Entropy

In previous studies by the author on binocular vision with the asymmetric eye (AE), which models a healthy human eye with misaligned optical components, the results were primarily presented in the Rodrigues vector (RV) framework and supported by simulations and 3D visualizations in GeoGebras dynamic geometry environment. In this paper, the novel geometric kinematics of the human eye, that is, the eye with misaligned optics, and simplified assumptions about the eye rotations (the eyes translational movements are disregarded), are developed within the framework of rigid-body rotations. The originality of the analysis lies in a precise geometric decomposition of a full rotation of the eyes posture into a torsion-free rotation (the geodesic part) and a torsional rotation (the non-geodesic extension of the geodesic part). This decomposition is extended to the corresponding decomposition of the angular velocity. A novel derivation of the eyes angular velocity from the RV formulation of the eye kinematics is proposed.

Categorisation is often treated as a form of compression: a high-dimensional stimulus space is reduced to a smaller set of behaviourally or cognitively useful classes. However, compression alone does not determine whether a category map is useful. The present manuscript develops an information-theoretic framework for evaluating categorisation in terms of both category complexity and target-relevant information preservation. Across a set of synthetic demonstrations, alternative category maps over the same stimulus space are shown to preserve different target variables, including identity, action, nuisance, and hierarchical category structure. The framework is then extended to learned visual representations by analysing layer-derived category maps from a pretrained ResNet-50 network applied to CIFAR-10 images. Two scenarios are compared: a clean-only object run and a pooled nuisance run containing clean, blurred, pixelated, and noise-perturbed images. The results show that category maps can have substantial entropy while preserving information about a variable that is not aligned with the specified target, and that the value of a categorisation depends on the target variable to be preserved. The manuscript argues that categorisation should therefore be evaluated not only by compression or separability, but by the information retained about a specified cognitive, behavioural, or computational target.

Curvature evolution on a deforming surface is governed by the full change in the surface metric, but on biological surfaces captured by serial three-dimensional imaging, only the local area change is observable. The loss of the shear component leaves prediction of curvature evolution underdetermined from imaging alone. On the thoracic aorta, where curvature change marks disease progression, we derive a closed-form equation that predicts the change in integrated Gaussian curvature from the area dilation and initial geometry. The equation combines a conformal term in the area dilation with a leading anisotropy correction from the initial geometry. These two analytic levels, augmented by multi-scale spatial features at neighboring regions and a graph neural network trained on residuals, form a four-level nested predictor. On a synthetic aortic geometry under prescribed isotropic expansion, the equation recovers the analytic coefficient exactly. Across a continuum from pure expansion to pure shear, it holds R2 [≥] 0.71. On 236 paired thoracic aortic surfaces spanning dissection, aneurysm, traumatic injury, and non-pathologic controls, the equation recovers within-surface curvature change patterns with per-patient median Pearson [Formula] and pooled R2 = +0.238 [+0.225, +0.250], matching the graph neural network on the same inputs. The residual is a direct measurement of how far the observed growth field departs from conformality. HighlightsO_LIClosed-form equation predicts aortic curvature change from paired computed tomography scans. C_LIO_LIRecovers analytic predictions exactly on synthetic aortic geometries. C_LIO_LIAnisotropy proxy holds R2 [≥] 0.71 from pure expansion to pure shear. C_LIO_LICoefficients tie to geometric mechanisms ensuring interpretability. C_LIO_LIAnisotropy term, computable from one CT, is twice as large on diseased aortas. C_LI

