Spectral and wave function statistics in Quantum digraphs

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Spectral and wave function statistics of the quantum directed graph, QdG, are studied. The crucial feature of this model is that the direction of a bond (arc) corresponds to the direction of the waves propagating along it. We pay special attention to the full Neumann digraph, FNdG, which consists of pairs of antiparallel arcs between every node, and differs from the full Neumann graph, FNG, in that the two arcs have two incommensurate lengths. The spectral statistics of the FNG (with incommensurate bond lengths) is believed to be universal, i.e. to agree with that of the random matrix theory, RMT, in the limit of large graph size. However, the standard perturbative treatment of the field theoretical representation of the 2-point correlation function [1, 2] for a FNG, does not account for this behaviour. The nearest-neighbor spacing distribution of the closely related FNdG is studied numerically. An original, efficient algorithm for the generation of the spectrum of large graphs allows for the observation that the distribution approaches indeed universality at increasing graph size (although the convergence cannot be ascertained), in particular "level repulsion" is confirmed. The numerical technique employs a new secular equation which generalizes the analogous object known for undirected graphs [3, 4], and is based on an adaptation to digraphs of the idea of wave function continuity. In view of the contradiction between the field theory [2] and the strong indications of universality, a non-perturbative approach to analysing the universal limit is presented. The substitution of the FNG by the FNdG results in a field theory with fewer degrees of freedom. Despite this simplification, the attempt is inconclusive. Possible applications of this approach are suggested. Regarding the wave function statistics, a field theoretical representation for the spectral average of the wave intensity on an fixed arc is derived and studied in the universal limit. The procedure originates from the study of wave function statistics on disordered metallic grains [5] and is used in conjunction with the field theory approach pioneered in [2]

Modeling Network Interdiction Tasks

Mission planners seek to target nodes and/or arcs in networks that have the greatest benefit for an operational plan. In joint interdiction doctrine, a top priority is to assess and target the enemy\u27s vulnerabilities resulting in a significant effect on its forces. An interdiction task is an event that targets the nodes and/or arcs of a network resulting in its capabilities being destroyed, diverted, disrupted, or delayed. Lessons learned from studying network interdiction model outcomes help to inform attack and/or defense strategies. A suite of network interdiction models and measures is developed to assist decision makers in identifying critical nodes and/or arcs to support deliberate and rapid planning and analysis. The interdiction benefit of a node or arc is a measure of the impact an interdiction task against it has on the residual network. The research objective is achieved with a two-fold approach. The measures approach begins with a network and uses node and/or arc measures to assess the benefit of each for interdiction. Concurrently, the models approach employs optimization models to explicitly determine the nodes and/or arcs that are most important to the planned interdiction task

Auroral Image Processing Techniques - Machine Learning Classification and Multi-Viewpoint Analysis

Every year, millions of scientific images are acquired in order to study the auroral phenomena. The accumulated data contain a vast amount of untapped information that can be used in auroral science. Yet, auroral research has traditionally been focused on case studies, where one or a few auroral events have been investigated and explained in detail. Consequently, theories have often been developed on the basis of limited data sets, which can possibly be biased in location, spatial resolution or temporal resolution. Advances in technology and data processing now allow for acquisition and analysis of large image data sets. These tools have made it feasible to perform statistical studies based on auroral data from numerous events, varying geophysical conditions and multiple locations in the Arctic and Antarctic. Such studies require reliable auroral image processing techniques to organize, extract and represent the auroral information in a scientifically rigorous manner, preferably with a minimal amount of user interaction. This dissertation focuses on two such branches of image processing techniques: machine learning classification and multi-viewpoint analysis. Machine learning classification: This thesis provides an in-depth description on the implementation of machine learning methods for auroral image classification; from raw images to labeled data. The main conclusion of this work is that convolutional neural networks stand out as a particularly suitable classifier for auroral image data, achieving up to 91 % average class-wise accuracy. A major challenge is that most auroral images have an ambiguous auroral form. These images can not be readily labeled without establishing an auroral morphology, where each class is clearly defined. Multi-viewpoint analysis: Three multi-viewpoint analysis techniques are evaluated and described in this work: triangulation, shell-projection and 3-D reconstruction. These techniques are used for estimating the volume distribution of artificially induced aurora and the height and horizontal distribution of a newly reported auroral feature: Lumikot aurora. The multi-viewpoint analysis techniques are compared and methods for obtaining uncertainty estimates are suggested. Overall, this dissertation evaluates and describes auroral image processing techniques that require little or no user input. The presented methods may therefore facilitate statistical studies such as: probability studies of auroral classes, investigations of the evolution and formation of auroral structures, and studies of the height and distribution of auroral displays. Furthermore, automatic classification and cataloging of large image data sets will support auroral scientists in finding the data of interest, reducing the needed time for manual inspection of auroral images

Proceedings, MSVSCC 2013

Proceedings of the 7th Annual Modeling, Simulation & Visualization Student Capstone Conference held on April 11, 2013 at VMASC in Suffolk, Virginia

