Results for “math”

Infers person-to-person transmission from pathogen genomes using outbreaker2 (Campbell 2018), TransPhylo (Didelot 2017), phybreak (Klinkenberg 2017), BadTrIP (De Maio 2018), SCOTTI (De Maio 2016), BEASTLIER (Hall 2015), and SNP-distance / cluster-picker approaches (HIV-TRACE for HIV; transcluster). Defines outbreak clusters using pathogen-specific SNP thresholds (NOT a universal cutoff -- TB <=12 SNPs / Walker 2013; MRSA <=15 / Coll 2017; C. difficile <=2 / Eyre 2013; Klebsiella <=21 / Snitkin 2012), models within-host diversity and transmission bottlenecks (Worby-Lipsitch-Hanage 2014; McCrone 2018; Sobel Leonard 2017; Lythgoe 2021 SARS-CoV-2), integrates contact-tracing data, distinguishes generation interval from serial interval (Britton & Scalia Tomba 2019; Ali 2020), attributes source via Bayesian source attribution (Mather 2013 DT104; islandR), and reconciles transmission-network reconstruction with epi metadata. Use when investigating outbreaks for who-infected-whom, defining SNP-cluster outbreak definitions, accounting for unsampled intermediates, choosing between outbreaker2 (rich epi data) and TransPhylo (genomic-only after dated phylogeny), running source attribution between host populations, calling HIV-TRACE thresholds appropriate to the local subtype, or distinguishing recent transmission from reactivation in TB / chronic HIV.

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Designs and analyzes in vivo CRISPR screens in animal tumor models, organoids, and immune-cell adoptive transfers. Covers bottleneck math (250x cells/sgRNA requires ~25M cells implanted; impossible for most syngeneic models, forcing focused libraries), focused library design (Manguso 2017 Nature 547:413 immune screen; Chen 2015 tumor screens), CRISPR-StAR intrinsic-control screening (Uijttewaal 2025 Nat Biotechnol 43:1848), clonal-dynamics-limited detection, tumor-explant DNA recovery, syngeneic vs xenograft vs PDX considerations, and the relationship to downstream MAGeCK / drugZ analysis. Use when designing in vivo CRISPR screens for tumor / immune / metastasis biology, choosing focused vs genome-wide for animal models, addressing bottleneck-induced clonal collapse, picking the syngeneic / xenograft / PDX model, integrating in vivo with in vitro results, or applying CRISPR-StAR for animal experiments.

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Analyzes base-editing screens for variant function. Covers library design (Sanson 2020 GRACE, Hanna 2021 BRCA1/2 SNV scanning, Cuella-Martin 2021), CBE vs ABE chemistry choice (BE3/BE4 vs ABE7.10/ABE8.20/ABE8e), editing-window math (positions 4-8 from PAM-distal end, wider for ABE8e), bystander-edit quantification and the variant-call ambiguity it creates, sgRNA-efficiency filtering before hit calling, indel byproduct interpretation, the substitution-vs-indel diagnostic, variant annotation against ClinVar / COSMIC, and the Broad be-validation-pipeline. Use when designing a BE variant screen, choosing CBE vs ABE for a specific edit, interpreting bystander-confounded hits, distinguishing functional signal from indel artifact, integrating CRISPResso2 output with screen scoring, or deciding BE vs PE for SNV installation.

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Runs JACKS (Joint Analysis of CRISPR/Cas9 Knockout Screens; Allen et al 2019 Genome Research) which models per-sgRNA log-fold-change as the product of a treatment-dependent gene-essentiality term and a treatment-independent guide-efficacy term. Covers the Bayesian decomposition math, the hierarchical efficacy prior shared across screens performed with the same library, when JACKS outperforms MAGeCK (multi-screen joint analysis, libraries with broad efficacy variance) and when it does not (single screen, novel libraries with no prior efficacy), library-reuse efficacy transfer, downstream essentiality interpretation, and the 2.5x sample-size reduction enabled by efficacy-aware testing. Use when running multiple screens with the same library, when guide-level noise is suspected to dominate per-gene signal, when reusing published essentiality reference screens for efficacy priors, or when comparing screens performed across cell lines that share library but differ biologically.

