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Keywords = memory-based random walk step sizes

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20 pages, 1391 KB  
Article
A Hybrid Model of Elephant and Moran Random Walks: Exact Distribution and Symmetry Properties
by Rafik Aguech and Mohamed Abdelkader
Symmetry 2025, 17(10), 1709; https://doi.org/10.3390/sym17101709 - 11 Oct 2025
Viewed by 388
Abstract
This work introduces a hybrid memory-based random walk model that combines the Elephant Random Walk with a modified Moran Random Walk. The model introduces a sequence of independent and identically distributed random variables with mean 1, representing step sizes. A particle starts at [...] Read more.
This work introduces a hybrid memory-based random walk model that combines the Elephant Random Walk with a modified Moran Random Walk. The model introduces a sequence of independent and identically distributed random variables with mean 1, representing step sizes. A particle starts at the origin and moves upward with probability r or remains stationary with probability 1−r. From the second step onward, the particle decides its next action based on its previous movement, repeating it with probability p or taking the opposite action with probability 1−p. The novelty of our approach lies in integrating a short-memory mechanism with variable step sizes, which allows us to derive exact distributions, recurrence relations, and central limit theorems. Our main contributions include (i) establishing explicit expressions for the moment-generating function and the exact distribution of the process, (ii) analyzing the number of stops through a symmetry phenomenon between repetition and inversion, and (iii) providing asymptotic results supported by simulations. Full article
(This article belongs to the Section Mathematics)
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11 pages, 1928 KB  
Communication
Stack LSTM-Based User Identification Using Smart Shoes with Accelerometer Data
by Do-Yun Kim, Seung-Hyeon Lee and Gu-Min Jeong
Sensors 2021, 21(23), 8129; https://doi.org/10.3390/s21238129 - 5 Dec 2021
Cited by 5 | Viewed by 3054
Abstract
In this study, we propose a long short-term memory (LSTM)-based user identification method using accelerometer data from smart shoes. In general, for the user identification with human walking data, we require a pre-processing stage in order to divide human walking data into individual [...] Read more.
In this study, we propose a long short-term memory (LSTM)-based user identification method using accelerometer data from smart shoes. In general, for the user identification with human walking data, we require a pre-processing stage in order to divide human walking data into individual steps. Next, user identification can be made with divided step data. In these approaches, when there exist partial data that cannot complete a single step, it is difficult to apply those data to the classification. Considering these facts, in this study, we present a stack LSTM-based user identification method for smart-shoes data. Rather than using a complicated analysis method, we designed an LSTM network for user identification with accelerometer data of smart shoes. In order to learn partial data, the LSTM network was trained using walking data with random sizes and random locations. Then, the identification can be made without any additional analysis such as step division. In the experiments, user walking data with 10 m were used. The experimental results show that the average recognition rate was about 93.41%, 97.19%, and 98.26% by using walking data of 2.6, 3.9, and 5.2 s, respectively. With the experimental results, we show that the proposed method can classify users effectively. Full article
(This article belongs to the Special Issue Smart Sensors: Applications and Advances in Human Motion Analysis)
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