Scope: Math, algorithms, and CS Theory references and links. Interested in the approaches of Lipton/Regan and Tao research on the internet, specifically, of establishing publication outlets through blogs. PBC has a different longer term goal than Tao’s polymath blog, I suspect. PBC is looking to establish and demonstrate expertise in a very specific portion of applied quantitative financial modeling that underlies the U.S. Retail Banking system, Think of it like Garabedian doing supersonic flow past a wing back in the day at Courant. At some point according to both Dave Korn and Tony Jamison, Garabedian cornered the market in numerical supersonic flow simulations. I suspect the math needed here is somewhat pedestrian. The simulation is not quite so pedestrian – we are looking for a 5 year daily security-by-security Monte Carlo simulation of all the US bank balance sheets ex-secondary trading. We want a model for dynamic optimization of the banks’ capital plans v.v. the accrual portfolio w. partial or incomplete information. For rank speculation it looks like there is at least 10 basis points up for grabs for banks carrying multiple trillion USD assets. There are several other personal mathematical interests that I will track here, as well.
People: Lipton, Tao, Woit, Baez, Gelman, Aaronson, Jordan Ellenberg, Nick Higham, Shewchuck, Sedgewick, Knuth, Peter Hellekalek, Trefethen, …
Organizations: Chebfun arxiv.org mathworld Computational Complexity The polymath blog Notices of the AMS Cambridge Numerical Analysis, Quanta Magazine, …
Open Problems:
- How does Dynamic Programming work with NIMo?
- What, including tradeoffs, is the best practical form of numerical optimization for NIMo?
- Application of Consensus MC to NIMo
Bib Stack:
Bibliography v0.0:
Bellman, R. (2003). Dynamic Programming. Dover Publications, Inc.
Drmota, M. (2017). Quasi-Monte Carlo Methods: Theory and Applications. Retrieved from http://www.sfb-qmc.jku.at/leaders/
Gelman, A., & et.al. (2013). Bayesian Data Analysis (Third ed.). CRC Press.
Hellekalek, P. (2017). pLab. Retrieved from Arithmetic Primitives: http://random.mat.sbg.ac.at
Holmes, M. (2009). Introduction to the Foundations of Applied Mathematics. Springer.
Knuth, D. Semi Numerical Algorithms. Addison Wesley.
Lehman, E., Leighton, F. T., & Meyer, A. R. (2015). Mathematics for Computer Science. https://people.csail.mit.edu/meyer/mcs.pdf.
Mittelmann, H. D. (2017). Decision Tree for Optimization Software. Retrieved from http://plato.asu.edu/guide.html
Niederreiter, H. (1992). Random Number Generation and Quasi-Monte Carlo Methods. Philadelphia: SIAM.
Scott, e. (2013). Bayes and Big Data: The Consensus Monte Carlo Algorithm. Retrieved from http://www.rob-mcculloch.org/some_papers_and_talks/papers/working/consensus-mc.pdf
Sedgewick, R. Algorithms. Addison Wesley.
Sipser, M. (2012). Introduction to the Theory of Computation (Third ed.). Cengage Learning.
Wigderson, A. (2017, Oct.). Mathematic and Computation. Retrieved from https://www.math.ias.edu: https://www.math.ias.edu/files/mathandcomp.pdf#page=1
Pink Iguana 