Analysis code, derived result tables, figures and validation-cohort inputs for a study of non-extensive (Tsallis) statistics in the glioblastoma transcriptome. Expression deviations of each sample are fitted with q-Gaussian laws by maximum likelihood. In a longitudinal GLASS cohort (230 libraries from 115 IDH-wildtype patients, at diagnosis and at recurrence after temozolomide chemoradiotherapy) the entropic index has a cohort mean of 1.330 with a standard error of 0.007, and reproduces in two further independent cohorts analysed identically: 1.331 in CGGA-693 (n = 109) and 1.372 in TCGA-GBM (391 libraries from 293 participants). What is new in version 4. Estimator validated against data with a known answer. On 350 synthetic samples drawn from q-Gaussians with known parameters at the observed gene counts, the estimator recovers q with a bias of -0.0008, no fit fails to converge, and the nominal 95% profile-likelihood intervals achieve 94.0% empirical coverage. Two further cohorts. Both CGGA mRNA-seq releases, stratified to match the GLASS design (primary, WHO IV, IDH-wildtype). Three cohorts agree to within 0.042, inside the a priori equivalence margin. A discrepant fourth cohort, with three explanations tested and excluded. CGGA-325 gives 1.420. Sequencing depth was tested by binomial thinning of real integer counts (shift -0.004), cohort size by subsampling (+0.003 at n = 74), and clinical composition by a pre-registered test of MGMT status (predicts 0.002 of 0.089, and the gap survives within both strata). Reported as unexplained. Model comparison against Laplace. The q-Gaussian is preferred by AIC in 87% of samples against an exponential-tailed alternative, with median dAIC above 120 in every cohort. A cohort-size effect in the estimator, characterised. Deviations from a cohort-median reference inflate the fitted tails when few samples are present (+0.032 at n = 20, +0.003 at n = 74); a fixed reference profile removes the effect, identifying the pathway. Applies to any index built the same way. Carried over from version 3. Estimation error measured by within-sample gene splitting (1–14% of the observed variance); a repeatability floor of 0.070 from 90 TCGA participants with replicate libraries, shown not to be explained by library composition; the finding that chemoradiotherapy moves the index no more than re-sampling the same tumour (F = 0.86, p = 0.78); equivalence testing with patient-clustered standard errors verified by a pairs-cluster bootstrap; and a circular covariate documented (the interquartile range of the deviation vector predicts q at R² = 0.94 but is a deterministic function of the fitted parameters). Contents. code/ analysis scripts in execution order; data/ open-access TCGA-GBM inputs with the GDC manifest; results/ one CSV per analysis; figures/ main and supplementary; legacy/ superseded artefacts, each with a file explaining why it is retired, including one retracted analysis. Reproducibility. The deposit is built from a git commit, recorded in the README. code/19_verify_manuscript_numbers.py recomputes every number printed in the manuscript from the tables in results/, confirms that each appears in the manuscript source, and exits non-zero if any disagrees. It passes on this build: 107 checks, 0 failures. Data availability. Raw RNA-seq and clinical data for the primary cohort are available from the GLASS consortium (Synapse syn17038081) under its terms of use and are not redistributed here; derived per-sample values remain subject to those terms, including a prohibition on commercialisation. See NOTICE.txt. TCGA-GBM data are open access from the NCI Genomic Data Commons and are included. CGGA data are openly available from cgga.org.cn and are not redistributed. Use of AI-assisted tools. Part of the analysis code was written with the assistance of a large language model (Claude, Anthropic), as described in the manuscript. All code was read, executed and verified by the authors, who take full responsibility for its correctness.
Sérgio Assunção Monteiro, Fabrício Alves Barbosa da Silva· Zenodo (CERN European Organi...· 0 citations
Abstract Clustering is an unsupervised learning technique used to discover hidden structures in data. By identifying patterns and similarities among objects, this methodology enables the organization of datasets into homogeneous groups. This work presents a new perspective on a specific class of partition-based algorithms for unsupervised discrete clustering in complete finite-dimensional Riemannian manifolds by introducing statistical shape analyses to classify clusters and improve label selection. To achieve this aim, we extend the statistical concepts of skewness and kurtosis to Riemannian settings, based on vector operations in the tangent plane at each point of the manifold. Assumptions regarding the injectivity radius and the boundedness of the sectional curvature are initially adopted to enable local convex analysis. Nevertheless, the well-posedness of Riemannian weighted centroids is ensured by analyzing the coercivity and quasiconvexity properties of the distance function’s powers. In addition, we demonstrate that well-posedness and continuity extend to any positive power of the distance function, rather than being limited to powers greater than or equal to 1. Computational experiments involving diffusion tensor imaging and hyperspectral image segmentation are performed. We also present a statistical analysis to demonstrate the practical applicability and computational performance of our technique compared with leading clustering approaches. Ultimately, our methodology is applicable to any field where data modeling resides in a complete finite-dimensional Riemannian manifold.
