HPC Methods for Domains of Attraction Computation

2015 ◽  
Author(s):  
Pierpaolo Belardinelli ◽  
Stefano Lenci
Keyword(s):  
Memory Management ◽  
Large Scale ◽  
Basins Of Attraction ◽  
Mapping Method ◽  
Cell Mapping ◽  
Double Step ◽  
Optimal Balance ◽  
A Cell ◽  
Step Algorithm ◽  
Computational Resources

The work is devoted to the development of efficient parallel algorithms for the computation of large-scale basins of attraction. Since the required computational resources increase exponentially with the dimension of a dynamical system, it is common to get into memory saturation or in a secular elaboration time. This paper presents a code, based on a cell mapping method, that evaluates basins of attraction for high-dimensional systems by exploiting the parallel programming. The proposed approach, by using a double-step algorithm, permits, i) to fully determine the basins in all the dimensions ii) to evaluate 2D Poincaré sections of the system. The code is described in all its parts: the shell, in charge of the core management, permits to split over a multi-core environment the computing domain, it carries out an efficient use of the memory. A preliminary analysis of the performances is undertaken also by considering different dimensional grids; the optimal balance between computing cores and memory management cores is studied.

A Cell Mapping Method for Nonlinear Deterministic and Stochastic Systems—Part II: Examples of Application

1986 ◽  
Vol 53 (3) ◽  
pp. 702-710 ◽  
Author(s):  
H. M. Chiu ◽  
C. S. Hsu
Keyword(s):  
Present Method ◽  
Stochastic Systems ◽  
Random Excitation ◽  
Mapping Method ◽  
Cell Mapping ◽  
Generalized Cell Mapping ◽  
Deterministic Systems ◽  
Strongly Nonlinear ◽  
Stochastic Problems ◽  
A Cell

In this second part of the two-part paper we demonstrate the viability of the compatible simple and generalized cell mapping method by applying it to various deterministic and stochastic problems. First we consider deterministic problems with non-chaotic responses. For this class of problems we show how system responses and domains of attraction can be obtained by a refining procedure of the present method. Then, we consider stochastic problems with stochasticity lying in system parameters or excitation. Next, deterministic systems with chaotic responses are considered. By the present method, finding the statistical responses of such systems under random excitation also presents no difficulties. Some of the systems studied here are well-known. New results are, however, also obtained. These are results on Duffing systems with a stochastic coefficient, the global results of a Duffing system shown in Section 4, the results on strongly nonlinear Duffing systems under random excitations reported in Section 7.2, and the strange attractor results for systems subjected to random excitations.

A Cell Mapping Method for Nonlinear Deterministic and Stochastic Systems—Part I: The Method of Analysis

1986 ◽  
Vol 53 (3) ◽  
pp. 695-701 ◽  
Author(s):  
C. S. Hsu ◽  
H. M. Chiu
Keyword(s):  
Stochastic Systems ◽  
Mapping Method ◽  
Cell Mapping ◽  
Generalized Cell Mapping ◽  
Strongly Nonlinear ◽  
Cell Mapping Methods ◽  
The Past ◽  
Simple Cell Mapping ◽  
A Cell ◽  
Vibration Problems

In the past few years as an attempt to devise more efficient and more practical ways of determining the global behavior of strongly nonlinear systems, two cell-to-cell mapping methods have been proposed, namely, the simple cell mapping and the generalized cell mapping. In this first part of the two-part paper we present a different and more efficient cell mapping method for treating nonlinear vibration problems. The vibratory systems may be deterministic or stochastic. The method utilizes compatible simple and generalized cell mapping and it combines the advantages of both. Applications to various systems will be presented in the second part of the paper.

scholarly journals Nebula: ultra-efficient mapping-free structural variant genotyper

2021 ◽  
Author(s):  
Parsoa Khorsand ◽  
Fereydoun Hormozdiari
Keyword(s):  
Large Scale ◽  
Structural Variants ◽  
Sequencing Technologies ◽  
Generic Framework ◽  
Common Genetic Variants ◽  
Order Of Magnitude ◽  
Complex Events ◽  
Comparable Accuracy ◽  
Using Data ◽  
Computational Resources

