Local Causal States and Discrete Coherent Structures

Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate dynamics. Phenomenologically, they appear as key components that organize the macroscopic behaviors in such systems. Despite a century of effort, they have eluded rigorous analysis and empirical prediction, with progress being made only recently. As a step in this, we present a formal theory of coherent structures in fully-discrete dynamical field theories. It builds on the notion of structure introduced by computational mechanics, generalizing it to a local spatiotemporal setting. The analysis' main tool employs the \localstates, which are used to uncover a system's hidden spatiotemporal symmetries and which identify coherent structures as spatially-localized deviations from those symmetries. The approach is behavior-driven in the sense that it does not rely on directly analyzing spatiotemporal equations of motion, rather it considers only the spatiotemporal fields a system generates. As such, it offers an unsupervised approach to discover and describe coherent structures. We illustrate the approach by analyzing coherent structures generated by elementary cellular automata, comparing the results with an earlier, dynamic-invariant-set approach that decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht

Expanding the Use of Cellular Automata

Cellular automata are a type of simulation based upon dividing space into cells. More specifically, cellular automata are characterized by parallelism, locality, and homogeneity. A simulation is run by conducting a series of updates, consisting of running a set of rules that all cells follow. The rules typically consist of looking at a cell\u27s immediate neighbors and/or itself to determine what will be in the cell at the next step. The rules are applied to all the cells at exactly the same time in exactly the same manner. The use of cellular automata has been limited to computer scientists, those who can write code, and people who understand the traditional nomenclature. Physicists, mathematicians, or even those who are just interested in different types of simulations should be able to fully explore the full potential of cellular automata. In order to expand the use of cellular automata to additional fields, my research has led to the creation of a program that allows users to easily create cellular automata without having to have foreknowledge of cellular automata terminology. The user is taken through a series of steps where they can control the size of the system, the number and speed of iterations, define the system variables in their own terms, populate the system however they wish, and make their own rules. The program also allows extreme flexibility so that non-traditional simulations can potentially be explored

Computational composition strategies in audiovisual laptop performance

We live in a cultural environment in which computer based musical performances have become ubiquitous. Particularly the use of laptops as instruments is a thriving practice in many genres and subcultures. The opportunity to command the most intricate level of control on the smallest of time scales in music composition and computer graphics introduces a number of complexities and dilemmas for the performer working with algorithms. Writing computer code to create audiovisuals offers abundant opportunities for discovering new ways of expression in live performance while simultaneously introducing challenges and presenting the user with difficult choices. There are a host of computational strategies that can be employed in live situations to assist the performer, including artificially intelligent performance agents who operate according to predefined algorithmic rules. This thesis describes four software systems for real time multimodal improvisation and composition in which a number of computational strategies for audiovisual laptop performances is explored and which were used in creation of a portfolio of accompanying audiovisual compositions

Urban land use change analysis and modelling: a case study of Setubal-Sesimbra, Portugal

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial TechnologiesIn this paper urban land use change analysis and modeling of the Concelhos of Setúbal and Sesimbra, Portugal is accomplished using multitemporal and multispectral satellite images acquired in the years 2000 and 2006 and other vector datasets. The LULC maps are first obtained using an object-oriented image classification approach with the Nearest Neighbour algorithm in Definiens. Classification is assessed using the overall accuracy and Kappa measure of agreement. These measures of accuracies are above minimum standard accepted levels. The land use dynamics, both for pattern and quantities are also studied using a post classification change detection technique together with the following selected spatial/landscape metrics: class area, number of patches, edge density, largest patch index, Euclidian mean nearest neighbor distance, area weighted mean patch fractal dimension and contagion. Urban sprawl has also been measured using Shannon Entropy approach to describe the dispersion of land development or sprawl. Results indicated that the study area has undergone a tremendous change in urban growth and pattern during the study period. A Cellular Automata Markov (CA_Markov) modeling approach has also been applied to predict urban land use change between 1990 and 2010 with two scenarios: MMU 1ha and MMU 25ha. The suitability maps (change drivers) are calibrated with the LULC maps of 1990 and 2000 using MCE and a contiguity filter. The maps of 1990 and 2000 are also used for the transition probability matrix. Then, the land use maps of 2006 are simulated to compare the result of the “prediction” with the actual land use map in that year so that further prediction can be carried out for the year 2010. This is evaluated based on the Kappa measure of agreement (Kno, Klocation and Kquanity) and produced a satisfactory level of accuracy. After calibrating the model and assessing its validity, a “real” prediction for the year 2010 is carried out. Analysis of the prediction revealed that the rate of urban growth tends to continue and would threaten large areas that are currently reserved for forest cover, farming lands and natural parks. Finally, the modeling output provides a building block for successive urban planning, for exploring how an

