Patch-Wise-Based Self-Supervised Learning for Anomaly Detection on Multivariate Time Series Data DOI Creative Commons
Seungmin Oh, Le Hoang Anh, Dang Thanh Vu

et al.

Mathematics, Journal Year: 2024, Volume and Issue: 12(24), P. 3969 - 3969

Published: Dec. 17, 2024

Multivariate time series anomaly detection is a crucial technology to prevent unexpected errors from causing critical impacts. Effective in such data requires accurately capturing temporal patterns and ensuring the availability of adequate data. This study proposes patch-wise framework for detection. The proposed approach comprises four key components: (i) maintaining continuous features through patching, (ii) incorporating various information by learning channel dependencies adding relative positional bias, (iii) achieving feature representation self-supervised learning, (iv) supervised based on augmentation downstream tasks. method demonstrates strong performance leveraging patching maintain continuity while effectively representations handling Additionally, it mitigates issue insufficient supporting diverse types anomalies. experimental results show that our model achieved 23% 205% improvement F1 score compared existing methods datasets as MSL, which has relatively small amount training Furthermore, also delivered competitive SMAP dataset. By systematically both local global dependencies, strikes an effective balance between accuracy, making valuable tool real-world multivariate applications.

Language: Английский

Fixed-time neural consensus control for nonlinear multiagent systems with state and input quantization DOI
Wenjing Cheng,

Huidong Cheng,

Fang Wang

et al.

Chaos Solitons & Fractals, Journal Year: 2025, Volume and Issue: 194, P. 116145 - 116145

Published: Feb. 21, 2025

Language: Английский

Citations

0
Bifurcation analysis of a non linear 6D financial system with three time delay feedback DOI

Animesh Phukan,

Hemanta Kumar Sarmah

Chaos Solitons & Fractals, Journal Year: 2025, Volume and Issue: 194, P. 116248 - 116248

Published: March 13, 2025

Language: Английский

Citations

0
A novel fractal fractional mathematical model for HIV/AIDS transmission stability and sensitivity with numerical analysis DOI Creative Commons

Mukhtiar Khan,

Nadeem Alam Khan,

Ibad Ullah

et al.

Scientific Reports, Journal Year: 2025, Volume and Issue: 15(1)

Published: March 18, 2025

Understanding the complex dynamics of HIV/AIDS transmission requires models that capture real-world progression and intervention impacts. This study introduces an innovative mathematical framework using fractal-fractional calculus to analyze dynamics, emphasizing memory effects nonlocal interactions critical disease spread. By dividing populations into four distinct compartments-susceptible individuals, infected those undergoing treatment, individuals in advanced AIDS stages-the model reflects key phases infection therapeutic interventions. Unlike conventional approaches, proposed nonlinear function, $$\frac{\nabla (\mathscr {I}+\alpha _1\mathscr {T}+\alpha _2\mathscr {A})}{\mathscr {N}}$$ , accounts for varying infectivity levels across stages (where $$\mathscr {N}$$ is total population $$\nabla$$ denotes effective contact rate), offering a nuanced view how treatment efficacy ( $$\alpha _1$$ ) _2$$ shape transmission. The analytical combines rigorous exploration with practical insights. We derive basic reproduction number {R}_0$$ assess outbreak potential employ Lyapunov theory establish global stability conditions. Using Schauder fixed-point theorem, we prove existence uniqueness solutions, while bifurcation analysis via center manifold reveals thresholds persistence or elimination. use computational scheme Adams-Bashforth method interpolation-based correction technique ensure numerical precision confirm theoretical results. Sensitivity highlights medication accessibility delaying spread as vital control strategy by identifying parameters. simulations illustrate predictive ability model, which shows order affects trajectories long-term burden. outperforms integer produces more accurate epidemiological predictions integrating memory-dependent fractional flexibility. These findings demonstrate model's value developing targeted public health initiatives, particularly environments limited resources where monitoring balancing allocation essential. In end, our work provides tool better predict manage evolving challenges bridging gap between mathematics actual control.

Language: Английский

Citations

0
An Anomaly Detection Method for Multivariate Time Series Data Based on Variational Autoencoders and Association Discrepancy DOI Creative Commons
Haodong Wang, Huaxiong Zhang

Mathematics, Journal Year: 2025, Volume and Issue: 13(7), P. 1209 - 1209

Published: April 7, 2025

Driven by rapid advancements in big data and Internet of Things (IoT) technologies, time series are now extensively utilized across diverse industrial sectors. The precise identification anomalies data—especially within intricate ever-changing environments—has emerged as a key focus contemporary research. This paper proposes multivariate anomaly detection framework that synergistically combines variational autoencoders with association discrepancy analysis. By incorporating prior knowledge associations sequence mechanisms, the model can capture long-term dependencies effectively between different points. Through reconstructing data, enhances distinction normal anomalous points, learning during reconstruction to strengthen its ability identify anomalies. combining errors discrepancy, achieves more accurate detection. Extensive experimental validation demonstrates proposed methodological statistically significant improvements over existing benchmarks, attaining superior F1 scores public datasets. Notably, it exhibits enhanced capability modeling temporal identifying nuanced patterns. work establishes novel paradigm for profound theoretical implications practical implementations.

