Category Archives: Mathematics

Seminar: Arithmetic Dynamics and Sarkovskii’s Theorem

Tuesday, November 6, 2012. Colloquium / Pizza Pi.
Prof. Ben Weiss, Bates College
“Arithmetic Dynamics and Sarkovskii’s Theorem”
421 Neville Hall. Pizza at 12:15, lecture from 12:30-1:20pm.

Given a function f(x), and a number A, what does the orbit {A, f(A), f(f(A)), f(f(f(A))), ….} look like? Can it be finite? If so how big can it be? These questions are part of dynamics, which studies functions by analyzing their orbits. The study of orbits has very wide applications to number theory, ergodic theory, and is a beautiful subject in its own right. We’ll discuss how dynamics of polynomials over the integers and rational numbers can tell us about units and arithmetical properties of these sets. Then we’ll discuss Sarkovskii’s Theorem, which classifies possible orbit sizes of continuous functions over the real numbers, and time permitting will discuss related open problems. This talk will be accessible to all.

New Times Opinion Piece References Markowsky’s Article on the Golden Ratio

The New York Times

The Opinion Pages

ME, MYSELF AND MATH September 24, 2012, 9:00 PM103 Comments

Proportion Control

By STEVEN STROGATZ

 

Me, Myself and Math, a six-part series by Steven Strogatz, looks at us through the lens of math.

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No other number attracts such a fevered following as the golden ratio. Approximately equal to 1.618 and denoted by the Greek letter phi, it’s been canonized as the “Divine Proportion.” Its devotees will tell you it’s ubiquitous in nature, art and architecture. And there are plastic surgeons and financial mavens who will tell you it’s the secret to pretty faces and handsome returns.

Not bad for the second-most famous irrational number. In your face, pi!

It even made a cameo appearance in “The Da Vinci Code.” Go to http://opinionator.blogs.nytimes.com/2012/09/24/proportion-control/ for the full article.

School of Computing & Information Science Seminar: Cases of Spatial, Spatio-temporal and Temporal-spatial Analysis

2:10-3 PM, Wednesday September 5, 2012 Room 336, Boardman Hall

Cases of Spatial, Spatio-temporal and Temporal-spatial Analysis

Presenter: Dr. Sytze de Bruin, University of Wageningen, the Netherlands

Abstract:
Including the temporal dimension in spatial analysis often considerably affects computational complexity and may render some problems virtually infeasible on regular hardware and software configurations. In this presentation I present three recent research projects that relate to modelling states in space, states in space-time and rates in space.

The first example concerns a spatial optimisation problem producing tracks for auto-steering of agricultural machinery. The project has resulted in a semi-operational web service providing near real-time results to a group of innovative farmers.

The second is about representation of a dynamic spatial field (toxic plume) using optimally located mobile sensors. The objective function involves the expected accumulated misclassification costs, which are data dependent and hence change over time.

The third case concerns analysis of spatial relationships between climatologies and
changes in global vegetation activity within the context of a project on land degradation assessment. This problem was computationally very demanding because of the size of the global data set (remote sensing data).

In the end, all three cases deal with changing states of the world but they do so using different modelling decisions which depend on dynamics, needs and possibilities. Fully integrated spatio-temporal analysis calls for efficient algorithms and adequate computational power.