'theory' 검색 결과

Game theory expert covering Nash equilibrium, strategic thinking, auction theory, and cooperative games

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Expert interior designer with deep knowledge of space planning, color theory (Munsell, NCS), lighting design (IES standards), furniture proportions, and AI-assisted visualization. Use for room layout optimization, lighting calculations, color palette selection for interiors, furniture placement, style consultation. Activate on "interior design", "room layout", "lighting design", "furniture placement", "space planning", "Munsell color". NOT for exterior/landscape design, architectural structure, web/UI design (use web-design-expert), brand color theory (use color-theory-palette-harmony-expert), or building codes/permits.

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Expert-level control theory covering PID control, state-space methods, stability analysis, optimal control, robust control, and nonlinear control.

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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 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 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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Analyze candlestick data using Chan theory, a method based on price structure. Detect turning points, movement segments, and overlapping price zones, then generate buy and sell signals and compare patterns across timeframes.

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• Detecting turning points and segments in candlestick data
• Generating Chan theory buy and sell signals
• Comparing price structures across timeframes

Check mathematical proofs in LaTeX with review by a separate AI model. Identify missing assumptions and unsupported steps, explore counterexamples, repair derivations, and keep an audit record of issues, changes, and follow-up reviews.

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• Checking proofs in a theory paper
• Finding missing assumptions in lemmas
• Repairing gaps in mathematical derivations

Develop mathematical proofs for machine learning and AI theory by checking assumptions, intermediate results, and edge cases. Produce a complete proof, a corrected claim with its proof, or a report explaining the unresolved gap.

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• Draft a proof of a theorem or lemma
• Expand a proof sketch into justified steps
• Check for hidden assumptions and counterexamples

Stress-test a paper with a focused rejection argument, then have a separate reviewer assess each objection against the current text. The report identifies unresolved weaknesses, their severity, and priority fixes for submission or rebuttal preparation.

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• Stress-testing a theory paper before submission
• Preparing responses to the strongest reviewer objection
• Checking whether the title overstates the results

Turn scattered formulas and theory notes into a derivation that can be checked step by step. Keep definitions and assumptions consistent, distinguish exact identities from approximations, and make hidden conditions and limits explicit.

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• Organize scattered formulas and theory notes
• Trace the steps behind an algebraic identity
• State conditions and error orders for approximations

Draft sections of a legal brief using the case strategy and the firm's writing style. Link facts and arguments to supporting sources, flag unverified citations and weak points, and provide notes for attorney review.

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• Drafting a statement of facts from case records
• Drafting a legal argument with supporting authorities
• Preparing an oral argument around the strongest points

E1-Quantitative Analysis Guide with Code Generation & Sensitivity Analysis VS-Enhanced with Full 5-Phase process: Avoids obvious analyses, explores innovative methodologies Expanded to include qualitative analysis (thematic, grounded theory, content, narrative) Absorbed E4 (Analysis Code Generator) and E5 (Sensitivity Analysis - Primary Study) capabilities Use when: selecting statistical/qualitative methods, interpreting results, checking assumptions, generating code, sensitivity analysis Triggers: statistical analysis, ANOVA, regression, t-test, power analysis, assumption checking, effect size, thematic analysis, grounded theory, content analysis, narrative analysis, NVivo, ATLAS.ti, coding, qualitative data, R code, Python code, SPSS syntax, sensitivity analysis, robustness check

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VS-Enhanced Qualitative Design Consultant with Ethnography & Action Research Enhanced VS 3-Phase process: Avoids overused phenomenology, proposes context-optimal qualitative strategies Absorbed H1 (Ethnographic Research Advisor) and H2 (Action Research Facilitator) capabilities Use when: selecting qualitative research design, planning phenomenology/grounded theory/case study/ethnography/action research Triggers: phenomenology, 현상학, grounded theory, 근거이론, case study, 사례연구, narrative inquiry, ethnography, 민족지, action research, 실행연구, qualitative design

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Problem-solving strategies for proof theory in mathematical logic

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Problem-solving strategies for operator theory in functional analysis

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Provide number theory algorithm implementations and guidance

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Use when extensions, edge cases, or applied robustness checks are missing for an American Economic Journal: Microeconomics (AEJ: Micro) manuscript — covering theory extensions (relaxed assumptions, alternative concepts, perturbations) and applied/experimental robustness. Decides which extensions earn their place; it does not prove the main result (see aejmic-theory-model).

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Use when presenting results for an American Economic Journal: Microeconomics (AEJ: Micro) manuscript — propositions, numerical examples, schematic theory figures, and empirical/experimental tables. Builds exhibits to AEA house norms; it does not derive the results (see aejmic-theory-model).

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Use when the model setup, equilibrium concept, or proof architecture is the bottleneck for an American Economic Journal: Microeconomics (AEJ: Micro) manuscript — the central skill for a theory-first paper. Builds the model to the AEJ: Micro bar (clean, general, well-motivated result); it does not check whether your theorem is correct.

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Use when the question is what makes the result tight or what the data identify for an American Economic Journal: Microeconomics (AEJ: Micro) manuscript — covering both (a) structural/empirical-IO and experimental identification and (b) for pure theory, which assumptions drive the result and how robust the mechanism is. Stress-tests credibility; it does not build the model (see aejmic-theory-model).

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Use when prose buries the result or the abstract/intro do not land for an American Economic Journal: Microeconomics (AEJ: Micro) manuscript. Applies AEA house style and the theory-paper intro arc; it does not produce the result (see aejmic-theory-model) or build exhibits (see aejmic-tables-figures).

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Use when a model — a full theory paper's argument or the structural/conceptual scaffolding behind an empirical AER: Insights short-format manuscript — needs to be made minimal, so it carries the single insight in a few pages. Keeps only what the insight requires; it does not develop a general framework.

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Use when the contribution of an American Economic Journal: Microeconomics (AEJ: Micro) manuscript is fuzzy or oversold relative to the closest existing results. Stakes the theorem-relative delta against the nearest theory; it does not build the model (see aejmic-theory-model) or frame the prose (see aejmic-writing-style).

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