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Washington DC Area Mathematica Special Interest Group
Mathematica SIG (http://web.me.com/hrbishop.pmsi) MEETING 18 June 2010, 7:30 am Science Applications International Corporation (SAIC) 8301 Greensboro Drive McLean VA Southern Corner of Westpark Drive and Greensboro Drive Agenda 1. Prepared Talks "Find the probability that the discriminant will be negative and produce imaginary roots", by Harry Bishop ABSTRACT. I use Mathematica to set up the problem statement/conditions and to graph domain variables. Next, solve the problem by integrating the joint pdf over the domain variables. I will then demonstrate integrating over regions. A numerical solution will also be provided using Mathematica and a comparative LISP program (both converge slowly). "Using Mathematica to conduct analyses of multi-sourced data and timed events between competing risks", by Harry Bishop ABSTRACT. An in-depth data analysis was conducted using Mathematica which required retrieving data, merging, and building a high quality history into a statistical database. Many data sources were merged using database and text based information. Data from these sources were brought together with consistency as the measure of quality. Time-based events were assimilated to produce an analysis of competing risks. A Bayesian analysis of the competing risk factors was then conducted with Mathematica as the primary tool. "Application of Mathematica to the card game 'Set' ", by Dave Vasholz ABSTRACT. Recently I was introduced to a card game which is known as "Set" (see Wikipedia). It was extremely fortunate for me that we were not playing for money. To compensate for my slowness in understanding what the heck was going on, I am using Mathematica to gain a better understanding of the game. The results of various forays into this endeavor will be presented. "History of the Washington DC-Area Mathematica Special Interest Group", by Dan Martinez ABSTRACT. This brief talk graphically depicts the history of our small but mighty SIG. "Visualization Tools for Benefit:Risk Assessment", by Richard Forshee (if not present, then Dr. Anne Fernando, Mathematics Department, Norfolk State University) ABSTRACT. Regulating medical products, such as drugs, biologics, and devices, is a complex and challenging enterprise. All medical products have their own unique benefit and risk profiles, and our understanding of the true benefits and risks of a product are known only with uncertainty because of limited data and the limitations of our scientific knowledge. Visualization tools can help decision-makers better understand the total body of scientific knowledge relating to a medical product as well as the amount of uncertainty that remains. We present two visualization tools developed in Mathematica that illustrate important concepts in benefit and risk analysis. First, we present an interactive graph that explores the tradeoff between expected losses from a risk and the costs of abatement and how that tradeoff is affected by the inclusion of estimates of uncertainty about the expected losses and the costs of abatement. A theoretical curve to represent abatement costs is the reciprocal curve where AC=K1/(x-K2)+K3 with values of x positive and K1, K2, K3 chosen so that y values are positive. For this same range of risk, represented by the independent variable x, we can model the expected cost of losses. The total cost is TC = AC + EL. This function will have a global minimum which can be found using simple calculus as any continuous (differentiable) function on a closed interval has to have a maximum and minimum either at the end points of the interval or at some interior point. Uncertainty about the true expected losses and abatement costs are introduced by adding stochastic terms to the loss and cost functions. Second, we will demonstrate a three-dimensional visualization tool where the height of the surface represents the probability that the treatment has a particular risk-benefit coordinate pair. For this presentation we will use simulated data representing the evolving scientific knowledge about the benefits and risks of a scientific product as new studies are conducted. For this demonstration, we have a bivariate normal Gaussian whose parameters-mean for risk, mean for benefit, standard error for risk, standard error for benefit, covariance-are gathered from (perhaps incomplete) data sets and with these 'base' parameters, our simulation model incorporates incoming periodic (annual) data into these parameters so that the model is updated and the user (stake holder) can assess what this new data does for the issues of risk and benefit. "Estimating Probability of Real Roots For A Quadratic Equation", by Mel Friedman ABSTRACT. The probability of real and imaginary roots is calculated using both simulation and probability theory when the coefficients of a quadratic equation are drawn from uniform, exponential and normal distributions. The results of the simulations agree with probability theory. When the coefficients are normally distributed, Kac's formula is compared with the simulation and analytical calculations. Note: This talk adds to that of Harry Bishop (above) by discussing diverse distributions and offering other insights. "Hold those Inputs!", by Bruce Colletti ABSTRACT. This brief talk presents a solution (by Paritosh Mokhasi, Wolfram Technical Support) to a problem that had stumped me: convert a list of "input expressions" into a list of strings. This simple solution clarifies the roles of HoldAll and Unevaluated. 2. Mathematica Gems and Discoveries Sharing of Mathematica programming oddities Applications of Mathematica to some areas of science Something recently read and worth sharing 3. Mathematica Questions, Possible Approaches and Discussion 4. New Business Select next meeting presentation, time and place Directions to 8301 Greensboro Drive, McLean VA (tall, boxy and white SAIC Enterprise Building at south corner of Westpark Drive and Greensboro Drive): >From the Beltway, go northwest on Route 7 (Leesburg Pike) and proceed past Route 123 (Chain Bridge Road). Turn right onto Westpark Drive (Gosnell oad in the other direction). Turn right at the next light onto Greensboro Drive and then right into the parking lot. Visitor's Parking is adjacent to Westpark Drive. A SIG representative will meet you in the lobby. Please arrive no later than 6:50AM if you wish to join us for a dutch-treat breakfast, and no later than 7:20AM to attend the meeting only. The desk officer will ask for a driver's license before issuing a visitor's badge.