'math' 검색 결과

Use when stuck on a hard problem, decomposition is unclear, a related problem is needed, or explicit looking-back review will improve transfer. NOT for routine execution with a known procedure, rote checklist work, or domain questions that need specialized subject matter expertise instead of heuristic search.

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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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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.

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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 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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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 (Colic et al. 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 greater sensitivity to small-effect hits than 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).

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Analyzes base-editing screens for variant function. Covers library design (Hanna 2021 ClinVar-scale CBE screen benchmarked on BRCA1/2, Cuella-Martin 2021 DDR saturation), CBE vs ABE chemistry choice (BE3/BE4 vs ABE7.10/ABE8.20/ABE8e), editing-window math (positions 4-8 from PAM-distal end; 4-7 for ABE7.10), 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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Search arXiv preprint repository for papers in physics, mathematics, computer science, quantitative biology, and related fields

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Manim CE animations: 3Blue1Brown math/algo videos.

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Think like Fable 5 — natural, flowing, purposeful reasoning distilled from 4,665 real chain-of-thought traces with mathematical precision. Use this skill EVERY TIME before writing code, making decisions, or taking action.

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[Document Processing] Use when converting between Word DOCX and Markdown (GFM, math rendering). --to={markdown|docx}.

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Mescle múltiplos modelos ajustados usando mergekit para combinar capacidades sem retreinar. Use ao criar modelos especializados misturando expertise específica de domínio (math + coding + chat), melhorando performance além de modelos únicos, ou experimentando rapidamente variantes de modelos. Cobre SLERP, TIES-Merging, DARE, Task Arithmetic, mesclagem linear e estratégias de deploy em produção.

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Converts Markdown to styled HTML with WeChat-compatible themes. Supports code highlighting, math, Mermaid (rendered to PNG via headless Chrome), PlantUML, footnotes, alerts, infographics, and optional bottom citations for external links. Use when user asks for "markdown to html", "convert md to html", "md 转 html", "微信外链转底部引用", or needs styled HTML output from markdown.

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Generate flat, minimal light/dark-aware SVG diagrams as standalone HTML files, using a unified educational visual language with 9 semantic color ramps, sentence-case typography, and automatic dark mode. Best suited for educational and non-software visuals — physics setups, chemistry mechanisms, math curves, physical objects (aircraft, turbines, smartphones, mechanical watches), anatomy, floor plans, cross-sections, narrative journeys (lifecycle of X, process of Y), hub-spoke system integrations (smart city, IoT), and exploded layer views. If a more specialized skill exists for the subject (dedicated software/cloud architecture, hand-drawn sketches, animated explainers, etc.), prefer that — otherwise this skill can also serve as a general-purpose SVG diagram fallback with a clean educational look. Ships with 15 example diagrams.

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Mathematical foundations, logical structures, and formal verification guidance. Trigger when: - Designing protocol contracts, formal specifications, verifying state spaces, or using proof assistants. - Tasks involve: TLA+, Alloy, Lean, Coq, model checkers, invariants, temporal logic. - Prompt contains keywords: formal verification, alloy, tla+, lean, coq, invariant, state machine, model checker, liveness, safety.

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Formally verify programs by writing Lean 4 proofs. Trigger this skill whenever the user wants to formally verify code, generate Lean 4 proofs, prove properties about algorithms or smart contracts, verify invariants, convert program logic into formal specifications, or anything involving Lean 4 and formal verification. Also trigger when the user mentions "qedgen", "lean proof", "formal proof", "verify my code", "prove correctness", "formal verification", or wants mathematical guarantees about their implementation.

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Constant-product AMM bonding curve math for Pump token pricing — buy/sell quoting, fee-aware calculations, market cap computation, tiered fees, ceiling division, virtual vs real reserves, and edge-case handling.

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Manim CE animations: 3Blue1Brown math/algo videos.

