Saturday April 29th at San Jose State University

The 34th Bay Area Discrete Math Day (BAD Math Day) will take place at San Jose State on Saturday, April 29th, 2017. 


BAD Math Days are one-day meetings aimed at facilitating communication between researchers and graduate students of discrete mathematics around the San Francisco Bay Area. These days happen twice a year and strive to create an informal atmosphere to talk about discrete mathematics. The term "discrete mathematics" is chosen to include at least the following topics: Algebraic and Enumerative Combinatorics, Discrete Geometry, Graph Theory, Coding and Design Theory, Combinatorial Aspects of Computational Algebra and Geometry, Combinatorial Optimization, Probabilistic Combinatorics, Combinatorial Aspects of Statistics, and Combinatorics in Mathematical Physics.


  • Registration  
  • Speakers and Schedule  
  • Directions and Parking  
  • Carpooling  
  • Organizers and Sponsors 

  • Registration

    Registration is free.  Please register here by Friday, April 21.  


    Schedule

    All talks will take place in Boccardo Business Complex, Room 202 (campus map)

    9:00-10:00am

    Welcome and refreshments

    10:00-10:30am

    Christopher O'Neill
    UC Davis

    Title: Frobenius numbers of shifted numerical monoids


    Abstract: A numerical monoid S is a subset of the nonnegative integers that is closed under addition, and the Frobenius number F(S)  is the largest integer that lies outside of S.  In this talk, we present a structural result about "shifted" monoids S_n obtained by adding a positive integer n to each minimal generator of S. We apply our result to obtain an asymptotic description of the Frobenius numbers F(S_n), as well as several other quantities. 

    10:45-11:15am

    Vijay D'Silva
    Google

    Title: Lattice Duality and the Foundations of Program Analysis

    Abstract: Programming tools like compilers and error analyzers attempt to automatically prove properties of programs. There are three distinct approaches to performing such proofs:The deductive approach uses logic, the automata-theoretic approach reduces questions about programs to algorithmic questions about state machines, and a third approach, called abstract interpretation, uses fixed points in lattices. These three approaches have been considered fundamentally distinct. We demonstrate how the theory of lattice dualities shows that these approaches are duals in a precise sense. The duality is an algorithmic variant of Stone duality between lattices, posets and topological spaces. These duality results have practical consequences as they indicate how the approaches can be combined.

    11:30-12:30pm

    Abel Rodriguez
    UC Santa Cruz

    Title: On species sampling sequences induced by residual allocation models


    Abstract: We discuss a general class of probability distributions on exchangeable partitions of n elements induced by residual allocation (sometimes called stick-breaking) models on almost-surely discrete random measures. This class provides a generalization of the well-known Ewens sampling formula that allows for additional flexibility while retaining computational tractability. In particular, the procedure is used to derive the exchangeable predictive probability functions associated with a number of well known nonparametric Bayesian priors. In addition to describing a constructive mechanism for deriving new probability models for random partitions, we introduced simulation-based algorithms for approximate full Bayesian inference from observed data.

    12:30-2:00pm

    Lunch

    2:00-
    2:30pm

    Ohad Feldheim
    Stanford University

    Title: The power of two-choices in reducing discrepancy


    Abstract: It is a classical observation that if N points are tossed uniformly and independently on the interval [0,1], then the discrepancy of the empirical distribution, i.e., the maximum difference between the proportion of points on any interval and the length of that interval, is of order 1/sqrt{N}. Now consider a similar online process in which at every step an overseer is allowed to choose between two independent, uniformly chosen points on [0,1]. 


      -- By how much can the overseer reduce the discrepancy of the selected points?


    This question, asked by Benjamini, is motivated by applications in both harmonic analysis and statistics. It is also related to the general setting of "power of two choices", i.e. the ability to significantly reduce imbalance by allowing slight amount of choice. We answer this question by adopting a new probabilistic perspective on the power of two-choices. In particular, we show that it is possible to obtain discrepancy of O(log^3 N/N), even if at every step the overseer is oblivious to the location of one of the two points from which he is allowed choose. 


    Joint work with Ori Gurel-Gurevich

    2:45-
    3:15pm

    Dashiell Fryer
    San Jose State University

    Title: Stationary Stability for Evolutionary Dynamics in Finite Populations

    Abstract: We extend the theory of evolutionary stability to multidimensional finite populations with mutation, connecting the theory of the stationary distribution of the Moran process with the Lyapunov theory of evolutionary stability for the replicator dynamic. We show essentially that the local extrema of the stationary distribution minimize the relative entropy of the current population state and the "expected next state" computed by weighting the adjacent states by the appropriate transition probabilities. This holds for a variety of selection processes including the increasingly popular Fermi selection. We present several complete computational examples for illustration and we show that the classical stability theory of the replicator dynamic is recovered in the large population limit. If time allows, we describe extensions to populations evolving on graphs.

    3:15-
    4:00pm

    Coffee break

    4:00-
    5:00pm

    Ruriko Yoshida
    Naval Postgraduate School

    Title: Tropical Fermat-Weber points

    Abstract: We investigate the computation of Fermat-Weber points under the tropical metric, motivated by its application to the space of equidistant phylogenetic trees with N leaves realized as the tropical linear space of all ultrametrics. While the Fréchet mean with the CAT(0)-metric of Billera-Holmes-Vogtman has been studied by many authors, the Fermat-Weber point under tropical metric in tree spaces is not well understood. In this talk we investigate the Fermat-Weber points under the tropical metric and we will show that the set of tropical Fermat-Weber points is a classical convex polytope. Then, we will identify conditions under which this set is a singleton.  This is joint work with Bo Lin. 




    Directions and Parking

    Parking: The North Garage (campus map) is the closest garage to the meeting place. Parking is $5 for the entire day. 

    Public Transportation: From Davis/Berkeley/East Bay, the most straightforward option is to take Amtrak's Capitol Corridor train.  The campus is a 1.3 mile walk from the Amtrak station. 

    From SF, you can take Caltrain (although the earliest train on Saturday arrives at 9:53am).  The campus is a 1.3 mile walk from the Caltrain station.
    Another option from the East Bay/SF is to take BART to Fremont and transfer to VTA Bus 181. One-way travel time is around 2 hours from the East Bay, more from SF.


    Carpooling

    If you need a ride, or if you are able to give rides, please contact your local member of the BAD Math Committee. 


    Organizers and Sponsors

    The BAD Math Committee:


    The 34nd BAD Math Day is kindly supported by Elsevier and the College of Science at San Jose State University: