Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices, and an algorithm […]
Joan Ponce Purdue University Abstract: One of the main challenges of mathematical modeling is the balance between simplifying assumptions and incorporating sufficient complexity for the model to provide more accurate and […]
At the turn of the twentieth century, physicist Henri Bénard heated a shallow plate of fluid from below. For temperatures above a critical value, the fluid’s evenly heated state became unstable as thermal convection took hold; heated fluid rose in localized areas while cooler fluid fell nearby. The rising and falling fluid created hexagonal convection cells, […]
Shannons sampling theorem provides a link between the continuous and thediscrete realms stating that bandlimited signals are uniquely determined by itsvalues on a discrete set. This theorem is realized in practice using so called analog to digital converters (ADCs). Unlike Shannons sampling theorem, the ADCs are limited in dynamic range. Whenever a signal exceeds some […]
Individuals may choose to create social groups where their individual fitness and success is influenced by those around them. A group may increase an individual's success in finding food, shelter, and safety; […]
Antibodies are the standard biomolecule for marking molecular structures and delivering drugs due to their specific binding capabilities. However, they are expensive to produce and their relatively large size prevents […]
Data coming from Monte Carlo experiments is often analyzed in the same way as data from more traditional sources. The unique nature of Monte Carlo data, where it is easy […]
In this talk I will discuss a rather unique collection of tools and how they have been used to understand the spread of Influenza virus in the State of Montana. […]
Biological invasions often have outsized consequences for the invaded ecosystem and represent an interesting challenge to model mathematically. Landscape heterogeneity, non-local or time-dependent spreading mechanisms, coarse data, and air or […]
In water-limited regions, competition for water resources results in the formation of vegetation patterns; on sloped terrain, one finds that the vegetation typically aligns in stripes or arcs. The dynamics […]
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