Bucknell Mathematics Department Blog

Spatial interpolation of atmospheric pollutants using Kriging

Thursday, January 25, 12:00 p.m. Room 268 in the Olin Science Building.

Abstract: Have you ever wondered how meteorologists produce prediction maps of temperature and rainfall volume across large geographic regions? They surely can’t monitor temperature and rainfall in every neighborhood across the country, yet there is a prediction available for any location. This challenge of estimating a spatial process at unsampled locations based on known (sampled) values of the process at neighboring sites is called spatial interpolation, and has a number of applications in geosciences and elsewhere: atmospheric scientists estimate concentrations of pollutants across cities or states using concentrations monitored at select sites; oceanic scientists graph salinity across water basins using water tested in certain areas; and mining engineers determine the volume of oil, gas, or other minerals underground in a region based on samples collected at a few sites. In this talk, I will present a popular statistical approach used for spatial interpolation, called Kriging. Unlike deterministic interpolation techniques, such as Inverse Distance Weighting, Kriging provides both unbiased estimates at unsampled locations, and a measure of the uncertainty associated with the estimates. I will demonstrate an application of Kriging by estimating the concentration of nitrogen dioxide, an atmospheric pollutant, over the state of Connecticut using concentrations monitored at a few locations within the state.

From Academia to Data Science, One Woman’s Journey

Getting into data science seems to be a unique path for each data scientist.  This talk will chronicle the path Dr. Mandi Traud took from graduate school in North Carolina to Data Science Lead at Tuple Health and President of Data Community DC.  She will talk about her data science projects all along the way and how she moved from academia to working for a company and volunteering in the data science community.

A special panel discussion featuring:

Maddie Brown `18 – NSF REU in mathematical analysis and applications at University of Michigan – Dearborn.

Caroline Edelman `18 – REU in dynamical systems at Boston College

Nate Mattis `19 – TEU program at Brown University

Alexander Murph `18 – Nielsen Professional Summer Analytics Experience (PSAE)

Leo Orozco `18 – Summer Security Intensive, IT Lab Fellow at Carnegie Mellon University

Pizza and sodas for everyone!

Title: What Do You Mean, It’s Hard?

Abstract: Suppose someone gives you a computer and asks you to perform one of the following tasks:

1. solve a 17 × 17 × 17 Rubik’s cube, or
2. decide if a given list of 100 integers can be broken into two parts having equal sums.

If your life depended on it, which task would you choose? Which is harder, computationally?

In 1971, Stephen Cook proposed a strong measure of efficiency – polynomial time, or simply P – as a desirable standard to which we should hold solutions to computational problems. Task A is an instance of a problem with such a solution. He also identified a seemingly less stringent measure – nondeterministic polynomial time, or simply NP – in which one merely has to check, efficiently, that a given solution is correct. Tasks A and B are both instances of problems satisfying this condition. The big question raised by Cook is whether these two measures of computational efficiency are actually distinct.

One can argue that the “P ≠ NP Problem,” as it is now known, is the most important open problem in all of mathematics and computer science. Certainly, it has far-reaching implications both within these two fields and beyond. Cook showed in his 1971 paper that there are NP problems that seem really hard: remarkably, if you can solve any one of these problems efficiently, then you can solve every NP problem efficiently. Problem B is an instance of one of these “NP-complete” problems. To solve P ≠ NP, one could look for NP problems that are unlikely to be hard in this sense and try to show that they’re also not easy. We have yet to find such a problem, but in this talk I will try to persuade you that there are some candidates worthy of further scrutiny!