Cellular Automata

Modelling and simulation are disciplines of major importance for science and engineering. There is no science without models, and simulation has nowadays become a very useful tool, sometimes unavoidable, for development of both science and engineering. The main attractive feature of cellular automata is that, in spite of their conceptual simplicity which allows an easiness of implementation for computer simulation, as a detailed and complete mathematical analysis in principle, they are able to exhibit a wide variety of amazingly complex behaviour. This feature of cellular automata has attracted the researchers' attention from a wide variety of divergent fields of the exact disciplines of science and engineering, but also of the social sciences, and sometimes beyond. The collective complex behaviour of numerous systems, which emerge from the interaction of a multitude of simple individuals, is being conveniently modelled and simulated with cellular automata for very different purposes. In this book, a number of innovative applications of cellular automata models in the fields of Quantum Computing, Materials Science, Cryptography and Coding, and Robotics and Image Processing are presented

Lattice-gas cellular automata for the analysis of cancer invasion

Cancer cells display characteristic traits acquired in a step-wise manner during carcinogenesis. Some of these traits are autonomous growth, induction of angiogenesis, invasion and metastasis. In this thesis, the focus is on one of the latest stages of tumor progression, tumor invasion. Tumor invasion emerges from the combined effect of tumor cell-cell and cell-microenvironment interactions, which can be studied with the help of mathematical analysis. Cellular automata (CA) can be viewed as simple models of self-organizing complex systems in which collective behavior can emerge out of an ensemble of many interacting "simple" components. In particular, we focus on an important class of CA, the so-called lattice-gas cellular automata (LGCA). In contrast to traditional CA, LGCA provide a straightforward and intuitive implementation of particle transport and interactions. Additionally, the structure of LGCA facilitates the mathematical analysis of their behavior. Here, the principal tools of mathematical analysis of LGCA are the mean-field approximation and the corresponding Lattice Boltzmann equation. The main objective of this thesis is to investigate important aspects of tumor invasion, under the microscope of mathematical modeling and analysis: Impact of the tumor environment: We introduce a LGCA as a microscopic model of tumor cell migration together with a mathematical description of different tumor environments. We study the impact of the various tumor environments (such as extracellular matrix) on tumor cell migration by estimating the tumor cell dispersion speed for a given environment. Effect of tumor cell proliferation and migration: We study the effect of tumor cell proliferation and migration on the tumor’s invasive behavior by developing a simplified LGCA model of tumor growth. In particular, we derive the corresponding macroscopic dynamics and we calculate the tumor’s invasion speed in terms of tumor cell proliferation and migration rates. Moreover, we calculate the width of the invasive zone, where the majority of mitotic activity is concentrated, and it is found to be proportional to the invasion speed. Mechanisms of tumor invasion emergence: We investigate the mechanisms for the emergence of tumor invasion in the course of cancer progression. We conclude that the response of a microscopic intracellular mechanism (migration/proliferation dichotomy) to oxygen shortage, i.e. hypoxia, maybe responsible for the transition from a benign (proliferative) to a malignant (invasive) tumor. Computing