「closed-form」の検索結果

Render mathematically-faithful Turkish marbling (Ebru) and paper-marbling with closed-form coordinate-deformation maps — a drop is a radial outward push, a comb/tine is a decaying shear, all composed as homeomorphisms over colored region boundaries. No fluid solver, runs 60fps on a 2D canvas. Use when building a marbling/Ebru toy or generative-art renderer, implementing drop/comb/wave/swirl deformations, scripting traditional patterns (Battal, Gel-Git, Şal, Bülbül Yuvası), keeping combed edges crisp via adaptive resampling, modeling ox-gall shouldering for crisp ring-in-ring drops, or exporting high-DPI marbled prints. NOT for real fluid / Navier-Stokes simulation, metaball / alpha-blended "smoke" blob effects, raster image-processing filters, or non-marbling generative art.

日本語の概要は準備中です。原文の説明を表示しています。

Calculates sample sizes and statistical power for study planning. Applies when someone asks "how many subjects/samples/replicates do I need", wants an a priori power analysis, a minimum detectable effect (MDE), a power curve, or needs to justify a sample size for a grant, IRB protocol, or pre-registration. Covers closed-form power for t-tests, ANOVA, proportions, correlations, chi-square, and regression, plus simulation-based (Monte Carlo) power for complex designs — logistic/Poisson regression, mixed models, cluster-randomized trials, survival, and interactions. Also handles requests that only mention an effect size, alpha, or "80% power" without saying "power analysis" explicitly. For laying out the study (randomization, blocking, factorial/DOE, crossover, sequential designs) use experimental-design; for analyzing data already collected and reporting it use statistical-analysis.

日本語の概要は準備中です。原文の説明を表示しています。

Sample-size and statistical power calculations for planning studies. Use whenever someone asks "how many subjects/samples/replicates do I need", wants an a priori power analysis, a minimum detectable effect (MDE), a power curve, or needs to justify a sample size for a grant, IRB protocol, or pre-registration. Covers closed-form power for t-tests, ANOVA, proportions, correlations, chi-square, and regression, plus simulation-based (Monte Carlo) power for designs with no formula — logistic/Poisson regression, mixed models, cluster-randomized trials, survival, and interactions. Use this skill even when the request only mentions an effect size, alpha, or "80% power" without saying "power analysis" explicitly. For laying out the study (randomization, blocking, factorial/DOE, crossover, sequential designs) use experimental-design; for analyzing data already collected and reporting it use statistical-analysis.

日本語の概要は準備中です。原文の説明を表示しています。

Calculates statistical power for high-dimensional genomics experiments (bulk RNA-seq, scRNA-seq, ATAC-seq, ChIP-seq, methylation, proteomics) under negative-binomial count models using RNASeqPower, PROPER, and simulation via powsimR, distinguishing per-gene from marginal (transcriptome-wide) power, the role of mean expression and dispersion, and the sequencing-depth-versus-replicate tradeoff. Covers simulation as the honest default for overdispersed counts, FDR-aware average power versus single-test power, observed/post-hoc power as an anti-pattern, and the winner's-curse / Type-S / Type-M consequences of underpowering. Use when planning replicate number for a sequencing experiment, deciding whether to add depth or samples, choosing closed-form versus simulation power, estimating power from pilot dispersions, or justifying replication in a grant. For clinical-trial power see clinical-biostatistics/power-and-sample-size; for the inverse sample-size question see experimental-design/sample-size.

日本語の概要は準備中です。原文の説明を表示しています。

Analyze the dynamics of diffusion processes using stochastic differential equations, Fokker-Planck equations, first-passage time distributions, and parameter sensitivity analysis. Use when deriving probability density evolution for a continuous-time diffusion process, computing mean first-passage times for bounded diffusion, analyzing how drift and diffusion parameters affect process behavior, or validating closed-form solutions against stochastic simulation.

