「math」の検索結果

Full-stack autonomous math modeling agent for CUMCM (全国大学生数学建模竞赛). Reads the problem statement and data, iterates through research → coding → verification → LaTeX writing, and produces a publication-quality PDF paper. Use when the user provides a CUMCM problem and wants end-to-end automated modeling, coding, and paper generation.

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AutoMCM-Pro industrial-grade math modeling agent. Supports AP (AI-led) and Manual (human-spec-led) dual modes with mandatory GitOps checkpoints, forced self-verification of all solver code before LaTeX inclusion, and structured human cross-validation at each pipeline stage. Use for both CUMCM (Chinese) and MCM/ICM (English) competitions.

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AutoMCM-Pro industrial-grade math modeling agent (DeepSeek Harness binding). Supports AP (AI-led) and Manual (human-spec-led) dual modes with mandatory GitOps checkpoints, forced self-verification of all solver code before LaTeX inclusion, and structured human cross-validation at each pipeline stage. Use for both CUMCM (Chinese) and MCM/ICM (English) competitions.

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Full-stack autonomous math modeling agent for MCM/ICM (美国大学生数学建模竞赛). Handles team control number, problem choice (A–F), English academic writing, mcmthesis LaTeX template, and optional practical deliverable (memo/letter/report). Use when the user provides an MCM/ICM problem and wants end-to-end automated modeling, coding, and paper generation in English.

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Generate test cases using metamorphic testing by applying transformations based on metamorphic properties. Use when you need to expand test suites, test programs without oracles, validate mathematical or algorithmic properties, or detect subtle bugs through input-output relationships. The skill takes a program, original test cases, and metamorphic properties as input, generates new test cases by applying transformations, executes tests, verifies outputs satisfy properties, reports violations and anomalies, and outputs an expanded test suite with property coverage summary. Supports multiple programming languages and property types.

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Design, audit, or repair mathematical benchmark verifiers, submission contracts, and scoring.

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Design or audit a Jacobian operation’s mathematical contract, boundedness, exact results, and composition.

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Author, package, validate, or run mathematical evaluations as Jacobian Harbor datasets.

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Find the papers that answer a research query in Firecrawl's research paper index — a corpus of paper abstracts whose largest share is biomedical and life-science literature (PubMed, bioRxiv, medRxiv), alongside arXiv preprints in CS, physics, and math — using semantic search, semantic and structural expansion, and in-body verification. Use this skill for literature-finding and paper-retrieval tasks of any kind, including clinical, biomedical, drug, gene, disease, and other life-science questions, whether the answer is a single paper or a full multi-paper set. The index is reached only through the `firecrawl_research_*` MCP tools or the `firecrawl research` CLI subcommands. Calling `firecrawl_search` with its `categories` option set to `["research"]` is a different feature — it filters ordinary web search to research-affiliated websites (the list includes PubMed, bioRxiv, medRxiv, arXiv, and publisher sites) and returns page results from them, without querying the paper records in this index.

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Think and work like an expert Logician. Use when a task calls for Logician judgment. Reasons from syntax-versus-semantics and object-versus-metalanguage discipline, the ⊢/⊨ distinction, and matching each logic to its intended semantics through natural deduction and sequent calculus (cut-elimination, subformula property), compactness and Löwenheim–Skolem, forcing and diagonalization, and proof assistants (Lean 4/mathlib, Coq, Isabelle/HOL, Agda) with Z3/CVC5/Vampire/Mace4 automation while treating use–mention conflation, second-order misuse of compactness, mis-stated incompleteness hypotheses (ω-consistency vs consistency), and Gödel philosophical overreach as first-class failure modes.

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Think and work like an expert Combinatorialist. Use when a task calls for Combinatorialist judgment. Reasons from labelled vs unlabelled enumeration, EGF/OGF and species, bijective and probabilistic proofs, Turán/Ramsey/extremal bounds, and BIBD/OA design parameters through SageMath/GAP/nauty, OEIS, House of Graphs, and Colbourn–Dinitz tables while treating isomorphism double-counting, parity barriers, and OEIS false matches as first-class failure modes.