in vivo tumor invasion: Finally, we propose an evolutionary algorithm that estimates the parameters of a tumor growth LGCA model based on time-series of patient medical data (in particular Magnetic Resonance and Diffusion Tensor Imaging data). These parameters may allow to reproduce clinically relevant tumor growth scenarios for a specific patient, providing a prediction of the tumor growth at a later time stage.Krebszellen zeigen charakteristische Merkmale, die sie in einem schrittweisen Vorgang während der Karzinogenese erworben haben. Einige dieser Merkmale sind autonomes Wachstum, die Induktion von Angiogenese, Invasion und Metastasis. Der Schwerpunkt dieser Arbeit liegt auf der Tumorinvasion, einer der letzten Phasen der Tumorprogression. Die Tumorinvasion ensteht aus der kombinierten Wirkung von den Wechselwirkungen Tumorzelle-Zelle und Zelle-Mikroumgebung, die mit die Hilfe von mathematischer Analyse untersucht werden können. Zelluläre Automaten (CA) können als einfache Modelle von selbst-organisierenden komplexen Systemen betrachtet werden, in denen kollektives Verhalten aus einer Kombination von vielen interagierenden "einfachen" Komponenten entstehen kann. Insbesondere konzentrieren wir uns auf eine wichtige CA-Klasse, die sogenannten Zelluläre Gitter-Gas Automaten (LGCA). Im Gegensatz zu traditionellen CA bieten LGCA eine einfache und intuitive Umsetzung der Teilchen und Wechselwirkungen. Zusätzlich erleichtert die Struktur der LGCA die mathematische Analyse ihres Verhaltens. Die wichtigsten Werkzeuge der mathematischen Analyse der LGCA sind hier die Mean-field Approximation und die entsprechende Lattice - Boltzmann - Gleichung. Das wichtigste Ziel dieser Arbeit ist es, wichtige Aspekte der Tumorinvasion unter dem Mikroskop der mathematischen Modellierung und Analyse zu erforschen: Auswirkungen der Tumorumgebung: Wir stellen einen LGCA als mikroskopisches Modell der Tumorzellen-Migration in Verbindung mit einer mathematischen Beschreibung der verschiedenen Tumorumgebungen vor. Wir untersuchen die Auswirkungen der verschiedenen Tumorumgebungen (z. B. extrazellulären Matrix) auf die Migration von Tumorzellen dürch Schätzung der Tumorzellen-Dispersionsgeschwindigkeit in einem gegebenen Umfeld. Wirkung von Tumor-Zellenproliferation und Migration: Wir untersuchen die Wirkung von Tumorzellenproliferation und Migration auf das invasive Verhalten der Tumorzellen durch die Entwicklung eines vereinfachten LGCA Tumorwachstumsmodells. Wir leiten die entsprechende makroskopische Dynamik und berechnen die Tumorinvasionsgeschwindigkeit im Hinblick auf die Tumorzellenproliferation- und Migrationswerte. Darüber hinaus berechnen wir die Breite der invasiven Zone, wo die Mehrheit der mitotischer Aktivität konzentriert ist, und es wird festgestellt, dass diese proportional zu den Invasionsgeschwindigkeit ist. Mechanismen der Tumorinvasion Entstehung: Wir untersuchen Mechanismen, die für die Entstehung von Tumorinvasion im Verlauf des Krebs zuständig sind. Wir kommen zu dem Schluss, dass die Reaktion eines mikroskopischen intrazellulären Mechanismus (Migration/Proliferation Dichotomie) zu Sauerstoffmangel, d.h. Hypoxie, möglicheweise für den Übergang von einem gutartigen (proliferative) zu einer bösartigen (invasive) Tumor verantwortlich ist. Berechnung der in-vivo Tumorinvasion: Schließlich schlagen wir einen evolutionären Algorithmus vor, der die Parameter eines LGCA Modells von Tumorwachstum auf der Grundlage von medizinischen Daten des Patienten für mehrere Zeitpunkte (insbesondere die Magnet-Resonanz-und Diffusion Tensor Imaging Daten) ermöglicht. Diese Parameter erlauben Szenarien für einen klinisch relevanten Tumorwachstum für einen bestimmten Patienten zu reproduzieren, die eine Vorhersage des Tumorwachstums zu einem späteren Zeitpunkt möglich machen

