Browsing by Author "Mirza, F.K."

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Citation - Scopus: 0
Decoding Rhythmic Complexity: a Nonlinear Dynamics Approach Via Visibility Graphs for Classifying Asymmetrical Rhythmic Frameworks of Turkish Classical Music
(Elsevier Inc., 2025) Mirza, F.K.; Baykaş, T.; Hekimoğlu, M.; Pekcan, Ö.; Tunçay, G.P.
The non-isochronous, hierarchical rhythmic cycles (usuls) of Turkish Classical Music (TCM) exhibit emergent temporal structures that challenge conventional rhythm analysis based on metrical regularity. To address this challenge, this study presents a complexity-oriented framework for usul classification, grounded in nonlinear time series analysis and network-based representations. Rhythmic signals are processed through energy envelope extraction, diffusion entropy analysis, and spectral transformations to capture multiscale temporal dynamics. Visibility graphs (VGs) are constructed from these representations to encode underlying structural complexity and temporal dependencies. Features derived from VG adjacency matrices serve as complexity-sensitive descriptors and enable high-accuracy classification (0.99) across 40 usul classes and 628 compositions. Energy envelope-derived graphs provide the most discriminative information, highlighting the importance of amplitude modulation in encoding rhythmic structure. Beyond classification, the analysis reveals self-organizing patterns and signatures of complexity, such as quasi-periodicity, scale-dependent variability, and entropy saturation, suggesting that usuls function as adaptive, nonlinear systems rather than metrically constrained patterns. The topological features extracted from the resulting graphs align with theoretical constructs from complexity science, such as modularity and long-range temporal correlations. This positions usul as an exemplary case for studying structured temporal complexity in cultural artifacts through the lens of dynamical systems. These findings contribute to computational rhythm analysis by demonstrating the efficacy of complexity measures in characterizing culturally specific rhythmic systems. © 2025
Citation - Scopus: 0
Stock Price Forecasting Through Symbolic Dynamics and State Transition Graphs With a Convolutional Recurrent Neural Network Architecture
(Springer Science and Business Media Deutschland GmbH, 2025) Mirza, F.K.; Pekcan, Ö.; Hekimoğlu, M.; Baykaş, T.
Accurate stock price forecasting remains a critical challenge in financial analytics due to volatile market conditions, non-stationary dynamics, and abrupt regime shifts that often defy traditional modeling techniques. This study proposes a comprehensive framework for stock price forecasting that integrates symbolic dynamics, graph-based state representations, and deep learning. By converting continuous-valued stock prices into discrete symbolic states representing amplitude and trend information, the method constructs transition matrices capturing probabilistic relationships within financial time series. These transition matrices are then processed by a convolutional recurrent neural network (CRNN), in which convolutional layers isolate local spatial dependencies in the symbolic-state domain, while recurrent LSTM layers capture multi-scale temporal dynamics extending across multiple time horizons. Experimental evaluations are conducted over prediction horizons of 1 day, 10 days, and 100 days, spanning pre-COVID, COVID, and post-COVID market regimes. The results indicate that while longer prediction horizons naturally incur greater forecasting uncertainty due to compounding variability, the integration of symbolic-state preprocessing with deep temporal modeling demonstrates significant robustness in handling non-stationary financial environments. During the stable pre-COVID period, the proposed methodology achieves reductions in mean squared error (MSE) of up to 98% relative to the volatile COVID phase, highlighting its capability to effectively leverage well-defined market patterns in stable economic conditions. Furthermore, the model consistently delivers competitive forecasting performance across all prediction horizons and market regimes. Collectively, these findings emphasize the potential of symbolic-state-based deep learning architectures as a viable pathway to address the complexity and volatility characteristic of modern financial markets. © The Author(s) 2025.