Inductive Pattern Formation

With the extended computational limits of algorithmic recursion, scientific investigation is transitioning away from computationally decidable problems and beginning to address computationally undecidable complexity. The analysis of deductive inference in structure-property models are yielding to the synthesis of inductive inference in process-structure simulations. Process-structure modeling has examined external order parameters of inductive pattern formation, but investigation of the internal order parameters of self-organization have been hampered by the lack of a mathematical formalism with the ability to quantitatively define a specific configuration of points. This investigation addressed this issue of quantitative synthesis. Local space was developed by the Poincare inflation of a set of points to construct neighborhood intersections, defining topological distance and introducing situated Boolean topology as a local replacement for point-set topology. Parallel development of the local semi-metric topological space, the local semi-metric probability space, and the local metric space of a set of points provides a triangulation of connectivity measures to define the quantitative architectural identity of a configuration and structure independent axes of a structural configuration space. The recursive sequence of intersections constructs a probabilistic discrete spacetime model of interacting fields to define the internal order parameters of self-organization, with order parameters external to the configuration modeled by adjusting the morphological parameters of individual neighborhoods and the interplay of excitatory and inhibitory point sets. The evolutionary trajectory of a configuration maps the development of specific hierarchical structure that is emergent from a specific set of initial conditions, with nested boundaries signaling the nonlinear properties of local causative configurations. This exploration of architectural configuration space concluded with initial process-structure-property models of deductive and inductive inference spaces. In the computationally undecidable problem of human niche construction, an adaptive-inductive pattern formation model with predictive control organized the bipartite recursion between an information structure and its physical expression as hierarchical ensembles of artificial neural network-like structures. The union of architectural identity and bipartite recursion generates a predictive structural model of an evolutionary design process, offering an alternative to the limitations of cognitive descriptive modeling. The low computational complexity of these models enable them to be embedded in physical constructions to create the artificial life forms of a real-time autonomously adaptive human habitat

The structured phase of concurrency

This extended abstract summarizes the state-of-the-art solution to the structuring problem for models that describe existing real world or envisioned processes. Special attention is devoted to models that allow for the true concurrency semantics. Given a model of a process, the structuring problem deals with answering the question of whether there exists another model that describes the process and is solely composed of structured patterns, such as sequence, selection, option for simultaneous execution, and iteration. Methods and techniques for structuring developed by academia as well as products and standards proposed by industry are discussed. Expectations and recommendations on the future advancements of the structuring problem are suggested

Practical Considerations and Applications for Autonomous Robot Swarms

In recent years, the study of autonomous entities such as unmanned vehicles has begun to revolutionize both military and civilian devices. One important research focus of autonomous entities has been coordination problems for autonomous robot swarms. Traditionally, robot models are used for algorithms that account for the minimum specifications needed to operate the swarm. However, these theoretical models also gloss over important practical details. Some of these details, such as time, have been considered before (as epochs of execution). In this dissertation, we examine these details in the context of several problems and introduce new performance measures to capture practical details. Specifically, we introduce three new metrics: (1) the distance complexity (reflecting power usage and wear-and-tear of robots), (2) the spatial complexity (reflecting the space needed for the algorithm to work), and (3) local computational complexity (reflecting the computational requirements for each robot in the swarm). We apply these metrics in the study of some well-known and important problems, such as Complete Visibility and Arbitrary Pattern Formation. We also introduce and study a new problem, Doorway Egress, that captures the essence of a swarm’s navigation through restricted spaces. First, we examine the distance and spatial complexity used across a class of Complete Visibility algorithms. Second, we provide algorithms for Complete Visibility on an integer plane, including some that are asymptotically optimal in terms of time, distance complexity, and spatial complexity. Third, we introduce the problem of Doorway Egress and provide algorithms for a variety of robot swarm models with various optimalities. Finally, we provide an optimal algorithm for Arbitrary Pattern Formation on the grid

Using Neural Networks for Pattern Association for the Online Purchase of Products

