其他技能

Expert-level marine biology covering ocean ecosystems, marine organisms, coral reef ecology, deep sea biology, fisheries science, ocean chemistry, and marine conservation.

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Expert-level probability theory knowledge. Use when working with probability spaces, random variables, distributions, expectation, variance, conditional probability, stochastic processes, Markov chains, martingales, or measure-theoretic probability. Also use when the user mentions 'sample space', 'random variable', 'expected value', 'variance', 'conditional probability', 'independence', 'Markov chain', 'Poisson process', 'moment generating function', 'law of large numbers', 'central limit theorem', or 'stochastic process'.

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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.

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Expert-level evolutionary biology covering natural selection, genetic drift, molecular evolution, phylogenetics, speciation, macroevolution, and the modern synthesis.

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Expert-level numerical methods knowledge. Use when working with root finding, numerical integration, numerical differentiation, interpolation, numerical linear algebra, ODEs, PDEs, or optimization algorithms. Also use when the user mentions 'Newton method', 'bisection', 'Runge-Kutta', 'finite difference', 'finite element', 'interpolation', 'numerical integration', 'quadrature', 'iterative solvers', 'condition number', 'round-off error', or 'truncation error'.

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Expert-level molecular biology knowledge. Use when working with DNA replication, transcription, translation, gene regulation, cloning, PCR, sequencing, CRISPR, epigenetics, or molecular techniques. Also use when the user mentions 'DNA replication', 'transcription', 'translation', 'gene expression', 'PCR', 'cloning', 'restriction enzyme', 'gel electrophoresis', 'Western blot', 'CRISPR', 'epigenetics', 'promoter', 'enhancer', or 'RNA splicing'.

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Expert-level neuroscience covering neuronal physiology, synaptic transmission, brain regions and circuits, neuroplasticity, neurodegenerative diseases, and computational neuroscience.

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Expert-level biochemistry from a biology perspective covering metabolic pathways, enzyme kinetics, bioenergetics, signal transduction, and the biochemical basis of cellular processes.

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Expert-level microbiology covering bacterial and viral biology, microbial physiology, pathogenesis, antimicrobial resistance, microbiome science, and industrial microbiology.

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Expert-level plasma physics knowledge. Use when working with plasma state, Debye shielding, plasma oscillations, magnetohydrodynamics, plasma confinement, fusion plasmas, space plasmas, plasma waves, or plasma instabilities. Also use when the user mentions 'plasma', 'Debye length', 'plasma frequency', 'MHD', 'magnetic confinement', 'tokamak', 'plasma instability', 'Alfven wave', 'Langmuir probe', 'ionosphere', or 'solar wind'.

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Expert-level optics knowledge. Use when working with geometric optics, wave optics, interference, diffraction, polarization, lasers, fiber optics, optical instruments, or photonics. Also use when the user mentions 'reflection', 'refraction', 'Snell law', 'lens', 'mirror', 'interference', 'diffraction', 'polarization', 'laser', 'fiber optic', 'holography', 'aberration', or 'optical instrument'.

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Expert-level number theory knowledge. Use when working with divisibility, prime numbers, modular arithmetic, congruences, Diophantine equations, cryptography, quadratic residues, or analytic number theory. Also use when the user mentions 'prime', 'divisibility', 'modular arithmetic', 'congruence', 'GCD', 'Euler totient', 'Fermat little theorem', 'Chinese remainder theorem', 'quadratic residue', 'Diophantine equation', 'RSA', or 'prime factorization'.

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Expert-level mathematical logic knowledge. Use when working with propositional logic, first-order logic, proof theory, model theory, computability theory, Godel incompleteness theorems, set theory, type theory, or formal verification. Also use when the user mentions 'formal proof', 'Godel', 'incompleteness', 'Turing machine', 'decidability', 'Zermelo-Fraenkel', 'axiom of choice', 'model theory', 'completeness theorem', 'computability', 'formal language', or 'type theory'.

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Expert-level graph theory knowledge. Use when working with graph algorithms, network flows, matching, graph coloring, planar graphs, spectral graph theory, random graphs, or graph applications in computer science and networks. Also use when the user mentions 'shortest path', 'minimum spanning tree', 'network flow', 'bipartite matching', 'graph coloring', 'clique', 'independent set', 'vertex cover', 'planarity', 'graph isomorphism', 'adjacency matrix', or 'Laplacian'.

