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Dynamical systems are frequently used to model biological systems. When these models are fit to data, it is necessary to ascertain the uncertainty in the model fit. Here, we present prediction deviation, a metric of uncertainty that determines the extent to which observed data have constrained the model's predictions. This is accomplished by solving an optimization problem that searches for a pair of models that each provides a good fit for the observed data, yet has maximally different predictions. We develop a method for estimating a priori the impact that additional experiments would have on the prediction deviation, allowing the ...

Contributors
Letham, Benjamin, Letham, Portia, Rudin, Cynthia, et al.
Created Date
2016-06-14

Synchronization of neuronal activity is associated with neurological disorders such as epilepsy. This process of neuronal synchronization is not fully understood. To further our understanding, we have experimentally studied the progression of this synchronization from normal neuronal firing to full synchronization. We implemented nine FitzHugh-Nagumo neurons (a simplified Hodgkin-Huxley model) via discrete electronics. For different coupling parameters (synaptic strengths), the neurons in the ring were either unsynchronized or completely synchronized when locally coupled in a ring. When a single long-range connection (nonlocal coupling) was introduced, an intermediate state known as a chimera appeared. The results indicate that (1) epilepsy is ...

Contributors
Arumugam, Easwara Moorthy Essaki, Spano, Mark, Ira A. Fulton Schools of Engineering, et al.
Created Date
2015-01-01

The interplay between individual behaviors and epidemic dynamics in complex networks is a topic of recent interest. In particular, individuals can obtain different types of information about the disease and respond by altering their behaviors, and this can affect the spreading dynamics, possibly in a significant way. We propose a model where individuals' behavioral response is based on a generic type of local information, i.e., the number of neighbors that has been infected with the disease. Mathematically, the response can be characterized by a reduction in the transmission rate by a factor that depends on the number of infected neighbors. ...

Contributors
Zhang, Haifeng, Xie, Jia-Rong, Tang, Ming, et al.
Created Date
2014-12-01

In 2013, the community of mathematical scientists and educators focused its collective attention on the mathematics of planet Earth. In the course of the year, a grassroots organization grew into an international partnership of more than 150 scientific societies, universities, research institutes, and organizations. The project, known as “Mathematics of Planet Earth 2013” (MPE2013), received the patronage of UNESCO and was a truly unique event. It brought the challenges facing our planet to the attention of the mathematics research community in numerous lectures, seminars, workshops, and special sessions at conferences of the professional societies; it sponsored the development of curriculum ...

Contributors
Anderies, John, Kaper, Hans G., Shuckburgh, Emily F., et al.
Created Date
2015-03-01

A fundamental result in the evolutionary-game paradigm of cyclic competition in spatially extended ecological systems, as represented by the classic Reichenbach-Mobilia-Frey (RMF) model, is that high mobility tends to hamper or even exclude species coexistence. This result was obtained under the hypothesis that individuals move randomly without taking into account the suitability of their local environment. We incorporate local habitat suitability into the RMF model and investigate its effect on coexistence. In particular, we hypothesize the use of “basic instinct” of an individual to determine its movement at any time step. That is, an individual is more likely to move ...

Contributors
Park, Junpyo, Do, Younghae, Huang, Zi-Gang, et al.
Created Date
2014