The Mathematics of Homeland Security
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May 31 and June 1, 2007 Getting early warning of the outbreak of a disease or a biological attack - Donna Schneider Slides:
Mathematical Prerequisites Knowledge of functions and graphs of functions and familiarity with some basic ideas in descriptive and inferential statistics. Supplementary Information
Statistical Approaches to Authorship Attribution - David Madigan Slides: Statistical Approaches to Authorship Attribution Mathematical Prerequisites To understand Bayes Rule you would need to do the chapter on Probability Theory in any Elementary Statistics textbook. The chapter usually starts with the definition of probability in terms of sets, so some basic set theory notation is essential. Then we do the rules of probability like the sum rule. Following that is conditional probability and then comes Bayes Rule. You also need to have an understanding of random variables and in particular discrete random variables. You could do this from the purely probabilistic perspective, but to really understand this you should know some statistics - basic terminology, representing data by bar graphs and histograms, measures of central tendency, measures of dispersion, and a good understanding of "randomness." The above material forms the bulk of descriptive statistics (excluding correlation and least-squares regression) in a college freshman level statistics course or an AP Stats course and usually gets done half way through the semester (or year). Naive Bayes teachnique simply means we assume the events are independent. Besides authorship attribution, Naive Bayes techniques are also used in, for example, medical expert systems including systems that produce differential diagnoses based on a list of symptoms. A differential diagnosis is a list of the diseases that could possibly cause a patient's symptoms, arranged in decreasing order by probability. For example, for a patient with a runny nose and sore throat, common cold would be at or near the top of the list. Supplementary Information
Inspecting containers at ports - Fred Roberts Slides: Algorithms for Port of Entry Inspection for WMDs Graph Theoretical Problems arising from defending against bioterrorism and controlling the spread of fires - Fred Roberts Locating Sensors to detect chemical, biological, or nuclear threats - Fred Roberts Slides: Locating Sensors to Detect Chem, Bio, or Nuclear Threats Mathematical Prerequisites The first half of the lectures require familiarity with elementary rules of counting including the product rule, the sum rule, permutations and combinations, bit strings, boolean functions and graph theory concepts including paths, trees, and binary rooted trees. The second half of the lectures need more advanced topics such as cost functions, sensitivity analysis including the Stroud-Saeger method, network theory, theory of algorithms, and location theory. Supplementary Information
Relationship Discovery in Large Text Collections Using Latent Semantic Indexing - Bill Pottenger Slides:
Mathematical Prerequisites Latent semantic indexing is based on a matrix factoring method called singular value decomposition (SVD). This topic is usually covered toward the end of a college-level sophomore linear algebra course. To understand this factoring technique you must first know LU factoring and the computational edge it has over Gaussian Elimination. These topics fall under the broad area of numerical linear algebra. So it would not be unusual to cover them in a college-level junior or senior numerical analysis course. Supplementary Information
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