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Expert-level general relativity knowledge. Use when working with curved spacetime, Einstein field equations, geodesics, black holes, gravitational waves, cosmology, Schwarzschild metric, or tensor calculus. Also use when the user mentions 'Einstein field equations', 'curved spacetime', 'geodesic', 'black hole', 'event horizon', 'Schwarzschild', 'gravitational waves', 'spacetime curvature', 'Riemann tensor', 'metric tensor', 'cosmological constant', or 'gravitational lensing'.

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Expert-level fluid physics knowledge. Use when working with fluid statics, fluid dynamics, Bernoulli equation, viscosity, turbulence, Navier-Stokes equations, boundary layers, vorticity, compressible flow, or surface tension. Also use when the user mentions 'Bernoulli', 'Navier-Stokes', 'Reynolds number', 'turbulence', 'viscosity', 'boundary layer', 'vorticity', 'continuity equation', 'laminar flow', 'pressure', 'buoyancy', or 'surface tension'.

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Expert-level electromagnetism knowledge. Use when working with electric fields, magnetic fields, Maxwell's equations, electromagnetic waves, circuits, Coulomb's law, Gauss's law, Faraday's law, Ampere's law, or electromagnetic induction. Also use when the user mentions 'electric field', 'magnetic field', 'Maxwell', 'Gauss law', 'Faraday', 'Ampere', 'capacitor', 'inductor', 'electromagnetic wave', 'Lorentz force', 'Poynting vector', or 'dielectric'.

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Expert-level discrete mathematics knowledge. Use when working with logic, set theory, combinatorics, graph theory, relations, functions, induction, recursion, boolean algebra, or discrete probability. Also use when the user mentions 'combinatorics', 'permutations', 'combinations', 'pigeonhole principle', 'inclusion-exclusion', 'generating functions', 'recurrence relations', 'graph theory', 'trees', 'logic', 'propositional calculus', or 'boolean algebra'.

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Expert-level biochemistry knowledge. Use when working with proteins, enzymes, metabolism, DNA, RNA, carbohydrates, lipids, cell signaling, or bioenergetics. Also use when the user mentions 'enzyme kinetics', 'metabolism', 'glycolysis', 'Krebs cycle', 'DNA replication', 'protein folding', 'amino acids', 'ATP', 'oxidative phosphorylation', 'gene expression', 'lipid bilayer', or 'signal transduction'.

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Expert-level real analysis knowledge. Use when working with limits, continuity, differentiability, Riemann and Lebesgue integration, sequences and series of functions, metric spaces, measure theory, or functional analysis foundations. Also use when the user mentions 'epsilon-delta', 'uniform continuity', 'uniform convergence', 'Lebesgue integral', 'measure theory', 'sigma-algebra', 'Banach space', 'Hilbert space', 'completeness', 'compactness', 'Heine-Borel', or 'dominated convergence'.

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Expert-level topology knowledge. Use when working with topological spaces, continuity, compactness, connectedness, metric spaces, homeomorphisms, fundamental groups, homology, manifolds, or algebraic topology. Also use when the user mentions 'open set', 'closed set', 'compactness', 'connectedness', 'homeomorphism', 'homotopy', 'fundamental group', 'covering space', 'manifold', 'homology', 'Euler characteristic', or 'topological invariant'.

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Expert-level cell biology knowledge. Use when working with cell structure, organelles, cell signaling, cell cycle, cell division, cytoskeleton, membrane biology, vesicular trafficking, apoptosis, or cell biology techniques. Also use when the user mentions 'organelle', 'mitochondria', 'endoplasmic reticulum', 'Golgi', 'cytoskeleton', 'cell cycle', 'mitosis', 'meiosis', 'apoptosis', 'signal transduction', 'membrane potential', 'endocytosis', or 'cell migration'.

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Expert-level computational chemistry knowledge. Use when working with molecular dynamics, density functional theory, force fields, quantum chemistry calculations, molecular docking, free energy calculations, or cheminformatics. Also use when the user mentions 'DFT', 'molecular dynamics', 'force field', 'AMBER', 'GROMACS', 'Gaussian', 'basis set', 'geometry optimization', 'molecular docking', 'free energy perturbation', 'QSAR', or 'cheminformatics'.

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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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