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Item Restricted Synchronization, Learning and Classification for a System of Kuramoto Models(University of Exeter, 2024) Alanazi, Faizah; Townley, Stuart; Mueller, MarkusKuramoto systems or Kuramoto networks model the behaviour of large sets of coupled oscillators. Arising initially in the context of systems of chemical and biological oscillators, they now find applications in various areas of science, engineering and medicine, including neuroscience. A key property of Kuramoto networks is their synchronization behaviour: for a network with N oscillators, it is possible that all N oscillators synchronize, that several clusters of synchronized oscillators emerge, or that there is no synchronization of the oscillators. The behaviour is a function of the network parameters, namely coupling strengths and natural frequencies for the oscillators, as well as their initial conditions. In this thesis, we consider control systems theory approaches for Kuramoto networks that focus on adaptive learning of system parameters and phase tracking, observation-based classification of synchrony, and a combination of both. We first consider synchronization and learning approaches for pairs of Kuramoto networks. One network plays the role of a training network, the other is a learning network. We consider synchronization and system parameter learning based on phase information. Our main result is an adaptive learning strategy that tunes the system parameters of the learning oscillator – the Kuramoto coupling strengths and the natural frequencies – to achieve phase tracking, i.e. synchronization, between the training and learning phases. Tracking is proved using a Lyapunov stability approach. The adaptive strategy also guarantees partial convergence of the learning weights and frequencies to those of the training oscillator. Partial convergence is characterized by the linear dependence of the phase differences of the states of the training oscillator. The results are illustrated by a Kuramoto network with N = 4 oscillators. Secondly, and generalizing the synchronization and learning result, we consider networks where only output information is available and not all phases of the network i may be measured independently. A crucial aspect of this approach is the concept of observability and observer design for dynamical systems, i.e. how to make use of output information to recreate phase information. This is an unsolved problem for Kuramoto networks where a training system is not necessarily in an equilibrium state. To overcome this problem we develop a machine learning-based approach using so-called “fingerprints” of the networks output signals, i.e. spectrogram images that represent the possible synchronization behaviours. We use a simple artificial neural network architecture to develop a pattern recognition tools that classifies the “fingerprints” and thus the types synchrony as observed by outputs of Kuramoto networks of a fixed size. The approach is illustrated by simulation and classification results for Kuramoto networks with N = 4 and N = 7 oscillators. Using the classifier approach we then develop a switched systems adaptive control framework to determine the type of Kuramoto network responsible or able to create a given “fingerprint” that matches the “fingerprint” of the training system. Our second main result is an adaptive algorithm that can learn the behaviour of a Kuramoto network, from a set or family of possible networks, to match the output-based “fingerprint” of the training system. The results are illustrated for networks of N = 4 and N = 7 oscillators with a variety of synchrony outputs, respectively26 0Item Restricted Predicting Customer Attrition in B2B SaaS Using Machine Learning Classification(Saudi Digital Library, 2023-09-15) Alalawi, Zainab; Fiaschetti, MaurizioCustomer retention and customer loss are crucial metrics in subscription-based industries like SaaS companies. Customer discharge is a significant concern for this type of business, as clients have the flexibility to terminate the service at any time. This can lead to adverse effects on the company’s revenue stream. If SaaS businesses can accurately predict the number of customers who will cancel their subscriptions and those who will continue using their services within a specific timeframe, they can more effectively forecast their revenue, cash flow, and any future growth plan accordingly. Predicting subscription renewals and cancelations remains a challenging problem for any SaaS company. However, with the ongoing advancement in machine learning and artificial intelligence, the potential for accurately forecasting this issue has significantly improved. The study examines customer attrition and customer retention prediction in a quantitative method by utilizing several different machine learning algorithms with Python, namely Logistics regression, Naïve Baye, and random forest algorithms. Data was collected from the case company’s database and manipulated to fit the algorithms. The dataset includes the customers' business data such as spend, customer platform usage data, customer service history data, and the date of the next payment. To identify the best hyperparameters for each machine- learning algorithm, A tuning technique, in particular Grid Search, was employed. Subsequently, the algorithm models were trained and assessed using optimized hyperparameters on the fitted data. Once the models were trained, they were applied to test data to obtain the analysis results. The model’s performance was measured on the quantitative model performance metrics. including F1-Score, Area under Curve (AUC), and Accuracy.37 0Item Restricted Optimal 0−1 Loss Classification In Linear, Overlapping And Interpolation Settings(University of Birmingham, 2022-09-07) Alanazi, Reem; Max, LittleClassification problems represent a major subject in machine learning, and addressing them requires solving underlying optimization problems. Optimis- ing the 0–1 loss function is the natural pathway to address the classification problem. Because of the properties of 0–1 loss, which are that it is non-convex and non-differentiable, 0–1 loss is mathematically intractable and classified as non-deterministic polynomial-time hard (NP-hard). Consequently, the 0– 1 loss function has been replaced by surrogate loss functions that can be optimized more efficiently, where their optimal solution is guaranteed with respect to these surrogate losses. At the same time, these functions may not provide the same optimal solution as the 0–1 loss function. Indeed, the loss function used during the empirical risk minimization (ERM) is not the same loss function used in the evaluation; the mismatch of the loss functions leads to an approximate solution that may not be an ideal solution for 0–1 loss. Thus, an additional source of error is produced because of this replacement.16 0