Behavioral neuroscience — NIH NIMH / NIDA / NIAAA mechanistic grain; study of the neural substrate of behavior in intact, behaving organisms, spanning classical and operant conditioning, instinctive and learned behavior, reward and…
behavioral-neuroscience
Rescorla-Wagner: ΔV = α·β·(λ − V); trial-by-trial error-driven update
The Rescorla-Wagner model (1972) is the foundational formal account of Pavlovian conditioning as error-driven learning. Setup: a…
Matching law (Herrnstein 1961): R₁/R₂ = r₁/r₂ under concurrent VI schedules
Herrnstein's matching law (1961) is foundational in the quantitative analysis of operant choice. Setup: an organism faces two response…
Weber's law: ΔI/I = k (constant); Fechner's log-perception derivation
Weber's law (1834) is the foundational psychophysical invariant: the just-noticeable difference (JND) in stimulus magnitude is proportional…
Rescorla-Wagner asymptote: ΔV(V=λ)=0; ΔV(V=0)=α·β·λ
Sympy-exact witness of the Rescorla-Wagner asymptote and initial-trial identities. Setup: ΔV = α · β · (λ − V). Identity 1 (asymptote):…
Matching law identity: R_i = k·r_i ⟹ R₁/R₂ − r₁/r₂ = 0
Sympy-exact witness of the matching-law ratio identity. Setup: the matching law asserts R₁ / R₂ = r₁ / r₂; equivalently, R_i = k · r_i for…
Weber fraction: ΔI/I = k; at ΔI=3, I=100 → k=3/100
Sympy-exact witness of the Weber-fraction invariance. Setup: ΔI / I as a two-symbol rational function; Weber's law asserts this is…