Quantum kernel methods offer a potential advantage for classification tasks in high-dimensional feature spaces, yet their practical benefit critically depends on how input features are prepared. We compare five dimensionality reduction strategies--principal component analysis (PCA), Gaussian random projection (RP Gaussian), sparse random projection (RP Sparse), partial least squares (PLS), and uniform manifold approximation and projection (UMAP) -- as pre-processing steps for quantum kernel support vector machines (SVMs) applied to trabecular bone classification from synthetic micro-computed tomography (micro-CT) data. Using a custom procedural generator based on Gaussian random field zero-crossings, we produced 500 synthetic trabecular bone volumes with controlled morphometric properties such as bone volume fraction (BV/TV), trabecular thickness (Tb.Th), number (Tb.N) and spacing (Tb.Sp). Texture features extracted from grayscale slices are reduced to 8-dimensional quantum circuit inputs via each method, then classified using both classical radial basis function (RBF)-SVMs and quantum kernel SVMs with ZZ feature maps on a statevector simulator, both evaluated with 5 x 5 repeated stratified cross-validation (25 folds). Our results show that UMAP is the only reduction method where the quantum kernel remains competitive with the classical baseline. Under repeated cross-validation, UMAP showed a +0.032 accuracy gap favouring the quantum kernel (Dietterich 5 x 2 CV p = 0.177); however, validation on 10 fully independent datasets--each with independently generated samples, separate reduction fits, and separate kernel matrices -- reversed the sign to -0.030 (paired t-test p = 0.123; Wilcoxon p = 0.193; quantum wins 3/10 datasets), indicating that the apparent advantage was likely inflated by fold dependence. Nevertheless, UMAPs gap remains small and non-significant in both analyses, whereas all linear methods (PCA, RP Gaussian, PLS) show substantial quantum deficits of -0.090 to -0.116 across BV/TV classification, with PCA and PLS remaining significant under corrected tests (5 x 2 CV p = 0.004 and p = 0.007 respectively). We additionally evaluate quantum kernel ridge regression for continuous morphometric prediction, finding that ZZ quantum kernels fail uniformly at regression (negative R2 for all methods except PLS at 4 qubits), suggesting that the ZZ kernel captures decision boundaries but not smooth metric structure. These findings provide practical guidance for feature engineering in near-term quantum machine learning pipelines and demonstrate that the choice of dimensionality reduction can determine whether quantum kernels remain competitive with classical baselines.

BackgroundThis study examines a competition-based model (C-model) designed to capture the temporal dynamics of successive brain microstates derived from electroencephalography (EEG) recordings during eyes-open conditions. The analyzed data were obtained from a public repository comprising microstate sequences from 60 sessions of a single subject [1]. When applied to microstate dynamics, the C-model posits a stochastic competition among neural circuits underlying the expression of individual microstates. MethodsThe model is formulated at a conceptual level (computational level in Marrs framework) and employs a geometric distribution to account for the long right tail of microstate duration distributions, interpreted as the probability of "failure" of the currently active microstate to persist. To account for the short-lived left tail, the model incorporates a transient increase in the stability of the currently active network, or equivalently, a temporary decrease in the activation probability of competing microstates (refractory period). ResultsThe model provides a good fit to the microstate duration distributions across all 60 sessions. One third of sessions showed microstate identity sequential dependency with respect to the previous microstates. DiscussionThese results suggest that the C-model captures key aspects of microstate temporal structure. Moreover, because microstate probabilities can be modulated by psychophysiological conditions--including the influence of previously active networks--the model may serve as a building block for more comprehensive neurobiological frameworks of neural and behavioral dynamics. In such frameworks, microstate sequences could emerge from structured competition and flow among neural networks supporting microstate expression.

Adolescence is an important developmental period during which there are diverse changes in the brain and behavior. Goal-directed behaviors and the component processes underlying those behaviors improve during adolescence, including working memory, response inhibition, and reinforcement learning. At the same time there is substantial pruning of excitatory connections in prefrontal cortex and ongoing myelination of axons. However, psychiatric disorders also become increasingly prevalent in late adolescence and early adulthood. In this study, we develop computational models that suggest a hypothesis for how the ongoing changes in the brain can give rise to the increased prevalence of psychiatric disorders. We show that both myelination and pruning during adolescence lead to attractor landscapes in which strongly encoded memories, driven by three-factor learning rules that modulate Hebbian plasticity, come to dominate the landscape of brain activity, at the expense of weakly encoded memories. Pruning and myelination lead to large, strong attractors which, if they are related to aversive emotions, can drive intrusive thoughts and compulsions in obsessive compulsive disorder, rumination in depression, and aversive memories in post-traumatic stress disorder. The link between pruning, myelination and the emergence of dominant attractors for emotionally salient memories is well supported by the models. The way these effects map onto forebrain circuits requires more work.

