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Description
We model communication among social insects as an interacting particle system in which individuals perform one of two tasks and neighboring sites anti-mimic one another. Parameters of our model are a probability of defection 2 (0; 1) and relative cost ci > 0 to the individual performing task i. We

We model communication among social insects as an interacting particle system in which individuals perform one of two tasks and neighboring sites anti-mimic one another. Parameters of our model are a probability of defection 2 (0; 1) and relative cost ci > 0 to the individual performing task i. We examine this process on complete graphs, bipartite graphs, and the integers, answering questions about the relationship between communication, defection rates and the division of labor. Assuming the division of labor is ideal when exactly half of the colony is performing each task, we nd that on some bipartite graphs and the integers it can eventually be made arbitrarily close to optimal if defection rates are sufficiently small. On complete graphs the fraction of individuals performing each task is also closest to one half when there is no defection, but is bounded by a constant dependent on the relative costs of each task.
ContributorsArcuri, Alesandro Antonio (Author) / Lanchier, Nicolas (Thesis director) / Kang, Yun (Committee member) / Fewell, Jennifer (Committee member) / Barrett, The Honors College (Contributor) / School of International Letters and Cultures (Contributor) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
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Description
Serge Galams voting systems and public debate models are used to model voting behaviors of two competing opinions in democratic societies. Galam assumes that individuals in the population are independently in favor of one opinion with a fixed probability p, making the initial number of that type of opinion a

Serge Galams voting systems and public debate models are used to model voting behaviors of two competing opinions in democratic societies. Galam assumes that individuals in the population are independently in favor of one opinion with a fixed probability p, making the initial number of that type of opinion a binomial random variable. This analysis revisits Galams models from the point of view of the hypergeometric random variable by assuming the initial number of individuals in favor of an opinion is a fixed deterministic number. This assumption is more realistic, especially when analyzing small populations. Evolution of the models is based on majority rules, with a bias introduced when there is a tie. For the hier- archical voting system model, in order to derive the probability that opinion +1 would win, the analysis was done by reversing time and assuming that an individual in favor of opinion +1 wins. Then, working backwards we counted the number of configurations at the next lowest level that could induce each possible configuration at the level above, and continued this process until reaching the bottom level, i.e., the initial population. Using this method, we were able to derive an explicit formula for the probability that an individual in favor of opinion +1 wins given any initial count of that opinion, for any group size greater than or equal to three. For the public debate model, we counted the total number of individuals in favor of opinion +1 at each time step and used this variable to define a random walk. Then, we used first-step analysis to derive an explicit formula for the probability that an individual in favor of opinion +1 wins given any initial count of that opinion for group sizes of three. The spatial public debate model evolves based on the proportional rule. For the spatial model, the most natural graphical representation to construct the process results in a model that is not mathematically tractable. Thus, we defined a different graphical representation that is mathematically equivalent to the first graphical representation, but in this model it is possible to define a dual process that is mathematically tractable. Using this graphical representation we prove clustering in 1D and 2D and coexistence in higher dimensions following the same approach as for the voter model interacting particle system.
ContributorsTaylor, Nicole Robyn (Co-author) / Lanchier, Nicolas (Co-author, Thesis director) / Smith, Hal (Committee member) / Hurlbert, Glenn (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2013-05
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Description
We study two models of a competitive game in which players continuously receive points and wager them in one-on-one battles. In each model the loser of a battle has their points reset, while the points the winner receives is what sets the two models apart. In the knockout model the

We study two models of a competitive game in which players continuously receive points and wager them in one-on-one battles. In each model the loser of a battle has their points reset, while the points the winner receives is what sets the two models apart. In the knockout model the winner receives no new points, while in the winner-takes-all model the points that the loser had are added to the winner's total. Recurrence properties are assessed for both models: the knockout model is recurrent except for the all-zero state, and the winner-takes-all model is transient, but retains some aspect of recurrence. In addition, we study the population-level allocation of points; for the winner-takes-all model we show explicitly that the proportion of individuals having any number j of points, j=0,1,... approaches a stationary distribution that can be computed recursively. Graphs of numerical simulations are included to exemplify the results proved.
ContributorsVanKirk, Maxwell Joshua (Author) / Lanchier, Nicolas (Thesis director) / Foxall, Eric (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2016-12
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Description
The Axelrod Model is an agent-based adaptive model. The Axelrod Model shows the eects of a mechanism of convergent social inuence. Do local conver- gences generate global polarization ? Will it be possible for all dierences between individuals in a population comprised of neighbors to disappear ? There are many