日本語の概要は準備中です。原文の説明を表示しています。

Calculates statistical power for high-dimensional genomics experiments (bulk RNA-seq, scRNA-seq, ATAC-seq, ChIP-seq, methylation, proteomics) under negative-binomial count models using RNASeqPower, PROPER, and simulation via powsimR, distinguishing per-gene from marginal (transcriptome-wide) power, the role of mean expression and dispersion, and the sequencing-depth-versus-replicate tradeoff. Covers simulation as the honest default for overdispersed counts, FDR-aware average power versus single-test power, observed/post-hoc power as an anti-pattern, and the winner's-curse / Type-S / Type-M consequences of underpowering. Use when planning replicate number for a sequencing experiment, deciding whether to add depth or samples, choosing closed-form versus simulation power, estimating power from pilot dispersions, or justifying replication in a grant. For clinical-trial power see clinical-biostatistics/power-and-sample-size; for the inverse sample-size question see experimental-design/sample-size.

日本語の概要は準備中です。原文の説明を表示しています。

Calculates statistical power for high-dimensional genomics experiments (bulk RNA-seq, scRNA-seq, ATAC-seq, ChIP-seq, methylation, proteomics) under negative-binomial count models using RNASeqPower, PROPER, and simulation via powsimR, distinguishing per-gene from marginal (transcriptome-wide) power, the role of mean expression and dispersion, and the sequencing-depth-versus-replicate tradeoff. Covers simulation as the honest default for overdispersed counts, FDR-aware average power versus single-test power, observed/post-hoc power as an anti-pattern, and the winner's-curse / Type-S / Type-M consequences of underpowering. Use when planning replicate number for a sequencing experiment, deciding whether to add depth or samples, choosing closed-form versus simulation power, estimating power from pilot dispersions, or justifying replication in a grant. For clinical-trial power see clinical-biostatistics/power-and-sample-size; for the inverse sample-size question see experimental-design/sample-size.

日本語の概要は準備中です。原文の説明を表示しています。

Calculates statistical power for high-dimensional genomics experiments (bulk RNA-seq, scRNA-seq, ATAC-seq, ChIP-seq, methylation, proteomics) under negative-binomial count models using RNASeqPower, PROPER, and simulation via powsimR, distinguishing per-gene from marginal (transcriptome-wide) power, the role of mean expression and dispersion, and the sequencing-depth-versus-replicate tradeoff. Covers simulation as the honest default for overdispersed counts, FDR-aware average power versus single-test power, observed/post-hoc power as an anti-pattern, and the winner's-curse / Type-S / Type-M consequences of underpowering. Use when planning replicate number for a sequencing experiment, deciding whether to add depth or samples, choosing closed-form versus simulation power, estimating power from pilot dispersions, or justifying replication in a grant. For clinical-trial power see clinical-biostatistics/power-and-sample-size; for the inverse sample-size question see experimental-design/sample-size.

日本語の概要は準備中です。原文の説明を表示しています。

Calculates statistical power for high-dimensional genomics experiments (bulk RNA-seq, scRNA-seq, ATAC-seq, ChIP-seq, methylation, proteomics) under negative-binomial count models using RNASeqPower, PROPER, and simulation via powsimR, distinguishing per-gene from marginal (transcriptome-wide) power, the role of mean expression and dispersion, and the sequencing-depth-versus-replicate tradeoff. Covers simulation as the honest default for overdispersed counts, FDR-aware average power versus single-test power, observed/post-hoc power as an anti-pattern, and the winner's-curse / Type-S / Type-M consequences of underpowering. Use when planning replicate number for a sequencing experiment, deciding whether to add depth or samples, choosing closed-form versus simulation power, estimating power from pilot dispersions, or justifying replication in a grant. For clinical-trial power see clinical-biostatistics/power-and-sample-size; for the inverse sample-size question see experimental-design/sample-size.

日本語の概要は準備中です。原文の説明を表示しています。