SummaryAssociation measurements, such as mutual information (MI), are fundamental in the analysis of cancer multi-omics data for identifying cancer-related genes, gene signatures, and gene regulatory networks, thereby shedding light on tumor development, progression, and treatment. Confounding factors, including tumor purity and mutation burden, can bias association measurements in MI, potentially leading to the misclassification of passenger events as drivers. Conditional mutual information (CMI) provides a robust framework for assessing both linear and non-linear associations while effectively accounting for different confounding factors. An R package called conMItion is introduced to estimate CMI and its statistical significance for multi-omics data, with flexibility to adjust for one or two confounding factors. We demonstrated the utilization of conMItion through two use cases. First, we identified co-occurring somatic alterations in bladder cancer genomic data. Second, we applied conMItion to a single-cell RNA sequencing dataset of lung cancer patients and identified positively or negatively associated cell types within the lung cancer tumor microenvironment. Availability and ImplementationThe conMItion package is freely available on CRAN at https://CRAN.R-project.org/package=conMItion. The two use cases described in the paper can be accessed at https://github.com/GJYWang/conMItion. A supplementary document is available online.

Developing parsimonious, mechanism-aware quantitative models that predict how biological effectiveness changes with different modifiers remains, in general, an unsolved problem. Advances in radiobiological research have created a large knowledge base of first-principles mechanistic models of radiation response that, in principle, could accurately predict radiosensitivity across different experimental and clinical conditions. However, in practice these mechanistic models come with an overabundance of parameters, the majority of which are practically unidentifiable and, moreover, likely unnecessary if one simply wishes to predict how radiosensitivity changes for some specific modifier of interest. Nevertheless, determining which few details in the full mechanistic model are relevant for a given purpose, as well as how to remove any other extraneous details, remains a highly non-trivial task. In this study, we demonstrate the potential of model reduction, starting from a detailed mechanistic description, as a systematic strategy for deriving parsimonious, experimentally falsifiable radiobiological descriptors. As a proof-of-concept demonstration, we apply the Manifold Boundary Approximation Method (MBAM) to a Mechanistic Model of DNA Repair and Survival (MEDRAS), for the problem of cell survival prediction following an acute exposure. Our findings reveal that the complete MEDRAS model for an arbitrary mixed-quality exposure can be structurally simplified to a reduced three-parameter model for an effective uniform-quality, named MEDRAS-LPL. Additional MBAM analysis on MEDRAS-LPL identifies two boundaries in parameter space, corresponding to sparsely ionizing and densely ionizing radiation. Mapping of MEDRAS-LPL parameter space on to effective LQ space further demonstrates that parameters close to the sparsely ionizing boundary line up with expectations from the theory of dual radiation, while parameters close to the densely ionizing boundary line up with expectations from a purely linear model based on a target-theory description. Moreover, our formalism predicts enhanced synergistic interactions between sparsely ionizing and densely ionizing radiation beyond the Zaider Rossi model (ZRM) paradigm, in line with empirical observations. The results highlight the potential for using reduced-order models not only for predictive applications but also for generating novel hypotheses that can inform future experimental designs and optimization strategies in radiobiology.

Improving long-term memory in artificial neural networks remains an open challenge. To address this, we developed a novel brain-inspired framework for memory prioritization based on the principle of emotional valence. Our framework includes: (i) a valence-weighted cross-entropy loss that scales the learning signal by the valence magnitude, analogous to neuromodulation; (ii) an amygdala-inspired module that learns high-dimensional valence embeddings; and (iii) a hippocampus-inspired module that integrates valence embeddings into the attention mechanism to modulate information retrieval. We demonstrated the generalization of our framework across spatial, episodic, and language-based memory tasks, consistently improving memory prioritization and long-term retention of high-salience information. In addition to improving long-term memory, we also showed that our framework can help mitigate the "lost-in-the-middle" problem in language modeling. More generally, this research provides further evidence of the potential of brain-inspired algorithms to advance the field of machine learning.

