WSU Vancouver Mathematics and Statistics Seminar
 WSU Vancouver Mathematics and Statistics Seminar (Spring 2018) Welcome to the WSU Vancouver Seminar in Mathematics and Statistics! The Seminar meets on Wednesdays at 1:10-2 PM in VLIB 240. This is the building marked "H" in the campus map, and is near the Undergraduate building (marked "N") where all Math/Stat faculty have offices. The seminar is open to the public, and here is some information for visitors. Students could sign up for Math 592 (titled Seminar in Analysis) for 1 credit. Talks will be given by external speakers, as well as by WSUV faculty and students. Contact the organizer Bala Krishnamoorthy if you want to invite a speaker, or to give a talk.
Date Speaker Topic Slides
Jan 10 No seminar     Science on Tap Lecture by Leslie New
Jan 17 Angelica Osorno, Reed College Why Should We Care About Category Theory?

#### Abstract (click to read)

One of the first mathematical concepts we learn as children is counting, and when we do so, we think of counting the number of elements in a specific set. Soon after, we forget about sets and we just consider the abstract numbers themselves. This abstraction simplifies many things, but it also makes us forget about some structure that we had when we were thinking about sets. That structure can be encoded by a category. In this talk we will describe certain concepts in category theory, and you will realize that in most of your mathematics classes you have been working with categories, you just didn't know about it. There will be plenty of examples that will show that category theory provides a unifying language for mathematics, and that many constructions are more naturally understood when they are seen through the categorical lens.

Jan 24 Alex Dimitrov, WSU Modeling of Perceptual Invariances in Biological Sensory Processing

#### Abstract (click to read)

A problem faced by all perceptual systems is natural variability in sensory stimuli associated with the same object. This is a common problem in sensory perception: Interpreting varied optical signals as originating from the same object requires a large degree of tolerance [1]. Understanding speech requires identifying phonemes, such as the consonant /g/, that constitute spoken words. A /g/ is perceived as a /g/, despite tremendous variability in acoustic structure that depends on the surrounding vowels and consonants [2]. A major goal of an object recognition problem then is the ability to identify individual objects while being invariant to changes stemming from multiple stimulus transformations.

In an ongoing project [3], we are testing the hypothesis that broad perceptual invariance is achieved through specific combinations of what we term locally invariant elements. The main questions we would like to address are: 1. What are the characteristics of locally-invariant units in sensory pathways? 2. How are biological locally-invariant units combined to achieve broadly invariant percepts? 3. What are the appropriate mathematical structures with which to address and model these sensory processes? The mathematical aspects of the research involve an interesting combination of probability theory (a must in the study of biological sensory systems) and group theory, needed to characterize invariants and symmetries.

video
Jan 31 Nathaniel Saul, WSU Snippets from the Joint Mathematics Meetings, 2018
Feb   7 No seminar
Feb 14 Zachary Robbins, PSU The Parameterization of PPA Formulas Using a SORTIE-ND Model for Harvard Forest

#### Abstract (click to read)

Spatially-implicit forest growth models, such as the perfect plasticity approximation (PPA), allow for the computationally efficient scaling of forest dynamics to the landscape scale, by using simplified mechanisms of individual tree competition. The parameterization and calibration of PPA using empirical data is challenging, limiting its applications in biogeochemistry and forest modeling. In contrast, the statistical methodology for parameterization of spatially explicit individual-based forest models, such as SORTIE, is well developed. In this work we parameterize the spatially-implicit PPA model by calibrating the spatially-explicit SORTIE-ND model using Harvard forest as a test site. Despite the two models using different tree competition mechanisms, both predicted similar biomass dynamics. Community composition diverged in the two models: between an Eastern hemlock dominated system in SORTIE-ND and a red maple dominated in PPA. This illustrates that the different competition mechanisms employed in spatially-explicit and -implicit models can lead to different predictions of forest successions, and provides a method for an initial parametrization of PPA using SORTIE-ND which is sufficient for scaling of biomass dynamics, but requires further calibration for species dynamics.

