Frequency-Domain Analysis of Time-Dependent Multiomic Data in Progressive Neurodegenerative Diseases: A Proposed Quantum-Classical Hybrid Approach with Quaternionic Extensions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911101550067712 |
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| author | Mayfield, John D. |
| author_facet | Mayfield, John D. |
| contents | Progressive neurodegenerative diseases, including Alzheimer's disease (AD), multiple sclerosis (MS), Parkinson's disease (PD), and amyotrophic lateral sclerosis (ALS), exhibit complex, nonlinear trajectories that challenge deterministic modeling. Traditional time-domain analyses of multiomic and neuroimaging data often fail to capture hidden oscillatory patterns, limiting predictive accuracy. We propose a theoretical mathematical framework that transforms time-series data into frequency or s-domain using Fourier and Laplace transforms, models neuronal dynamics via Hamiltonian formulations, and employs quantum-classical hybrid computing with variational quantum eigensolvers (VQE) for enhanced pattern detection. This theoretical construct serves as a foundation for future empirical works in quantum-enhanced analysis of neurodegenerative diseases. We extend this to quaternionic representations with three imaginary axes ($i, j, k$) to model multistate Hamiltonians in multifaceted disorders, drawing from quantum neuromorphic computing to capture entangled neural dynamics \citep{Pehle2020, Emani2019}. This approach leverages quantum advantages in handling high-dimensional amplitude-phase data, enabling outlier detection and frequency signature analysis. Potential clinical applications include identifying high-risk patients with rapid progression or therapy resistance using s-domain biomarkers, supported by quantum machine learning (QML) precedents achieving up to 99.89% accuracy in Alzheimer's classification \citep{Belay2024, Bhowmik2025}. This framework aims to lay the groundwork for redefining precision medicine for neurodegenerative diseases through future validations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_07948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frequency-Domain Analysis of Time-Dependent Multiomic Data in Progressive Neurodegenerative Diseases: A Proposed Quantum-Classical Hybrid Approach with Quaternionic Extensions Mayfield, John D. Other Quantitative Biology Emerging Technologies Quantum Physics 81P68, 92C20, 42A38, 15A18, 81R05 F.0; F.1.1; F.2.1; G.1.0; G.1.3; I.2; I.2.1; I.2.6; I.5; J.3 Progressive neurodegenerative diseases, including Alzheimer's disease (AD), multiple sclerosis (MS), Parkinson's disease (PD), and amyotrophic lateral sclerosis (ALS), exhibit complex, nonlinear trajectories that challenge deterministic modeling. Traditional time-domain analyses of multiomic and neuroimaging data often fail to capture hidden oscillatory patterns, limiting predictive accuracy. We propose a theoretical mathematical framework that transforms time-series data into frequency or s-domain using Fourier and Laplace transforms, models neuronal dynamics via Hamiltonian formulations, and employs quantum-classical hybrid computing with variational quantum eigensolvers (VQE) for enhanced pattern detection. This theoretical construct serves as a foundation for future empirical works in quantum-enhanced analysis of neurodegenerative diseases. We extend this to quaternionic representations with three imaginary axes ($i, j, k$) to model multistate Hamiltonians in multifaceted disorders, drawing from quantum neuromorphic computing to capture entangled neural dynamics \citep{Pehle2020, Emani2019}. This approach leverages quantum advantages in handling high-dimensional amplitude-phase data, enabling outlier detection and frequency signature analysis. Potential clinical applications include identifying high-risk patients with rapid progression or therapy resistance using s-domain biomarkers, supported by quantum machine learning (QML) precedents achieving up to 99.89% accuracy in Alzheimer's classification \citep{Belay2024, Bhowmik2025}. This framework aims to lay the groundwork for redefining precision medicine for neurodegenerative diseases through future validations. |
| title | Frequency-Domain Analysis of Time-Dependent Multiomic Data in Progressive Neurodegenerative Diseases: A Proposed Quantum-Classical Hybrid Approach with Quaternionic Extensions |
| topic | Other Quantitative Biology Emerging Technologies Quantum Physics 81P68, 92C20, 42A38, 15A18, 81R05 F.0; F.1.1; F.2.1; G.1.0; G.1.3; I.2; I.2.1; I.2.6; I.5; J.3 |
| url | https://arxiv.org/abs/2508.07948 |