For decades, the photon counting histogram (PCH) was used as the sole method to quantify fluorophore numbers in a diffraction-limited focal volume. This technique combines spatial excitation profiles, and the distribution of photon counts to register the photon emission statistics of individual fluorophores. However, this approach has not yet been transferred to widefield fluorescent imaging due to the lack of fast and single photon sensitive camera sensors which can capture the photon emission statistics of a single fluorophore. Here, we explore avenues towards quantitative analysis of the active fluorophore number by leveraging recent advancements in single photon avalanche diode (SPAD) array technology. Binary exposures of a SPAD array can be synchronized with picosecond laser pulses to measure the PCH in a widefield setting. Then, by modeling the statistical relationship between the active fluorophore number and the PCH in a region of interest following a laser pulse, we can perform Bayesian inference of this number. The model is demonstrated experimentally by counting quantum dots and various numbers of fluorescent dye molecules bound to DNA origamis. We find that this method has several important applications in widefield microscopy, including enhanced localization microscopy and constrained fitting of multiple unresolvable fluorescent emitters.

The increasing number of computational methods designed to predict the effects of genetic perturbations on cellular gene expression profiles has led to a need for rigorous evaluation metrics. Recent benchmarking studies rely on correlation or cosine similarity of differential expression relative to a shared population of control cells. We show that these metrics are systematically inflated by statistical bias induced by reusing the same control population to define both quantities being compared. As a result, even non-informative methods can appear to perform well, particularly in datasets with limited numbers of control cells. Reanalysis of published datasets using a simple control-splitting procedure that removes this bias leads to a substantial reduction in performance previously attributed to biological signal.

Glioblastoma multiforme (GBM) is characterised by profound genomic heterogeneity and heavy-tailed gene-expression distributions that challenge conventional machine-learning methods. We introduce the Tsallis-Gated Autoencoder (Tsallis-GAE), a physics-informed architecture that replaces classical softmax attention with a learnable Tsallis q-softmax followed by mean-field smoothing iterations, motivated by recent work on curved statistical manifolds and dense associative networks. Trained on the full TCGA-GBM RNA-seq cohort (391 samples, top 2,000 high-variance genes) under a rigorous 80/20 hold-out protocol, the Tsallis-GAE achieves a mean AUC-ROC of 0.977 {+/-} 0.002 across five independent seeds, compared to 0.906 {+/-} 0.003 for a matched-capacity Vanilla autoencoder trained under the identical protocol. The matched-capacity Vanilla autoencoder is statistically indistinguishable from a LocalOutlierFactor baseline (AUC 0.906 vs 0.906), confirming that the +0.07 AUC gain over the Vanilla AE stems from the gated attention architecture rather than from the use of a neural network per se. A fixed-q Softmax-AE ablation (q {equiv}1 by construction) achieves AUC 0.976 {+/-}0.001, only +0.001 below the Tsallis-GAE (DeLong p = 0.44); the physically meaningful contribution of the learnable q is its spontaneous convergence to the non-extensive regime described below. The three attention blocks each carry an independent learnable entropic index q; across 5 seeds x3 blocks = 15 measurements, q converges spontaneously to 1.554{+/-} 0.019, strictly bounded away from the Boltzmann-Gibbs limit q = 1 and in the moderate non-extensivity regime characteristic of complex biological systems. Cross-detector validation against OneClassSVM and LocalOutlier-Factor pseudo-labels yields Tsallis-GAE AUCs of 0.998 and 0.992 respectively, indicating that the learned representation captures anomaly structure intrinsic to the data rather than the decision boundary of any single labeling heuristic. We declare that DeLongs paired test on the present test-set size (n = 79) does not certify the +0.07 AUC gap as formally significant (p{approx} 0.26); a 5-fold cross-validation over the full cohort, which would supply the needed statistical power, is left to future work. The source code is available upon reasonable request to the corresponding author.

