Pub Date : 2026-10-17DOI: 10.1007/s10867-026-09726-9
Gualtiero Piccinini
I present three proofs that idealized neurocomputational architectures capable of navigation guided by allocentric maps with landmark structure can be computationally universal. Navigation may occur online, in the environment, or offline, in the animal’s head. The first proof encodes the counters of a two-counter machine as positions of movable markers on orthogonal axes. The second directly simulates a one-tape Turing machine using a writable tape-path embedded in the map. The third realizes the tape-path’s predecessor/successor relation through local cues at a two-row landmark track rather than through a globally indexed path primitive. I establish universality in two senses: each class of navigation models is Turing-complete, and each contains a single machine that simulates every machine in its class. These constructions are mathematically close to classical graph-based models, including Kolmogorov–Uspensky machines, storage-modification machines, and graph Turing machines, so the bare computability results are unsurprising. My contribution is to reconstruct them explicitly within an allocentric cognitive-map architecture whose representational and computational primitives are drawn from empirical and theoretical work on spatial navigation and cognitive control. This shows that an allocentric navigation-based architecture can be computationally universal and opens the possibility of reconstructing aspects of biological cognition, including symbolic processing, in navigation-based terms.
{"title":"Allocentric navigation is computationally universal","authors":"Gualtiero Piccinini","doi":"10.1007/s10867-026-09726-9","DOIUrl":"10.1007/s10867-026-09726-9","url":null,"abstract":"<div><p>I present three proofs that idealized neurocomputational architectures capable of navigation guided by allocentric maps with landmark structure can be computationally universal. Navigation may occur online, in the environment, or offline, in the animal’s head. The first proof encodes the counters of a two-counter machine as positions of movable markers on orthogonal axes. The second directly simulates a one-tape Turing machine using a writable tape-path embedded in the map. The third realizes the tape-path’s predecessor/successor relation through local cues at a two-row landmark track rather than through a globally indexed path primitive. I establish universality in two senses: each class of navigation models is Turing-complete, and each contains a single machine that simulates every machine in its class. These constructions are mathematically close to classical graph-based models, including Kolmogorov–Uspensky machines, storage-modification machines, and graph Turing machines, so the bare computability results are unsurprising. My contribution is to reconstruct them explicitly within an allocentric cognitive-map architecture whose representational and computational primitives are drawn from empirical and theoretical work on spatial navigation and cognitive control. This shows that an allocentric navigation-based architecture can be computationally universal and opens the possibility of reconstructing aspects of biological cognition, including symbolic processing, in navigation-based terms.</p></div>","PeriodicalId":612,"journal":{"name":"Journal of Biological Physics","volume":"52 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10867-026-09726-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-15DOI: 10.1007/s10867-026-09727-8
Tahir Abbas, Saima Rashid, Muhammad Imran
Obesity, hyperglycemia, and aging are major risk factors for dementia-related disorders, particularly Alzheimer’s disease. We develop a time-fractional reaction–diffusion mathematical framework integrating nine interacting biological compartments governed by Michaelis–Menten kinetics and Hill functions to characterize the nonlinear interplay between metabolic dysfunction and neurodegeneration. Rigorous analysis establishes boundedness, stability, and the existence of a global attractor describing long-term system behavior. To enhance biological realism and predictive capability, we implement fractional physics-informed neural networks that embed fractional partial differential equations within deep learning architectures. This approach captures memory-dependent and spatiotemporal diffusion dynamics characteristic of neurological disorders while enabling estimation of time-varying parameters, fractional orders, and latent states. Global sensitivity analysis using partial-rank correlation coefficients identifies key drivers of tau pathology, insulin dysregulation, and dementia progression. Simulations reveal heterogeneous diffusion patterns linking obesity to accelerated neurodegenerative processes. An optimal control framework incorporating behavioral interventions and personalized anti-amyloid therapies is proposed to delay obesity-induced cognitive decline. The model highlights the critical roles of neuroinflammation and blood–brain barrier permeability in disease acceleration. The proposed FPI-NN framework achieves high predictive accuracy, with (mathcal {R}^{2}) values of 0.95, 0.93, 0.92, and 0.92 for (textrm{Y}_{1}), (textrm{W}_{beta }), (textrm{W}_{tau }), and (textrm{V}_{textrm{d}}), respectively. The corresponding RMSE values are 0.078, 0.094, 0.098, and 0.099, while the MAE values are 0.065, 0.079, 0.082, and 0.084, respectively. The MAPE values are (6.50%), (7.90%), (8.20%), and (8.40%), respectively. Cross-validation further confirms the stability and robustness of the proposed framework. This work provides a reproducible and interpretable computational platform for modeling fractional-order neurodegenerative dynamics and optimizing therapeutic strategies in obesity-associated dementia.
