A library of reproducible analyses.
Each module ships with typed parameters, versioned code, and structured result viewers — so every run is inspectable, shareable, and replayable.
Neurobioinformatics
scRNA-seq QC & filtering
Per-cell QC metrics and MAD-based outlier filtering for single-cell/single-nucleus RNA-seq.
Differential expression
Compare expression between two groups of cells/samples; volcano + table.
Neuro-GWAS association
Single-variant case/control association with a Manhattan plot and top hits.
Brain atlas expression
Region-level expression browsing across a brain atlas.
Connectome graph metrics
Density, degree distribution, clustering and hubs from a connectivity matrix.
Sequence QC (FASTA/FASTQ)
Read counts, GC%, N50, length distribution, mean quality from FASTA/FASTQ.
VCF variant statistics
Ts/Tv, het/hom, SNP vs indel counts, and allele-frequency spectrum from VCF.
k-mer frequency spectrum
Distinct/total k-mers, top-k table, and occurrence histogram from sequences.
Gene-set enrichment (hypergeometric)
Over-representation of pathways via hypergeometric test + BH-FDR.
Kaplan–Meier survival + log-rank
Survival curves per group with log-rank hypothesis test.
One-way ANOVA
F-test across ≥2 groups with eta-squared effect size.
Linear regression
OLS y = a + b·x with R², slope SE, residuals, and fitted line.
Mann–Whitney U (Wilcoxon rank-sum)
Non-parametric two-sample test with tie-corrected normal approximation.
Kruskal–Wallis H-test
Non-parametric ≥2-group comparison of ranks with tie correction.
Pearson correlation matrix
Pairwise Pearson r for numeric columns with two-sided p-values.
Logistic regression (IRLS)
Binary logistic regression via Newton-Raphson; coefficients, z, p, AUC.
Spearman rank correlation
Non-parametric rank correlation between two numeric vectors.
Fisher's exact test (2×2)
Exact two-sided p-value and odds ratio for a 2×2 contingency table.
Chi-square test of independence
Independence test for an R×C contingency table with Cramér's V.
K-means clustering
k-means++ initialization + Lloyd's algorithm; labels, centroids, inertia.
Hierarchical clustering (agglomerative)
Agglomerative clustering with average/single/complete linkage; flat cut at k.
Two-proportion z-test
Compare two binomial proportions with pooled SE + 95% CI on the difference.
Diversity indices (Shannon / Simpson / Chao1)
Richness, Shannon H', Gini-Simpson, Pielou J', Chao1, and rarefaction curve.
Wilcoxon signed-rank (paired)
Non-parametric paired-sample test with tie correction.
GWAS QQ plot + λ (genomic inflation)
QQ plot of observed vs expected -log10 p-values with genomic inflation factor.
ORF finder + codon usage
Six-frame ORF discovery on a DNA sequence with codon-usage table.
Pairwise alignment (Needleman–Wunsch)
Global pairwise sequence alignment with configurable match/mismatch/gap scores.
Motif enrichment (k-mer overrepresentation)
k-mer counts in foreground vs background sequences with binomial p and BH-FDR.
Local alignment (Smith–Waterman)
Local pairwise sequence alignment with configurable scoring.
Population stratification (genotype PCA)
Top PCs on a standardised genotype matrix to reveal population structure.
t-SNE 2D embedding
Non-linear dimensionality reduction to a 2D map (exact O(N²) t-SNE).
Neighbor-joining phylogeny
Neighbor-joining tree from a square distance matrix; returns Newick string.
Poisson GLM (log link, IRLS)
Count-data regression via iteratively re-weighted least squares.
DBSCAN clustering
Density-based clustering with ε-neighbourhoods; labels noise points as -1.
ROC curve & AUC
Receiver-operating characteristic curve, AUC, and Youden's-J optimal threshold.
Bland–Altman agreement
Bias, 95% limits of agreement, and proportional-bias check for two paired measurements.