The awake brain is known to display asynchronous (AS) states during periods of attention and arousal, but the responsiveness properties of such states remain unclear. Here, we investigate this question using computational models of spiking networks of excitatory and inhibitory neurons, mimicking recurrently-connected networks in layer 2/3 of the cerebral cortex. The networks can generate a continuum of AS states, but with different responsiveness characteristics. By using a mean-field model to infer the dynamic properties of the system, we find that there are two families of AS states, which we call "underdamped" (UD) and "overdamped" (OD). Responsiveness is maximised at the transition between OD and UD states, which identifies a "working point" that may present advantageous computational properties.

Understanding how neuronal populations interact to encode and transform sensory information is a fundamental challenge in computational neuroscience. Most existing studies, however, study neural encoding, behavioral readout, and functional connectivity as disjoint problems. Two-photon calcium imaging enables simultaneous recording of large neuronal ensembles in vivo, driven by diverse stimuli and eliciting distinct behaviors. However, extracting directional functional connectivity metrics as well as encoding and readout properties of neurons from such data remains difficult due to indirect and noisy observations of spiking activity, slow temporal dynamics, and the latent interplay between external stimuli and endogenous neural processes. Here, we introduce a unified conceptual and operational modeling and inference framework for directly extracting functional Granger causal (GC) effects between neurons, from external stimuli to neurons, and from neurons to behavior, from two-photon imaging data, in the sense of Granger. Inspired by the intersection information framework, we also identify neurons that encode features of sensory stimuli that inform behavioral readout. The resulting GC networks together with the taxonomy of functional sensori-behavioral relevance, which we call G-taxonomy, provides a powerful statistical analysis framework, enabled by the integration of several techniques including state-space modeling and inference, variational inference, and point processes. We applied the proposed framework to simulated and experimentally-recorded two-photon imaging from the mouse auditory cortex (A1) during both passive listening and active tone discrimination. Our simulation studies reveal significant improvement of our proposed methodology over existing techniques. Analysis of experimental data from the mouse A1 identifies distinct groups of cells with diverse sensori-behavioral relevance, as well as changes in functional connectivity associated with correct vs. incorrect behavior. In summary, this work provides a principled and data-driven methodology for uncovering directional interactions among the neurons, sensory stimuli, and behavior, all within the same statistical framework, offering new insights into how distributed cortical populations transform sensory inputs into behaviorally relevant representations. Author SummaryThe brain processes sensory inputs through the coordinated activity of large networks of neurons and produces readouts that elicit behavior. Understanding how information flows and is processed through these networks is a central goal of neuroscience. In this study, we present a new computational framework that identifies directional interactions among neurons in an ensemble as well as from sensory stimuli to neurons and from neurons to behavior. Utilizing the Granger formalism to identify directional effects, as opposed to common correlational measures, our framework extracts said effects directly from two-photon calcium imaging data. We tested our proposed method on both simulated data and recordings from the auditory cortex of mice during passive listening and active tone discrimination tasks. Our method revealed diverse groups of neurons in the auditory cortex with distinct functional roles and relevance to sensori-behavioral integration. Our framework provides a new way to study the flow of information in the brain and can be broadly applied to uncover neural computations across sensory and cognitive systems.

The learning dynamics of biological brains and artificial neural networks are of interest to both neuroscience and machine learning. A key difference between them is that neural networks are often trained from a randomly initialized state whereas each brain is the product of generations of evolutionary optimization, yielding innate structures that enable few-shot learning and inbuilt reflexes. Artificial neural networks, by contrast, require non-ethological quantities of training data to attain comparable performance. To investigate the effect of evolutionary optimization on the learning dynamics of neural networks, we combined algorithms simulating natural selection and online learning to produce a method for evolutionarily conditioning artificial neural networks, and applied it to both reinforcement and supervised learning contexts. We found the evolutionary conditioning algorithm, by itself, performs comparably to an unoptimized baseline. However, evolutionarily conditioned networks show signs of unique and latent learning dynamics, and can be rapidly fine-tuned to optimal performance. These results suggest evolution constitutes an inductive bias that tunes neural systems to enable rapid learning.