Abstract Large scale catalogs of common genetic variants (including indels and structural variants) are being created using data from second and third generation whole-genome sequencing technologies. However, the genotyping of these variants in newly sequenced samples is a nontrivial task that requires extensive computational resources. Furthermore, current approaches are mostly limited to only specific types of variants and are generally prone to various errors and ambiguities when genotyping complex events. We are proposing an ultra-efficient approach for genotyping any type of structural variation that is not limited by the shortcomings and complexities of current mapping-based approaches. Our method Nebula utilizes the changes in the count of k-mers to predict the genotype of structural variants. We have shown that not only Nebula is an order of magnitude faster than mapping based approaches for genotyping structural variants, but also has comparable accuracy to state-of-the-art approaches. Furthermore, Nebula is a generic framework not limited to any specific type of event. Nebula is publicly available at https://github.com/Parsoa/Nebula.

An improved cell mapping method based on dimension-extension for fractional systems

2021 ◽  
Vol 31 (6) ◽  
pp. 063132
Author(s):  
Minjuan Yuan ◽  
Liang Wang ◽  
Yiyu Jiao ◽  
Wei Xu
Keyword(s):  
Mapping Method ◽  
Cell Mapping ◽  
Fractional Systems

scholarly journals Vehicular Crowdsourcing for Congestion Support in Smart Cities

Smart Cities ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 662-685
Author(s):  
Stephan Olariu
Keyword(s):  
Smart City ◽  
Large Scale ◽  
Smart Cities ◽  
Traffic Signal Control ◽  
Signal Timing ◽  
Adaptive Traffic Signal Control ◽  
Traffic Conditions ◽  
Direct Benefits ◽  
Traffic Signal Control Systems ◽  
Computational Resources

Under present-day practices, the vehicles on our roadways and city streets are mere spectators that witness traffic-related events without being able to participate in the mitigation of their effect. This paper lays the theoretical foundations of a framework for harnessing the on-board computational resources in vehicles stuck in urban congestion in order to assist transportation agencies with preventing or dissipating congestion through large-scale signal re-timing. Our framework is called VACCS: Vehicular Crowdsourcing for Congestion Support in Smart Cities. What makes this framework unique is that we suggest that in such situations the vehicles have the potential to cooperate with various transportation authorities to solve problems that otherwise would either take an inordinate amount of time to solve or cannot be solved for lack for adequate municipal resources. VACCS offers direct benefits to both the driving public and the Smart City. By developing timing plans that respond to current traffic conditions, overall traffic flow will improve, carbon emissions will be reduced, and economic impacts of congestion on citizens and businesses will be lessened. It is expected that drivers will be willing to donate under-utilized on-board computing resources in their vehicles to develop improved signal timing plans in return for the direct benefits of time savings and reduced fuel consumption costs. VACCS allows the Smart City to dynamically respond to traffic conditions while simultaneously reducing investments in the computational resources that would be required for traditional adaptive traffic signal control systems.

scholarly journals Secure Large-Scale Airport Simulations Using Distributed Computational Resources

2001 ◽  
Author(s):  
William J. Mcdermott ◽  
David A. Maluf ◽  
Yuri Gawdiak ◽  
Peter Tran
Keyword(s):  
Large Scale ◽  
Computational Resources

scholarly journals Reaction Diffusion and Chemotaxis for Decentralized Gathering on FPGAs

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Bernard Girau ◽  
César Torres-Huitzil ◽  
Nikolaos Vlassopoulos ◽  
José Hugo Barrón-Zambrano
Keyword(s):  
Large Scale ◽  
Complex Dynamics ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Fpga Implementation ◽  
Cellular Slime Mold ◽  
Reaction Diffusion Model ◽  
Cellular Slime ◽  
Computational Resources ◽  
Embedded Implementation

We consider here the feasibility of gathering multiple computational resources by means of decentralized and simple local rules. We study such decentralized gathering by means of a stochastic model inspired from biology: the aggregation of theDictyostelium discoideumcellular slime mold. The environment transmits information according to a reaction-diffusion mechanism and the agents move by following excitation fronts. Despite its simplicity this model exhibits interesting properties of self-organization and robustness to obstacles. We first describe the FPGA implementation of the environment alone, to perform large scale and rapid simulations of the complex dynamics of this reaction-diffusion model. Then we describe the FPGA implementation of the environment together with the agents, to study the major challenges that must be solved when designing a fast embedded implementation of the decentralized gathering model. We analyze the results according to the different goals of these hardware implementations.

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