Cox proportional hazards
Univariate survival regression with hazard ratio, Wald test, partial likelihood, and concordance.
Gaussian mixture model
Diagonal-covariance EM clustering with responsibilities, BIC/AIC, and component summaries.
Kaplan–Meier + log-rank
Kaplan–Meier survival curves for two groups with the log-rank χ² test and median survival.
Fisher LDA (2-class)
Fisher's linear discriminant projection, decision threshold, accuracy, and Fisher ratio.
Permutation two-sample test
Non-parametric permutation test on the difference of two group means with an empirical null.
Ridge regression (CV)
L2-penalised linear regression with k-fold cross-validated λ selection and coefficient table.
Partial least-squares regression
PLS1 regression for high-dimensional, collinear predictors with latent scores and fitted-vs-observed diagnostics.
Non-negative matrix factorization
Parts-based decomposition of non-negative matrices into sample loadings and component signatures.
PageRank centrality
Weighted directed-graph centrality for citation, regulatory, interaction, or connectivity edge lists.
Mutual information
Binned mutual information and normalized MI for non-linear association between two numeric variables.
Kendall's τ rank correlation
Non-parametric τ-b rank correlation with concordant/discordant pair counts and asymptotic z-test.
Bootstrap CI for the mean
Percentile bootstrap confidence interval for the sample mean with standard error and bias estimate.
Jarque-Bera normality test
Normality test based on sample skewness and excess kurtosis with chi-square (df=2) p-value.
Welch's t-test
Two-sample t-test with unequal variances (Satterthwaite df) for comparing group means.
Theil-Sen robust regression
Median-of-slopes linear regression with a Kendall-based slope confidence interval; resistant to outliers.
Two-sample Poisson rate test
Compare two event rates (counts / exposure) with rate ratio, 95% CI and Wald p-value.
Wald-Wolfowitz runs test
Randomness test on a numeric sequence dichotomised at its median; detects clustering or drift.
Levene's test (variance equality)
Tests whether ≥2 groups have equal variances using mean-centered absolute deviations (F-test).
Chi-square goodness-of-fit
Compares observed category counts to an expected distribution with a chi-square test.
Friedman test (repeated measures)
Non-parametric repeated-measures ANOVA on ranked within-subject conditions with tie correction.
Kolmogorov-Smirnov normality
One-sample two-sided KS test against a normal distribution with sample-estimated mean and SD.
Shapiro-Francia normality
Normality test via correlation of ordered values with normal scores; Royston p-value.
Cohen's d effect size
Standardized mean difference between two groups with Hedges' g bias correction and 95% CI.
Benjamini-Hochberg FDR
BH step-up FDR adjustment turning a vector of p-values into q-values with rejection flags.
Paired t-test
Matched-pair t-test for before/after or paired-condition measurements with confidence interval.
Exact sign test
Non-parametric paired sign test using exact binomial probabilities and explicit tie handling.
McNemar paired binary test
Tests marginal symmetry for paired binary outcomes or classifier disagreements using McNemar statistics.
Partial correlation
Pearson partial correlation between X and Y after controlling for one numeric covariate Z.
Grubbs outlier test
Two-sided test for a single extreme outlier using the maximum standardized deviation.
Mann-Kendall trend test
Non-parametric monotonic trend test with Kendall S, τ, p-value, and Sen slope estimate.
Cochran's Q test
Repeated-measures test for equality of related binary outcomes across three or more conditions.
Anderson-Darling normality test
Empirical distribution test for normality with A² statistic, A* adjustment, and p-value.
Bartlett equal-variance test
Chi-square test for homogeneity of variance across two or more normally distributed groups.
Brown-Forsythe test
Robust Levene-type variance equality test using absolute deviations from group medians.
Dixon's Q outlier test
Classical Q test for a single outlier in small samples (n = 3..30) with 95% critical values.
One-sample t-test
Tests whether a numeric sample mean differs from a specified null mean.
