Convergence results for continuous-time dynamics arising in ant colony optimization

This paper studies the asymptotic behavior of several continuous-time dynamical systems which are analogs of ant colony optimization algorithms that solve shortest path problems. Local asymptotic stability of the equilibrium corresponding to the shortest path is shown under mild assumptions. A complete study is given for a recently proposed model called EigenAnt: global asymptotic stability is shown, and the speed of convergence is calculated explicitly and shown to be proportional to the difference between the reciprocals of the second shortest and the shortest paths.Comment: A short version of this paper was published in the preprints of the 19th World Congress of the International Federation of Automatic Control, Cape Town, South Africa, 24-29 August 201

On a preferential attachment and generalized Pólya's urn model

We study a general preferential attachment and Pólya's urn model. At each step a new vertex is introduced, which can be connected to at most one existing vertex. If it is disconnected, it becomes a pioneer vertex. Given that it is not disconnected, it joins an existing pioneer vertex with probability proportional to a function of the degree of that vertex. This function is allowed to be vertex-dependent, and is called the reinforcement function. We prove that there can be at most three phases in this model, depending on the behavior of the reinforcement function. Consider the set whose elements are the vertices with cardinality tending a.s. to infinity. We prove that this set either is empty, or it has exactly one element, or it contains all the pioneer vertices. Moreover, we describe the phase transition in the case where the reinforcement function is the same for all vertices. Our results are general, and in particular we are not assuming monotonicity of the reinforcement function. Finally, consider the regime where exactly one vertex has a degree diverging to infinity. We give a lower bound for the probability that a given vertex ends up being the leading one, i.e. its degree diverges to infinity. Our proofs rely on a generalization of the Rubin construction given for edge-reinforced random walks, and on a Brownian motion embedding.Preferential attachment; Reinforcement processes; Species sampling sequence; Pólya's urn process

On a preferential attachment and generalized P\'{o}lya's urn model

We study a general preferential attachment and Polya's urn model. At each step a new vertex is introduced, which can be connected to at most one existing vertex. If it is disconnected, it becomes a pioneer vertex. Given that it is not disconnected, it joins an existing pioneer vertex with probability proportional to a function of the degree of that vertex. This function is allowed to be vertex-dependent, and is called the reinforcement function. We prove that there can be at most three phases in this model, depending on the behavior of the reinforcement function. Consider the set whose elements are the vertices with cardinality tending a.s. to infinity. We prove that this set either is empty, or it has exactly one element, or it contains all the pioneer vertices. Moreover, we describe the phase transition in the case where the reinforcement function is the same for all vertices. Our results are general, and in particular we are not assuming monotonicity of the reinforcement function. Finally, consider the regime where exactly one vertex has a degree diverging to infinity. We give a lower bound for the probability that a given vertex ends up being the leading one, that is, its degree diverges to infinity. Our proofs rely on a generalization of the Rubin construction given for edge-reinforced random walks, and on a Brownian motion embedding.Comment: Published in at http://dx.doi.org/10.1214/12-AAP869 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

2008,06: Evolutionary modelling in economics : a survey of methods and building blocks

In this paper we present an overview of methods and components of formal economic models employing evolutionary approaches. This compromises two levels: (1) techniques of evolutionary modelling, including multi-agent modelling, evolutionary algorithms and evolutionary game theory; (2) building blocks or components of formal models classified into core processes and features of evolutionary systems - diversity, innovation and selection - and additional elements, such as bounded rationality, diffusion, path dependency and lock-in, co-evolutionary dynamics, multilevel and group selection, and evolutionary growth. We focus our attention on the characteristics of models and techniques and their underlying assumptions. -- bounded rationality ; evolutionary algorithms ; evolutionary game theory ; evolutionary growth ; innovation ; multilevel evolution ; neo-Schumpeterian models

Why knot?

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, 1991.Includes bibliographical references (p. 535-551).Carol Strohecker.Ph.D

1999-2001 Wright State University Undergraduate Course Catalog

This is a Wright State University undergraduate course catalog from 1999-2001.https://corescholar.libraries.wright.edu/archives_catalogs/1044/thumbnail.jp

Diffusion of Technologies and Social Behavior

The diffusion of innovations is at the core of the dynamic processes that underlie social, economic, and technological change. Diffusion phenomena are not limited to the spread of new process technologies and the market penetration of new products but extend also to changes in the forms of social organization and transformations in the social fabric and cultural traits. This book is the outcome of the diffusion of the concept of diffusion as a fundamental process in society. Originating from biology, diffusion research is now carried out in many disciplines including economics, geography, history, technological change, sociology, and management science. The book illustrates the progress that has been made in understanding the nature of diffusion processes and their underlying driving forces. The contributions by leading scholars provide a novel interdisciplinary perspective and span a wide range of modeling and empirical research backgrounds

Compact Anthology of World Literature II: Volumes 4, 5, and 6

The Compact Anthology of World Literature, Parts 4, 5, and 6 is designed as an e-book to be accessible on a variety of devices: smart phone, tablet, e-reader, laptop, or desktop computer. Students have reported ease of accessibility and readability on all these devices. To access the ePub text on a laptop, desktop, or tablet, you will need to download a program through which you can read the text. We recommend Readium, an application available through Google. If you plan to read the text on an Android device, you will need to download an application called Lithium from the App Store. On an iPhone, the text will open in iBooks. Affordable Learning Georgia has also converted the .epub files to PDF. Because .epub does not easily convert to other formats, the left margin of the .pdf is very narrow. ALG recommends using the .epub version. Although the text is designed to look like an actual book, the Table of Contents is composed of hyperlinks that will take you to each introductory section and then to each text. The three parts of the text are organized into the following units: Part 4—The Seventeenth and Eighteenth Centuries Unit I: The Age of Reason Unit II: The Near East and Asia Part 5—The Long Nineteenth Century Unit I Romanticism Unit II Realism Part 6—The Twentieth Century and Contemporary Literature Unit I Modernism Unit II Postcolonial Literature Unit III Contemporary Literature Texts from a variety of genres and cultures are included in each unit. Additionally, each selection or collection includes a brief introduction about the author and text(s), and each includes 3 – 5 discussion questions. Texts in the public domain--those published or translated before 1923--are replicated here. Texts published or translated after 1923 are not yet available in the public domain. In those cases, we have provided a link to a stable site that includes the text. Thus, in Part 6, most of the texts are accessible in the form of links to outside sites. In every case, we have attempted to connect to the most stable links available. The following texts have been prepared with the assistance of the University of North Georgia Press in its role as Affordable Learning Georgia\u27s Partner Press. Affordable Learning Georgia partners with the University of North Georgia Press to assist grantees with copyright clearance, peer review, production and design, and other tasks required to produce quality Open Educational Resources (OER). The University Press is a peer-reviewed, academic press. Its mission is to produce scholarly work that contributes to the fields of innovative teaching, textbooks, and Open Educational Resources. Affordable Learning Georgia Textbook Transformation Grant funds may be used for services provided by the Press. To determine how the University Press can assist ALG grantees or anyone interested in developing OER with ALG, the University Press will provide advance free consultations. Please contact the Press at 706-864-1556 or [email protected]. “Textbook Transformation Grants” from Affordable Learning Georgia Accessible files with optical character recognition (OCR) and auto-tagging provided by the Center for Inclusive Design and Innovation.https://oer.galileo.usg.edu/english-textbooks/1018/thumbnail.jp