The second meeting of the seminar is, as usual, in **Grainger Library**, *room 335*.

*Steven Levinson*, ECE, talks on A Geometric Interpretation and Proof of Baum's Algorithm for Estimation of the Parameters of a Probabilistic Function of a Markov Process,

There are two standard proofs of this result, one based on the convexity of and another based on Hölder’s inequality. These proofs are long and rather opaque giving little insight into the remarkable properties of . We give a new, short, and intuitively appealing geometric interpretation and proof of Baum’s algorithm. This proof begins by noticing that has the form of a homogeneous polynomial in with positive coefficients and restricts to lie on a manifold defined as that part of the hyperplane bounded by the first orthant of the space . From these observations it follows that the line segment from to has a positive projection on the gradient of everywhere on the the segment. Thus is, as Baum shows, a growth transformation.

*Nikolaos Tzirakis*, Math, reporting on Talbot effect for a nonlinear Schrödinger equation on the torus.

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