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542EDUCATIONFORUM I n 2003, the National Research Council's BIO2010 report recommended aggressive curriculum restructuring to educate the "quantitative biologists" of the future ( 1). The number of undergraduate and graduate programs in mathematical and computational biology has since increased, and some institutions have added courses in mathematical biology related to biomedical research ( 2, 3). The National Science Foundation (NSF) and the National Institutes of Health are funding development workshops and discussion forums for faculty ( 4, 5), research-related experiences ( 6, 7), and specialized research conferences in mathematical biology for students ( 8, 9).This new generation of biologists will routinely use mathematical models and computational approaches to frame hypotheses, design experiments, and analyze results. To accomplish this, a toolbox of diverse mathematical approaches will be needed.Nowhere is this trend more evident than in systems biology. At the molecular level, this involves understanding a complex network of interacting molecular species that incorporates gene regulation, protein-protein interactions, and metabolism. Two types of models have been used successfully to organize insights of molecular biology and to capture network structure and dynamics: (i) discreteand continuous-time models built from difference equations or differential equations (DE) models, which focus on the kinetics of biochemical reactions; and (ii) discretetime algebraic models built from functions of fi nite-state variables (in particular Boolean networks), which focus on the logic of the network variables' interconnections. Algebraic models were introduced in 1969 to study dynamic properties of gene regulatory networks ( 10). They have proven useful in cases where network dynamics are determined by the logic of interactions rather than fi nely tuned kinetics, which often are not known. Published algebraic models include the metabolic network in Escherichia coli ( 11) and the abscisic acid signaling pathway ( 12).The use of algebraic methods is extending beyond systems biology. Methods from algebraic geometry have been used in evolutionary biology to develop new approaches to sequence alignment ( 13), and new modeling of viral capsid assembly has been developed using geometric constraint theory ( 14). Algorithms based on algebraic combinatorics have been used to study RNA secondary structures ( 15).Training in developing algebraic models is often overlooked but can be valuable to biologists and mathematicians. ) M E L G e L e DE and Boolean models of the lac operon mechanism. Each component of the shaded part of the wiring diagram is a variable in the model, and the compartments outside of the shaded region are parameters. Directed links represent infl uences between the variables: A positive infl uence is indicated by an arrow; a negative infl uence is depicted by a circle.tional ideas (hierarchical clustering, pattern classification, and feature selection) are introduced as part of the "story" to promote ease ...

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Manifestations of ADHD are observed at both psychological and physiological levels and assessed via various psychometric, EEG, and imaging tests. However, no test is 100% accurate in its assessment of ADHD. This study introduces a stochastic assessment combining psychometric tests with previously reported (Consistency Index) and newly developed (Alpha Blockade Index) EEG-based physiological markers of ADHD. The assessment utilizes classical Bayesian inference to refine after each step the probability of ADHD of each individual. In a pilot study involving six college females with ADHD and six matched controls, the assessment achieved correct classification for all ADHD and non-ADHD participants. In comparison, the classification of ADHD versus non-ADHD participants was < 85% for any one of the tests separately. The procedure significantly improved the score separation between ADHD versus non-ADHD groups. The final average probabilities for ADHD were 76% for the ADHD group and 8% for the control group. These probabilities correlated (r = .87) with the Brown ADD scale and (r = .84) with the ADHD-Symptom Inventory used for the screening of the participants. We conclude that, although each separate test was not completely accurate, a combination of several tests classified correctly all ADHD and all non-ADHD participants. The application of the proposed assessment is not limited to the specific tests used in this study--the assessment represents a general paradigm capable of accommodating a variety of ADHD tests into a single diagnostic assessment.