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- Genre: Academic theses
Description
Parallel Monte Carlo applications require the pseudorandom numbers used on each processor to be independent in a probabilistic sense. The TestU01 software package is the standard testing suite for detecting stream dependence and other properties that make certain pseudorandom generators ineffective in parallel (as well as serial) settings. TestU01 employs two basic schemes for testing parallel generated streams. The first applies serial tests to the individual streams and then tests the resulting P-values for uniformity. The second turns all the parallel generated streams into one long vector and then applies serial tests to the resulting concatenated stream. Various forms of stream dependence can be missed by each approach because neither one fully addresses the multivariate nature of the accumulated data when generators are run in parallel. This dissertation identifies these potential faults in the parallel testing methodologies of TestU01 and investigates two different methods to better detect inter-stream dependencies: correlation motivated multivariate tests and vector time series based tests. These methods have been implemented in an extension to TestU01 built in C++ and the unique aspects of this extension are discussed. A variety of different generation scenarios are then examined using the TestU01 suite in concert with the extension. This enhanced software package is found to better detect certain forms of inter-stream dependencies than the original TestU01 suites of tests.
ContributorsIsmay, Chester (Author) / Eubank, Randall (Thesis advisor) / Young, Dennis (Committee member) / Kao, Ming-Hung (Committee member) / Lanchier, Nicolas (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2013
Description
Rabies disease remains enzootic among raccoons, skunks, foxes and bats in the United States. It is of primary concern for public-health agencies to control spatial spread of rabies in wildlife and its potential spillover infection of domestic animals and humans. Rabies is invariably fatal in wildlife if untreated, with a non-negligible incubation period. Understanding how this latency affects spatial spread of rabies in wildlife is the concern of chapter 2 and 3. Chapter 1 deals with the background of mathematical models for rabies and lists main objectives. In chapter 2, a reaction-diffusion susceptible-exposed-infected (SEI) model and a delayed diffusive susceptible-infected (SI) model are constructed to describe the same epidemic process -- rabies spread in foxes. For the delayed diffusive model a non-local infection term with delay is resulted from modeling the dispersal during incubation stage. Comparison is made regarding minimum traveling wave speeds of the two models, which are verified using numerical experiments. In chapter 3, starting with two Kermack and McKendrick's models where infectivity, death rate and diffusion rate of infected individuals can depend on the age of infection, the asymptotic speed of spread $c^\ast$ for the cumulated force of infection can be analyzed. For the special case of fixed incubation period, the asymptotic speed of spread is governed by the same integral equation for both models. Although explicit solutions for $c^\ast$ are difficult to obtain, assuming that diffusion coefficient of incubating animals is small, $c^\ast$ can be estimated in terms of model parameter values. Chapter 4 considers the implementation of realistic landscape in simulation of rabies spread in skunks and bats in northeast Texas. The Finite Element Method (FEM) is adopted because the irregular shapes of realistic landscape naturally lead to unstructured grids in the spatial domain. This implementation leads to a more accurate description of skunk rabies cases distributions.
ContributorsLiu, Hao (Author) / Kuang, Yang (Thesis advisor) / Jackiewicz, Zdzislaw (Committee member) / Lanchier, Nicolas (Committee member) / Smith, Hal (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2013
Description
By the von Neumann min-max theorem, a two person zero sum game with finitely many pure strategies has a unique value for each player (summing to zero) and each player has a non-empty set of optimal mixed strategies. If the payoffs are independent, identically distributed (iid) uniform (0,1) random variables, then with probability one, both players have unique optimal mixed strategies utilizing the same number of pure strategies with positive probability (Jonasson 2004). The pure strategies with positive probability in the unique optimal mixed strategies are called saddle squares. In 1957, Goldman evaluated the probability of a saddle point (a 1 by 1 saddle square), which was rediscovered by many authors including Thorp (1979). Thorp gave two proofs of the probability of a saddle point, one using combinatorics and one using a beta integral. In 1965, Falk and Thrall investigated the integrals required for the probabilities of a 2 by 2 saddle square for 2 × n and m × 2 games with iid uniform (0,1) payoffs, but they were not able to evaluate the integrals. This dissertation generalizes Thorp's beta integral proof of Goldman's probability of a saddle point, establishing an integral formula for the probability that a m × n game with iid uniform (0,1) payoffs has a k by k saddle square (k ≤ m,n). Additionally, the probabilities of a 2 by 2 and a 3 by 3 saddle square for a 3 × 3 game with iid uniform(0,1) payoffs are found. For these, the 14 integrals observed by Falk and Thrall are dissected into 38 disjoint domains, and the integrals are evaluated using the basic properties of the dilogarithm function. The final results for the probabilities of a 2 by 2 and a 3 by 3 saddle square in a 3 × 3 game are linear combinations of 1, π2, and ln(2) with rational coefficients.