Two-sample KS test
Distribution-free comparison of two numeric samples using the maximum ECDF distance.
Mood's median test
Non-parametric test for equal medians across two or more independent groups.
Cohen's kappa (inter-rater)
Two-rater categorical agreement corrected for chance; kappa, SE, z, p.
Cronbach's alpha (reliability)
Internal consistency reliability across items with per-item variance.
Lin's concordance correlation
Concordance correlation coefficient with Pearson r, bias, location and scale shift.
Wald-Wolfowitz runs test (2-sample)
Non-parametric two-sample test based on runs in the pooled ordered sequence.
Mahalanobis outlier screening
Multivariate outlier detection using squared Mahalanobis distances and chi-square tail probabilities.
Hotelling two-sample T²
Multivariate two-sample mean-vector test with pooled covariance and F approximation.
Mardia multivariate normality
Multivariate normality diagnostics via Mardia skewness and kurtosis tests.
Intraclass correlation (ICC)
Two-way random-effects reliability estimate for subjects rated by multiple raters or methods.
Bonferroni correction
Family-wise error-rate correction by multiplying p-values by the number of tests.
Holm-Bonferroni correction
Sequential step-down family-wise correction that is uniformly more powerful than Bonferroni.
Benjamini-Yekutieli FDR
False-discovery-rate correction valid under arbitrary dependence among tests.
Storey q-values
Adaptive FDR q-values using a pi-zero estimate from the high-p-value tail.
G-test of independence
Log-likelihood-ratio test of independence for contingency tables; chi-square approximation.
Cochran-Armitage trend test
Tests for a linear trend in binary proportions across ordered groups (e.g. dose-response).
Breusch-Pagan heteroscedasticity
Tests whether residual variance from a linear regression depends on the predictor.
Fligner-Killeen variance test
Non-parametric, median-centered test for homogeneity of variances across groups.
Anderson-Darling k-sample
Tests whether ≥2 samples are drawn from the same continuous distribution.
Epps-Singleton two-sample
Characteristic-function-based two-sample test; sensitive to shape and scale differences.
Page's trend test
Non-parametric ordered-alternatives test for randomized blocks (monotone treatment trend).
Skillings-Mack test
Friedman-style test for repeated measures that tolerates missing block-treatment observations.
Rayleigh test (circular uniformity)
Tests whether a set of angles (radians) is uniformly distributed around the circle.
Hodges-Lehmann shift estimator
Median of pairwise differences between two samples with a Mann-Whitney based confidence interval.
Siegel-Tukey scale test
Non-parametric two-sample test for equality of dispersion (scale).
Turning-points test (Wallis-Moore)
Tests a time series for randomness by counting local peaks and troughs.
Ansari-Bradley scale test
Distribution-free two-sample test for a difference in scale or dispersion.
Quade randomized-block test
Rank-based treatment comparison for complete randomized blocks, weighted by block ranges.
Watson U² circular uniformity
Omnibus circular uniformity test based on deviations from the wrapped empirical CDF.
Kuiper circular uniformity test
Rotation-invariant circular uniformity test using upper and lower empirical-CDF deviations.
Fligner-Policello robust rank test
Two-sample location test robust to unequal variances, based on placement counts.
Jonckheere-Terpstra trend test
Non-parametric test for monotone trend across k ordered independent samples.
Bowker symmetry test
Chi-square test of symmetry for a square k×k contingency table (extends McNemar).
Stuart-Maxwell marginal homogeneity
Chi-square test that row and column marginal distributions match in a k×k table.
Fisher's combined probability test
Combines independent p-values via X² = -2 Σ ln(p_i) with df = 2k.
Stouffer's Z meta-analysis
Weighted Z-score combination of independent p-values (column 1 = p, column 2 = optional weights).
TOST equivalence test
Two one-sided Welch t-tests establishing equivalence within [lower, upper] on the mean difference.
