and non-malignant respiratory disease (2.04 (1.55 to 2.65)). Average concentration and duration of exposure to silica were, taken together, significantly related to the presence of small opacities (> or = 1/0). In a nested case-referent analysis of 52 cases of lung cancer and 197 matched referents, conditional logistic regression gave a significantly increased odds ratio (OR) for average silica concentration (micrograms/m3.100), after adjustment for smoking, of 1.66 (1.14 to 2.41) but not for duration of exposure nor, in consequence, for cumulative exposure. CONCLUSION: The association between risk of lung cancer and quantitative estimates of silica exposure supports the SMR analysis and implies that crystalline silica may well be a human carcinogen.     

Simple mathematical models with very complicated dynamics

First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hiearchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them.     

Family history of cancer and risk of lung cancer in lifetime non-smokers and long-term ex-smokers

Primary hepatocyte cultures prepared from male beagle dog liver were used to determine susceptibility of the canine liver to tetracycline-induced steatosis. The effects of the drug on mitochondrial lipid metabolism and intracellular triglyceride accumulation were monitored at the same time that steatosis was detected by light microscopy and quantitated using lipid-specific stains. Exposure of primary canine hepatocyte cultures to tetracycline for 24-48 h resulted in concentration-dependent, significant increases in the Oil Red O-stained lipid inclusions. Microscopic examination of the total stained areas suggested that increases over control levels were due primarily to the increase in the size of the lipid inclusions rather than in the number. Biochemical analyses for triglyceride content and histological staining with Nile red, another neutral lipid-specific dye, confirmed a specific increase in intracellular triglyceride following a 24-h exposure to noncytotoxic levels of tetracycline beta-oxidation studies based on the oxidation of [14C]palmitic acid or [14C]palmitoyl carnitine demonstrated a concentration-dependent inhibition of mitochondrial but not peroxisomal beta-oxidation in hepatocytes after a 24-h exposure to tetracycline. In vitro incubation of tetracycline with mitochondria isolated from dog liver showed similar concentration-dependent inhibition. This study clearly indicates that the canine hepatocyte is susceptible to tetracycline-induced steatosis. Triglyceride accumulation was concomitant with the inhibition of mitochondrial lipid metabolism, indicating that this is a primary mechanism leading to steatosis in dog hepatocytes following tetracycline exposure.     

Spatio-temporal models with errors in covariates: mapping Ohio lung cancer mortality

In estimating spatial disease patterns, as well as in related assessments of environmental equity, regional morbidity and mortality rate maps are widely used. Hierarchical Bayes methods are increasingly popular tools for creating such maps, since they permit smoothing of the fitted rates toward spatially local mean values, with more unreliable estimates (those arising in low-population regions) receiving more smoothing. In this paper we blend methods for spatial-temporal mapping with those for handling errors in covariates in a single hierarchical model framework. Estimated posterior distributions for the resulting highly-parameterized models are obtained via Markov chain Monte Carlo (MCMC) methods, which also play a key role in our approach to model evaluation and selection. We apply our approach to a data set of county-specific lung cancer rates in the state of Ohio during the period 1968-1988. Our model uses age-adjusted death rates, and incorporates recent information regarding smoking prevalence, population density, and the socio-economic status of the counties. This information is critical to understanding the role played by a certain depleted uranium fuel processing facility on the elevated lung cancer rates in the counties that neighbour it.     

Is low selenium status a risk factor for lung cancer?

The hypothesis that low selenium may in some circumstances be a risk factor for lung cancer was investigated in a case-control study nested within a longitudinal study. Serum samples from 9,101 cancer-free individuals were collected and stored at -20 degrees C by the Finnish Mobile Clinic in 1968-1971 and 1973-1976. During follow-up until the end of 1991, 95 cases of lung cancer were diagnosed. Selenium concentrations were determined from the serum samples of the cases and 190 controls, individually matched for sex, age, and place of residence. Mean levels of serum selenium in cases and controls were 53.2 microg/liter and 57.8 microg/liter, respectively. The relative risk of lung cancer between the highest and lowest tertiles of serum selenium, adjusted for smoking, serum alpha-tocopherol, serum cholesterol, serum copper, serum orosomucoid, and body mass index (kg/m2), was 0.41 (95% confidence interval (CI) 0.17-0.94). The association was stronger at lower levels (<5.9 mg/liter) of alpha-tocopherol (relative risk=0.24, 95% CI 0.07-0.85). The association was also pronounced among current smokers and at higher levels of serum orosomucoid and serum copper. The relative risk for smokers who were twice ranked in higher selenium tertiles, at an interval of 4-7 years, in comparison with smokers who remained in the lowest tertile was 0.16 (95% CI 0.04-0.74). In accordance with the hypothesis, the findings suggest that very low selenium status may contribute to the risk of lung cancer.     