ContributorsManley, Michael (Author) / Kadell, Kevin W. J. (Thesis advisor) / Kao, Ming-Hung (Committee member) / Lanchier, Nicolas (Committee member) / Lohr, Sharon (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2011
Description
This dissertation examines six different models in the field of econophysics using interacting particle systems as the basis of exploration. In each model examined, the underlying structure is a graph G = (V , E ), where each x ∈ V represents an individual who is characterized by the number of coins in her possession at time t. At each time step t, an edge (x, y) ∈ E is chosen at random, resulting in an exchange of coins between individuals x and y according to the rules of the model. Random variables ξt, and ξt(x) keep track of the current configuration and number of coins individual x has at time t respectively. Of particular interest is the distribution of coins in the long run. Considered first are the uniform reshuffling model, immediate exchange model and model with saving propensity. For each of these models, the number of coins an individual can have is nonnegative and the total number of coins in the system is conserved for all time. It is shown here that the distribution of coins converges to the exponential distribution, gamma distribution and a pseudo gamma distribution respectively. The next two models introduce debt, however, the total number of coins again remains fixed. It is shown here that when there is an individual debt limit, the number of coins per individual converges to a shifted exponential distribution. Alternatively, when a collective debt limit is imposed on the whole population, a heuristic argument is given supporting the conjecture that the distribution of coins converges to an asymmetric Laplace distribution. The final model considered focuses on the effect of cooperation on a population. Unlike the previous models discussed here, the total number of coins in the system at any given time is not bounded and the process evolves in continuous time rather than in discrete time. For this model, death of an individual will occur if they run out of coins. It is shown here that the survival probability for the population is impacted by the level of cooperation along with how productive the population is as whole.
ContributorsReed, Stephanie Jo (Author) / Lanchier, Nicolas (Thesis advisor) / Smith, Hal (Committee member) / Gumel, Abba (Committee member) / Motsch, Sebastien (Committee member) / Camacho, Erika (Committee member) / Arizona State University (Publisher)
Created2019
Description
This dissertation investigates the dynamics of evolutionary games based on the framework of interacting particle systems in which individuals are discrete, space is explicit, and dynamics are stochastic. Its focus is on 2-strategy games played on a d-dimensional integer lattice with a range of interaction M. An overview of related past work is given along with a summary of the dynamics in the mean-field model, which is described by the replicator equation. Then the dynamics of the interacting particle system is considered, first when individuals are updated according to the best-response update process and then the death-birth update process. Several interesting results are derived, and the differences between the interacting particle system model and the replicator dynamics are emphasized. The terms selfish and altruistic are defined according to a certain ordering of payoff parameters. In these terms, the replicator dynamics are simple: coexistence occurs if both strategies are altruistic; the selfish strategy wins if one strategy is selfish and the other is altruistic; and there is bistability if both strategies are selfish. Under the best-response update process, it is shown that there is no bistability region. Instead, in the presence of at least one selfish strategy, the most selfish strategy wins, while there is still coexistence if both strategies are altruistic. Under the death-birth update process, it is shown that regardless of the range of interactions and the dimension, regions of coexistence and bistability are both reduced. Additionally, coexistence occurs in some parameter region for large enough interaction ranges. Finally, in contrast with the replicator equation and the best-response update process, cooperators can win in the prisoner's dilemma for the death-birth process in one-dimensional nearest-neighbor interactions.
