scholarly journals Modeling of Dynamic Systems With Interval Parameters

2019 ◽  
Vol 09 (4) ◽  
pp. 5-31
Author(s):  
A.Y. Morozov ◽  
D.L. Reviznikov
Keyword(s):  
Dynamic Systems ◽  
Interval Analysis ◽  
Interpolation Algorithm ◽  
Interval Parameters ◽  
Estimates Of Solutions ◽  
Software Libraries ◽  
Adaptive Interpolation ◽  
Over Time

The paper provides a review of existing libraries and methods of modeling dynamic systems with interval parameters. Available software libraries AWA, VNODELP, COZY Infinity, RiOT, FlowStar, as well as the author’s adaptive interpolation algorithm are considered. The traditional software for interval analysis gives guaranteed estimates of solutions, however, over time, these estimates become extremely significantly overstated. Due to the use of a fundamentally different approach to constructing solutions, the adaptive interpolation algorithm is not subject to the accumulation of errors, determines the boundaries of solutions with controlled accuracy, and works much faster than analogues.

scholarly journals Sparse Grid Adaptive Interpolation in Problems of Modeling Dynamic Systems with Interval Parameters

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 298
Author(s):  
Alexander Yu Morozov ◽  
Andrey A. Zhuravlev ◽  
Dmitry L. Reviznikov
Keyword(s):  
Dynamic Systems ◽  
Materials Science ◽  
Sparse Grids ◽  
Interpolation Algorithm ◽  
Piecewise Polynomial Function ◽  
Interval Parameters ◽  
Adaptive Interpolation ◽  
Interval Uncertainties ◽  
Computational Materials ◽  
Interval Problems

The paper is concerned with the issues of modeling dynamic systems with interval parameters. In previous works, the authors proposed an adaptive interpolation algorithm for solving interval problems; the essence of the algorithm is the dynamic construction of a piecewise polynomial function that interpolates the solution of the problem with a given accuracy. The main problem of applying the algorithm is related to the curse of dimension, i.e., exponential complexity relative to the number of interval uncertainties in parameters. The main objective of this work is to apply the previously proposed adaptive interpolation algorithm to dynamic systems with a large number of interval parameters. In order to reduce the computational complexity of the algorithm, the authors propose using adaptive sparse grids. This article introduces a novelty approach of applying sparse grids to problems with interval uncertainties. The efficiency of the proposed approach has been demonstrated on representative interval problems of nonlinear dynamics and computational materials science.

Parallel Adaptive Interpolation Algorithm based on Sparse Grids for Modeling Dynamic Systems with Interval Parameters

2021 ◽  
Vol 12 (8) ◽  
pp. 395-403
Author(s):  
A. Yu. Morozov ◽  
Keyword(s):  
Dynamic Systems ◽  
Polynomial Interpolation ◽  
Parallel Implementation ◽  
Sparse Grids ◽  
Piecewise Polynomial Function ◽  
Call Graph ◽  
Interval Parameters ◽  
Computational Costs ◽  
Adaptive Interpolation ◽  
Grid Nodes

The paper presents a parallel algorithm for adaptive interpolation based on sparse grids for modeling dynamic systems with interval parameters. The idea of the algorithm is to construct a piecewise polynomial function that interpolates the dependence of the solution to the problem on the point values of the interval parameters. In the classical version of the algorithm, polynomial interpolation on complete grids is used, and with a large number of uncertainties, the algorithm becomes difficult to apply due to the exponential growth of computational costs. The use of sparse grids can significantly reduce the computational costs, but nevertheless the complexity of the algorithm in the general case remains exponential with respect to the number of interval parameters. In this regard, the issue of accelerating the algorithm is relevant. The algorithm can be divided into several sets of independent subtasks: updating the values corresponding to the grid nodes; calculation of weighting factors; interpolation of values at new nodes. The last two sets imply parallelization of recursion, so here the techniques for traversing the width of the call graph are mainly used. The parallel implementation of the algorithm was tested on two ODE systems containing two and six interval parameters, respectively, using a different number of computing cores. The results obtained demonstrate the effectiveness of the approaches used.

KD-Tree based adaptive interpolation algorithm for chemical kinetics problems with interval parameters

2018 ◽  
Vol 30 (12) ◽  
pp. 129-144
Author(s):  
A. Morozov ◽  
◽  
D. Reviznikov ◽  
V. Gidaspov ◽  
◽  
...  
Keyword(s):  
Chemical Kinetics ◽  
Interpolation Algorithm ◽  
Interval Parameters ◽  
Adaptive Interpolation

Dualities, Dialectics, and Paradoxes in Organizational Life

2018 ◽  
Keyword(s):  
Dynamic Systems ◽  
Empirical Studies ◽  
Organizational Studies ◽  
Organizational Life ◽  
Organizational Processes ◽  
Organization Studies ◽  
Process Studies ◽  
Convergence And Divergence ◽  
Insight Into ◽  
Over Time

Organizational contradictions and process studies offer interwoven and complementary insights. Studies of dialectics, paradox, and dualities depict organizational contradictions that are oppositional as well as interrelated such that they persistently morph and shift over time. Studies of process often examine how contradictions fuel emergent, dynamic systems and stimulate novelty, adaptation, and transformation. Drawing from rich conversations at the Eighth International Symposium on Process Organization Studies, the contributors to this volume unpack these relationships in more depth. The chapters explore three main, connected themes through both conceptual and empirical studies, including (1) offering insight into how process theorizing advances understandings of organizational contradictions; (2) shedding light on how dialectics, paradoxes, and dualities fuel organizational processes that affect persistence and transformation; and (3) exploring the convergence and divergence of dialectics, paradox, and dualities lenses. Taken together, this book offers key insights in order to inform persistent, contradictory dynamics in organizations and organizational studies.

scholarly journals Variability as normal as apple pie

2021 ◽  
Vol 7 (s2) ◽  
Author(s):  
Marjolijn Verspoor ◽  
Wander Lowie ◽  
Kees de Bot
Keyword(s):  
Dynamic Systems ◽  
Dynamic Systems Theory ◽  
Complex Dynamic ◽  
Controlled Processes ◽  
Complex Dynamic Systems ◽  
L2 Development ◽  
Limited Degree ◽  
Development Phases ◽  
Longitudinal Case Studies ◽  
Over Time

Abstract In recent studies in second language (L2) development, notably within the focus of Complex Dynamic Systems Theory (CDST), non-systematic variation has been extensively studied as intra-individual variation, which we will refer to as variability. This paper argues that variability is functional and is needed for development. With examples of four longitudinal case studies we hope to show that variability over time provides valuable information about the process of development. Phases of increased variability in linguistic constructions are often a sign that the learner is trying out different constructions, and as such variability can be evidence for change, and change can be learning. Also, a limited degree of variability is inherent in automatic or controlled processes. Conversely, the absence of variability is likely to show that no learning is going on or the system is frozen.

Video image scaling technology based on adaptive interpolation algorithm and TTS FPGA implementation

2021 ◽  
Vol 76 ◽  
pp. 103516
Author(s):  
Guangyu Liu ◽  
Bao Zhou ◽  
Yi Huang ◽  
Longfei Wang ◽  
Wei Wang ◽  
...  
Keyword(s):  
Fpga Implementation ◽  
Video Image ◽  
Interpolation Algorithm ◽  
Image Scaling ◽  
Adaptive Interpolation
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