Prev: Divergent integration result
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From: Bruce Colletti on 15 Jun 2010 02:30
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.



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