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2013 | Book

Numerical Computations with Infinite and Infinitesimal Numbers: Theory and Applications Read chapter Read first chapter

Dynamics of Information Systems: Algorithmic Approaches

Editors: Alexey Sorokin, Panos M. Pardalos

Publisher: Springer New York

Book Series : Springer Proceedings in Mathematics & Statistics

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

Dynamics of Information Systems: Algorithmic Approaches presents recent developments and results found by participants of the Fourth International Conference on the Dynamics of Information Systems, which took place at the University of Florida, Gainesville FL, USA on February 20-22, 2012. The purpose of this conference was to bring together scientists and engineers from industry, government, and universities to exchange knowledge and results in a broad range of topics relevant to the theory and practice of the dynamics of information systems.​​​Dynamics of Information plays an increasingly critical role in our society. The influence of information on social, biological, genetic, and military systems must be better understood to achieve large advances in the capability and understanding of these systems. Applications are widespread and include: detection of terrorist networks, design of highly efficient businesses, computer networks, quantum entanglement, genome modeling, multi-robotic systems, and industrial and manufacturing safety.

The book contains state-of-the-art work on theory and practice relevant to the dynamics of information systems. It covers algorithmic approaches to numerical computations with infinite and infinitesimal numbers; presents important problems arising in service-oriented systems, such as dynamic composition and analysis of modern service-oriented information systems and estimation of customer service times on a rail network from GPS data; addresses the complexity of the problems arising in stochastic and distributed systems; and discusses modulating communication for improving multi-agent learning convergence. Network issues—in particular minimum-risk maximum-clique problems, vulnerability of sensor networks, influence diffusion, community detection, and link prediction in social network analysis, as well as a comparative analysis of algorithms for transmission network expansion planning—are described in later chapters.

Table of Contents

Frontmatter
Numerical Computations with Infinite and Infinitesimal Numbers: Theory and Applications
Abstract
A new computational methodology for executing calculations with infinite and infinitesimal quantities is described in this chapter. It is based on the principle “The part is less than the whole” introduced by Ancient Greeks and applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). It is shown that it becomes possible to write down finite, infinite, and infinitesimal numbers by a finite number of symbols as particular cases of a unique framework that is not related to non-standard analysis theories. The Infinity Computer working with numbers of a new kind is described (its simulator has already been realized). The concept of accuracy of mathematical languages and its importance for a number of theoretical and practical issues regarding computations is discussed. Numerous examples dealing with divergent series, infinite sets, probability, limits, fractals, etc. are given.
Yaroslav D. Sergeyev
Dynamic Composition and Analysis of Modern Service-Oriented Information Systems
Abstract
Despite all the advantages brought by service-oriented architecture (SOA), experts argue that SOA introduces more complexity into information systems rather than resolving it. The problem of service integration challenges modern companies taking the risk of implementing SOA. One of important aspects of this problem relates to dynamic service composition, which has to take into account many types of information and restrictions existing in each enterprise. Moreover, all the changes in business logic should also be promptly reflected. This chapter proposes the approach to solution of the stated problem based on such concepts as model-driven architecture (MDA), ontology modelling and logical analysis. The approach consists of several steps of modelling and finite scope logical analysis for automated translation of business processes into the sequence of service invocations. Formal language of relational logic is proposed as a key element of the proposed approach which is responsible for logical analysis and service workflow generation. We present a logical theory to automatically specialize generic orchestration templates which are close to semantic specification of abstract services in OWL-S. The developed logical theory is described formally in terms of Relational Logic. Our approach is implemented and tested using MIT Alloy Analyzer software.
Habib Abdulrab, Eduard Babkin, Jeremie Doucy
Estimating Customer Service Times on a Rail Network from GPS Data
Abstract
A key input to managing and scheduling customer service on a rail network is an accurate characterization of the time a particular train takes to serve a customer, based on the quantity of work the customer requires. The algorithm presented here estimates the customer service times of a train on a given day utilizing global positioning system (GPS) data from train locomotives, the known customers to be served on the day and some geographic knowledge of the customer’s tracks. The algorithm was built and evaluated on real data sets provided by CSX. This research was conducted as a joint effort between the University of Florida in Gainesville, FL and CSX Transportation, Inc. in Jacksonville, Florida.
Shantih M. Spanton, Joseph Geunes
A Risk-Averse Game-Theoretic Approach to Distributed Control
Abstract
The research article gives a comprehensive presentation of the broad and still developing area of risk-averse decision-making approach to control of distributed stochastic systems. A distributed stochastic system considered here consists of the interconnection of two or more stochastic systems with the structural constraints of linear system dynamics, quadratic cost functionals, and additive stationary Wiener noises corrupting the system dynamics and measurements. Each system has an input from its incumbent agent or controller and an output to its local environment, in addition to links with the other neighboring systems. The problem of distributed control without communications between incumbent agents or controllers is formulated as a nonzero-sum stochastic differential game. Local best responses by each incumbent agents with risk-averse attitudes toward performance uncertainty are determined by a person-by-person equilibrium and subject to decentralized output-feedback information structures.
Khanh D. Pham, Meir Pachter
Static Teams and Stochastic Games
Abstract
Radner’s solution of the static team decision problem is revisited. A careful and complete statement of the static decentralized optimization problem, also referred to as the team decision problem, is given. Decentralized optimization is considered in the framework of nonzero-sum game theory, and the impact of the partial information pattern on the structure of the optimal strategies is analyzed. The complete solution of the static decentralized multivariate Quadratic Gaussian (QG) optimization problem is obtained.
Meir Pachter, Khanh Pham
A Framework for Coordination in Distributed Stochastic Systems: Output Feedback and Performance Risk Aversion
Abstract
This research article considers a class of distributed stochastic systems where interconnected systems closely keep track of reference signals issued by a coordinator. Much of the existing literature concentrates on conducting decisions and control synthesis based solely on expected utilities and averaged performance. However, research in psychology and behavioral decision theory suggests that performance risk plays an important role in shaping preferences in decisions under uncertainty. Thus motivated, a new equilibrium concept, called “person-by-person equilibrium” for local best responses is proposed for analyzing signaling effects and mutual influences between an incumbent system, its coordinator, and immediate neighbors. Individual member objectives are defined by the multi-attribute utility functions that capture both performance expectation and risk measures to model the satisfaction associated with local best responses with risk-averse attitudes. The problem class and approach of coordination control of distributed stochastic systems proposed here are applicable to and exemplified in military organizations and flexibly autonomous systems.
Khanh D. Pham
Modulating Communication to Improve Multi-agent Learning Convergence
Abstract
The problem of getting interacting agents to learn simultaneously to improve their joint performance has received significant attention in the literature. One of the key challenges is to manage the system-wide effects that occur due to learning in a non-stationary environment. In this paper, we look at the impact on the system-wide dynamics and the learning convergence due to communication between the agents. Specifically, we look at the problem of learning routes between locations in a graph in the case where agents using the same edge at the same time slow each other down. We implemented and empirically examined a model where the agents simply try to model each edge in the graph as being either slow, medium, or fast due to the other agents using that edge. Communication on a fixed social network occurs only when an agent changes the speed category it has for a particular link, e.g., when it changes from believing a link is slow to believing it is medium. We find that the system dynamics are very sensitive to the ratio between the influence of direct observations on local beliefs to the influence of communicated beliefs. For some values of this ratio, convergence to good behavior can occur very quickly, but for others a brief period of good performance is followed by wild oscillations.
Paul Scerri
Minimum-Risk Maximum Clique Problem
Abstract
In this work, we consider the minimum-risk maximum clique problem on stochastic graphs. Namely, assuming that each vertex of the graph is associated with a random variable describing a cost or a loss, such that the joint distribution of all variables on the graph is known, the goal is to determine a clique in the graph that has the lowest risk, given a specific risk measure. It is shown that in the developed problem formulation, minimization of risk is facilitated through inclusion of additional vertices in the partial solution, whereby an optimal solution represents a maximal clique in the graph. In particular, two instances of risk-averse maximum clique problems are considered, where risk exposures of a graph’s vertices are “isolated” (i.e., not dependent on risk profiles of other vertices) and “neighbor-dependent,” or dependent on the risk profiles of adjacent vertices. Numerical experiments on randomly generated Erdos–Renyi demonstrating properties of optimal risk-averse maximum cliques are conducted.
Maciej Rysz, Pavlo A. Krokhmal, Eduardo L. Pasiliao
Models for Assessing Vulnerability in Imperfect Sensor Networks
Abstract
We examine a directed network on which sensors exist at a subset of the nodes. At each node, a target (e.g., an intruder in a physical network, a fire in a building, or a virus in a computer network) may or may not exist. Sensors detect the presence of these targets by monitoring the nodes at which they are located and all nodes adjacent from their positions. However, in practical settings a limited-cardinality subset of sensors might fail. A failed sensor may report false positives or negatives and, as a result, the network owner may not be able to ascertain whether or not targets exist at some nodes. If it is not possible to deduce whether or not a target exists at a node with a given set of sensor readings, then the node is said to be ambiguous. We show that a network owner must solve a series of combinatorial optimization problems to determine which nodes are ambiguous. Furthermore, we determine the worst-case number of ambiguous nodes by optimizing over the set of all sensor readings that could possibly arise. We also present mathematical programming formulations for these problems under varying assumptions on how sensors fail, and on what assumptions a network owner makes on how sensors fail. Our computational results illustrate how these varying assumptions impact the number of ambiguous nodes.
Sibel B. Sonuç, J. Cole Smith
Minimum Connected Sensor Cover and Maximum-Lifetime Coverage in Wireless Sensor Networks
Abstract
Energy efficiency is an important issue in the study of wireless sensor networks. The minimum connected sensor cover problem and the maximum lifetime coverage problem are very well known in the literature on energy efficiency. In recent years, there are important developments in the study of these two problems through studying the relationship between the connected sensor cover and the group Steiner tree and the relationship between coverage and weighted dominating set. In this article, we introduce those relationships and related new developments on the minimum connected sensor cover problem and the maximum lifetime coverage problem.
Lidong Wu, Weili Wu, Kai Xing, Panos M. Pardalos, Eugene Maslov, Ding-Zhu Du
Influence Diffusion, Community Detection, and Link Prediction in Social Network Analysis
Abstract
Social networks have received extensive attention among researchers across a wide range of disciplines such as computer science, physics, and sociology. This paper mainly overviews a variety of approaches for three problems in real-world life scenarios. The first problem is about influence diffusion, in which influence represents news, ideas, information, and so forth; the second one concerns with partitioning social networks into communities efficiently; and the third one is to predict the hidden or possible new links between individuals in the future based on the existing or observed information.
Lidan Fan, Weili Wu, Zaixin Lu, Wen Xu, Ding-Zhu Du
Comparative Analysis of Local Search Strategies for Transmission Network Expansion Planning
Abstract
The demands for electricity and the electrical power generation in various areas may change significantly with time. These changes require additional transmission corridors to be installed in the existing electrical power network. The problem of electrical grid expansion can be formulated as a nonlinear mixed integer programming problem. The local search algorithms, which employ constructive heuristics for defining a neighborhood, could be used iteratively to find approximate solutions for this problem. In this study, we compare a number of local search strategies using statistical analysis techniques.
Alla Kammerdiner, Alex Fout, Russell Bent
Metadata
Title
Dynamics of Information Systems: Algorithmic Approaches
Editors
Alexey Sorokin
Panos M. Pardalos
Copyright Year
2013
Publisher
Springer New York
Electronic ISBN
978-1-4614-7582-8
Print ISBN
978-1-4614-7581-1
DOI
https://doi.org/10.1007/978-1-4614-7582-8