Feb 21 Andrew Bray, Reed College   postponed to Mar 21 due to snow
Feb 28 Brandon Edwards, Intel The Curse of Dimensionality and Image Recognition

#### Abstract (click to read)

Despite the high test-accuracy of state of the art image recognition models, optimization methods can be used to find "worst-case" images that are similar to test images from a human perspective, but for which the model fails its image recognition task. Though high test-accuracy would indicate that these images are rare, this phenomenon can be used by an adversary who will benefit from model failure and can alter either the physical space or image stream to match the worst-case image. For this reason, these worst-case images are known in the literature as "adversarial examples". I will give an overview of this space, and present recent results from another group that further highlight the connection between the existence of adversarial examples and the large dimensionality of the model input.

slides
Mar  7 WA State High School Regional Math Contest (no seminar)
Mar 14 No seminar (Spring break)
Mar 21 Andrew Bray, Reed College infer: A Framework for Tidy Statistical Inference

#### Abstract (click to read)

The classical paradigm for null hypothesis significance testing has suffered from misapplication and misinterpretation for many years but it reached a fevered pitch when the American Statistical Association issued a statement on p-values in 2014. In this talk we will consider an approach to formulating classical inference that is expressive of the underlying concepts. This approach is implemented in infer, a new package for the R statistical language.

Mar 28 No seminar
Apr   4 Bala Krishnamorthy and Nathaniel Saul, WSUV Robustness of Solutions to Systems of Quadratic Equations AND
A Stitchfix for Mapper
Apr 11 Olga Rumyantseva, WSUV Forest Canopy Stability in the Perfect Plasticity Approximation (PPA) Model

#### Abstract (click to read)

The Perfect Plasticity Approximation (PPA) is system of equations that predicts the large-scale dynamics of forest stands. The model is computationally efficient and is employed to scaling of vegetation dynamics and carbon and nutrient cycles using parameter values and functional forms of individual tree species. The model includes the system of McKendrick–von Foerster partial differential equations (one for every tree species) and an integral equation (the PPA equation). The McKendrick–von Foerster equation is a conservation law-based first-order hyperbolic partial-differential equation similar to the advection or transport equations that can be solved using the method of characteristics; however, the non-linear PPA integral equation presents a substantial challenge. In this presentation we will discuss structural stability of the PPA model, including the observed tendency of trees with particular shapes to produce unstable canopies. We will introduce analytic conditions of canopy stability an arbitrary crown shapes.

Apr 18 Noah Doss, WSUV Pick-Up Parity: An Exploration of Optimal Partitioning for Competitive Team Activities

#### Abstract (click to read)

For situations in which a population of individuals may be divided into groups, a complete graph with weighted edges captures the complete system of pairing decisions and their value to the individuals. I will discuss how assigning particular discrete weights and participating in "graph pruning", among other methods, provides strategies for creating "fair teams", defined as groups of relatively even total skill rating, while also paying attention to teammate preference. Focusing on cliques of thresholded subgraphs, and contracted edges derived from the stable marriage algorithm, I will approach the problem of practically maximizing a participant response-dependent utility function and balancing the need for team equity with the desire of individuals to participate alongside favored or satisfactory teammates.

Apr 25 Adam Erickson, WSUV Toward the efficient approximation of energetic and biogeochemical processes in terrestrial biosphere models: next-generation forest models

#### Abstract (click to read)

Over the past 80 years, forest models have progressed from empirical linear models to physiological process models to hybrids of both. Early empirical models simulated the growth and yield of pure even-aged forest stands. Four decades later, individual-based multi-species physiological gap models emerged with JABOWA and FORET. Despite reasonable fidelity to Moore's Law, efforts to upscale gap models remain limited by algorithmic and parametric complexity, with existing solutions relying on sampling strategies. Following model reduction techniques demonstrated in LANDSIM, a new class of model emerged blending empirical and physiological components. Such hybrid models include the two popular cohort models, LANDIS-II and Sortie-PPA. While the former is based on species life history strategies and the CENTURY model, the latter is based on phototropism and crown plasticity combined with recent biogeochemistry models. Here, I discuss approximations used in LANDIS-II and Sortie-PPA. I also discuss combining the PPA cohort model with a big-leaf biogeochemistry model in the latest version of Sortie-PPA, known as Sortie-PPA-BGC, intended to inform future terrestrial biosphere models. Finally, I discuss the development of the forestmodels Python library, designed to provide a unified interface to forest biogeochemistry models, including helper functions for data acquisition, parameter estimation, and model intercomparison. This is joint work with Robert Scheller, Nikolay Strigul, and Melissa Lucash.

Last modified: Wed Apr 25 11:11:18 PDT 2018