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Designs and analyzes pooled prime-editor (PE) screens for installing precise genetic variants without bystander confounding. Covers pegRNA design with PRIDICT and PRIDICT2 (Mathis 2023/2024) for predicting per-pegRNA editing efficiency, pegRNA architecture (spacer + scaffold + PBS + RTT), PE2 / PE3 / PE3b / PEmax / PEAR variants, MOSAIC in situ saturation mutagenesis (Hsu JY et al 2024 bioRxiv), the PRIME pooled-screen methodology (Erwood/Doman 2023 Nat Biotechnol 41:885; ~3,699 ClinVar variant screens), chromatin context as a primary determinant of PE efficiency, scaffold-incorporation and indel byproduct quantification with CRISPResso2, and the cross-modal validation strategy of PE + base-editor screens for variant function. Use when designing a pegRNA library for variant installation, choosing between BE and PE for a specific edit, predicting pegRNA efficiency before library synthesis, analyzing PE screen output, distinguishing intended-edit from scaffold-incorporation, or scaling PE screens to thousands of variants.

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Quantifies CRISPR editing outcomes with CRISPResso2 (Clement 2019 Nat Biotechnol) across Cas9-nuclease (indels, HDR), CBE and ABE base editors (target conversion + bystander), and prime editor (pegRNA-templated) modes. Covers single-amplicon (CRISPResso), multi-sample batch (CRISPRessoBatch), pooled-amplicon (CRISPRessoPooled), WGS off-target (CRISPRessoWGS), and sample-comparison (CRISPRessoCompare) workflows; quantification-window math that controls what is called edited; substitution-vs-indel diagnostic to distinguish BE from Cas9 contamination; MMEJ deletion pattern interpretation; allele-frequency tables; and failure modes from amplicon misalignment or contamination. Use when quantifying editing from amplicon sequencing, choosing CRISPResso mode by design, distinguishing intended edits from bystanders and indel byproducts, debugging low-alignment runs, or generating publication-grade editing reports.

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Analyzes CRISPR drug-modifier (chemogenomic) screens with drugZ (Li & Hart 2019 Genome Med), a bidirectional Z-score method that identifies synthetic-lethal sensitizing genes and resistance-conferring suppressor genes from vehicle vs drug comparisons. Covers vehicle-anchored design (not Day-0), the bidirectional Z math giving 2-3x sensitivity over MAGeCK / STARS / edgeR / RIGER on drug screens, per-gene sumZ and normZ, synth (sensitizer) vs supp (suppressor) FDR, multi-dose handling, integration with control sgRNAs, and comparison with MAGeCK MLE with dose covariate. Use when running a drug-modifier CRISPR screen, identifying sensitizing or resistance genes for a drug candidate, choosing drugZ vs MAGeCK MLE for chemogenomic analysis, troubleshooting low-effect drug screens where MAGeCK lacks sensitivity, or designing a drug-screen layout (vehicle vs drug arms).

The English summary is being prepared. Showing the original description.

Infers person-to-person transmission from pathogen genomes using outbreaker2 (Campbell 2018), TransPhylo (Didelot 2017), phybreak (Klinkenberg 2017), BadTrIP (De Maio 2018), SCOTTI (De Maio 2016), BEASTLIER (Hall 2015), and SNP-distance / cluster-picker approaches (HIV-TRACE for HIV; transcluster). Defines outbreak clusters using pathogen-specific SNP thresholds (NOT a universal cutoff -- TB <=12 SNPs / Walker 2013; MRSA <=15 / Coll 2017; C. difficile <=2 / Eyre 2013; Klebsiella <=21 / Snitkin 2012), models within-host diversity and transmission bottlenecks (Worby-Lipsitch-Hanage 2014; McCrone 2018; Sobel Leonard 2017; Lythgoe 2021 SARS-CoV-2), integrates contact-tracing data, distinguishes generation interval from serial interval (Britton & Scalia Tomba 2019; Ali 2020), attributes source via Bayesian source attribution (Mather 2013 DT104; islandR), and reconciles transmission-network reconstruction with epi metadata. Use when investigating outbreaks for who-infected-whom, defining SNP-cluster outbreak definitions, accounting for unsampled intermediates, choosing between outbreaker2 (rich epi data) and TransPhylo (genomic-only after dated phylogeny), running source attribution between host populations, calling HIV-TRACE thresholds appropriate to the local subtype, or distinguishing recent transmission from reactivation in TB / chronic HIV.

The English summary is being prepared. Showing the original description.