ContributorsEvilsizor, Stephen (Author) / Lanchier, Nicolas (Thesis advisor) / Kang, Yun (Committee member) / Motsch, Sebastien (Committee member) / Smith, Hal (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2016
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
Description
For fifty years, inquiry has attempted to capture how groups of people experience microaggression phenomena through multiple methodological and analytic applications grounded in psychology-influenced frameworks. Yet, despite theoretical advancements, the phenomenon has met criticisms trivializing its existence, falsifiability, and social significance. Unpacking possible interactive factors of a microaggressive moment invites a revisitation of the known and unknown pragmatic conditions that may produce and influence its discomforting situational “content.” This study employs an intentional, game-theoretic methodology based on brief, publicly-recorded, everyday conversation segments. Conversation segments of social interactions provide a means to conduct a mathematically-solid, computationally-tractable analysis of explaining what is happening during encounters where disability microaggressions are likely the result of partial (non)cooperation between communicators. Such analysis extends the microaggression research program (MRP) by: (1) proposing theoretical consequences for conversational repair phenomena, algorithmic programming, and experimental designs in negotiation research; and (2) outlining practical approaches for preventing microaggressions with new communication pedagogy, anti-oppression/de-escalation training programs, and calculable, focus-oriented psychotherapy. It concludes with an invitation for scholars to “be” in ambiguity so that they may speculate possible trajectories for the study of microaggressions as a communicative phenomenon.
ContributorsReutlinger, Corey Jon (Author) / de la Garza, Sarah Amira (Thesis advisor) / Alberts, Janet (Committee member) / Lanchier, Nicolas (Committee member) / Cherney, James L. (Committee member) / Arizona State University (Publisher)
Created2021
Description
The main objective of this work is to study novel stochastic modeling applications to cybersecurity aspects across three dimensions: Loss, attack, and detection. First, motivated by recent spatial stochastic models with cyber insurance applications, the first and second moments of the size of a typical cluster of bond percolation on finite graphs are studied. More precisely, having a finite graph where edges are independently open with the same probability $p$ and a vertex $x$ chosen uniformly at random, the goal is to find the first and second moments of the number of vertices in the cluster of open edges containing $x$. Exact expressions for the first and second moments of the size distribution of a bond percolation cluster on essential building blocks of hybrid graphs: the ring, the path, the random star, and regular graphs are derived. Upper bounds for the moments are obtained by using a coupling argument to compare the percolation model with branching processes when the graph is the random rooted tree with a given offspring distribution and a given finite radius. Second, the Petri Net modeling framework for performance analysis is well established; extensions provide enough flexibility to examine the behavior of a permissioned blockchain platform in the context of an ongoing cyberattack via simulation. The relationship between system performance and cyberattack configuration is analyzed. The simulations vary the blockchain's parameters and network structure, revealing the factors that contribute positively or negatively to a Sybil attack through the performance impact of the system. Lastly, the denoising diffusion probabilistic models (DDPM) ability for synthetic tabular data augmentation is studied. DDPMs surpass generative adversarial networks in improving computer vision classification tasks and image generation, for example, stable diffusion. Recent research and open-source implementations point to a strong quality of synthetic tabular data generation for classification and regression tasks. Unfortunately, the present state of literature concerning tabular data augmentation with DDPM for classification is lacking. Further, cyber datasets commonly have highly unbalanced distributions complicating training. Synthetic tabular data augmentation is investigated with cyber datasets and performance of well-known metrics in machine learning classification tasks improve with augmentation and balancing.
