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Mathematics Department

Basic Notions Seminars

Spring 2018

All talks are from 1200 - 1300 in the Seminar room, unless otherwise specified.

  • Apr
    26
  • An Introduction to Machine Learning
    Will Traves
    USNA, Mathematics
    Time: 12:00 PM

    View Abstract

    Machine learning (ML) and artificial intelligence are all over the news: self driving cars use ML to learn to drive, doctors use ML to diagnose illnesses, computer scientists use ML to detect spam ... the list goes on and on. I've been learning about ML in preparation for teaching a ML course in the Fall. One of my sources has been a Massive Open Online Course (MOOC) offered by Stanford Professor Andrew Ng. I'll give an introduction to ML and reflect on my experience in the MOOC.
  • Apr
    24
  • Data assimilation and its applications
    Evelyn Lunasin
    USNA, Mathematics
    Time: 12:00 PM

    View Abstract

    What exactly is data assimilation? Data assimilation is a method to approximate the true state of a system by combining, in an optimal way, information obtained from a dynamic model with observational measurements of the state of the system. Do we really need data assimilation in order to accurately predict the state of the system? Why not rely on models alone? Or, why not rely on observational measurements alone and use usual averaging or regression techniques? In this talk I will introduce basic methods and algorithms for data assimilation, its importance in atmospheric sciences and geophysical fluid dynamics, and its role in control of complex engineering systems and chemical processes.
  • Apr
    12
  • If a “Flap of a Butterfly’s Wings in Brazil Sets off a Tornado”, How Can Computer Simulations Have Any Relevance?
    Irina Popovici
    USNA, Mathematics
    Time: 12:00 PM

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    A great deal of models in science use ordinary differential equations (ODE) that are non-linear and that can’t be explicitly integrated. Understanding them often relies on the use of an ODE solver to approximate trajectories (such as Euler or Runge Kutta on a finite-precision computer). Even very simple ODEs, such as the ones modeling a forced damped pendulum, exhibit sensitive dependence on initial conditions, meaning that two trajectories with initial conditions that are extremely close diverge quickly from one another, (and although they remain bounded, they have no periodic limit state, thus are chaotic). The phenomenon was immortalized by Lorenz in 1972, with the question “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” The 2-min short videos https://youtu.be/FYE4JKAXSfY (OK to skip ahead to second 45) and https://www.youtube.com/watch?v=tHnT6AHO1tU are an illustration of that. This leads to a modern day paradox: the rounding off at any step during a numerical approximation will be greatly magnified as the ODE system evolves in time. Does the computed trajectory resemble (i.e. “shadow”) any actual trajectory? Not all ODEs allow shadowing, so the question is: which systems do? The talk will go through some familiar ODEs (1 and 2-dimensional systems) where shadowing can/can’t hold, and will give insight on how to find an appropriate initial condition whose true trajectory stays close a numerically computed one when possible. It will state and explain a few versions of Shadowing Lemmas for higher dimensions (by Anosov; Bowen; Yorke & all). The talk is to be accessible to students who completed SM222 (Diff. Eqs) and SM333 (Analysis).
  • Apr
    05
  • Statistical Power
    Elizabeth McGuffey
    USNA, Mathematics
    Time: 12:00 PM

    View Abstract

    When study results are reported, often the focus is on the statistical significance of the results. Although an important component to consider, significance does not tell the whole story. In this talk, I will describe and discuss power, a statistical attribute that provides more context for any significant findings, or lack thereof. I'll present the mathematical definition of power, derive the power curve for a particular hypothesis test, and discuss what elements should be reported in a conclusion to provide a holistic view of study outcomes.

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