Designs and analyzes pooled prime-editor (PE) screens for installing precise genetic variants without bystander confounding. Covers pegRNA design with PRIDICT and PRIDICT2 (Mathis 2023/2024) for predicting per-pegRNA editing efficiency, pegRNA architecture (spacer + scaffold + PBS + RTT), PE2 / PE3 / PE3b / PEmax / PEAR variants, MOSAIC in situ saturation mutagenesis (Hsu JY et al 2024 bioRxiv), the PRIME pooled-screen methodology (Erwood/Doman 2023 Nat Biotechnol 41:885; ~3,699 ClinVar variant screens), chromatin context as a primary determinant of PE efficiency, scaffold-incorporation and indel byproduct quantification with CRISPResso2, and the cross-modal validation strategy of PE + base-editor screens for variant function. Use when designing a pegRNA library for variant installation, choosing between BE and PE for a specific edit, predicting pegRNA efficiency before library synthesis, analyzing PE screen output, distinguishing intended-edit from scaffold-incorporation, or scaling PE screens to thousands of variants.

The English summary is being prepared. Showing the original description.

Analyzes base-editing screens for variant function. Covers library design (Sanson 2020 GRACE, Hanna 2021 BRCA1/2 SNV scanning, Cuella-Martin 2021), CBE vs ABE chemistry choice (BE3/BE4 vs ABE7.10/ABE8.20/ABE8e), editing-window math (positions 4-8 from PAM-distal end, wider for ABE8e), bystander-edit quantification and the variant-call ambiguity it creates, sgRNA-efficiency filtering before hit calling, indel byproduct interpretation, the substitution-vs-indel diagnostic, variant annotation against ClinVar / COSMIC, and the Broad be-validation-pipeline. Use when designing a BE variant screen, choosing CBE vs ABE for a specific edit, interpreting bystander-confounded hits, distinguishing functional signal from indel artifact, integrating CRISPResso2 output with screen scoring, or deciding BE vs PE for SNV installation.

The English summary is being prepared. Showing the original description.

Quantifies CRISPR editing outcomes with CRISPResso2 (Clement 2019 Nat Biotechnol) across Cas9-nuclease (indels, HDR), CBE and ABE base editors (target conversion + bystander), and prime editor (pegRNA-templated) modes. Covers single-amplicon (CRISPResso), multi-sample batch (CRISPRessoBatch), pooled-amplicon (CRISPRessoPooled), WGS off-target (CRISPRessoWGS), and sample-comparison (CRISPRessoCompare) workflows; quantification-window math that controls what is called edited; substitution-vs-indel diagnostic to distinguish BE from Cas9 contamination; MMEJ deletion pattern interpretation; allele-frequency tables; and failure modes from amplicon misalignment or contamination. Use when quantifying editing from amplicon sequencing, choosing CRISPResso mode by design, distinguishing intended edits from bystanders and indel byproducts, debugging low-alignment runs, or generating publication-grade editing reports.

The English summary is being prepared. Showing the original description.

Analyzes CRISPR drug-modifier (chemogenomic) screens with drugZ (Li & Hart 2019 Genome Med), a bidirectional Z-score method that identifies synthetic-lethal sensitizing genes and resistance-conferring suppressor genes from vehicle vs drug comparisons. Covers vehicle-anchored design (not Day-0), the bidirectional Z math giving 2-3x sensitivity over MAGeCK / STARS / edgeR / RIGER on drug screens, per-gene sumZ and normZ, synth (sensitizer) vs supp (suppressor) FDR, multi-dose handling, integration with control sgRNAs, and comparison with MAGeCK MLE with dose covariate. Use when running a drug-modifier CRISPR screen, identifying sensitizing or resistance genes for a drug candidate, choosing drugZ vs MAGeCK MLE for chemogenomic analysis, troubleshooting low-effect drug screens where MAGeCK lacks sensitivity, or designing a drug-screen layout (vehicle vs drug arms).

The English summary is being prepared. Showing the original description.

Designs and analyzes in vivo CRISPR screens in animal tumor models, organoids, and immune-cell adoptive transfers. Covers bottleneck math (250x cells/sgRNA requires ~25M cells implanted; impossible for most syngeneic models, forcing focused libraries), focused library design (Manguso 2017 Nature 547:413 immune screen; Chen 2015 tumor screens), CRISPR-StAR intrinsic-control screening (Uijttewaal 2025 Nat Biotechnol 43:1848), clonal-dynamics-limited detection, tumor-explant DNA recovery, syngeneic vs xenograft vs PDX considerations, and the relationship to downstream MAGeCK / drugZ analysis. Use when designing in vivo CRISPR screens for tumor / immune / metastasis biology, choosing focused vs genome-wide for animal models, addressing bottleneck-induced clonal collapse, picking the syngeneic / xenograft / PDX model, integrating in vivo with in vitro results, or applying CRISPR-StAR for animal experiments.

The English summary is being prepared. Showing the original description.

