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12:00pm - Zoom - Probability and Analysis Webinar Marcin Bownik - (University of Oregon) TBA |
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2:00pm to 3:00pm - 440R - Mathematical Physics Michael Campbell - (Eureka) An Elementary Humanomics Approach to Boundedly Rational Quadratic Models
We take a refreshing new look at boundedly rational quadratic models in economics using some elementary modeling of the principles put forward in the book Humanomics by Vernon L. Smith and Bart J. Wilson. A simple model is introduced built on the fundamental Humanomics principles of gratitude/resentment felt and the corresponding action responses of reward /punishment in the form of higher/lower payoff transfers. There are two timescales: one for strictly self-interested action, as in economic equilibrium, and another governed by feelings of gratitude/resentment. One of three timescale scenarios is investigated: one where gratitude /resentment changes much more slowly than economic equilibrium (“quenched model”). Another model, in which economic equilibrium occurs over a much slower time than gratitude /resentment evolution (“annealed” model) is set up, but not investigated. The quenched model with homogeneous interactions turns out to be a non-frustrated spin-glass model. For this particular model, the Nash equilibrium has no predictive power of Humanomics properties since the rewards are the same for self-interested behavior, resentful behavior, and gratitude behavior. Accordingly, we see that the boundedly rational Gibbs equilibrium does indeed lead to richer properties. |
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4:00pm to 5:00pm - Zoom - https://uci.zoom.us/j/97796361534 - Applied and Computational Mathematics Bangti Jin - (University College London) Conductivity imaging from current density magnitude using neural networks Conductivity imaging represents one of the most important tasks in medical imaging. In this talk we discuss a neural network-based technique for imaging the conductivity from the magnitude of the internal current density. It is achieved by formulating the problem as the relaxed weighted least-gradient problem, and then approximating the minimizer by standard feedforward neural networks. We derive bounds on two components of the generalization error, i.e., approximation error and statistical error, explicitly in terms of properties of the neural networks (i.e., depth, total number of parameters, and the bound of the network parameters). We illustrate the performance and distinct features of the proposed approach on several numerical experiments. |
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1:00pm to 2:00pm - Zoom - Dynamical Systems Grisha Monakov - (UC Irvine) Shadowing in dynamical systems We say that a dynamical system satisfies shadowing property if for any pseudotrajectory there exists an exact trajectory that is pointwise close to it. This property was introduced by Anosov in 1970th and plays an important role in the theory of dynamical systems. Shadowing property is known to have strong connections with hyperbolicity and structural stability. In this talk I will give an overview of classical results in shadowing theory and will present a new proof of Anosov shadowing lemma. |
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4:00pm - NS2 1201 - Differential Geometry Kai-Wei Zhao - (UC Irvine) On blowup of regularized solutions to Jang equation and constant expansion surfaces Schoen-Yau proved the spacetime positive energy theorem by reducing |