Alves Barbosa da Silva, F.

bioRxiv2026

The Tsallis index of the human cortical transcriptome is invariant between bipolar II disorder and control: a pre-registered, cross-platform null with the disease question relocated to correlation structure

Gene-expression fluctuations are heavy-tailed and resist description by additive (Boltzmann-Gibbs) statistics, motivating a non-extensive (Tsallis) account in which the index q summarizes the departure from Gaussianity. We ask two separable questions of the human cortical transcriptome in bipolar II disorder: whether the model-free value of q differs between cases and controls, and, if not, whether any disease signal instead resides in the correlation structure. Using a per-sample maximum-likelihood q-Gaussian estimator under a leakage-free, pre-registered protocol, we find the index concentrated near [Formula] (GSE80655), [Formula] (GSE12649), [Formula] (GSE53987), with no case-control difference in any cohort. Per-sample model comparison favours the q-Gaussian over a Gaussian in 99-100% of samples (median {Delta}BIC << 0), so q is a meaningful descriptor rather than an artefact of fitting. The BD-CTRL difference is null in every cohort. Pooling the three homogeneous cohorts, we test invariance by equivalence (TOST) rather than by non-rejection: the data establish equivalence at the bound |{Delta}q| [≥] 0.037, but do not reach the pre-registered bound of 0.03, which would require roughly twice the present sample. We report this shortfall explicitly: the null is bounded and informative, but the study is underpowered against its own pre-registered minimum effect of interest. A random-matrix test finds no between-group structural difference surviving label permutation. We argue that non-extensivity behaves as a conserved organizational property of the cortical transcriptome and that the disease question, for bipolar II, is relocated from the marginal index to the collective correlation modes and to dynamics (companion work). We report, and do not paper over, a failed cross-tissue scale anchor: a glioma RNA-seq reference is depth-confounded in a cohort-inconsistent way and therefore cannot license a same-value claim across tissues.

genomics↗

bioRxiv2026

Tsallis-Gated Autoencoder: A Nonextensive Physics-Informed Approach for Unsupervised Anomaly Detection in Glioblastoma Multiforme RNA-seq Data

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.

bioinformatics↗