I will discuss the concept of transfinite ζ-metrics. In some details I will discuss transfinite Apollonian metric in the settings of semi-metric spaces. I will discuss specific examples of domains […]
Joint work with Larry Shepp & Philip Ernst In this paper we develop a mathematical model to address an ongoing politico-economic debate between Democrats and Republicans. Democrats in the US […]
The Navier-Stokes existence and smoothness problem is one of the most important open problems in modern mathematics. Ya. Sinai and D. Li have proposed a renormalization approach to constructing a counter-example […]
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 […]
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 […]
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 […]
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 […]
Locust swarms pose a major threat to agriculture, notably in northern Africa and the Middle East. In the early stages of aggregation, locusts form hopper bands. These are coordinated groups that march in columnar structures that are often kilometers long and may contain millions of individuals. We propose a model for the formation of locust […]
Once a new commercial product, technology, political opinion, or social norm is adopted by a few people, these few often put peer pressure on others to consider adopting it as […]
We will have an organizational meeting for the applied math seminar today. Anyone who is interested in suggesting speakers and/or organizing applied math seminar is welcome to come.