Runs JACKS (Joint Analysis of CRISPR/Cas9 Knockout Screens; Allen et al 2019 Genome Research) which models per-sgRNA log-fold-change as the product of a treatment-dependent gene-essentiality term and a treatment-independent guide-efficacy term. Covers the Bayesian decomposition math, the hierarchical efficacy prior shared across screens performed with the same library, when JACKS outperforms MAGeCK (multi-screen joint analysis, libraries with broad efficacy variance) and when it does not (single screen, novel libraries with no prior efficacy), library-reuse efficacy transfer, downstream essentiality interpretation, and the 2.5x sample-size reduction enabled by efficacy-aware testing. Use when running multiple screens with the same library, when guide-level noise is suspected to dominate per-gene signal, when reusing published essentiality reference screens for efficacy priors, or when comparing screens performed across cell lines that share library but differ biologically.

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Use this skill when the user asks about truck purchase financing, leasing options, factoring, fuel surcharge math, lease-purchase agreements, the total-cost-of-ownership (TCO) comparison between buying + leasing, and how owner-operators finance their first truck. Cover Section 179 + Bonus Depreciation tax treatment.

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Use this skill when the user asks about trucking rate negotiation — cost-plus pricing, market rate benchmarking via DAT/Truckstop, fuel surcharge math, how to negotiate with brokers/shippers, when to walk away, contract pricing vs spot rates. Reference DAT Rate Analytics + freight market reports.

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Use when a dispatcher, operations manager, or owner asks how to plan loads to minimize empty (deadhead) miles, sequence freight efficiently, balance regional capacity, design dedicated loops, or build a load-pairing strategy across customers. Covers loaded-ratio math, lane balance, region-pair pricing, and software-supported optimization.

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Builds comprehensive design systems and design bibles with production-ready CSS. Expert in design tokens, component libraries, CSS architecture. Use for design system creation, token architecture, component documentation, style guide generation. Activate on "design system", "design tokens", "CSS architecture", "component library", "style guide", "design bible". NOT for typography deep-dives (use typography-expert), color theory mathematics (use color-theory-palette-harmony-expert), brand identity strategy (use web-design-expert), or actual UI implementation (use web-design-expert or native-app-designer).

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Audit or design server-side indexes, directories, reputations, or aggregates that are DERIVED from traffic a platform witnesses (chain heads, run verdicts, heartbeats, publish activity) so that consent gates the derivation, not merely the read: no shadow index over non-consenting principals, post-consent-only evidence windows, retention bounds and delete-propagation into derived rows, activity-oracle threat modeling, and audit-logged ranking discretion. Use when building a capability directory / whois from witnessed activity, a reputation ledger from settled outcomes, vitals aggregation across tenants, or any "the yellow pages can't lie because they index signatures" feature. Keywords: shadow index, derived index, consent gates derivation, activity oracle, phone book not a log, delist propagation, ranking weight audit, k-anonymous aggregate, subpoena surface. NOT for the consent-screen UX and scope-ladder mechanics themselves (use local-first-tenancy-boundary), reputation scoring math and Sybil economics (use agent-identity-continuity-reputation), or discovery-layer architecture L1/L2/L3 (use agent-discovery-directories-guilds).

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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.

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Building resilient distributed systems with circuit breakers, retries with full-jitter exponential backoff, retry budgets (per-request 3-attempt + per-client 10% ratio per Google SRE), deadline propagation, and the cascading-failure math (4 layers × 3 retries = 64x amplification). Grounded in Resilience4j, Microsoft Cloud Patterns, AWS Architecture Blog (Marc Brooker), and Google SRE Book. NOT for server-side rate limiting, bulkhead isolation, backpressure protocols, or database-specific retry.

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Design and build mathematically rigorous, high-density, interactive data graphics and streaming telemetry visualizations following Mike Bostock's D3.js and Observable methodologies. Use when crafting custom SVG/Canvas charts, reactive streaming time-series, multi-dimensional brush-and-link coordinates, small multiples, or topological swarm graphs. NOT for generic dashboard template clones, basic spreadsheet charts, or off-the-shelf low-effort wrapper libraries.

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Search academic paper repositories (arXiv, Semantic Scholar) for scholarly articles in physics, mathematics, computer science, quantitative biology, AI/ML, and related fields

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Interactive review sessions with academic PDFs (lectures, research papers, book chapters). Extract concepts, run Q&A sessions, generate quizzes with scoring. Preserves mathematical formulas in LaTeX format. Privacy-preserving local processing - PDFs never uploaded. Use when studying academic materials, reviewing research, or preparing for exams.

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