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Think and work like an expert Algebraist. Use when a task calls for Algebraist judgment. Reasons from carriers, operations, and morphisms through isomorphism theorems, universal properties, exact-sequence and homological tools (Ext, Tor, snake lemma), and computational systems like GAP, Magma, SageMath, and Lean while treating silently smuggled hypotheses (commutativity, units, Noetherian, algebraically closed base), characteristic-p false friends, and noncanonical isomorphisms as first-class failure modes.

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Track real-time events, announcements, and breaking developments across Twitter, Reddit, news outlets, and web search. Monitors event progression, public reaction, key moments, and aftermath coverage for crisis response and opportunity detection.

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Create code-driven explanatory animations and precise vector graphics with Manim, optionally using SandBase for generated images, narration, music, or transcription. Use for mathematical, scientific, algorithmic, or diagrammatic animation; use a video-generation workflow for photoreal footage.

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Use when an agent must make TwelveLabs do real video-understanding work: indexing footage, semantic/visual search across an archive, generating descriptions, summaries, chapters, highlights, and tags from video, producing multimodal embeddings, or wiring TwelveLabs into a media-production pipeline (NLE panels, logging, compliance review, metadata). Covers the current model families (Marengo for search/embeddings, Pegasus for video-to-text analysis), the v1.3 Video Understanding API (indexes, assets, tasks, search, analyze, embed), prompt construction for analysis, capability and format limits, pricing/quota math, output quality review (hallucination and timestamp accuracy), and privacy/rights obligations when footage shows real people. Not for generating or editing video pixels — this is analysis and retrieval.

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Provider-independent production workflow for creating Manim-based explainer animations. Use when an agent must plan, code, render, QA, or hand off precise math, science, data, diagram, algorithm, or concept animations with Manim, including storyboard, scene architecture, formulas, coordinate systems, voiceover timing, accessibility, reproducibility, provenance, and delivery decisions.

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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).

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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 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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Find and synthesize research papers, whitepapers, PDFs, technical reports, and academic sources with Firecrawl Research, using semantic paper search, related-paper expansion, and in-body verification over Firecrawl's paper index — largely biomedical and life-science literature from PubMed, bioRxiv, and medRxiv, plus arXiv preprints in CS, physics, and math. Use when the user wants a literature review, systematic review, survey of studies, paper summary, research landscape, or sourced synthesis from scholarly and industry publications, including clinical, drug, gene, disease, epidemiology, and public-health topics. Prefer this over a general web-research workflow whenever the evidence base is published papers rather than web pages.

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Implement consumer-driven contract testing with Pact-JS (v16). Covers consumer test writing, broker-driven provider verification, Pact Broker setup, can-i-deploy as a deployment gate, webhook-triggered verification, pending pacts, and schema-first vs consumer-first approaches (OpenAPI/Ajv, Schemathesis). Use when: "contract test," "Pact," "consumer-driven," "API contract," "provider verification," "can-i-deploy." Not for: stubbing or mocking a dependency to isolate a test — use service-virtualization; general REST/GraphQL endpoint assertions against your own API — use api-testing. Related: api-testing, service-virtualization, ci-cd-integration, test-environments.

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Build or resume mathematical-modeling competition work, including CUMCM, MCM/ICM, graduate and regional contests, data challenges, and open-topic statistical modeling. Guide problem framing, modeling, computation, validation, Chinese or English LaTeX writing, and reviewed PDF/source delivery using current official requirements. Not for ordinary paper polishing.

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Founders face unique challenges in how they work. Maker vs manager schedule conflicts. Default alive vs dead math. Time and money slowly leaking away. Effective founders develop systems for navigating these challenges. This skill synthesizes PG's essays on founder productivity and decision-making into an operating system for founder effectiveness. Use when "keywords, contexts, " mentioned.

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When things go wrong - and they will - how you communicate determines whether you lose customers for a day or lose trust forever. Crisis communications isn't about spin or damage control. It's about being human when your company is at its most vulnerable. This skill covers incident response communications, public apologies, data breach notifications, service outages, PR crises, and the aftermath. The goal isn't to look good - it's to be good, and communicate that clearly. Use when "crisis, incident, outage, down, breach, apology, we messed up, customers are angry, PR disaster, viral complaint, status page, postmortem, trust recovery, bad press, crisis, incident, communications, apology, trust, status-page, outage, breach, postmortem, recovery" mentioned.

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