Modeling the interplay of mechanics and self-assembly in the actin cytoskeleton

Many cellular processes such as cell migration or division require a trade-off between structural integrity and dynamic reorganization of the load-bearing elements. The actin cytoskeleton has evolved to provide this function for animal cells, but a physical understanding of the interplay between its mechanics and self-assembly is missing. Here I model theoretically two paradigmatic situations of this kind. First, I consider the self-assembly of non-muscle myosin II minifilaments, with a special focus on the stochastic effects that arise due to the small system size of around 30 load bearing elements that turn-over simultaneously to producing contractile force. The self-assembly model follows a consensus architecture, thereby relating the geometrical neighborhood relations of the myosin II monomers with associated binding energies. I find that the turn-over of monomers depends on the mechanochemistry of the cross-bridge cycle by simulating the associated master equation explicitly and by a mean-field approach that maps the complex assembly structure to a simple monomer-addition scheme. Using a rheological framework, I characterize the distinct mechanical properties of non-muscle myosin II minifilaments that arise due to differences in the cross-bridge cycle of the different myosin II isoforms, that can co-assemble in one hetero-filament. Quantitative analysis of the frequency dependent response by a complex modulus, reveals a cross over from viscous to elastic behavior as the ratio of slow to fast isoforms working together is increased. Second I consider the dynamical stability of a peripheral stress fiber, that depends on the interplay of contraction by myosin II minifilaments, self-assembly of new actin filaments at both ends of the fiber and cortical tension. In collaboration with an experimental group, we could show how the myosin II isoform content is differentially reflected by the phenotype of peripheral stress fibers and show their position in a stability phase diagram of the stress fiber. These results demonstrate quantitatively how mechanics and self-assembly interact on different scales in the actin cytoskeleton

Adhesive Interactions Delineate the Topography of the Immune Synapse

T cells form adhesive contacts with antigen-presenting cells (APCs) as part of the normal surveillance process that occurs in lymph nodes and other tissues. Most of these adhesive interactions are formed by integrins that interact with ligands expressed on the surface of the APC. The interactive strength of integrins depends on their degree of membrane proximity as well as intracellular signals that dictate the conformation of the integrin. Integrins appear in different conformations that endow them with different affinities for their ligand(s). Integrin conformation and thus adhesive strength between the T cell and the APC is tuned by intracellular signals that are turned on by ligation of the T cell receptor (TCR) and chemokine receptors. During the different stages of the process, integrins, the TCR and chemokine receptors may be interconnected by the actin cytoskeleton underneath the plasma membrane, forming a chemical and physical network that facilitates the spatiotemporal dynamics, positioning, and function of these receptors and supports cell-cell adhesion during T cell activation, allowing it to perform its effector function

The role of hydrodynamic interactions in the dynamics and viscoelasticity of actin networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 143-146).Actin, the primary component of the cytoskeleton, is the most studied semi-flexible filament, yet its dynamics remains elusive. We show that hydrodynamic interactions (HIs) significantly alter the time scale of actin deformation by 2-20 fold at different levels of network structure. For a single fiber, HIs between the mesh-sized segments can change the net force by up to 7 fold. Relaxation times are underestimated, if HIs are ignored, but mode shapes are not affected. HIs can explain deviation of the relaxation times from standard worm like chain models, speculated to be due to internal viscosity of the filament. HIs affect filament alignment, a necessary step for bundle formation. Ignoring HIs can result in up to 20-fold overestimation of shear loss modulus in the 2 ym range investigated. Even for a 1 mg/ml F-actin (0.1% volume fraction), HIs cannot be neglected whether the network is discretized into beads or rods. A shear loss modulus, slightly dependent on system-size, can be defined consistent with (intrinsic) viscoelasticity. However, axial loss modulus follows a quadratic system-size dependency consistent with poroelasticity. Our results suggest that including HIs is critical for consistency in theoretical models or analyzing experimental observation in cytoskeleton mechanics and dynamics. We also propose a new rod method to incorporate the HIs accurately and effectively. This method includes HIs in the larger systems, the same way as typical bead models, but it can decrease the computational cost by up to 100,000 fold. The primary part of this thesis deals with the viscous properties of the cytoskeletal actin networks investigated via theoretical bottom-up approaches in the nm to pm ranges. However, initially we focus on elastic properties of arterial tissue in the pm to mm ranges via an experimental top-down approach. We develop a combined robust registration and inverse elasticity method to investigate the mechanical properties of arterial tissue. We quantify the accuracy of this method with simulated problems and in vitro gels. This method can identify lipid pools via OCT (optical coherence tomography) and assess plaque rupture risk for cardiovascular diagnosis. The method can also be used as a model-based registration technique.Key words: Actin, Hydrodynamic Interactions, Relaxation Time, Cytoskeleton, Rod Model, Brownian Dynamics, Viscoelasticity, Poroelasticity, Length-Scale Dependent, Inverse Elasticity Problem, Registration, Optical Coherence Tomography (OCT), Atherosclerotic Plaque, Cardiovascular Mechanics.by Reza Karimi.Ph.D

Recent advances in petri nets and concurrency

CEUR Workshop Proceeding

Magnetic shell enhancements during magnetic disturbances

Magnetic shell enhancements during magnetic field disturbances from Langmuir probe observations of electron density on Ariel I satellit