Ronaldo Malheiros Gregório, Charlan Dellon da Silva Alves, Sérgio Assunção Monteiro et al.· Soft Computing· 0 citations
Analysis code, derived result tables, figures and validation-cohort inputs for a study of non-extensive (Tsallis) statistics in the glioblastoma transcriptome. Expression deviations of each sample are fitted with q-Gaussian laws by maximum likelihood. In a longitudinal GLASS cohort (230 libraries from 115 IDH-wildtype patients, at diagnosis and at recurrence after temozolomide chemoradiotherapy) the entropic index has a cohort mean of 1.330 with a standard error of 0.007, and reproduces in two further independent cohorts analysed identically: 1.331 in CGGA-693 (n = 109) and 1.372 in TCGA-GBM (391 libraries from 293 participants). What is new in version 4. Estimator validated against data with a known answer. On 350 synthetic samples drawn from q-Gaussians with known parameters at the observed gene counts, the estimator recovers q with a bias of -0.0008, no fit fails to converge, and the nominal 95% profile-likelihood intervals achieve 94.0% empirical coverage. Two further cohorts. Both CGGA mRNA-seq releases, stratified to match the GLASS design (primary, WHO IV, IDH-wildtype). Three cohorts agree to within 0.042, inside the a priori equivalence margin. A discrepant fourth cohort, with three explanations tested and excluded. CGGA-325 gives 1.420. Sequencing depth was tested by binomial thinning of real integer counts (shift -0.004), cohort size by subsampling (+0.003 at n = 74), and clinical composition by a pre-registered test of MGMT status (predicts 0.002 of 0.089, and the gap survives within both strata). Reported as unexplained. Model comparison against Laplace. The q-Gaussian is preferred by AIC in 87% of samples against an exponential-tailed alternative, with median dAIC above 120 in every cohort. A cohort-size effect in the estimator, characterised. Deviations from a cohort-median reference inflate the fitted tails when few samples are present (+0.032 at n = 20, +0.003 at n = 74); a fixed reference profile removes the effect, identifying the pathway. Applies to any index built the same way. Carried over from version 3. Estimation error measured by within-sample gene splitting (1–14% of the observed variance); a repeatability floor of 0.070 from 90 TCGA participants with replicate libraries, shown not to be explained by library composition; the finding that chemoradiotherapy moves the index no more than re-sampling the same tumour (F = 0.86, p = 0.78); equivalence testing with patient-clustered standard errors verified by a pairs-cluster bootstrap; and a circular covariate documented (the interquartile range of the deviation vector predicts q at R² = 0.94 but is a deterministic function of the fitted parameters). Contents. code/ analysis scripts in execution order; data/ open-access TCGA-GBM inputs with the GDC manifest; results/ one CSV per analysis; figures/ main and supplementary; legacy/ superseded artefacts, each with a file explaining why it is retired, including one retracted analysis. Reproducibility. The deposit is built from a git commit, recorded in the README. code/19_verify_manuscript_numbers.py recomputes every number printed in the manuscript from the tables in results/, confirms that each appears in the manuscript source, and exits non-zero if any disagrees. It passes on this build: 107 checks, 0 failures. Data availability. Raw RNA-seq and clinical data for the primary cohort are available from the GLASS consortium (Synapse syn17038081) under its terms of use and are not redistributed here; derived per-sample values remain subject to those terms, including a prohibition on commercialisation. See NOTICE.txt. TCGA-GBM data are open access from the NCI Genomic Data Commons and are included. CGGA data are openly available from cgga.org.cn and are not redistributed. Use of AI-assisted tools. Part of the analysis code was written with the assistance of a large language model (Claude, Anthropic), as described in the manuscript. All code was read, executed and verified by the authors, who take full responsibility for its correctness.
Sérgio Assunção Monteiro, Fabrício Alves Barbosa da Silva· Zenodo (CERN European Organi...· 0 citations
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