The Poisson-Nernst-Planck (PNP) system is an accurate model of electrodiffusion of ionic species. It is commonly used in situations where nanoscale resolution is required, for instance close to ion channels in the membranes of biological cells. The inherent stiffness of the equations has made them challenging to solve and has limited the applicability of the system. In particular, the time step required for stable solutions has typically needed to be very short (nanoseconds), which makes simulations on the time scale of an action potential (milliseconds) difficult. Recently, it has been observed that avoiding operator splitting and instead solving the concentration equations and the electrostatic equation in a coupled manner relaxes the time-step limitation considerably. However, no theoretical explanation of this observation has been provided. Here, we aim to explain why the coupled scheme allows much larger time steps. We illustrate the mechanism by considering special cases that define necessary, but not sufficient, conditions for stability. We also show that these conditions remain relevant for the fully coupled PNP model in 3D.

Wild-type T4 lysozyme (T4L) is used as a benchmark to evaluate conformational sampling across generative AI, AI-accelerated molecular simulation (AMS), and physics-based enhanced molecular dynamics (EMD). A four-state model: exposed/open, exposed/closed, buried/open, and buried/closed; is defined using physically meaningful collective variables. While generative AI methods (AF-cluster, MSA subsampling of AlphaFold2, ConforFold, AlphaFlow, ESMFlow, ConfRover, BioEmu) largely sample only the exposed/open state, AMS integrating generative ensembles with iterative molecular dynamics, recovering all states and reproducing equilibrium populations similar to EMD and experimental smFRET signatures.

BackgroundThe relevance of spontaneous activity has been unlocked thanks to recent large scale recordings that revealed, via Shared Variance Component Analysis (SVCA), the high-dimensional nature of the ongoing activity. A fundamental problem is how the dimension modifies when more neurons are included in the analysis. Contradictory results have been reported on this subject based on SVCA and Principal Component Analysis (PCA). New MethodWe investigate pro et contra of SVCA and PCA for the identification of reliable responses encoding underlying state variables. We focus on common features of the spectra of the reliable variances (RVs) and on their dimensionality. The analysis is demonstrated on previously published Ca2+ data from the visual and the dorsal cortex in head fixed mice during spontaneous behavior. ResultsRVs grow proportionally to the number N of neurons and show a power-law decay k- with the k-th SVC dimension over a range bounded by a maximal dimension kc, initially diverging as N 1/ and then saturating at sufficiently large N. The reliable dimensionality, estimated with different methodologies, also shows a clear saturation to an asymptotic value for large N. Furthermore, its value decreases when becomes larger, as demonstrated by employing experimental data as well as theoretical predictions. ConclusionWe have shown that SVCA is an extremely effective tool to extract reliable features from the neural signals, and that the exponent represents a biomarker able to reveal the level of correlation of the neurons as well as the dimensionality of the reliable space. HighlightsO_LIAdvantages and drawbacks of Shared Variance Component Analysis to extract reliable signals from neural data C_LIO_LIComparison of different methods to estimate reliable neural dimensionality associated to spontaneous activity C_LIO_LIAnalytical expressions of embedding dimensionality for power-law decaying reliable variances C_LIO_LIBounded growth of the dimensionality with the number of neurons C_LI