Random-effects meta-analysis (DerSimonian-Laird)
Pools per-study effects (column 1) and variances (column 2) with DL τ² and reports Q, I², CI.
Concordance C-index (survival)
Harrell's C for survival: 3 columns (time, event 0/1, risk score) → concordance of predicted risk with observed event order.
Two-sample t-test power calculator
Power and required per-group N for a two-sample t-test given effect, sd, alpha, target power (normal approximation).
Correlation sample-size calculator
Required N to detect a Pearson correlation of magnitude r at given alpha and power (Fisher z transform).
Simon's two-stage design
Phase-II single-arm design finding (r1, n1, r, n) minimising max N subject to type-I ≤ α and power ≥ 1-β.
Gaussian Naive Bayes
Gaussian Naive Bayes classifier: per-class means/variances with independence assumption; returns training accuracy and per-class precision/recall/F1. Input: numeric matrix, label = last column.
k-Nearest Neighbours classifier
Euclidean k-NN classifier with leave-one-out cross-validation. Input: numeric matrix, label = last column.
Confusion matrix + precision/recall/F1
Confusion matrix, per-class precision, recall, F1 and macro-F1. Input: two columns (truth, prediction).
Stratified k-fold cross-validation
Stratified k-fold CV with Gaussian Naive Bayes: per-fold accuracy, mean/std and pooled confusion matrix. Input: numeric matrix, label = last column.
Multinomial logistic regression
Softmax multinomial logistic regression trained by batch gradient descent with L2 penalty; returns log loss, accuracy and per-class precision/recall/F1. Input: numeric matrix, label = last column.
Ordinal (proportional-odds) logistic
Proportional-odds ordinal logistic regression with cumulative link; returns beta coefficients, ordered thresholds and accuracy. Input: numeric matrix, ordered label = last column (≥3 classes).
Random forest classifier
Bagged decision-tree ensemble with √d random feature subset per split; returns training and out-of-bag accuracy plus per-class metrics. Input: numeric matrix, label = last column.
Gradient boosting regressor
Gradient boosting with regression stumps (squared-error loss) and learning-rate shrinkage; returns MSE, RMSE, R² and sample predictions. Input: numeric matrix, target = last column.
Polygenic risk score (PRS)
Additive PRS across risk variants under HWE; distribution, summary stats and top-effect variants.
Heritability regression (LDSC-style)
Regress χ² on LD score to estimate SNP-heritability ĥ² and intercept, following the LDSC framework.
cis-eQTL scan
Per-SNP linear regression of expression on genotype dosage with BH-FDR; reports top SNP and significant hits.
Rare-variant burden test
Collapse rare variants per individual; test carrier enrichment in cases vs. controls with Fisher's exact.
Differential methylation (DMPs)
Per-CpG Welch t-test on β-values across two groups with BH-FDR; volcano and top-CpG table.
CpG island detector
Sliding-window GC% and CpG obs/exp on a DNA sequence with island merging (Gardiner-Garden & Frommer criteria).
ChIP-seq peak calling
Sliding-window Poisson peak calling on read-count bins; reports peaks with fold-enrichment and −log₁₀ p.
Methylation age (Horvath-style clock)
Weighted linear methylation-age predictor with per-sample chronological vs. predicted age, MAE, RMSE and Pearson r.
Computational Neuroscience
Hodgkin-Huxley neuron
Simulate a single HH neuron under step-current injection and measure spiking.
Integrate-and-fire neuron
Leaky integrate-and-fire neuron f-I curve and voltage trace.
Spiking network (LIF)
Recurrent excitatory/inhibitory LIF network; population dynamics and raster.
Spike-train statistics
ISI distribution, firing rate, CV and Fano factor from a spike train.
LFP / EEG spectral analysis
Power spectral density and band power from a continuous signal.
fMRI functional connectivity
Region-by-region correlation matrix and graph summary from BOLD time series.
Peri-stimulus time histogram
Event-triggered firing rate around triggers.
