Complex Networks from Simple Rewrite Systems

Complex networks are all around us, and they can be generated by simple mechanisms. Understanding what kinds of networks can be produced by following simple rules is therefore of great importance. We investigate this issue by studying the dynamics of extremely simple systems where are `writer' moves around a network, and modifies it in a way that depends upon the writer's surroundings. Each vertex in the network has three edges incident upon it, which are colored red, blue and green. This edge coloring is done to provide a way for the writer to orient its movement. We explore the dynamics of a space of 3888 of these `colored trinet automata' systems. We find a large variety of behaviour, ranging from the very simple to the very complex. We also discover simple rules that generate forms which are remarkably similar to a wide range of natural objects. We study our systems using simulations (with appropriate visualization techniques) and analyze selected rules mathematically. We arrive at an empirical classification scheme which reveals a lot about the kinds of dynamics and networks that can be generated by these systems

An information geometrical evaluation of Shannon information metrics on a discrete n-dimensional digital manifold

The definition and nature of information have perplexed scientists due to its dual nature in measurements. The information is discrete and continuous when evaluated on a metric scale, and the Laplace-Beltrami operator and Gauss-Bonnet Theorem can map one to another. On the other hand, defining the information as a discrete entity on the surface area of an n-dimensional discrete digital manifold provides a unique way of calculating the entropy of a manifold. The software simulation shows that the surface area of the discrete n-dimensional digital manifold is an effectively computable function. Moreover, it also provides the information-geometrical evaluation of Shannon information metrics

Lexical measurements for information retrieval: a quantum approach

The problem of determining whether a document is about a loosely defined topic is at the core of text Information Retrieval (IR). An automatic IR system should be able to determine if a document is likely to convey information on a topic. In most cases, it has to do it solely based on measure- ments of the use of terms in the document (lexical measurements). In this work a novel scheme for measuring and representing lexical information from text documents is proposed. This scheme is inspired by the concept of ideal measurement as is described by Quantum Theory (QT). We apply it to Information Retrieval through formal analogies between text processing and physical measurements. The main contribution of this work is the development of a complete mathematical scheme to describe lexical measurements. These measurements encompass current ways of repre- senting text, but also completely new representation schemes for it. For example, this quantum-like representation includes logical features such as non-Boolean behaviour that has been suggested to be a fundamental issue when extracting information from natural language text. This scheme also provides a formal unification of logical, probabilistic and geometric approaches to the IR problem. From the concepts and structures in this scheme of lexical measurement, and using the principle of uncertain conditional, an “Aboutness Witness” is defined as a transformation that can detect docu- ments that are relevant to a query. Mathematical properties of the Aboutness Witness are described in detail and related to other concepts from Information Retrieval. A practical application of this concept is also developed for ad hoc retrieval tasks, and is evaluated with standard collections. Even though the introduction of the model instantiated here does not lead to substantial perfor- mance improvements, it is shown how it can be extended and improved, as well as how it can generate a whole range of radically new models and methodologies. This work opens a number of research possibilities both theoretical and experimental, like new representations for documents in Hilbert spaces or other forms, methodologies for term weighting to be used either within the proposed framework or independently, ways to extend existing methodologies, and a new range of operator-based methods for several tasks in IR

Homo deceptus: How language creates its own reality

Homo deceptus is a book that brings together new ideas on language, consciousness and physics into a comprehensive theory that unifies science and philosophy in a different kind of Theory of Everything. The subject of how we are to make sense of the world is addressed in a structured and ordered manner, which starts with a recognition that scientific truths are constructed within a linguistic framework. The author argues that an epistemic foundation of natural language must be understood before laying claim to any notion of reality. This foundation begins with Ludwig Wittgenstein’s Tractatus Logico-Philosophicus and the relationship of language to formal logic. Ultimately, we arrive at an answer to the question of why people believe the things they do. This is effectively a modification of Alfred Tarski’s semantic theory of truth. The second major issue addressed is the ‘dreaded’ Hard Problem of Consciousness as first stated by David Chalmers in 1995. The solution is found in the unification of consciousness, information theory and notions of physicalism. The physical world is shown to be an isomorphic representation of the phenomenological conscious experience. New concepts in understanding how language operates help to explain why this relationship has been so difficult to appreciate. The inclusion of concepts from information theory shows how a digital mechanics resolves heretofore conflicting theories in physics, cognitive science and linguistics. Scientific orthodoxy is supported, but viewed in a different light. Mainstream science is not challenged, but findings are interpreted in a manner that unifies consciousness without contradiction. Digital mechanics and formal systems of logic play central roles in combining language, consciousness and the physical world into a unified theory where all can be understood within a single consistent framework