{"title":"Fractional-order dynamical modelling of neurophysiological reaction–diffusion model of adiposity-induced cognitive decline using physics-informed neural networks","authors":"Tahir Abbas, Saima Rashid, Muhammad Imran","doi":"10.1007/s10867-026-09727-8","DOIUrl":"10.1007/s10867-026-09727-8","url":null,"abstract":"<div><p>Obesity, hyperglycemia, and aging are major risk factors for dementia-related disorders, particularly Alzheimer’s disease. We develop a time-fractional reaction–diffusion mathematical framework integrating nine interacting biological compartments governed by Michaelis–Menten kinetics and Hill functions to characterize the nonlinear interplay between metabolic dysfunction and neurodegeneration. Rigorous analysis establishes boundedness, stability, and the existence of a global attractor describing long-term system behavior. To enhance biological realism and predictive capability, we implement fractional physics-informed neural networks that embed fractional partial differential equations within deep learning architectures. This approach captures memory-dependent and spatiotemporal diffusion dynamics characteristic of neurological disorders while enabling estimation of time-varying parameters, fractional orders, and latent states. Global sensitivity analysis using partial-rank correlation coefficients identifies key drivers of tau pathology, insulin dysregulation, and dementia progression. Simulations reveal heterogeneous diffusion patterns linking obesity to accelerated neurodegenerative processes. An optimal control framework incorporating behavioral interventions and personalized anti-amyloid therapies is proposed to delay obesity-induced cognitive decline. The model highlights the critical roles of neuroinflammation and blood–brain barrier permeability in disease acceleration. The proposed FPI-NN framework achieves high predictive accuracy, with <span>(mathcal {R}^{2})</span> values of 0.95, 0.93, 0.92, and 0.92 for <span>(textrm{Y}_{1})</span>, <span>(textrm{W}_{beta })</span>, <span>(textrm{W}_{tau })</span>, and <span>(textrm{V}_{textrm{d}})</span>, respectively. The corresponding RMSE values are 0.078, 0.094, 0.098, and 0.099, while the MAE values are 0.065, 0.079, 0.082, and 0.084, respectively. The MAPE values are <span>(6.50%)</span>, <span>(7.90%)</span>, <span>(8.20%)</span>, and <span>(8.40%)</span>, respectively. Cross-validation further confirms the stability and robustness of the proposed framework. This work provides a reproducible and interpretable computational platform for modeling fractional-order neurodegenerative dynamics and optimizing therapeutic strategies in obesity-associated dementia.</p></div>","PeriodicalId":612,"journal":{"name":"Journal of Biological Physics","volume":"52 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hepatitis C virus (HCV) remains a major global health concern, causing chronic hepatitis, cirrhosis, and hepatocellular carcinoma (HCC), with an estimated 185 million people affected worldwide. In the absence of an FDA-approved vaccine, the development of effective antiviral strategies remains essential. The HCV NS3-4A protease, which mediates cleavage of the viral polyprotein at specific downstream sites of NS3 and is essential for replication-complex formation, represents a key therapeutic target. In this study, approximately 1,480 phytocompounds were compiled from the IMPPAT database and previously reported in vitro studies and subjected to drug-likeness, toxicity, and biological activity screening using pkCSM, SwissADME, and PASS. Twenty compounds were subsequently prioritized and docked against WT, R155K, and D168Y NS3/4A protease structures. Among these, Ladanein (LAD) and Diosmetin (DMT) exhibited favourable binding across all protein variants. MD simulations indicated stable protein–ligand interactions, while MM/GBSA calculations revealed more favourable binding free energies for LAD than DMT across the WT and mutant complexes. Residue-wise energy decomposition identified more energetically favourable hotspot residues in LAD-bound complexes, whereas DMT exhibited higher overall hydrogen-bond occupancy. PCA and free-energy landscape analyses further demonstrated ligand-dependent alterations in collective conformational states induced by the R155K and D168Y substitutions. Overall, these findings computationally prioritize LAD as a promising candidate against WT and mutant HCV NS3/4A protease, warranting further in vitro and biochemical validation.