The Axelrod Model is an agent-based adaptive model. The Axelrod Model shows the eects of a mechanism of convergent social inuence. Do local conver- gences generate global polarization ? Will it be possible for all dierences between individuals in a population comprised of neighbors to disappear ? There are many mechanisms to approach this issue ; the Axelrod Model is one of them.
ContributorsYu, Yili (Author) / Lanchier, Nicolas (Thesis director) / Kang, Yun (Committee member) / Brooks, Dan (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Finance (Contributor)
Created2013-05
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Description

This brief article, written for a symposium on "Collaboration and the Colorado River," evaluates the U.S. Department of the Interior's Glen Canyon Dam Adaptive Management Program ("AMP"). The AMP has been advanced as a pioneering collaborative and adaptive approach for both decreasing scientific uncertainty in support of regulatory decision-making and

This brief article, written for a symposium on "Collaboration and the Colorado River," evaluates the U.S. Department of the Interior's Glen Canyon Dam Adaptive Management Program ("AMP"). The AMP has been advanced as a pioneering collaborative and adaptive approach for both decreasing scientific uncertainty in support of regulatory decision-making and helping manage contentious resource disputes -- in this case, the increasingly thorny conflict over the Colorado River's finite natural resources. Though encouraging in some respects, the AMP serves as a valuable illustration of the flaws of existing regulatory processes purporting to incorporate collaboration and regulatory adaptation into the decision-making process. Born in the shadow of the law and improvised with too little thought as to its structure, the AMP demonstrates the need to attend to the design of the regulatory process and integrate mechanisms that compel systematic program evaluation and adaptation. As such, the AMP provides vital information on how future collaborative experiments might be modified to enhance their prospects of success.

ContributorsCamacho, Alejandro E. (Author)
Created2008-09-19
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Description

With a focus on resources of the Colorado River ecosystem below Glen Canyon Dam, the Glen Canyon Dam Adaptive Management Program has included a variety of experimental policy tests, ranging from manipulation of water releases from the dam to removal of non-native fish within Grand Canyon National Park. None of

With a focus on resources of the Colorado River ecosystem below Glen Canyon Dam, the Glen Canyon Dam Adaptive Management Program has included a variety of experimental policy tests, ranging from manipulation of water releases from the dam to removal of non-native fish within Grand Canyon National Park. None of these field-scale experiments has yet produced unambiguous results in terms of management prescriptions. But there has been adaptive learning, mostly from unanticipated or surprising resource responses relative to predictions from ecosystem modeling. Surprise learning opportunities may often be viewed with dismay by some stakeholders who might not be clear about the purpose of science and modeling in adaptive management. However, the experimental results from the Glen Canyon Dam program actually represent scientific successes in terms of revealing new opportunities for developing better river management policies. A new long-term experimental management planning process for Glen Canyon Dam operations, started in 2011 by the U.S. Department of the Interior, provides an opportunity to refocus management objectives, identify and evaluate key uncertainties about the influence of dam releases, and refine monitoring for learning over the next several decades. Adaptive learning since 1995 is critical input to this long-term planning effort. Embracing uncertainty and surprise outcomes revealed by monitoring and ecosystem modeling will likely continue the advancement of resource objectives below the dam, and may also promote efficient learning in other complex programs.

ContributorsMelis, Theodore S. (Author) / Walters, Carl (Author) / Korman, Josh (Author)
Created2015
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Description

The Glen Canyon Dam Adaptive Management Program (AMP) has been identified as a model for natural resource management. We challenge that assertion, citing the lack of progress toward a long-term management plan for the dam, sustained extra-programmatic conflict, and a downriver ecology that is still in jeopardy, despite over ten

The Glen Canyon Dam Adaptive Management Program (AMP) has been identified as a model for natural resource management. We challenge that assertion, citing the lack of progress toward a long-term management plan for the dam, sustained extra-programmatic conflict, and a downriver ecology that is still in jeopardy, despite over ten years of meetings and an expensive research program. We have examined the primary and secondary sources available on the AMP’s design and operation in light of best practices identified in the literature on adaptive management and collaborative decision-making. We have identified six shortcomings: (1) an inadequate approach to identifying stakeholders; (2) a failure to provide clear goals and involve stakeholders in establishing the operating procedures that guide the collaborative process; (3) inappropriate use of professional neutrals and a failure to cultivate consensus; (4) a failure to establish and follow clear joint fact-finding procedures; (5) a failure to produce functional written agreements; and (6) a failure to manage the AMP adaptively and cultivate long-term problem-solving capacity.