Language: Английский

Citations

0
Regulating spatiotemporal dynamics of tussock-sedge coupled map lattices model via PD control DOI

Yanhua Zhu,

Xiaohong Ma, Tonghua Zhang

et al.

Chaos Solitons & Fractals, Journal Year: 2025, Volume and Issue: 194, P. 116168 - 116168

Published: March 5, 2025

Language: Английский

Citations

0
Analyzing fractional glucose-insulin dynamics using Laplace residual power series methods via the Caputo operator: stability and chaotic behavior DOI Creative Commons
Sayed Saber,

Safa M. Mirgani

Beni-Suef University Journal of Basic and Applied Sciences, Journal Year: 2025, Volume and Issue: 14(1)

Published: March 31, 2025

Abstract Background The dynamics of glucose-insulin regulation are inherently complex, influenced by delayed responses, feedback mechanisms, and long-term memory effects. Traditional integer-order models often fail to capture these nuances, leading the adoption fractional-order using Caputo derivatives. This study applies Laplace residual power series method (LRPSM) explore regulatory system’s stability, oscillatory behaviors, chaotic transitions. Results Morphologically, system revealed transitions between oscillations, chaos. Key behaviors were characterized Lyapunov exponents, bifurcation diagrams, phase portraits. Numerical simulations validated effectiveness LRPSM in capturing essential dynamics, including sensitivity parameters such as insulin glucose uptake rates. observed emphasize initial conditions fractional order. Conclusion highlights utility modeling biological systems, offering significant advancements understanding diabetes pathophysiology. findings pave way for designing glycemic control strategies exploring optimized interventions management. Future research could integrate additional physiological real-time applications enhance control.

Language: Английский

Citations

0
A fractional-order multi-delayed bicyclic crossed neural network: Stability, bifurcation, and numerical solution DOI
Pushpendra Kumar, Tae-Hee Lee, Vedat Suat Ertürk

et al.

Neural Networks, Journal Year: 2025, Volume and Issue: unknown, P. 107436 - 107436

Published: April 1, 2025

Language: Английский

Citations

0
Integrative bioinformatics fractional analysis for co-infection dynamics of renal disease and paramyxoviridae virus and optimal control DOI

Maysaa Al-Qurashi,

Sehrish Ramzan, Saima Rashid

et al.

Computers in Biology and Medicine, Journal Year: 2025, Volume and Issue: 191, P. 110059 - 110059

Published: April 15, 2025

Language: Английский

Citations

0
Impact of alarm signals and mutualistic interactions in a food chain model of oxpeckers, zebras, and lions DOI Creative Commons
Ashraf Adnan Thirthar, Prabir Panja, Thabet Abdeljawad

et al.

Partial Differential Equations in Applied Mathematics, Journal Year: 2025, Volume and Issue: 14, P. 101189 - 101189

Published: April 25, 2025

Language: Английский

Citations

0
Patch-Wise-Based Self-Supervised Learning for Anomaly Detection on Multivariate Time Series Data DOI Creative Commons
Seungmin Oh, Le Hoang Anh, Dang Thanh Vu

et al.

Mathematics, Journal Year: 2024, Volume and Issue: 12(24), P. 3969 - 3969

Published: Dec. 17, 2024

Multivariate time series anomaly detection is a crucial technology to prevent unexpected errors from causing critical impacts. Effective in such data requires accurately capturing temporal patterns and ensuring the availability of adequate data. This study proposes patch-wise framework for detection. The proposed approach comprises four key components: (i) maintaining continuous features through patching, (ii) incorporating various information by learning channel dependencies adding relative positional bias, (iii) achieving feature representation self-supervised learning, (iv) supervised based on augmentation downstream tasks. method demonstrates strong performance leveraging patching maintain continuity while effectively representations handling Additionally, it mitigates issue insufficient supporting diverse types anomalies. experimental results show that our model achieved 23% 205% improvement F1 score compared existing methods datasets as MSL, which has relatively small amount training Furthermore, also delivered competitive SMAP dataset. By systematically both local global dependencies, strikes an effective balance between accuracy, making valuable tool real-world multivariate applications.

Language: Английский

Citations

0