Parallel asynchronous algorithms for discrete data

1990 ◽  
Vol 37 (3) ◽  
pp. 588-606 ◽  
Author(s):  
Aydin Üresin ◽  
Michel Dubois
Keyword(s):  
Discrete Data ◽  
Asynchronous Algorithms ◽  
Parallel Asynchronous Algorithms

scholarly journals A Relaxation of Üresin and Dubois’ Asynchronous Fixed-Point Theory in Agda

2019 ◽  
Vol 64 (5) ◽  
pp. 857-877
Author(s):  
Matthew L. Daggitt ◽  
Ran Zmigrod ◽  
Timothy G. Griffin
Keyword(s):  
Fixed Point ◽  
Numerical Analysis ◽  
Fixed Point Theory ◽  
Iterative Algorithms ◽  
Point Theory ◽  
Proof Assistant ◽  
Convergence Conditions ◽  
Counter Example ◽  
Asynchronous Algorithms ◽  
Parallel Asynchronous Algorithms

AbstractÜresin and Dubois’ paper “Parallel Asynchronous Algorithms for Discrete Data” shows how a class of synchronous iterative algorithms may be transformed into asynchronous iterative algorithms. They then prove that the correctness of the resulting asynchronous algorithm can be guaranteed by reasoning about the synchronous algorithm alone. These results have been used to prove the correctness of various distributed algorithms, including in the fields of routing, numerical analysis and peer-to-peer protocols. In this paper we demonstrate several ways in which the assumptions that underlie this theory may be relaxed. Amongst others, we (i) expand the set of schedules for which the asynchronous iterative algorithm is known to converge and (ii) weaken the conditions that users must prove to hold to guarantee convergence. Furthermore, we demonstrate that two of the auxiliary results in the original paper are incorrect, and explicitly construct a counter-example. Finally, we also relax the alternative convergence conditions proposed by Gurney based on ultrametrics. Many of these relaxations and errors were uncovered after formalising the work in the proof assistant Agda. This paper describes the Agda code and the library that has resulted from this work. It is hoped that the library will be of use to others wishing to formally verify the correctness of asynchronous iterative algorithms.

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

A two-dimensional sideways problem with random discrete data

2021 ◽  
Vol 86 ◽  
pp. 16-32
Author(s):  
Dang Duc Trong ◽  
Tran Quoc Viet ◽  
Vo Dang Khoa ◽  
Nguyen Thi Hong Nhung
Keyword(s):  
Discrete Data ◽  
Two Dimensional

scholarly journals The Performance of Post-Fall Detection Using the Cross-Dataset: Feature Vectors, Classifiers and Processing Conditions

Sensors ◽  
2021 ◽  
Vol 21 (14) ◽  
pp. 4638
Author(s):  
Bummo Koo ◽  
Jongman Kim ◽  
Yejin Nam ◽  
Youngho Kim
Keyword(s):  
Time Series ◽  
Fall Detection ◽  
Discrete Data ◽  
Classification Performance ◽  
Training Data ◽  
Processing Conditions ◽  
Feature Vectors ◽  
External Data ◽  
Public Dataset ◽  
The Cross

In this study, algorithms to detect post-falls were evaluated using the cross-dataset according to feature vectors (time-series and discrete data), classifiers (ANN and SVM), and four different processing conditions (normalization, equalization, increase in the number of training data, and additional training with external data). Three-axis acceleration and angular velocity data were obtained from 30 healthy male subjects by attaching an IMU to the middle of the left and right anterior superior iliac spines (ASIS). Internal and external tests were performed using our lab dataset and SisFall public dataset, respectively. The results showed that ANN and SVM were suitable for the time-series and discrete data, respectively. The classification performance generally decreased, and thus, specific feature vectors from the raw data were necessary when untrained motions were tested using a public dataset. Normalization made SVM and ANN more and less effective, respectively. Equalization increased the sensitivity, even though it did not improve the overall performance. The increase in the number of training data also improved the classification performance. Machine learning was vulnerable to untrained motions, and data of various movements were needed for the training.

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