「numerical」の検索結果

Think and work like an expert Dynamical Systems Theorist. Use when a task calls for Dynamical Systems Theorist judgment. Reasons from state spaces, invariant sets, bifurcations, and multiple time scales through normal-form classification, center-manifold reduction, Floquet/Poincaré maps, and continuation tools like AUTO, MatCont, and DynamicalSystems.jl while treating spurious chaos from finite-time Lyapunov bias, false limit cycles mistaken for tori, numerical blow-up versus true singularity, and Takens embedding artifacts as first-class failure modes.

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Think and work like an expert Applied Mathematician. Use when a task calls for Applied Mathematician judgment. Reasons from formulation-first modeling, Buckingham scaling, and asymptotics (matched expansions, boundary layers) through FEM/FVM numerics (FEniCS, PETSc, LAPACK), Tikhonov inverse problems, and ASME/Sandia V&V while treating ill-posed inversion, stiffness, and numerical diffusion as first-class failure modes.

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Review and adapt MetaX attention backends, MLA, sparse indexers, cache layouts, and their kernel wrappers against a target vLLM revision and the actually installed MetaX component APIs. Verify dispatch, supported configurations, and GPU numerical behavior. Use for attention adaptations outside vllm_metax/patch/; do not apply monkey-patch headers or patch audit requirements.

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Provides a pre-submission manuscript audit covering argument, numerical consistency, references and DOIs, writing, figures, CONSORT flow, pre-registration, and the replication archive. Use before paper submission or when a draft needs an adversarial, quote-grounded review with a journal-readiness checklist. Add `--codex` to run the specification independently on Claude and Codex, GPT-6 Astra, and cross-check findings.

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Formulate a quantum mechanics or quantum chemistry problem with proper mathematical framework including Hilbert space, operators, boundary conditions, and approximation method selection. Use when setting up a quantum mechanics problem for analytic or numerical solution, formulating a quantum chemistry calculation, translating a physical scenario into the Schrodinger or Dirac formalism, or choosing between perturbation theory, variational methods, DFT, and exact diagonalization.

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MATLAB R2026a workflow for control systems, system identification, robust control, MPC, Simulink Control Design, parameter tuning, constrained optimization, and numerical validation. Use whenever the user asks for controllers, transfer functions, state-space models, tuning, identification, optimal control, or solver-based engineering.

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"Apply Benford's Law to detect anomalies in numerical datasets by analyzing first-digit frequency distributions. Use this skill when the user needs to audit financial data for fraud indicators, validate data integrity, or detect fabricated numbers — even if they say 'data manipulation detection', 'first digit test', or 'accounting fraud screening'.".

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pyfixest demeaner_backend="cupy64" (including its CPU fallback when cupy is absent) is NOT numerically identical to the default numba backend and does NOT drop fully-absorbed/collinear regressors the same way. Use when: (1) adding demeaner_backend="cupy64" to existing pf.feols/fepois calls changes the printed coefficient table, (2) a regression report suddenly gains rows with absurd estimates (e.g. coef 435.8, SE 7106) for controls absorbed by the fixed effects, (3) diffing outputs before/after a backend change, or (4) anything parses a pyfixest text report by line position.

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Use when a task needs the judgment of a Computer Numerically Controlled (CNC) Tool Programmer — calculating stepover from a scallop-height/surface-finish spec instead of picking one by feel, deciding whether a toolpath needs a dry run before cutting material on an unfamiliar post-processor/machine pairing, verifying datum consistency across multiple part setups, or diagnosing why cycle time jumped after a "minor" parameter change.

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Advanced matrix theory expert covering spectral theory, matrix factorizations, and numerical linear algebra

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Expert-level astrodynamics covering orbit determination, trajectory optimization, launch vehicle ascent, re-entry dynamics, and numerical methods for space mission analysis.

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Expert-level meteorology covering atmospheric dynamics, thermodynamics, synoptic meteorology, mesoscale systems, numerical weather prediction, and climate dynamics.

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Expert-level differential equations knowledge. Use when working with ordinary differential equations, partial differential equations, systems of ODEs, Laplace transforms, Fourier methods, boundary value problems, stability analysis, or numerical methods for ODEs. Also use when the user mentions 'ODE', 'PDE', 'initial value problem', 'boundary value problem', 'Laplace transform', 'separation of variables', 'eigenvalue problem', 'heat equation', 'wave equation', 'Laplace equation', 'stability', or 'phase plane'.

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Phase 4 Turn 1 of disease-market-sizing-orchestration. Generates report HTML with mandatory citation anchors per fact claim. Reads contract + staging + sources/. Every drug/treatment/stat/recommendation MUST carry [pmid:.../guideline:.../nct:...] anchor that resolves to an actual file in sources/. NEVER hardcode drug names or numerical claims. Use AFTER evidence recall (phase 3), BEFORE content-verification-layer (Turn 2).

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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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Expert in JAX for high-performance numerical computing and machine learning

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Performs numerical and symbolic mathematics using NumPy, SciPy, SymPy, and mpmath. Use when the user needs linear algebra, arrays, optimization, integration, ODEs, symbolic expressions, equation solving, or arbitrary-precision arithmetic.

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SymPy is a Python library for symbolic mathematics that enables exact computation using mathematical symbols rather than numerical approximations.

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Tabular and numerical data analysis with descriptive statistics and insights. Use when the user provides data, tables, CSVs, or numbers and wants analysis.

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General mathematical methods skill for symbolic and numerical work; use when solving equations or deriving relationships.

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High-performance numerical and quantum compute skill for scientific workloads; use when working on numeric algorithms, simulation, or acceleration.

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Use this skill when working with symbolic mathematics in Python. This skill should be used for symbolic computation tasks including solving equations algebraically, performing calculus operations (derivatives, integrals, limits), manipulating algebraic expressions, working with matrices symbolically, physics calculations, number theory problems, geometry computations, and generating executable code from mathematical expressions. Apply this skill when the user needs exact symbolic results rather than numerical approximations, or when working with mathematical formulas that contain variables and parameters.

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Map observed site vegetation, species lists, land-cover descriptions, or plant management PFTs to EcoSIM vegetation codes using templates/ecosim_pftpar_20260303.nc.cdl. Use when choosing or validating EcoSIM pft_type values, pfts entries, pfts_short categories, pfts_long plant type meanings, or the combined short-code plus Koppen climate numerical code used by plant management inputs.

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Master Julia 1.10+ with modern features, performance optimization, multiple dispatch, and production-ready practices. Expert in the Julia ecosystem including package management, scientific computing, and high-performance numerical code. Use PROACTIVELY for Julia development, optimization, or advanced Julia patterns.

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