Time-frequency spectrogram (STFT)
Short-time Fourier transform with band power over time for EEG/LFP.
Event-related potential (ERP)
Trial-averaged waveform around event markers with bootstrap 95% CI.
Spike cross-correlogram
Pairwise coincident-spike histogram between two spike trains.
Seed-based functional connectivity
Correlation map from a seed region to all others in a BOLD time-series matrix.
Independent Component Analysis (FastICA)
FastICA on multichannel signals (e.g. BOLD, EEG) with logcosh nonlinearity.
ALFF / fALFF per region
Amplitude of low-frequency fluctuations and fractional ALFF from BOLD time series.
Granger causality (bivariate)
Tests whether x's past improves prediction of y beyond y's past (VAR + F-test).
Regional Homogeneity (ReHo)
Kendall's W concordance across each region and its neighbours in a BOLD time × region matrix.
Hidden Markov decoding
Scaled forward-backward posteriors plus Viterbi state decoding for discrete observations.
Dynamic time warping
Elastic alignment distance and warping path for neural, behavioural, or imaging time series.
Autocorrelation function
Biased autocorrelation estimator with Bartlett 95% white-noise confidence band for signal analysis.
Exponential smoothing forecast
Single exponential smoothing with grid-searched α, in-sample fit, and h-step-ahead forecast.
Ljung-Box autocorrelation test
Portmanteau test for serial correlation across multiple lags in neural or time-series signals.
Durbin-Watson diagnostic
Residual autocorrelation diagnostic with Durbin-Watson statistic and lag-1 correlation test.
Leaky integrate-and-fire (LIF)
Simulates a leaky integrate-and-fire neuron for a chosen input current — returns spike train, membrane trajectory, firing rate, ISI CV, and an F–I curve.
Izhikevich neuron
Izhikevich 2-variable model with canonical cortical regimes — regular spiking (RS), intrinsically bursting (IB), chattering (CH), fast spiking (FS), and low-threshold spiking (LTS). Returns V(t), rate, spike raster.
Spike-timing-dependent plasticity (STDP)
Classical exponential STDP learning window — Δw = A+·exp(−Δt/τ+) for pre→post and Δw = −A−·exp(Δt/τ−) for post→pre. Returns full Δw(Δt) curve, LTP/LTD peaks and areas.
Wilson–Cowan E/I dynamics
Two-population excitatory–inhibitory rate model with sigmoid activation. Simulates E(t), I(t), reports fixed-point vs limit-cycle behaviour and the dominant oscillation frequency.
FitzHugh–Nagumo neuron
Two-variable excitable neuron model. Simulates V(t), W(t), reports spike count, firing rate, and phase-plane trajectory.
Morris–Lecar neuron
Conductance-based Ca²⁺/K⁺ model of a barnacle muscle fiber. Produces V(t), gating variable n(t), spike times and firing rate under step current.
Kuramoto oscillator network
N phase oscillators with all-to-all coupling. Tracks the Kuramoto order parameter r(t) and detects synchronization vs incoherence.
Hopfield associative memory
Discrete Hopfield network with Hebbian weights. Recalls a stored ±1 pattern from a noisy probe and reports energy descent and per-pattern overlaps.
Adaptive exponential IF (AdEx)
Brette–Gerstner adaptive exponential integrate-and-fire neuron with subthreshold and spike-triggered adaptation. Returns V(t), w(t), spike raster and firing rate.
Hindmarsh–Rose bursting neuron
3-variable model producing spikes, bursts and chaotic dynamics. Reports spikes per burst, burst count and (x, z) phase-plane trajectory.
Ring attractor network
1-D ring of rate neurons with Mexican-hat coupling. Forms a persistent activity bump that encodes a stimulus angle after the input is removed.
Poisson spike train
Homogeneous Poisson spike generator. Reports empirical rate, ISI mean and coefficient of variation, and the 100 ms-bin Fano factor.