UIUC Dept. of Mathematics Seminar Calendar

    September 2009          October 2009          November 2009    
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Thursday, October 8, 2009

Mathematical Biology Seminar
1:00 pm in 345 Altgeld Hall, Thursday, October 8, 2009

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Submitted by zrapti.

Tsvi Achler (Department of Computer Science, University of Illinois at Urbana-Champaign)
Using Non-Oscillatory Dynamics to Disambiguate Simultaneous Patterns
Abstract: How does the brain contend with simultaneous patterns? Training methods required for machine learning and neural network algorithms are not optimal for simultaneous patterns. I introduce a nonlinear classifier method motivated by a feedback-inhibition/negative-feedback configuration. Indirect evidence for neuron-circuits and structures that support this configuration are found ubiquitously in brain regions responsible for sensory processing. With a focus on simultaneous pattern processing, the performance of machine learning, neural network and feedback inhibition algorithms are compared. Feedback inhibition networks are robust, inherently process mixtures of previously learned patterns, and predict several cognitive phenomena.

Number Theory Seminar
1:00 pm in 241 Altgeld Hall, Thursday, October 8, 2009

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Submitted by jarouse.

Bruce Berndt (UIUC Math)
Ramanujan's Lost Notebook
Abstract: In the spring of 1976, while searching through papers of the late G. N. Watson at Trinity College, Cambridge, George Andrews found a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan, generally regarded as India's greatest mathematician. In view of the fame of Ramanujan's earlier notebooks, Andrews naturally called these papers Ramanujan's "lost notebook." This work, comprising about 650 results with no proofs, arises from the last year of Ramanujan's life and represents some of his deepest work. First, we provide a history of the lost notebook. Second, a general description of the topics found in the lost notebook will be provided. For some of the topics, such as ranks and cranks of partitions, we offer some details. The third portion of the lecture will be devoted to a more detailed discussion of one of the topics prominently addressed in the lost notebook, namely continued fractions.