Adaptive management can be an effective approach for addressing complex ecosystem-related processes like the operation of the Glen Canyon Dam, particularly in the face of substantial complexity, uncertainty, and political contentiousness. However, the Glen Canyon Dam AMP shows that a stated commitment to collaboration and adaptive management is insufficient. Effective management of natural resources can only be realized through careful attention to the collaborative design and implementation of appropriate problem-solving and adaptive-management procedures. It also requires the development of an appropriate organizational infrastructure that promotes stakeholder dialogue and agency learning. Though the experimental Glen Canyon Dam AMP is far from a success of collaborative adaptive management, the lessons from its shortcomings can foster more effective collaborative adaptive management in the future by Congress, federal agencies, and local and state authorities.

ContributorsSusskind, Lawrence (Author) / Camacho, Alejandro E. (Author) / Schenk, Todd (Author)
Created2010-03-23
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DescriptionUnderstanding the evolution of opinions is a delicate task as the dynamics of how one changes their opinion based on their interactions with others are unclear.
ContributorsWeber, Dylan (Author) / Motsch, Sebastien (Thesis advisor) / Lanchier, Nicolas (Committee member) / Platte, Rodrigo (Committee member) / Armbruster, Dieter (Committee member) / Fricks, John (Committee member) / Arizona State University (Publisher)
Created2021
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Description
This dissertation consists of three papers about opinion dynamics. The first paper is in collaboration with Prof. Lanchier while the other two papers are individual works. Two models are introduced and studied analytically: the Deffuant model and the Hegselmann-Krause~(HK) model. The main difference between the two models is that the

This dissertation consists of three papers about opinion dynamics. The first paper is in collaboration with Prof. Lanchier while the other two papers are individual works. Two models are introduced and studied analytically: the Deffuant model and the Hegselmann-Krause~(HK) model. The main difference between the two models is that the Deffuant dynamics consists of pairwise interactions whereas the HK dynamics consists of group interactions. Translated into graph, each vertex stands for an agent in both models. In the Deffuant model, two graphs are combined: the social graph and the opinion graph. The social graph is assumed to be a general finite connected graph where each edge is interpreted as a social link, such as a friendship relationship, between two agents. At each time step, two social neighbors are randomly selected and interact if and only if their opinion distance does not exceed some confidence threshold, which results in the neighbors' opinions getting closer to each other. The main result about the Deffuant model is the derivation of a positive lower bound for the probability of consensus that is independent of the size and topology of the social graph but depends on the confidence threshold, the choice of the opinion space and the initial distribution. For the HK model, agent~$i$ updates its opinion~$x_i$ by taking the average opinion of its neighbors, defined as the set of agents with opinion at most~$\epsilon$ apart from~$x_i$. Here,~$\epsilon > 0$ is a confidence threshold. There are two types of HK models: the synchronous and the asynchronous HK models. In the former, all the agents update their opinion simultaneously at each time step, whereas in the latter, only one agent is selected uniformly at random to update its opinion at each time step. The mixed model is a variant of the HK model in which each agent can choose its degree of stubbornness and mix its opinion with the average opinion of its neighbors. The main results of this dissertation about HK models show conditions under which the asymptotic stability holds or a consensus can be achieved, and give a positive lower bound for the probability of consensus and, in the one-dimensional case, an upper bound for the probability of consensus. I demonstrate the bounds for the probability of consensus on a unit cube and a unit interval.
ContributorsLi, Hsin-Lun (Author) / Lanchier, Nicolas (Thesis advisor) / Camacho, Erika (Committee member) / Czygrinow, Andrzej (Committee member) / Fishel, Susanna (Committee member) / Motsch, Sebastien (Committee member) / Arizona State University (Publisher)
Created2021