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 […]
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 to existence. In this approach, existence of a blow-up solution (a solution whose energy becomes infinite in finite time) is equivalent to existence of fixed […]
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 say that government spending can be used to “grease the wheels’ of the economy, create wealth, and increase employment; the Republicans say that government spending […]
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 where the transfinite Apollonian metric can be computed explicitly. This is a preliminary work.
We will have an organizational meeting for the applied math seminar at 4:15pm in Emmy Noether Rm, Millikan 1021, Pomona on 1/28 (Monday). Anyone who in interested in suggesting speakers and/or organizing applied math seminar is welcome to come.
Approximately 500 million tweets are sent everyday. Scientists monitor these tweets to predict the spread of disease, better allocate social welfare services, help first responders during natural disasters, and many other important tasks. A key step in each of these tasks is estimating the location the tweet was sent from. In this talk, I discuss how to combine machine […]
Online social networks and other networks of interest are known to exhibit community structure, where a community is defined to be a highly interconnected group of nodes with possibly shared traits or features. However, classic network models, such as the preferential attachment model, do not account for community structure. In this talk, I will present […]
Measurement error, formally defined as the difference between the measured value and the true value of a quantity of interest, is ubiquitous. When a doctor takes your blood pressure, the […]
One very important concept in understanding a dynamical system is coherent structure. Such structure segments the domain into different regions with similar behavior according to a quantity. When we try […]
I will present mathematical and computational methods used to model interactions between a viscous fluid and elastic structures in biological processes. For example, microfluidic devices carry very small volumes of […]
We study the problems of clustering covariance stationary ergodic processes and locally asymptotically self-similar stochastic processes, when the true number of clusters is priorly known. A new covariance-based dissimilarity measure is introduced, […]
The traditional method of treating most human diseases is to direct a therapy against targets in the host patient, whereas conventional therapies against infectious diseases are directed against the pathogen. […]