Abstract: Today, a huge percentage of all the business transactions that take place in the domain of e-commerce are dominated by online shopping after the virtual market conceptualization of the business. This paper focuses on how pattern association rules may be obtained from the dynamic databases generated during purchases in an e-Store to maximize the profit of the marketer. In this paper, ANN has been used as a tool for generating pattern association rules during online purchases of products to aid the cross-selling of products. For getting the rules, a methodology using artificial neural networks has been adapted for usage using an extended Delta rule for initial training of the network and a hetero-associative neural network for generating and storing the associative rules. Also, a methodology has been proposed to filter out all rules which do not add economic value to the firm and then select that rule which will meet the profit maximization objective of the marketer

Faculty Publications and Creative Works 2004

Faculty Publications & Creative Works is an annual compendium of scholarly and creative activities of University of New Mexico faculty during the noted calendar year. Published by the Office of the Vice President for Research and Economic Development, it serves to illustrate the robust and active intellectual pursuits conducted by the faculty in support of teaching and research at UNM

Integration of tools for the Design and Assessment of High-Performance, Highly Reliable Computing Systems (DAHPHRS), phase 1

Systems for Space Defense Initiative (SDI) space applications typically require both high performance and very high reliability. These requirements present the systems engineer evaluating such systems with the extremely difficult problem of conducting performance and reliability trade-offs over large design spaces. A controlled development process supported by appropriate automated tools must be used to assure that the system will meet design objectives. This report describes an investigation of methods, tools, and techniques necessary to support performance and reliability modeling for SDI systems development. Models of the JPL Hypercubes, the Encore Multimax, and the C.S. Draper Lab Fault-Tolerant Parallel Processor (FTPP) parallel-computing architectures using candidate SDI weapons-to-target assignment algorithms as workloads were built and analyzed as a means of identifying the necessary system models, how the models interact, and what experiments and analyses should be performed. As a result of this effort, weaknesses in the existing methods and tools were revealed and capabilities that will be required for both individual tools and an integrated toolset were identified

Perplexing Complexity Human Modelling and Primacy of the Group as Essence of Complexity

This paper describes the emergence of complexity as duplicated evolutionary process. The first procedural source of complexity is the quantum jump of the evolution of the human species when it started to maintain certain brain-internal models of its environment. The second - parallel - procedural origin is the evolution of a communication structure, a language, with which an already existing group of primates could frame their internal models. In contrast to definitions of complexity which use the concept in the context of theoretical physics, this approach reveals some perplexing properties of model-building for a special subject of investigation; namely the human species: All adequate models of political economy (economics is just the sub-discipline that freezes political dynamics) have to be complex. Since today’s mainstream economic theory lends its formal apparatus from the mathematics of Newtonian physics, it misses the most essential features characterizing human social dynamics, i.e. its complexity

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this paper we present computational techniques to investigate the solutions of two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD systems, and extend them to operate on large-scale meshes for arbitrary surfaces. In particular, we use spectral techniques for a linear stability analysis to characterize and directly compose patterns emerging from homogeneities. We develop an implementation using surface finite element methods and a numerical eigenanalysis of the Laplace-Beltrami operator on surface meshes. In addition, we describe a technique to explore solutions of the nonlinear RD equations using numerical continuation. Here, we present a multiresolution approach that allows us to trace solution branches of the nonlinear equations efficiently even for large-scale meshes. Finally, we demonstrate the working of our framework for two RD systems with applications in biological pattern formation: a Brusselator model that has been used to model pattern development on growing plant tips, and a chemotactic model for the formation of skin pigmentation patterns. While these models have been used previously on simple geometries, our framework allows us to study the impact of arbitrary geometries on emerging patterns.Comment: This paper was submitted at the Journal of Mathematical Biology, Springer on 07th July 2015, in its current form (barring image references on the last page and cosmetic changes owning to rebuild for arXiv). The complete body of work presented here was included and defended as a part of my PhD thesis in Nov 2015 at the University of Ber