A single soap bubble has a spherical shape since it minimizes its surface area subject to a fixed enclosed volume of air. When two soap bubbles collide, they form a "double-bubble" composed of three spherical caps. The double-bubble minimizes total surface area among all sets enclosing two fixed volumes. This was proven mathematically in a […]
Algebraic geometry (AG) is a major generalization of linear algebra which is fairly influential in mathematics. Since the 1980's with the development of computer algebra systems like Mathematica, AG has been leveraged in areas of STEM as diverse as statistics, robotic kinematics, computer science/geometric modeling, and mirror symmetry. Part one of my talk will be a […]
Abstract: Bats in North America have been dying off due to the invasion of a fungal disease (White Nose Syndrome). In this talk, I'll present a very simple linear algebraic model to predict the magnitude of the die-offs. By comparing these models to some data about actual bat survival, my collaborator and I also hypothesized […]
TOPIC: Exploring the fascinating world of prime numbers, Part I The study of patterns in the sequence of prime numbers has fascinated mathematicians for centuries. Are there formulas that generate prime numbers? Are there patterns in the distribution of prime numbers and the distribution of gaps between consecutive primes? In this series of two workshops, beginning […]
The exchange algorithm enables Bayesian posterior inference for models with intractable likelihoods, such as Ising, Potts, or exponential random graph models (ERGM). Crucially, this algorithm relies on an auxiliary Markov […]
Moment generating functions (Laplace transforms) are a means for transforming probability problems into problems involving polynomials. Here I will concentrate on the binomial distribution, and use the mgf to link […]
Abstract: In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our […]
When Charles Darwin began writing “On the Origin of Species” he knew that explaining cooperative behavior in the context of “survival of the fittest” was problematic. In fact, this apparent […]
Frequency hopping is a method of transmitting signals by rapidly switching between many frequency channels, following some sequence of frequencies known to the transmitter and the receiver. This technique is used in […]
In this talk we use the unit-graphs and the special unit-digraphs on matrix rings to show that every n x n nonzero matrix over F_q can be written as a […]
Growth regulation and pattern formation are two main problems in developmental biol- ogy. How cells know when to stop growing at certain tissue size with specic shape is an important […]
It has been observed that motor neuron synapses in the worm C. elegans are remarkably evenly spaced, even during growth and development. In this work, we propose a novel mechanism […]
