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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Curvature: A Geometric Villain That Ruins Our Instinctive Perception Of Nature, Vehbi Emrah Paksoy
Curvature: A Geometric Villain That Ruins Our Instinctive Perception Of Nature, Vehbi Emrah Paksoy
Mathematics Colloquium Series
Our perception of nature is based on evolutionary wiring of our brain and observations we make via our senses. But, in reality, many scientific and technological advancements are based on non-intuitive rules and principles that can only be explained by the ultimate abstraction that is embedded in mathematics. In this talk, I will discuss the concept of curvature and argue how it explains the “unexplainable”. We will see how the curvature proves that the earth is rotating, how good the soap bubbles are at proving profound mathematical results, and if the two dimensional residents can determine the shape of their …
Bayes Multiple Binary Classifier - How To Make Decisions Like A Bayesian, Wensong Wu
Bayes Multiple Binary Classifier - How To Make Decisions Like A Bayesian, Wensong Wu
Mathematics Colloquium Series
This presentation will start by a general introduction of Bayesian statistics, which has become popular in the era of big data. Then we consider a two-class classification problem, where the goal is to predict the class membership of M units based on the values of high-dimensional categorical predictor variables as well as both the values of predictor variables and the class membership of other N independent units. We focus on applying generalized linear regression models with Boolean expressions of categorical predictors. We consider a Bayesian and decision-theoretic framework, and develop a general form of Bayes multiple binary classification functions with …
Flexible Gating Of Contextual Influences In Natural Vision, Odelia Schwartz
Flexible Gating Of Contextual Influences In Natural Vision, Odelia Schwartz
Mathematics Colloquium Series
An appealing hypothesis suggests that neurons represent inputs in a coordinate system that is matched to the statistical structure of images in the natural environment. I discuss theoretical work on unsupervised learning of statistical regularities in natural images. In the model, Bayesian inference amounts to a generalized form of divisive normalization, a canonical computation that has been implicated in many neural areas. In our framework, divisive normalization is flexible: it is recruited only when the image is inferred to contain dependencies, and muted otherwise. I particularly focus on recent work in which we have applied this approach to understanding spatial …
Learning From Lionfish: Modeling Marine Invaded Systems, Matthew Johnston
Learning From Lionfish: Modeling Marine Invaded Systems, Matthew Johnston
Mathematics Colloquium Series
Simulating marine invaded systems requires broad consideration of physical oceanographic processes, such as ocean circulation patterns and temperature, and biological traits of the invader, such as their reproductive strategy and tolerances to their environment. Through this understanding of baseline biological and oceanographic function, models can be developed in order to forecast the incursion patterns of marine invasive species - helpful both to predict their spread as well as forewarn of impacts. To facilitate this understanding, computer simulation is useful in order to quickly and efficiently assimilate large biological and oceanographic datasets into digestible products. Data derived from such simulations are …
Life As An Nfl Statistician, Dennis Lock
Life As An Nfl Statistician, Dennis Lock
Mathematics Colloquium Series
Over the last few years, the fields of statistics and mathematics have become more prevalent and popular in professional sports (with the help of mainstream books and movies like Moneyball). The use of advanced (and non-advanced) statistical methods is growing across the sporting landscape from the front office to the media, and even into business and ticket sales. This talk will discuss Lock’s experiences building an analytics department with the Miami Dolphins as well as the general role of statistics in sports today. It will also including the recent analytics boom in the front office framework, the coinciding need for …
Computing Invariant Dynamics For Differential Equations: Spectral Methods, Errors, And Computer Assisted Proof, J. D. Mireles James
Computing Invariant Dynamics For Differential Equations: Spectral Methods, Errors, And Computer Assisted Proof, J. D. Mireles James
Mathematics Colloquium Series
The qualitative theory of dynamical systems is concerned with studying the long time behavior discrete and continuous time models such as nonlinear differential equations. The long time behavior of such models is organized by landmarks called invariant sets. For complicated nonlinear equations these invariant sets are difficult to study via pen and paper analysis, and we typically employ numerical simulations to gain insights into the dynamics. If we now think of these computer assisted insights as mathematical conjectures, then it is natural to ask how we might obtain proofs. Since the conjectures themselves originate with the computer it is not …