Structural Network Properties and Their Relation to Cognitive Flexibility and Neurological Risk Factors in Adult Survivors of Pediatric Brain Tumors

Neuroimaging techniques have been used to investigate the neurobiological mechanisms of cognitive deficits in survivors of childhood brain tumors. Graph theory is a quantitative method that characterizes brains as a complex system. By modeling brain regions as ‘nodes’ and white matter tracts between each brain region pair as ‘edges,’ graph theory provides metrics that quantify the topological properties of networks. Given that brain tumor survivorship is associated with focal and diffuse impairments, a network analysis can provide complementary information to previous neuroimaging studies in this clinical group. This study used diffusion-weighted imaging and deterministic tractography to examine the properties of the structural networks in 38 adult survivors of pediatric brain tumors (Mean age=22.5, 55% female, mean years post diagnosis=14.1 (6.2), Range post diagnosis = 4.5-30 years). Results of this study suggest that long term survivorship is associated with altered structural networks with respect to measures of integration, segregation, and centrality. Further, properties of the network mediate differences in cognitive flexibility performance between survivors and healthy peers, and mediate the relationship between cumulative neurological risk and cognitive flexibility performance

Network Formation and Dynamics under Economic Constraints

Networks describe a broad range of systems across a wide variety of topics from social and economic interactions over technical infrastructures such as power grids and the internet to biological contexts such as food webs or neural networks. A number of large scale failures and events in these interconnected systems in recent years has shown that understanding the behavior of individual units of these networks is not necessarily sufficient to handle the increasing complexity of these systems. Many theoretical models have been studied to understand the fundamental mechanisms underlying the formation and function of networked systems and a general framework was developed to describe and understand networked systems. However, most of these models ignore a constraint that affects almost all realistic systems: limited resources. In this thesis I study the effects of economic constraints, such as a limited budget or cost minimization, both on the control of network formation and dynamics as well as on network formation itself. I introduce and analyze a new coupling scheme for coupled dynamical systems, showing that synchronization of chaotic units can be enhanced by restricting the interactions based on the states of the individual units, thus saving interactions costs. This new interaction scheme guarantees synchronizability of arbitrary networks of coupled chaotic oscillators, independent of the network topology even with strongly limited interactions. I then propose a new order parameter to measure the degree of phase coherence of networks of coupled phase oscillators. This new order parameter accurately describes the phase coherence in all stages of incoherent movement, partial and full phase locking up to full synchrony. Importantly, I analytically relate this order parameter directly to the stability of the phase locked state. In the second part, I consider the formation of networks under economic constraints from two different points of view. First I study the effects of explicitly limited resources on the control of random percolation, showing that optimal control can have undesired side effects. Specifically, maximal delay of percolation with a limited budget results in a discontinuous percolation transition, making the transition itself uncontrollable in the sense that a single link can have a macroscopic effect on the connectivity. Finally, I propose a model where network formation is driven by cost minimization of the individual nodes in the network. Based on a simple economically motivated supply problem, the resulting network structure is given as the solution of a large number of individual but interaction optimization problem. I show that these network states directly correspond to the final states of a local percolation algorithm and analyze the effects of local optimization on the network formation process. Overall, I reveal mechanisms and phenomena introduced by these economic constraints that are typically not considered in the standard models, showing that economic constraints can strongly alter the formation and function of networked systems. Thereby, I extend the theoretical understanding that we have of networked systems to economic considerations. I hope that this thesis enables better prediction and control networked systems in realistic settings

Control and Data Analysis of Complex Networks

abstract: This dissertation treats a number of related problems in control and data analysis of complex networks. First, in existing linear controllability frameworks, the ability to steer a network from any initiate state toward any desired state is measured by the minimum number of driver nodes. However, the associated optimal control energy can become unbearably large, preventing actual control from being realized. Here I develop a physical controllability framework and propose strategies to turn physically uncontrollable networks into physically controllable ones. I also discover that although full control can be guaranteed by the prevailing structural controllability theory, it is necessary to balance the number of driver nodes and control energy to achieve actual control, and my work provides a framework to address this issue. Second, in spite of recent progresses in linear controllability, controlling nonlinear dynamical networks remains an outstanding problem. Here I develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another. I introduce the concept of attractor network and formulate a quantifiable framework: a network is more controllable if the attractor network is more strongly connected. I test the control framework using examples from various models and demonstrate the beneficial role of noise in facilitating control. Third, I analyze large data sets from a diverse online social networking (OSN) systems and find that the growth dynamics of meme popularity exhibit characteristically different behaviors: linear, “S”-shape and exponential growths. Inspired by cell population growth model in microbial ecology, I construct a base growth model for meme popularity in OSNs. Then I incorporate human interest dynamics into the base model and propose a hybrid model which contains a small number of free parameters. The model successfully predicts the various distinct meme growth dynamics. At last, I propose a nonlinear dynamics model to characterize the controlling of WNT signaling pathway in the differentiation of neural progenitor cells. The model is able to predict experiment results and shed light on the understanding of WNT regulation mechanisms.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Recent Advances in Industrial and Applied Mathematics

This open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress