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2013 | Buch

Soliton Self-wave Number Downshift Compensation by the Increasing Second-Order Dispersion Kapitel lesen Erstes Kapitel lesen

Models, Algorithms, and Technologies for Network Analysis

Proceedings of the First International Conference on Network Analysis

herausgegeben von: Boris Goldengorin, Valery A. Kalyagin, Panos M. Pardalos

Verlag: Springer New York

Buchreihe : Springer Proceedings in Mathematics & Statistics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

​​ ​Network Analysis has become a major research topic over the last several years. The broad range of applications that can be described and analyzed by means of a network is bringing together researchers, practitioners and other scientific communities from numerous fields such as Operations Research, Computer Science, Transportation, Energy, Social Sciences, and more. The remarkable diversity of fields that take advantage of Network Analysis makes the endeavor of gathering up-to-date material in a single compilation a useful, yet very difficult, task. The purpose of these proceedings is to overcome this difficulty by collecting the major results found by the participants of the “First International Conference in Network Analysis,” held at The University of Florida, Gainesville, USA, from the 14th to the 16th of December 2011. The contributions of this conference not only come from different fields, but also cover a broad range of topics relevant to the theory and practice of network analysis, including the reliability of complex networks, software, theory, methodology and applications.

Inhaltsverzeichnis

Frontmatter
Soliton Self-wave Number Downshift Compensation by the Increasing Second-Order Dispersion
Abstract
Dynamics of solitons in the frame of the extended nonlinear Schrödinger equation (NSE) taking into account stimulated Raman scattering (SRS) and inhomogeneous second-order dispersion (SOD) is considered. Compensation of soliton Raman self-wave number downshift in media with increasing second-order linear dispersion is shown. Quasi-soliton solution with small wave number spectrum variation, amplitude and extension are found analytically in adiabatic approximation and numerically. The soliton is considered as the equilibrium of SRS and increasing SOD. For dominate SRS soliton wave number spectrum tends to long wave region. For dominate increasing SOD soliton wave number spectrum tends to shortwave region.
N. V. Aseeva, E. M. Gromov, V. V. Tyutin
Pattern-Based Heuristic for the Cell Formation Problem in Group Technology
Abstract
In this chapter we introduce a new pattern-based approach within the linear assignment model with the purpose to design heuristics for a combinatorial optimization problem (COP). We assume that the COP has an additive (separable) objective function and the structure of a feasible (optimal) solution to the COP is predefined by a collection of cells (positions) in an input file. We define a pattern as a collection of positions in an instance problem represented by its input file (matrix). We illustrate the notion of pattern by means of some well-known problems in COP, among them are the linear ordering problem (LOP) and cell formation problem (CFP), just to mention a couple. The CFP is defined on a Boolean input matrix, the rows of which represent machines and columns – parts. The CFP consists in finding three optimal objects: a block-diagonal collection of rectangles, a row (machines) permutation, and a column (parts) permutation such that the grouping efficacy is maximized. The suggested heuristic combines two procedures: the pattern-based procedure to build an initial solution and an improvement procedure to obtain a final solution with high grouping efficacy for the CFP. Our computational experiments with the most popular set of 35 benchmark instances show that our heuristic outperforms all well-known heuristics and returns either the best known or improved solutions to the CFP.
Mikhail Batsyn, Ilya Bychkov, Boris Goldengorin, Panos Pardalos, Pavel Sukhov
An Analytical Expression for the Distribution of the Sum of Random Variables with a Mixed Uniform Density and Mass Function
Abstract
The distribution of the sum of independent random variables plays an important role in many problems of applied mathematics. In this chapter we concentrate on the case when random variables have a continuous distribution with a discontinuity (or a probability mass) at a certain point r. Such a distribution arises naturally in actuarial mathematics when a responsibility or a retention limit is applied to every claim payment. An analytical expression for the distribution of the sum of i.i.d. random variables, which have a uniform distribution with a discontinuity, is reported.
Mikhail Batsyn, Valery Kalyagin
Modular Contractions and Their Application
Abstract
The notion of a metric modular on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces and Orlicz spaces, were recently introduced and studied by the author [Chistyakov: Dokl. Math. 73(1):32–35, 2006 and Nonlinear Anal. 72(1):1–30, 2010]. In this chapter we present yet one more application of the metric modulars theory to the existence of fixed points of modular contractive maps in modular metric spaces. These are related to contracting generalized average velocities rather than metric distances, and the successive approximations of fixed points converge to the fixed points in the modular sense, which is weaker than the metric convergence. We prove the existence of solutions to a Carathéodory-type differential equation with the right-hand side from the Orlicz space.
Vyacheslav V. Chistyakov
Network-Based Representation of Stock Market Dynamics: An Application to American and Swedish Stock Markets
Abstract
We consider three network-based models of the stock market (referred to as market graphs): one solely based on stock returns, another one based on stock returns with vertices weighted with a liquidity measure, and lastly one based on correlations of volume fluctuations. We utilize graph theory as a means for analyzing the stock market in order to show that one can potentially gain insight into structural properties and dynamics of the stock market by studying market graphs. The approach is applied to the data representing American and Swedish stock markets.
David Jallo, Daniel Budai, Vladimir Boginski, Boris Goldengorin, Panos M. Pardalos
On a Numerically Stable Algorithm for the Analysis of Generalized Volterra Lattice
Abstract
Volterra or Langmuir lattice is the dynamical model where the interaction of particle with the nearest neighbors is taken into account. It is known since J. Moser that the analysis of the Volterra lattice is related with isospectral deformation of a tridiagonal Jacobi operator. The main numerical problem in this setting is the inverse spectral problem for this Jacobi operator. Generalized Volterra lattice is a dynamical model where the interaction of particle with some fixed number of neighbors is taken into account. This model is a particular case of the discrete KP equation. The analysis of discrete KP equation is related with a class of Hessenberg operators. In this chapter we propose and study a stable algorithm for the numerical solution of the inverse spectral problem for the band Hessenberg operator with application to the analysis of generalized Volterra lattice.
Valery Kalyagin, Maxim Sokolov
How Close to Optimal Are Small World Properties of Human Brain Networks?
Abstract
A number of studies have reported small-world properties in human brain networks. Recently Barmpoutis et al. [2] have shown that there exist networks with optimal small-world structure, in the sense that they optimize all small-world attributes compared to other networks of given order and size. We wished to evaluate how close human brain network properties are compared to the properties of optimal small-world networks. We have constructed weighted functional human brain networks based on functional magnetic resonance imaging (fMRI) data and MNI anatomical parcellation of brain. These weighted networks were further thresholded in order to obtain a set of simple undirected graphs. In the obtained graphs we computed small-world characteristics and compared them to the characteristics of comparable optimal small-world networks.
Dmytro Korenkevych, Frank Skidmore, Boris Goldengorin, Panos M. Pardalos
Optimizing Network Topology to Reduce Aggregate Traffic in Systems of Mobile Agents
Abstract
Systems of networked mobile robots, such as unmanned aerial or ground vehicles, will play important roles in future military and commercial applications. The communications for such systems will typically be over wireless links and may require that the robots form an ad hoc network and communicate on a peer-to-peer basis. In this chapter, we consider the problem of optimizing the network topology to minimize the total traffic in a network required to support a given set of data flows under constraints on the amount of movement possible at each mobile robot. We consider a subclass of this problem in which the initial and final topologies are trees, and the movement restrictions are given in terms of the number of edges in the graph that must be traversed. We develop algorithms to optimize the network topology while maintaining network connectivity during the topology reconfiguration process. Our topology reconfiguration algorithm uses the concept of prefix labeling and routing to move nodes through the network while maintaining network connectivity. We develop three algorithms to determine the final network topology. These include an optimal, but computationally complex algorithm, as well as a greedy algorithm and a simulated annealing algorithm that trade optimality for reduced complexity. We present simulation results to compare the performance of these algorithms.
Leenhapat Navaravong, John M. Shea, Eduardo L. Pasiliao Jr, Gregory L. Barbette, Warren E. Dixon
Integrated Production Planning, Shift Planning, and Detailed Scheduling in a Tissue Paper Manufacturer
Abstract
In this study, we report an integrated planning system that we developed for a large tissue paper manufacturer in Turkey. The system is composed of three integrated models to solve the capacity planning, shift planning, and scheduling problems. All three problems are solved by a combination of optimization methods and heuristics. We also report the implementation process of the system in the manufacturing organization, and discuss observed benefits of the system in terms of the competitive position of the company.
Zehra Melis Teksan, Ali Tamer Ünal, Z. Caner Taşkın
Evacuation Through Clustering Techniques
Abstract
Evacuation and disaster management is of the essence for any advanced society. Ensuring the welfare and well-being of the citizens even in times of immense distress is of utmost importance. Especially in coastal areas where tropical storms and hurricanes pose a threat on a yearly basis, evacuation planning and management is vital. However, modern metropolitan city evacuations prove to be large-scale optimization problems which cannot be tackled in a timely manner with the computational power available. We propose a clustering technique to divide the problem into smaller and easier subproblems and present numerical results that prove our success.
Chrysafis Vogiatzis, Jose L. Walteros, Panos M. Pardalos
Economic Analysis of the N-k Power Grid Contingency Selection and Evaluation
Abstract
Contingency analysis is important for providing information about the vulnerability of power grids. Many methods have been purposed to use topological structures of power grids for analyzing contingency states. Considering failures of buses and lines, we present and compare several graph methods for selecting contingencies in this chapter. A new method, called critical node detection, is introduced for selecting contingencies consisting of failures on buses. Besides these methods, we include an interdiction model which provides the worst case contingency selection. Our measurement for contingency evaluation is to maximize the social benefit, or to minimize the generating and load shedding cost. Comparing with other measurements for contingency selection, our model is based on economic analysis and is reasonable for evaluating the selected contingency state. Additionally, a contingency consisting of both buses and lines is also studied.
Hongsheng Xu
Calcium Transient Imaging as Tool for Neuronal and Glial Network Interaction Study
Abstract
Signaling in neuronal networks plays a crucial role in regulating the processes of proper network formation during development and learning in the matured nervous system. Adaptation of neuronal networks to the cultured conditioning in the absence of external drive stimulates appearance of self-sustained spiking patterns without any specific stimuli. Some alteration like electrical stimulation, medium changing, metabolic activation, or depression of mature culture evokes to novel properties of spiking pattern. These properties are reversible usually and may be considered as a new function system occurring in consequence of strong stimulations. Intracellular calcium transients are the basic signaling mechanisms in nerve cells in addition to membrane potential. However, little is known about the transition of spontaneous intracellular calcium dynamics and the relationship between calcium transients and electrical activity during network development. To identify function neuronal networks in vitro we investigated spontaneous intracellular calcium transients in mouse hippocampal networks cultured on MEA for month after plating.
Yu. N. Zakharov, E. V. Mitroshina, O. Shirokova, I. V. Mukhina
Backmatter
Metadaten
Titel
Models, Algorithms, and Technologies for Network Analysis
herausgegeben von
Boris Goldengorin
Valery A. Kalyagin
Panos M. Pardalos
Copyright-Jahr
2013
Verlag
Springer New York
Electronic ISBN
978-1-4614-5574-5
Print ISBN
978-1-4614-5573-8
DOI
https://doi.org/10.1007/978-1-4614-5574-5

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