Antitumor activity of S 16020-2 in two orthotopic models of lung cancer

S 16020-2, a new olivacine derivative selected on the basis of its cytotoxicity in vitro and antitumor activity in vivo, was evaluated against the human A549 and the murine Lewis lung tumor models implanted s.c. and i.v. Against Lewis lung carcinoma implanted s.c., S 16020-2 was found to be curative, with an activity and therapeutic index (Ti = 4) similar to that of cyclophosphamide. S 16020-2 administered weekly demonstrated a high therapeutic efficacy against A549 non-small cell lung carcinoma implanted s.c. in nude mice and induced tumor regression at 80 mg/kg. When A549 tumor cells were injected i.v. in SCID mice, experimental metastases rapidly developed and the progressive invasion of the lung tissue by tumor preceded the death of animals. In this model, S 16020-2 administered at 40 mg/kg i.v. following an early (days 8, 18 and 28) or delayed (days 20, 30 and 40) treatment schedule prolonged the survival of tumor-bearing mice with T/C values of 150 and 145%, respectively. Against the i.v. Lewis lung carcinoma, S 16020-2 was also highly active since when administered at 60 mg/kg on days 5, 9 and 13 it totally inhibited tumor growth and cured up to 89% of mice. When administered on days 11, 15 and 19 to animals with established tumors, S 16020-2 was still active but not curative. In the presented studies, S 16020-2 antitumor activity was superior to that of adriamycin and comparable or superior to cyclophosphamide (used as reference compounds). Our results demonstrate the efficacy of S 16020-2 against these highly aggressive and chemoresistant tumor models.     

Reviving traditional blast furnace models with new mathematical approach

Abstract

This paper describes how traditional analytical blast furnace (BF) models can be revived by the inclusion of new mathematical tools. Combining some fundamental models with new mathematical algorithms can create efficient and simple to use hybrid models. A hybrid model based on artificial neural network (ANN) and its industrial application to the new BF No. 3 at Companhia Siderúrgica Nacional (CSN, Volta Redonda, Brazil) was developed, tested and put in use. In BF operation, which is a multivariable complex process subject to oscillations in raw material characteristics, a precise model is essential to adjust charging and blow conditions to match productivity, chemical quality and target costs. A neural model was developed in order to estimate chemical and thermal parameters to feed a first principles model capable of evaluating alternative operation standards. As a consequence, operation efficiency is being enhanced, leading to higher productivity and lower costs.     

铁碳合金凝固过程微观溶质偏析模型分析

为了选择正确的微观溶质偏析模型研究铁碳合金的凝固过程,利用Thermo-Calc商业软件计算了不同碳含量下铁碳合金的固相线温度、液相线温度和碳的平衡分配系数,利用数值方法研究了不同微观溶质偏析模型下铁碳合金的固液界面温度和无量纲液相溶质浓度.数值结果表明:文献中常用的碳平衡分配系数不准确;C lyne-Kurz模型和Sche il模型不能准确地预测固液界面温度,B rody-F lem ings模型不能正确地预测碳偏析,建议采用杠杆模型和大中逸雄模型计算铁碳合金凝固过程的微观溶质偏析.     

Simplified mathematical models of heat transfer in continuous fuel-fired furnaces

Introduction of the model based on the equations of radiative and convective heat transfer connected with equation of heat conduction in stock. Walking beam, roller-hearth and pusher furnaces. Radiative transport coefficients, mean beam lengths and configuration factors computation. Examples of furnace calculation. Use of the generalized temperature response charts.     

An introduction to the use of physiologically based pharmacokinetic models in risk assessment

Many extrapolation issues surface in quantitative risk assessments. The extrapolation from high-dose animal studies to low-dose human exposures is of particular concern. Physiologically based pharmacokinetic (PBPK) models are often proposed as tools to mitigate the problems of extrapolation. These models provide a representation of the disposition, metabolism, and excretion of xenobiotics that are believed to possess the potential of inducing adverse human health responses. Given a model of xenobiotic disposition that is applicable for multiple species and appropriate for nonlinearity of the xenobiotic biotransformation process, better extrapolation may be possible. Unfortunately, the true structure of these models (e.g. number of compartments, type of metabolism, etc.) is seldom known, and attributes of these models (tissue volumes, partition coefficients, etc.) are often experimentally determined and often only central measures of these quantities are reported. We describe the use of PBPK models in risk assessment, the structural and parameter uncertainty in these models, and provide a simple illustration of how these characteristics can be incorporated in a statistical analysis of PBPK models. Additional complexity in the analysis of variability in the models is also outlined. This discussion is illustrated using data from methylene chloride.