ContributorsLa Salle, Axel (Author) / Lanchier, Nicolas (Thesis advisor) / Jevtic, Petar (Thesis advisor) / Motsch, Sebastien (Committee member) / Boscovic, Dragan (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2023
Description
A leading crisis in the United States is the opioid use disorder (OUD) epidemic. Opioid overdose deaths have been increasing, with over 100,000 deaths due to overdose from April 2020 to April 2021. This dissertation presents two mathematical models to address illicit OUD (IOUD), treatment, and recovery within an epidemiological framework. In the first model, individuals remain in the recovery class unless they relapse. Due to the limited availability of specialty treatment facilities for individuals with OUD, a saturation treat- ment function was incorporated. The second model is an extension of the first, where a casual user class and its corresponding specialty treatment class were added. Using U.S. population data, the data was scaled to a population of 200,000 to find parameter estimates. While the first model used the heroin-only dataset, the second model used both the heroin and all-illicit opioids datasets. Backward bifurcation was found in the first IOUD model for realistic parameter values. Additionally, bistability was observed in the second IOUD model with the heroin-only dataset. This result implies that it would be beneficial to increase the availability of treatment. An alarming effect was discovered about the high overdose death rate: by 2038, the disease-free equilibrium would be the only stable equilibrium. This consequence is concerning because although the goal is for the epidemic to end, it would be preferable to end it through treatment rather than overdose. The IOUD model with a casual user class, its sensitivity results, and the comparison of parameters for both datasets, showed the importance of not overlooking the influence that casual users have in driving the all-illicit opioid epidemic. Casual users stay in the casual user class longer and are not going to treatment as quickly as the users of the heroin epidemic. Another result was that the users of the all-illicit opioids were going to the recovered class by means other than specialty treatment. However, the relapse rates for those individuals were much more significant than in the heroin-only epidemic. The results above from analyzing these models may inform health and policy officials, leading to more effective treatment options and prevention efforts.
ContributorsCole, Sandra (Author) / Wirkus, Stephen (Thesis advisor) / Gardner, Carl (Committee member) / Lanchier, Nicolas (Committee member) / Camacho, Erika (Committee member) / Fricks, John (Committee member) / Arizona State University (Publisher)
Created2022
Description
The increase in the photovoltaic (PV) generation on distribution grids may cause reverse power flows and challenges such as service voltage violations and transformer overloading. To resolve these issues, utilities need situational awareness, e.g., PV-feeder mapping to identify the potential back-feeding feeders and meter-transformer mapping for transformer overloading. As circuit schematics are outdated, this work relies on data. In cases where the advanced metering infrastructure (AMI) data is unavailable, e.g., analog meters or bandwidth limitation, the dissertation proposes to use feeder measurements from utilities and solar panel measurements from solar companies to identify PV-feeder mapping. Several sequentially improved methods based on quantitative association rule mining (QARM) are proposed, where a lower bound for performance guarantee is also provided. However, binning data in QARM leads to information loss. So, bands are designed to replace bins for increased robustness. For cases where AMI data is available but solar PV data is unavailable, the AMI voltage data and location data are used for situational awareness, i.e., meter-transformer mapping, to resolve voltage violation and transformer overloading. A density-based clustering method is proposed that leverages AMI voltage data and geographical information to efficiently segment utility meters such that the segments comprise meters of few transformers only. Although it is helpful for utilities, it may not directly recover the meter-transformer connectivity, which requires transformer-wise segmentation. The proposed density-based method and other past methods ignore two common scenarios, e.g., having large distance between a meter and parent transformer or high similarity of a meter's consumption pattern to a non-parent transformer's meters. However, going from meter-meter can lead to the parent transformer group meters due to the usual observation that the similarity of intra-cluster meter voltages is usually stronger than the similarity of inter-cluster meter voltages. Therefore, performance guarantee is provided via spectral embedding with voltage data under reasonable assumption. Moreover, the assumption is partially relaxed using location data. It will benefit the utility in many ways, e.g., mitigating voltage violations by transformer tap settings and identifying overloaded transformers.
ContributorsSaleem, Muhammad Bilal (Author) / Weng, Yang (Thesis advisor) / Lanchier, Nicolas (Committee member) / Wu, Meng (Committee member) / Cook, Elizabeth (Committee member) / Arizona State University (Publisher)
Created2022