Quantum effects in biology are unavoidable at the molecular scale; the unresolved question is whether they can remain functionally relevant across the timescale gap between femtosecond molecular dynamics and microsecond-to-millisecond biological function. Here we formalize this mismatch as an equilibrium-to-functionality gap and use tubulin as a stringent open-system test case. We combine secular Lindblad, Redfield, and hierarchical equations of motion (HEOM) treatments to quantify decoherence, non-perturbative relaxation, and the physical amplification required for functional relevance. Equilibrium dephasing yields a conservative [Formula] fs at 310 K, with a generic protein-bath baseline of {approx} 13 fs. A completed 30 ps HEOM trajectory for the full 1JFF tryptophan network shows distributed non-Markovian relaxation, with terminal purity Pur = 0.210 and stretched-exponential exponent {beta}KWW {approx} 0.44, confirming that Redfield is useful as a short-time perturbative comparator but not quantitatively interchangeable with HEOM in this intermediate-coupling regime. We introduce a coherence-utility criterion [U] = [K]{tau}coh/{tau}func, separating required amplification from empirically bounded gain. A thermodynamic uncertainty relation closure shows that neural-scale cascade amplification would require Pmin [~] 10-7 W, about five orders of magnitude above the local microtubule GTP budget. Frohlich pumping is found to be linewidth-gated rather than generically micron-scale; ordered-water cavity QED and geometric subradiance remain experimentally testable but severely constrained candidates. The result is not a model of consciousness, but a reproducible physical benchmark framework for evaluating biological quantum-coherence claims under explicit open-system, energetic, and experimental constraints. Six falsifiable experimental programmes are prioritized, and the full computational framework is released with a validation ledger, cryptographic audit trail, and living supplementary material. O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=107 SRC="FIGDIR/small/724047v1_ufig1.gif" ALT="Figure 1"> View larger version (20K): org.highwire.dtl.DTLVardef@19e4f42org.highwire.dtl.DTLVardef@65a719org.highwire.dtl.DTLVardef@1bd63beorg.highwire.dtl.DTLVardef@df77d8_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOGraphical abstract.C_FLOATNO Equilibrium tubulin coherence lies in the femtosecond regime, while functional neural timescales lie in the millisecond regime. Frohlich pumping, QED-cavity protection, and geometric subradiance remain experimentally discriminable non-equilibrium candidates requiring independently bounded amplification. C_FIG FundingThis research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. Versioned computational scope of this releaseThis manuscript reports the theoretical framework, calibrated equilibrium baseline, Redfield/HEOM validation ledger, stratified Bayesian evidence synthesis, classical comparators, and falsifiable experimental design. The release-specific reproduction audit, including the current validation-check total and the SHA-256 fingerprints of the binary production artefacts (.npz, .pkl), is documented in LIVING_SI.md and outputs_data/raw_json/structur al/validation_report.json. A completed 30 ps HEOM production trajectory has been validated on constrained hardware; the master dataset contains the full 8-site population trajectory. A summary of those results is provided in [§]2.2.5. All claims made below are restricted to the numerical and theoretical evidence reported in this manuscript and its associated repository artefacts. The public repository ships the calibrated phenomenological baseline for accessibility; the HEOM production artefacts serve as the non-perturbative validation benchmark. All source figure outputs associated with this release are maintained in the public repository under outputs_data/figures_final/.

Despite progress in predicting protein structures, how proteins arrive at their native state remains a subject of continuous debate. We present a single molecule force spectroscopy study of the unfolding and refolding intermediates of the conserved, diverse, and ancient Rossmann2x2 fold ({beta}12{beta}34{beta}56{beta}78). By inserting glycines at different locations in the protein, we can follow in real time and annotate its unfolding and refolding intermediates. This protein folds along a single reversible pathway involving the ordered and sequential organization of discrete and cooperative folding units or foldons: unfolded {rightleftarrows} {beta}12{beta}3 {rightleftarrows} {beta}12{beta}34{beta}5 {rightleftarrows} {beta}12{beta}34{beta}56{beta}7 {rightleftarrows} {beta}12{beta}34{beta}56{beta}78. This strict order results from the formation of an autonomously folding unit (primary foldon) and the subsequent organization of elements (secondary foldons) whose stability depends on their interactions with previously organized ones.