Algorithms for inverting Hodgkin-Huxley type neuron models

The study of neurons is of fundamental importance in biology and medicine. Neurons are the most basic unit of information processing in the nervous system of humans and all other vertebrates and in complex invertebrates. In addition, networks of neurons (the human brain) are the most sophisticated computational devices known, and the study of neurons individually and working in concert is seen as a step toward understanding consciousness and cognition. In the 1950's Hodgkin and Huxley developed a system of nonlinear ordinary differential equations to describe the behavior of a neuron found in the squid. Equations of this form have since been used to model the behavior of a multitude of neurons across a broad spectrum of species. Hodgkin-Huxley type neuron models helped lay the foundation for computational neuroscience, and they remain widely used in the study of neuron behavior almost sixty years after their development. Hodgkin-Huxley type models accept a set of parameters as input and generate data describing the electrical activity of the neuron as a function of time. We develop inversion algorithms to predict a set of input parameter values from the voltage trace data generated by the model. We test our algorithm on data from the Hodgkin-Huxley equations, and we extend the algorithm to solve the inverse problem associated with a more complex Hodgkin-Huxley type model for a lobster stomatogastric neuron. We find strong empirical evidence that the algorithms produce parameter values that generate a good fit to the target voltage trace, and we prove that under certain conditions the inversion algorithm for the Hodgkin-Huxley equations converges to a perfect match. To our knowledge this is the first parameter optimization procedure for which convergence has been shown theoretically. Understanding the relationship between the parameters of a neuron model and its output has implications for designing effective neuron models and for explaining the mechanisms by which neurons regulate their behavior. Inversion algorithms for Hodgkin-Huxley type neuron models are an important theoretical and practical step toward understanding the relationship between model parameters and model behavior, and toward the larger problem of inferring neuronal parameters from behavior observed experimentally.Ph.D.Committee Chair: Tovey, Craig; Committee Member: Butera, Rob; Committee Member: Nemirovski, Arkadi; Committee Member: Prinz, Astrid; Committee Member: Sokol, Joe

RE-EXAMINING THE EVIDENCE FOR LATE COLONIZATION ON EASTER ISLAND

One of the recent discussions to emerge among archaeologists regarding Rapa Nui (Easter Island) prehistory contrasts "early" and "late" estimates for initial human colonization of the island. These differing estimates, in tum, offer significantly different messages for the timing and rate of cultural evolution on the island. A recent study of eleven charcoal samples concluded that Rapa Nui was first colonized around 1200 CE. A new analysis of the same eleven charcoal samples suggests that the data are consistent with an earlier colonization date, around 900 CE. The three hundred year difference between the two estimates could mean the difference between a "short chronology" and "long chronology" to archaeologists and environmentalists alike.</p

The Wisdom of a Crowd of Near-Best Fits: Drug-Resistant Tuberculosis in the United States

Antibiotic-resistant tuberculosis (TB) strains pose a major challenge to TB eradication. Existing US epidemiological models have not fully incorporated the impact of antibiotic-resistance. To develop a more realistic model of US TB dynamics, we formulated a compartmental model integrating single-and multi-drug resistance. We fit twenty-seven parameters to twenty-two years of historical data using a genetic algorithm to minimize a non-differentiable error function. Since counts for several compartments are not available, many parameter combinations achieve very low error. We demonstrate that a crowd of near-best fits can provide compelling new evidence about the ranges of key parameters. While available data is sparse and insufficient to produce point estimates, our crowd of near-best fits computes remarkably consistent predictions about TB prevalence. We believe that our crowd-based approach is applicable to a common problem in mathematical biological research, namely situations where data are sparse and reliable point estimates cannot be directly obtained

Terevaka Archaeological Outreach 2014 field report: Meeting community objectives

Work completed in July of 2014 marks the eleventh year that Terevaka Archaeological Outreach (TAO) has offered educational opportunities for high school students local to the Rapa Nui community. Fifteen Rapanui students enrolled in this year’s program, representing La Aldea Educativa and Colegio Hermano Eugenio Eyraud—two of the high schools on the island. Five of those fifteen students were returning students, having successfully completed their first year of the TAO curriculum in July of 2013. The goals of the TAO program have remained the same since its inception in 2003. First, our work aims to utilize archaeology as a foundation for education and opportunity within Rapa Nui’s island community. Second, our projects promote awareness of and expertise in archaeology and cultural conservation. And third, we document, study, and conserve the remarkable treasures of the past that remain on Rapa Nui today. In order to fulfill these goals, TAO staff and students have undertaken a variety of innovative projects on the island and presented findings through various media (Rutherford et al. 2008; Shepardson 2006, 2010; Shepardson & Torres Hochstetter 2009; Shepardson et al. 2004, 2009, 2010, 2011, 2012, 2013; Torres Hochstetter & Shepardson 2005). As TAO becomes a more established institution on the island, one of our challenges is to make sure that projects are closely aligned with the everevolving community objectives in sustainable development. Our 2014 program focused on two specific projects: (1) non-invasive archaeological site documentation and surveillance, and (2) raising awareness of Rapanui artifacts that currently reside in museums overseas

Terevaka Archaeological Outreach (TAO) 2015 field report: Archaeology, conservation, and toponymy

Terevaka Archaeological Outreach (TAO) is a volunteer program that has provided educational opportunities for youths local to the Rapa Nui community since 2003. The long-term goals of TAO are: (1) to offer experiential learning opportunities specific to cultural and natural resources that surround the local community; (2) to promote awareness and expertise in conservation measures and sustainable development; and (3) to document and study both cultural and natural phenomena of the past today. TAO has now provided educational opportunities to approximately 115 local high school students. Our alumni have gained inspiration to complete university degrees in fields such as archaeology, conservation, history, and cultural anthropology. Several of these students now hold official positions in governmental, private, and educational organizations on the island that will be of critical importance in the island’s near and distant futur