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…
Temporal discounting: V_hyp = A/(1+k·t); V_exp = A·exp(−k·t); t_1/2 ratio = 1/ln 2
Temporal discounting — the canonical behavioral-economics framework for how organisms discount future rewards by delay. Physical setup:…
Generalization gradient: p_gauss(d) = exp(−d²/2σ²); p_shep(d) = exp(−d/σ); metric-space-dependent
Generalization gradient — the canonical framework for how organisms generalise learned responses from a training stimulus to novel test…
Dual-process habituation: dH/dt=−aH+I; dS/dt=−bS+J; R=R₀−H+S; H_ss=I/a, S_ss=J/b
Groves-Thompson 1970 dual-process habituation — the canonical two-opponent-process framework for habituation, sensitisation, and their…
Discount: V_hyp=A/(1+kt); V_exp=A·e^{−kt}; t½_hyp/t½_exp=1/ln2; ∫V_exp dt=A/k (V_hyp diverges)
Sympy-exact symbolic witness of temporal-discounting canonical forms (hyperbolic + exponential), their half-value delays, ratio, and…
Gradient: p_gauss(σ)=e^{−1/2}; p_shep(σ)=e^{−1}; d½_gauss=σ√(2ln2); d½_shep=σ·ln2
Sympy-exact symbolic witness of generalization-gradient canonical forms (Gaussian + Shepard-exponential), their 1-sigma anchors, and their…
Habituation: H(t)=(I/a)(1−e^{−at}); H_∞=I/a; t½_H=ln2/a; R_ss=R_0−I/a+J/b
Sympy-exact symbolic witness of the Groves-Thompson dual-process habituation canonical forms for step-input habituation trace and…
Place cells (O Keefe 1971)
J O Keefe 1971 (Nobel 2014) place-cells in hippocampus; modern May-Britt+Edvard Moser 2005 grid-cells (Nobel 2014).
Optogenetics (Deisseroth 2005)
Deisseroth-Boyden-Bamberg 2005 ChR2-optogenetics; modern step-function-opsins + soma-targeted; cellular causal manipulation.
Dopamine RPE (Schultz 1997)
W Schultz 1997 dopamine reward-prediction-error; modern computational reinforcement-learning Sutton-Barto-1998.
Addiction (Koob-Volkow 2010)
Koob-Volkow 2010 'Neural mechanisms of drug addiction'; 3-stage allostasis + brain-stress-systems; modern medication-assisted-treatment.
Fear (LeDoux 1996)
J LeDoux 1996 'Emotional Brain'; amygdala-fear-circuit; modern reconsolidation-update; PTSD therapeutic-window.
Circadian (Young-Rosbash-Hall Nobel 2017)
Young-Rosbash-Hall Nobel 2017 PER + TIM + dCRY clock; modern jet-lag + shift-work + chronotherapy.
Classical conditioning (Pavlov 1903)
I Pavlov 1903 (Nobel 1904) + Watson 1913 behaviorism; modern modern foundational text + 2024 ML-driven Pavlovian fear-conditioning circuits.
Operant (Skinner 1938)
B F Skinner 1938 'Behavior of Organisms' operant-conditioning; modern modern foundational text + 2024 reward-RL deep-RL biological-circuit…
Dopamine RPE (Schultz 1997)
W Schultz 1997 + Montague-Dayan-Sejnowski 1996 dopamine reward-prediction-error; modern modern foundational + 2024 deep-RL TD-learning…
Morris water maze (1981)
R Morris 1981 spatial-learning Morris-water-maze; modern modern foundational text + 2024 standardized hippocampal-disease cognitive-screen…
Equipotentiality (Lashley 1929)
K Lashley 1929 'Brain Mechanisms and Intelligence' mass-action; modern modern foundational text + 2024 distributed-representations +…
Amygdala fear (LeDoux 1996)
J LeDoux 1996 amygdala-fear-conditioning; modern modern foundational + Tonegawa 2014 engram + 2024 optogenetic-erasure PTSD therapy.