Data & Analytics

Expert-level computational biology covering molecular dynamics simulation, protein structure prediction, systems biology, network analysis, and machine learning in biology.

Expert-level neural engineering covering neural interfaces, brain-computer interfaces, neural signal processing, deep brain stimulation, and neuroprosthetics.

Expert-level hydraulics covering open channel flow, pipe systems, hydraulic structures, pumps and turbines, flood routing, and stormwater management.

Expert-level fluid mechanics covering fluid statics, continuity, Bernoulli, Navier-Stokes, boundary layers, turbulence, pipe flow, and external aerodynamics.

Expert-level ceramics covering ceramic bonding, processing, mechanical properties, thermal properties, electronic ceramics, and ceramic applications in engineering.

Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.

Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.

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

Expert-level exoplanet science covering detection methods, orbital dynamics, planetary atmospheres, habitability, and the search for biosignatures.

Expert-level climatology covering climate system components, climate forcing and feedbacks, paleoclimatology, climate modeling, and climate change science.

Expert-level bioinformatics covering sequence analysis, structural bioinformatics, database searching, phylogenetic analysis, NGS data processing, single-cell analysis, and machine learning in biology.

Expert-level thermodynamics knowledge. Use when working with heat, temperature, entropy, thermodynamic laws, heat engines, refrigerators, phase transitions, statistical mechanics, or thermodynamic cycles. Also use when the user mentions 'entropy', 'enthalpy', 'Carnot', 'heat engine', 'thermodynamic cycle', 'ideal gas', 'phase transition', 'Gibbs free energy', 'specific heat', 'thermal equilibrium', or 'second law'.

Expert-level statistics knowledge. Use when working with probability distributions, hypothesis testing, regression, Bayesian statistics, statistical inference, experimental design, ANOVA, or statistical modeling. Also use when the user mentions 'p-value', 'confidence interval', 'hypothesis test', 'regression', 'ANOVA', 'chi-square', 't-test', 'Bayesian', 'maximum likelihood', 'statistical significance', 'correlation', 'normal distribution', or 'sampling distribution'.

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'.

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 the...

Expert-level optimization knowledge. Use when working with linear programming, convex optimization, nonlinear programming, integer programming, dynamic programming, gradient methods, duality theory, or optimization algorithms. Also use when the user mentions 'linear programming', 'simplex method', 'convex optimization', 'Lagrangian', 'KKT conditions', 'gradient descent', 'Newton method', 'integer programming', 'dynamic programming', 'duality', 'Bellman equation', or 'branch and bound'.

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'.

Expert-level linear algebra knowledge. Use when working with vectors, matrices, determinants, eigenvalues, linear transformations, vector spaces, inner products, decompositions, or applications in machine learning and physics. Also use when the user mentions 'matrix', 'determinant', 'eigenvalue', 'eigenvector', 'linear transformation', 'vector space', 'basis', 'orthogonality', 'SVD', 'PCA', 'least squares', 'null space', or 'rank'.

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'.

Expert-level condensed matter physics knowledge. Use when working with crystal structure, band theory, semiconductors, superconductivity, magnetism, phase transitions, Fermi liquids, topological materials, or strongly correlated systems. Also use when the user mentions 'band gap', 'Fermi energy', 'semiconductor', 'superconductor', 'phonon', 'crystal lattice', 'Brillouin zone', 'Bloch theorem', 'Hall effect', 'magnetism', 'phase transition', or 'topological insulator'.

Expert-level complex analysis knowledge. Use when working with complex functions, holomorphic functions, Cauchy's theorem, contour integration, Laurent series, residues, conformal mappings, or analytic continuation. Also use when the user mentions 'holomorphic', 'analytic', 'Cauchy theorem', 'residue', 'contour integral', 'Laurent series', 'conformal map', 'Riemann mapping', 'Mobius transformation', 'harmonic function', 'entire function', or 'meromorphic'.

Expert-level financial modeling and valuation. Use when building financial models, LBO models, DCF models, merger models, three-statement models, scenario analysis, sensitivity tables, or forecasting financial statements. Also use when the user mentions 'financial model', 'LBO', 'merger model', 'DCF', 'three statement model', 'sensitivity analysis', 'scenario analysis', 'Excel model', 'forecast', 'assumptions', 'waterfall', or 'returns analysis'.

Expert-level finance and trading knowledge. Use when working with stock analysis, technical indicators, portfolio management, risk management, options, derivatives, crypto, forex, valuation models, or trading strategies. Also use when the user mentions 'moving average', 'RSI', 'P/E ratio', 'options', 'hedge', 'volatility', 'DCF', 'arbitrage', 'candlestick', 'order book', or 'alpha'.

Expert-level quantitative finance and algorithmic trading. Use when working with factor models, statistical arbitrage, backtesting, alpha research, portfolio optimization, time series analysis, machine learning for finance, or building systematic trading strategies. Also use when the user mentions 'alpha factor', 'Sharpe ratio', 'mean reversion', 'momentum factor', 'cointegration', 'pairs trading', 'Monte Carlo', 'portfolio optimization', 'systematic strategy', or 'quant model'.