Extending the Stochastic Two-Stage Model of Carcinogenesis to Include Self-Regulation of the Nonmalignant Cell Population

One of the challenges of introducing greater biological realism into stochastic models of cancer induction is to find a way to represent the homeostatic control of the normal cell population over its own size without complicating the analysis too much to obtain useful results. Current two-stage models of carcinogenesis typically ignore homeostatic control. Instead, a deterministic growth path is specified for the population of "normal" cells, while the population of "initiated" cells is assumed to grow randomly according to a birth-death process with random immigrations from the normal population. This paper introduces a simple model of homeostatically controlled cell division for mature tissues, in which the size of the nonmalignant population remains essentially constant over time. Growth of the nonmalignant cell population (normal and initiated cells) is restricted by allowing cells to divide only to fill the "openings" left by cells that die or differentiate, thus maintaining the constant size of the nonmalignant cell population. The fundamental technical insight from this model is that random walks, rather than birth-and-death processes, are the appropriate stochastic processes for describing the kinetics of the initiated cell population. Qualitative and analytic results are presented, drawn from the mathematical theories of random walks and diffusion processes, that describe the probability of spontaneous extinction and the size distribution of surviving initiated populations when the death/differentiation rates of normal and initiated cells are known. The constraint that the nonmalignant population size must remain approximately constant leads to much simpler analytic formulas and approximations, flowing directly from random walk theory, than in previous birth-death models.(ABSTRACT TRUNCATED AT 250 WORDS)     

THE TAX LITIGATION DECISION: AN ANALYSIS OF THE SMALL CLAIMS DIVISION OF THE U.S. TAX COURT*

One of the more difficult but intriguing problems in the tax field is the decision of when (and how) to settle tax disputes with the Internal Revenue Service (IRS) and when (and how) to litigate. Research in this area of decision making is limited and has concentrated on the probability of winning in the judicial system. This paper examines the tax litigation decision for suits in the Small Claims Division of the U.S. Tax Court. Four examples are presented which involve varying degrees of information regarding the likelihood of a settlement and differing risk attitudes. The maximum amount the taxpayer should be willing to spend in pursuing litigation is derived for each case.     

Purchasing management and business competitiveness in the coming decade

Changing dynamics of the marketplace require that old mind-sets of the procurement function radically shift directions. Cost-based practices of the past should be replaced by a value-added focus in today's organizational supply channel. This paper, based upon in-depth discussions with a focus group of experts, documents the upcoming challenges for purchasing professionals and defines a new role for purchasing managers. Additionally, key questions are suggested as an impetus for future research.     

DISTRIBUTIONAL CHARACTERIZATIONS THROUGH SCALING RELATIONS

Investigated here are aspects of the relation between the laws of X and Y where X is represented as a randomly scaled version of Y. In the case that the scaling has a beta law, the law of Y is expressed in terms of the law of X. Common continuous distributions are characterized using this beta scaling law, and choosing the distribution function of Y as a weighted version of the distribution function of X, where the weight is a power function. It is shown, without any restriction on the law of the scaling, but using a one‐parameter family of weights which includes the power weights, that characterizations can be expressed in terms of known results for the power weights. Characterizations in the case where the distribution function of Y is a positive power of the distribution function of X are examined in two special cases. Finally, conditions are given for existence of inverses of the length‐bias and stationary‐excess operators.     

Why Risk Is Not Variance: An Expository Note

Variance (or standard deviation) of return is widely used as a measure of risk in financial investment risk analysis applications, where mean‐variance analysis is applied to calculate efficient frontiers and undominated portfolios. Why, then, do health, safety, and environmental (HS&E) and reliability engineering risk analysts insist on defining risk more flexibly, as being determined by probabilities and consequences, rather than simply by variances? This note suggests an answer by providing a simple proof that mean‐variance decision making violates the principle that a rational decisionmaker should prefer higher to lower probabilities of receiving a fixed gain, all else being equal. Indeed, simply hypothesizing a continuous increasing indifference curve for mean‐variance combinations at the origin is enough to imply that a decisionmaker must find unacceptable some prospects that offer a positive probability of gain and zero probability of loss. Unlike some previous analyses of limitations of variance as a risk metric, this expository note uses only simple mathematics and does not require the additional framework of von Neumann Morgenstern utility theory.     

Village on the Border, anthropology at the crossroads: the significance of a classic British ethnography

Village on the Border was the seminal anthropological study of a mainland British rural community. It was written and published during a period of unsurpassed scholarship and creativity in British social science. To explain the impact it had on social anthropology, British studies and public discourse at the time, I look at the influences on Ronnie Frankenberg and his work of the then state of social anthropology; of the particular academic environment in which he was trained and worked; and of his personal background and political convictions. This analysis shows that although the book clearly bears particular historical and intellectual influences, it was explicitly set within comparative ethnographic frameworks, and in due course greatly influenced work elsewhere. Both methodologically and substantively, it should be seen as a significant contribution to the comparative study of local‐level politics, gender relations and the role of the ‘stranger’, as well as the authentic origin of modern anthropological studies of rural Britain.     

A performance measurement paradigm for integrating strategy formulation: A review of systems and frameworks

Measuring organizational performance plays a very important part in translating corporate strategy into results. Various emerging (non-traditional) performance systems have recently been devised to aid firms in selecting and implementing measures. This paper discusses the strategy/measurement initiatives and compares ten emerging performance measurement systems with respect to a list of performance dimensions, the characteristics of performance measures, and the requirements of development process. Although these systems have constraints borne with their own application domains, they stand by themselves empirically and/or theoretically, and provide guidance about what to measure and how to design performance measures that could be linked to the corporate strategy and objectives of an organization. This paper concludes that there is a need to develop a paradigm for integrating strategy formulation and performance measurement in organizations.     

How Probabilistic Risk Assessment Can Mislead Terrorism Risk Analysts

Traditional probabilistic risk assessment (PRA), of the type originally developed for engineered systems, is still proposed for terrorism risk analysis. We show that such PRA applications are unjustified in general. The capacity of terrorists to seek and use information and to actively research different attack options before deciding what to do raises unique features of terrorism risk assessment that are not adequately addressed by conventional PRA for natural and engineered systems—in part because decisions based on such PRA estimates do not adequately hedge against the different probabilities that attackers may eventually act upon. These probabilities may differ from the defender's (even if the defender's experts are thoroughly trained, well calibrated, unbiased probability assessors) because they may be conditioned on different information. We illustrate the fundamental differences between PRA and terrorism risk analysis, and suggest use of robust decision analysis for risk management when attackers may know more about some attack options than we do.