The Four-Color Theorem And Chromatic Numbers Of Graphs,
2010
Lynchburg College
The Four-Color Theorem And Chromatic Numbers Of Graphs, Sarah E. Cates
Undergraduate Theses and Capstone Projects
We study graph colorings of the form made popular by the four-color theorem. Proved by Appel and Haken in 1976, the Four-Color Theorem states that all planar graphs can be vertex-colored with at most four colors. We consider an alternate way to prove the Four-Color Theorem, introduced by Hadwiger in 1943 and commonly know as Hadwiger’s Conjecture. In addition, we examine the chromatic number of graphs which are not planar. More specifically, we explore adding edges to a planar graph to create a non-planar graph which has the same chromatic number as the planar graph which we started from.
Towards A Formal Theory Of Interoperability,
2010
Old Dominion University
Towards A Formal Theory Of Interoperability, Saikou Y. Diallo
Computational Modeling & Simulation Engineering Theses & Dissertations
This dissertation proposes a formal theory of interoperability that explains 1) what interoperability is as opposed to how it works, 2) how to tell whether two or more systems can interoperate and 3) how to identify whether systems are interoperating or merely exchanging bits and bytes. The research provides a formal model of data in M&S that captures all possible representations of a real or imagined thing and distinguishes between existential dependencies and transformational dependencies. Existential dependencies capture the relationships within a model while transformational dependencies capture the relationships between interactions with a model. These definitions are used to formally …
Non Bayesian Conditioning And Deconditioning,
2010
University of New Mexico
Non Bayesian Conditioning And Deconditioning, Jean Dezert, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
In this paper, we present a Non-Bayesian conditioning rule for belief revision. This rule is truly Non-Bayesian in the sense that it doesn’t satisfy the common adopted principle that when a prior belief is Bayesian, after conditioning by X, Bel(X|X) must be equal to one. Our new conditioning rule for belief revision is based on the proportional conflict redistribution rule of combination developed in DSmT (Dezert-Smarandache Theory) which abandons Bayes’ conditioning principle. Such Non-Bayesian conditioning allows to take into account judiciously the level of conflict between the prior belief available and the conditional evidence. We also introduce the deconditioning problem …
Sketch Of A Typology Of Abstract Memristic Machines,
2010
ThinkArt Lab Glasgow
Sketch Of A Typology Of Abstract Memristic Machines, Rudolf Kaehr
Rudolf Kaehr
A typology of memristic machines is sketched. This sketch gives an overview and orientation to the paper “Towards Abstract Memristic Machines”. It also intents to propose a concise systematization of the newly introduced terms and strategies to memristics and morphogrammatics. This sketch is introducing four types of sign-use for four types of machines of fundamentally different paradigms: 1. semiotic, 2. monomorphic, 3. polymorphic and 4. bisimilar abstract machines. Further definitions of abstract machines have to be based on those graphematic notational systems. A realization of such constructions of abstract machines, in contrast to existing abstract machines of the theory of …
Towards Abstract Memristic Machines,
2010
ThinkArt Lab Glasgow
From Universe To Polyverses,
2010
ThinkArt Lab Glasgow
From Universe To Polyverses, Rudolf Kaehr
Rudolf Kaehr
Some thoughts about the power of speculation behind important discoveries in mathematics, physics and computer science. The exercise shows that there is no need for a compulsory ultimate unifying universe. It is speculated that just this paradigm of a single ultimate universe is unmasking itself today as the main obstacle for further development in Western science and technology.
Morphogrammatics For Dummies: The Domino Approach,
2010
ThinkArt Lab Glasgow
Morphogrammatics For Dummies: The Domino Approach, Rudolf Kaehr
Rudolf Kaehr
Dominoes, morphograms, cellular automata, memristics. Topics: possible continuation, coalitions, cooperations, substitution, morphic bisimilarity.
Fusion Of Sources Of Evidence With Different Importances And Reliabilities,
2010
University of New Mexico
Fusion Of Sources Of Evidence With Different Importances And Reliabilities, Florentin Smarandache, Jean Dezert, J.M. Tacnet
Branch Mathematics and Statistics Faculty and Staff Publications
This paper presents a new approach for combining sources of evidences with different importances and reliabilities. Usually, the combination of sources of evidences with different reliabilities is done by the classical Shafer’s discounting approach. Therefore, to consider unequal importances of sources, if any, a similar reliability discounting process is generally used, making no difference between the notion of importance and reliability. In fact, in multicriteria decision context, these notions should be clearly distinguished. This paper shows how this can be done and we provide simple examples to show the differences between both solutions for managing importances and reliabilities of sources. …