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Create a study cheatsheet by extracting and synthesizing key concepts from lecture materials, homework, and past exams. Use this skill whenever a user asks for help making a cheatsheet, study sheet, formula sheet, exam reference sheet, or "one-pager" — especially when they upload lecture slides (PDF/PPTX/DOCX), problem sets, past exams, or scanned/handwritten notes. Trigger this even for casual phrasings like "help me prep for my final," "summarize my course materials into something I can bring to the exam," or "make me a study reference from these slides and homeworks." Tuned for math/science (formulas, proofs, theorems) and CS/engineering (code, algorithms). Processes one file at a time and persists intermediate summaries to disk to avoid blowing past the context window on large courses.

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Knowledge base from FAA-HDBK-006D (2020), the FAA's System Reliability, Maintainability, and Availability (RMA) Handbook for National Airspace System (NAS) hardware and software. Use for RMA figures of merit (MTBF, MTBO, MTTR, the availability variants), the bathtub curve and probability distributions, the four-stage RMA lifecycle mapped to the FAA Acquisition Management System (AMS), the six-task RMA technical-management/acquisition process, service-thread criticality and the NAS-RD severity-to-target table, the RMA analysis toolbox (RBD, FMEA/FMECA, FTA, Ishikawa, Monte Carlo, Bayesian, FRACAS, ALT, reliability-growth/recovery tests), software reliability (early prediction + reliability growth), and tailorable example RMA requirements for a Program Requirements Document. Scope limits: it is FAA/NAS-specific guidance (not a requirement, by its own statement), centred on hardware-plus-software availability — it brackets out human/service/facility/communications availability, names but does not reproduce the math derivations or external standards (MIL-STDs, IEEE 1633, RTCA DO-178C/DO-278A, SAE JA1011), is thin on detailed worked numerical examples and on safety-case method, and predates any current revision beyond 006D.

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Knowledge base from NASA-STD-8729.1A — NASA's R&M (Reliability and Maintainability) standard covering spaceflight and support systems (Revision A, 2017-06-13). Use for NASA's objectives-driven R&M framework — the R&M objectives hierarchy (one Top Objective decomposed into four sub-objectives, paired with tailorable strategies), how R&M requirements are established inside the SMA Plan required by NPR 7120.5, the SMA Technical Authority concurrence/independent-evaluation governance, milestone vs. readiness review gates, the reliability/maintainability/availability vocabulary (Ai vs. Ao, the failure causal chain, risk as a triplet), and the R&M Evidentiary Methods catalogue (FMEA/FMECA, FTA, RBDA, RCM, LORA, plus the space-environment and parts-pedigree analyses). Scoped to NASA spaceflight and support systems and to assurance planning: it is an objectives-and-strategies standard, so it deliberately does NOT prescribe step-by-step analysis procedures (those live in the referenced NASA Preferred Reliability Practices) and is thin on facility R&M, detailed math/derivations, and non-NASA or commercial life cycles.

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Use when the user asks to "run the weekly social readout", "which denominator does our engagement rate use", or "which posts won this week and what changes next cycle"; produces the organic-social metric dictionary (every rate names its denominator — ERR engagement-by-reach vs ERI by-impressions vs ER-by-follower — locked across periods), median-not-mean per-post rollups with organic and boosted separated, EMV as labeled exec-translation only (never inside any score), an attributed CHAOSS/Orbit-style community-health readout with employees excluded, and the best/worst-performer write-back the next calendar cycle consumes. Not for dollar-ROI math or the ECHO profile result gate verdict — use roi-calculator and social-quality-auditor. 社媒周报/互动率分母/指标字典/复盘回写

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Use when the user asks to "analyze influencer campaign performance", "compare influencers", or "find what content worked"; produces metric scorecards vs target and benchmark, platform/influencer/content rankings, engagement-quality and sentiment reads, conversion-attribution breakdowns, and ranked learnings. Not for dollar-level return math — use roi-calculator. 达人营销效果分析/投放复盘

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