Urban Informatics

This open access book is the first to systematically introduce the principles of urban informatics and its application to every aspect of the city that involves its functioning, control, management, and future planning. It introduces new models and tools being developed to understand and implement these technologies that enable cities to function more efficiently – to become ‘smart’ and ‘sustainable’. The smart city has quickly emerged as computers have become ever smaller to the point where they can be embedded into the very fabric of the city, as well as being central to new ways in which the population can communicate and act. When cities are wired in this way, they have the potential to become sentient and responsive, generating massive streams of ‘big’ data in real time as well as providing immense opportunities for extracting new forms of urban data through crowdsourcing. This book offers a comprehensive review of the methods that form the core of urban informatics from various kinds of urban remote sensing to new approaches to machine learning and statistical modelling. It provides a detailed technical introduction to the wide array of tools information scientists need to develop the key urban analytics that are fundamental to learning about the smart city, and it outlines ways in which these tools can be used to inform design and policy so that cities can become more efficient with a greater concern for environment and equity

Urban Informatics

This open access book is the first to systematically introduce the principles of urban informatics and its application to every aspect of the city that involves its functioning, control, management, and future planning. It introduces new models and tools being developed to understand and implement these technologies that enable cities to function more efficiently – to become ‘smart’ and ‘sustainable’. The smart city has quickly emerged as computers have become ever smaller to the point where they can be embedded into the very fabric of the city, as well as being central to new ways in which the population can communicate and act. When cities are wired in this way, they have the potential to become sentient and responsive, generating massive streams of ‘big’ data in real time as well as providing immense opportunities for extracting new forms of urban data through crowdsourcing. This book offers a comprehensive review of the methods that form the core of urban informatics from various kinds of urban remote sensing to new approaches to machine learning and statistical modelling. It provides a detailed technical introduction to the wide array of tools information scientists need to develop the key urban analytics that are fundamental to learning about the smart city, and it outlines ways in which these tools can be used to inform design and policy so that cities can become more efficient with a greater concern for environment and equity

Land-Cover and Land-Use Study Using Genetic Algorithms, Petri Nets, and Cellular Automata

Recent research techniques, such as genetic algorithm (GA), Petri net (PN), and cellular automata (CA) have been applied in a number of studies. However, their capability and performance in land-cover land-use (LCLU) classification, change detection, and predictive modeling have not been well understood. This study seeks to address the following questions: 1) How do genetic parameters impact the accuracy of GA-based LCLU classification; 2) How do image parameters impact the accuracy of GA-based LCLU classification; 3) Is GA-based LCLU classification more accurate than the maximum likelihood classifier (MLC), iterative self-organizing data analysis technique (ISODATA), and the hybrid approach; 4) How do genetic parameters impact Petri Net-based LCLU change detection; and 5) How do cellular automata components impact the accuracy of LCLU predictive modeling. The study area, namely the Tickfaw River watershed (711mi²), is located in southeast Louisiana and southwest Mississippi. The major datasets include time-series Landsat TM / ETM images and Digital Orthophoto Quarter Quadrangles (DOQQ’s). LCLU classification was conducted by using the GA, MLC, ISODATA, and Hybrid approach. The LCLU change was modeled by using genetic PN-based process mining technique. The process models were interpreted and input to a CA for predicting future LCLU. The major findings include: 1) GA-based LCLU classification is more accurate than the traditional approaches; 2) When genetic parameters, image parameters, or CA components are configured improperly, the accuracy of LCLU classification, the coverage of LCLU change process model, and/or the accuracy of LCLU predictive modeling will be low; 3) For GA-based LCLU classification, the recommended configuration of genetic / image parameters is generation 2000-5000, population 1000, crossover rate 69%-99%, mutation rate 0.1%-0.5%, generation gap 25%-50%, data layers 16-20, training / testing data size 10000-20000 / 5000-10000, and spatial resolution 30m-60m; 4) For genetic Petri nets-based LCLU change detection, the recommended configuration of genetic parameters is generation 500, population 300, crossover rate 59%, mutation rate 5%, and elitism rate 4%; and 5) For CA-based LCLU predictive modeling, the recommended configuration of CA components is space 6025 * 12993, state 2, von Neumann neighborhood 3 * 3, time step 2-3 years, and optimized transition rules