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1. Krishnan, Nikhil. Foraging in Stochastic Environments.

Degree: MS, Applied Mathematics, 2019, University of Colorado

URL: https://scholar.colorado.edu/appm_gradetds/145

For many organisms, foraging for food and resources is integral to survival. Mathematical models of foraging can provide insight into the benefits and drawbacks of different foraging strategies. We begin by considering the movement of a memoryless starving forager on a one-dimensional periodic lattice, where each location contains one unit of food. As the forager lands on sites with food, it consumes the food leaving the sites empty. If the forager lands consecutively on a certain number of empty sites, then it starves. The forager has two modes of movement: it can either diffuse by moving with equal probability to adjacent lattice sites, or it can jump uniformly randomly amongst the lattice sites. The lifetime of the forager can be approximated in either paradigm by the sum of the cover time plus the number of empty sites it can visit before starving. The lifetime of the forager varies nonmontonically according to the probability of jumping. The tradeoff between jumps and diffusion is explored using simpler systems as well as numerical simulation, and we demonstrate that the best strategy is one that incorporates both jumps and diffusion. When long range jumps are time-penalized, counterintuitively, this shifts the optimal strategy to pure jumping. We next consider optimal strategies for a group of foragers to search for a target (such as food in an environment where it is sparsely located). There is a single target in one of several patches, with a greater penalty if the foragers decide to switch their positions among the patches. Both in the case of a single searcher, and in the case of a group of searchers, efficient deterministic strategies can be found to locate the target.
*Advisors/Committee Members: Zachary Kilpatrick, Nancy Rodriguez, Juan Restrepo.*

Subjects/Keywords: Foraging; Dynamic Systems

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Krishnan, N. (2019). Foraging in Stochastic Environments. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/145

Chicago Manual of Style (16^{th} Edition):

Krishnan, Nikhil. “Foraging in Stochastic Environments.” 2019. Masters Thesis, University of Colorado. Accessed January 24, 2021. https://scholar.colorado.edu/appm_gradetds/145.

MLA Handbook (7^{th} Edition):

Krishnan, Nikhil. “Foraging in Stochastic Environments.” 2019. Web. 24 Jan 2021.

Vancouver:

Krishnan N. Foraging in Stochastic Environments. [Internet] [Masters thesis]. University of Colorado; 2019. [cited 2021 Jan 24]. Available from: https://scholar.colorado.edu/appm_gradetds/145.

Council of Science Editors:

Krishnan N. Foraging in Stochastic Environments. [Masters Thesis]. University of Colorado; 2019. Available from: https://scholar.colorado.edu/appm_gradetds/145

University of Colorado

2. Broido, Anna. Characterizing the tails of degree distributions in real-world networks.

Degree: PhD, Applied Mathematics, 2019, University of Colorado

URL: https://scholar.colorado.edu/appm_gradetds/143

This is a thesis about how to characterize the statistical structure of the tails of degree distributions of real-world networks. The primary contribution is a statistical test of the prevalence of scale-free structure in real-world networks. A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree k follows a power law, decaying like k^{-a}, often with 2 < a< 3. However, empirical evidence for this belief derives from a relatively small number of real-world networks. In the first section, we test the universality of scale-free structure by applying state-of-the-art statistical tools to a large corpus of nearly 1000 network data sets drawn from social, biological, technological, and informational sources. We fit the power-law model to each degree distribution, test its statistical plausibility, and compare it via a likelihood ratio test to alternative, non-scale-free models, e.g., the log-normal. Across domains, we find that scale-free networks are rare, with only 4% exhibiting the strongest-possible evidence of scale-free structure and 52% exhibiting the weakest-possible evidence. Furthermore, evidence of scale-free structure is not uniformly distributed across sources: social networks are at best weakly scale free, while a handful of technological and biological networks can be called strongly scale free. These results undermine the universality of scale-free networks and reveal that real-world networks exhibit a rich structural diversity that will likely require new ideas and mechanisms to explain. A core methodological component of addressing the ubiquity of scale-free structure in real-world networks is an ability to fit a power law to the degree distribution. In the second section, we numerically evaluate and compare, using both synthetic data with known structure and real-world data with unknown structure, two statistically principled methods for estimating the tail parameters for power-law distributions, showing that in practice, a method based on extreme value theory and a sophisticated bootstrap and the more commonly used method based an empirical minimization approach exhibit similar accuracy.
*Advisors/Committee Members: Aaron Clauset, Jem Corcoran, Daniel Larremore, Manuel Lladser, Juan Restrepo.*

Subjects/Keywords: networks; power law; scale free; Applied Statistics; Other Applied Mathematics; Probability; Statistical Methodology; Statistical Models

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Broido, A. (2019). Characterizing the tails of degree distributions in real-world networks. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/143

Chicago Manual of Style (16^{th} Edition):

Broido, Anna. “Characterizing the tails of degree distributions in real-world networks.” 2019. Doctoral Dissertation, University of Colorado. Accessed January 24, 2021. https://scholar.colorado.edu/appm_gradetds/143.

MLA Handbook (7^{th} Edition):

Broido, Anna. “Characterizing the tails of degree distributions in real-world networks.” 2019. Web. 24 Jan 2021.

Vancouver:

Broido A. Characterizing the tails of degree distributions in real-world networks. [Internet] [Doctoral dissertation]. University of Colorado; 2019. [cited 2021 Jan 24]. Available from: https://scholar.colorado.edu/appm_gradetds/143.

Council of Science Editors:

Broido A. Characterizing the tails of degree distributions in real-world networks. [Doctoral Dissertation]. University of Colorado; 2019. Available from: https://scholar.colorado.edu/appm_gradetds/143