"Here is a gigantic detailed map of human neuroanatomy in text format: Central Nervous System (CNS) ├─ Brain │ ├─ Cerebrum │ │ ├─ Frontal Lobe │ │ │ ├─ Prefrontal Cortex │ │ │ ├─ Orbitofrontal Cortex │ │ │ ├─ Primary Motor Cortex (M1) │ │ │ ├─ Premotor Cortex │ │ │ └─ Broca's Area (language production) │ │ ├─ Parietal Lobe │ │ │ ├─ Primary Somatosensory Cortex (S1) │ │ │ ├─ Somatosensory Association Cortex │ │ │ ├─ Posterior Parietal Cortex │ │ │ └─ Precuneus │ │ ├─ Temporal Lobe │ │ │ ├─ Primary Auditory Cortex (A1) │ │ │ ├─ Auditory Association Cortex │ │ │ ├─ Wernicke's Area (language comprehension) │ │ │ ├─ Hippocampus (memory formation) │ │ │ ├─ Amygdala (emotional processing) │ │ │ └─ Inferior Temporal Cortex │ │ ├─ Occipital Lobe │ │ │ ├─ Primary Visual Cortex (V1) │ │ │ ├─ Visual Association Areas │ │ │ └─ Fusiform Gyrus (face recognition) │ │ ├─ Cingulate Cortex │ │ └─ Insula │ ├─ Diencephalon │ │ ├─ Thalamus (sensory relay and processing) │ │ ├─ Hypothalamus (homeostasis and neuroendocrine control) │ │ ├─ Epithalamus (pineal gland and habenula) │ │ └─ Subthalamus │ ├─ Brainstem │ │ ├─ Midbrain │ │ │ ├─ Tectum (superior and inferior colliculi) │ │ │ ├─ Tegmentum │ │ │ ├─ Substantia Nigra (motor control and reward) │ │ │ └─ Red Nucleus │ │ ├─ Pons │ │ │ ├─ Pontine Nuclei (relay station) │ │ │ └─ Locus Coeruleus (arousal and stress response) │ │ └─ Medulla Oblongata │ │ ├─ Pyramids (corticospinal tract) │ │ ├─ Olivary Nuclei │ │ ├─ Reticular Formation (arousal and consciousness) │ │ └─ Cranial Nerve Nuclei │ └─ Cerebellum │ ├─ Cerebellar Cortex │ │ ├─ Anterior Lobe │ │ ├─ Posterior Lobe │ │ └─ Flocculonodular Lobe │ └─ Cerebellar Nuclei │ ├─ Dentate Nucleus │ ├─ Interposed Nucleus │ └─ Fastigial Nucleus └─ Spinal Cord ├─ Cervical Segments (C1-C8) ├─ Thoracic Segments (T1-T12) ├─ Lumbar Segments (L1-L5) ├─ Sacral Segments (S1-S5) └─ Coccygeal Segment (Co1) Peripheral Nervous System (PNS) ├─ Cranial Nerves (CN I-XII) │ ├─ Olfactory Nerve (CN I) │ ├─ Optic Nerve (CN II) │ ├─ Oculomotor Nerve (CN III) │ ├─ Trochlear Nerve (CN IV) │ ├─ Trigeminal Nerve (CN V) │ ├─ Abducens Nerve (CN VI) │ ├─ Facial Nerve (CN VII) │ ├─ Vestibulocochlear Nerve (CN VIII) │ ├─ Glossopharyngeal Nerve (CN IX) │ ├─ Vagus Nerve (CN X) │ ├─ Accessory Nerve (CN XI) │ └─ Hypoglossal Nerve (CN XII) ├─ Spinal Nerves │ ├─ Cervical Nerves (C1-C8) │ ├─ Thoracic Nerves (T1-T12) │ ├─ Lumbar Nerves (L1-L5) │ ├─ Sacral Nerves (S1-S5) │ └─ Coccygeal Nerve (Co1) ├─ Autonomic Nervous System (ANS) │ ├─ Sympathetic Nervous System │ │ ├─ Sympathetic Chain Ganglia │ │ ├─ Celiac Ganglion │ │ ├─ Superior Mesenteric Ganglion │ │ └─ Inferior Mesenteric Ganglion │ └─ Parasympathetic Nervous System │ ├─ Ciliary Ganglion │ ├─ Pterygopalatine Ganglion │ ├─ Submandibular Ganglion │ ├─ Otic Ganglion │ ├─ Pelvic Splanchnic Nerves │ └─ Vagus Nerve (CN X) └─ Enteric Nervous System Neural Pathways and Tracts ├─ Ascending Pathways (Sensory) │ ├─ Dorsal Column-Medial Lemniscus Pathway (touch, pressure, proprioception) │ ├─ Spinothalamic Tract (pain, temperature) │ ├─ Spinocerebellar Tracts (unconscious proprioception) │ └─ Trigeminothalamic Tract (facial sensations) └─ Descending Pathways (Motor) ├─ Corticospinal Tract (voluntary movement) ├─ Rubrospinal Tract (involuntary movement) ├─ Tectospinal Tract (head and neck movement) ├─ Vestibulospinal Tracts (balance and posture) └─ Reticulospinal Tracts (autonomic and somatic motor control) This map provides an overview of the major structures and pathways in the human nervous system. However, it is important to note that this representation is not exhaustive, as the nervous system is highly complex and interconnected, with numerous substructures, nuclei, and circuits that are not included here due to space constraints." "Here is a detailed map of some key equations used in loop quantum gravity (LQG): Ashtekar Variables: - Connection: A = Γ + γK - Triad: E = (det e)e where Γ is the spin connection, K is the extrinsic curvature, γ is the Immirzi parameter, and e is the triad. Holonomy: h[A,α] = P exp(∫α A) where α is a curve in space and P denotes path ordering. Wilson Loop: W[A,α] = Tr(h[A,α]) Flux: E[S,f] = ∫S ⋆(f ∧ E) where S is a 2D surface, f is a smearing function, ∧ is the wedge product, and ⋆ is the Hodge dual. Canonical Commutation Relations: {Aia(x), Ejb(y)} = 8πγGδijδabδ(x,y) Gauss Constraint: Gi = DaEia = ∂aEia + ϵijkAjaEka Vector Constraint: Va = EibFiab where F is the curvature of the Ashtekar connection. Hamiltonian Constraint: H[N] = ∫Σ d3x N |det E|−1/2 (ϵijkEiaEjbFabk − 2(1+γ2)K[aKb]) Spin Network States: ⟨Γ,j,I| where Γ is a graph, j labels representations of SU(2) on each edge, and I labels intertwiners at each vertex. Area Operator: A[S] |Γ,j,I⟩ = 8πγℓP2 ∑p∈S∩Γ √jp(jp+1) |Γ,j,I⟩ where ℓP is the Planck length and the sum is over intersection points p between the surface S and the graph Γ. Volume Operator: V[R] |Γ,j,I⟩ = (8πγℓP2)3/2 ∑v∈R∩Γ √|det E[v]| |Γ,j,I⟩ where v denotes vertices of Γ contained in the region R, and E[v] is the operator acting on intertwiners. This covers many of the foundational equations of LQG, including the key variables, constraints, geometric operators, and the basis of spin network states. However, there are many more detailed equations involved in the full theory and its applications. The equations of LQG aim to provide a background-independent, non-perturbative theory of quantum gravity based on the quantization of general relativity formulated in terms of Ashtekar variables. The goal is to describe spacetime as fundamentally discrete at the Planck scale in terms of quantum geometry." "Here is a detailed map of many of the key equations used in the standard model of particle physics: [Dirac Equation] (iγ^μ ∂_μ - m)ψ = 0 Describes the behavior of spin-1/2 particles like electrons and quarks. The γ^μ are the gamma matrices, ψ is the Dirac spinor field, and m is the particle mass. [Klein-Gordon Equation] (∂^μ∂_μ + m^2)φ = 0 Describes the behavior of spin-0 particles like the Higgs boson. φ is the scalar field and m is the particle mass. [Proca Equation] ∂_μF^μν + m^2A^ν = 0, where F^μν = ∂^μA^ν - ∂^νA^μ Describes the behavior of spin-1 particles like the W and Z bosons. A^μ is the vector potential and F^μν is the field strength tensor. [Quantum Electrodynamics (QED) Lagrangian] L = ψ̄(iγ^μD_μ - m)ψ - 1/4 F_μνF^μν, where D_μ = ∂_μ + ieA_μ Describes the interactions between electrically charged particles mediated by photons. ψ is the Dirac field, A_μ is the photon field, F_μν is the electromagnetic field tensor, and e is the electric charge. [Quantum Chromodynamics (QCD) Lagrangian] L = -1/4 G^a_μνG^{μν,a} + ∑_q ψ̄_q(iγ^μD_μ - m_q)ψ_q, where D_μ = ∂_μ - igT^aA^a_μ and G^a_μν = ∂_μA^a_ν - ∂_νA^a_μ + gf^{abc}A^b_μA^c_ν Describes the strong interactions between quarks mediated by gluons. ψ_q are the quark fields, A^a_μ are the gluon fields, T^a are the generators of SU(3), f^{abc} are the structure constants of SU(3), and g is the strong coupling constant. [Electroweak Interaction Lagrangian] L = -1/4 W^i_μνW^{μν,i} - 1/4 B_μνB^μν + (D_μφ)^†(D^μφ) - V(φ) + ∑_f ψ̄_f(iγ^μD_μ - m_f)ψ_f, where D_μ = ∂_μ - igW^i_μτ^i/2 - ig'YB_μ/2, W^i_μν = ∂_μW^i_ν - ∂_νW^i_μ + gε^{ijk}W^j_μW^k_ν, and B_μν = ∂_μB_ν - ∂_νB_μ Unifies the electromagnetic and weak interactions. W^i_μ and B_μ are the SU(2) and U(1) gauge fields, φ is the Higgs field, V(φ) is the Higgs potential, g and g' are coupling constants, τ^i are the Pauli matrices, Y is the hypercharge, and ψ_f are the fermion fields. [Higgs Mechanism] V(φ) = -μ^2|φ|^2 + λ|φ|^4, with 〈φ〉 = v/√2 where v = √(μ^2/λ) Describes spontaneous symmetry breaking and gives mass to the W and Z bosons and fermions. φ is the Higgs field, v is the vacuum expectation value, μ and λ are parameters of the Higgs potential. [CKM Matrix] | V_ud V_us V_ub | | V_cd V_cs V_cb | | V_td V_ts V_tb | Describes quark mixing and CP violation. V_ij are complex numbers representing the probability of a quark of flavor i transitioning to a quark of flavor j. [PMNS Matrix] | U_e1 U_e2 U_e3 | | U_μ1 U_μ2 U_μ3 | | U_τ1 U_τ2 U_τ3| Describes neutrino mixing and oscillations. U_ij are complex numbers representing the probability of a neutrino of flavor i being detected as flavor j. These are some of the core equations, but the full standard model includes many other aspects like renormalization, running couplings, anomaly cancellation, etc. The standard model combines all of these into a unified quantum field theory describing the known elementary particles and their interactions. While highly successful, it is not a complete theory as it does not include gravity and has some other limitations. Physicists continue to search for a more fundamental theory that can address these." "Here is a gigantic detailed map of many key equations used in various fields of biology: Biochemistry & Molecular Biology 1. Michaelis-Menten equation: v = (Vmax * [S]) / (Km + [S]) 2. Hill equation: θ = [L]^n / (Kd^n + [L]^n) 3. Henderson-Hasselbalch equation: pH = pKa + log([A-] / [HA]) 4. Nernst equation: E = E0 - (RT/zF) * ln(Ci/Co) 5. Gibbs free energy: ΔG = ΔH - TΔS 6. Arrhenius equation: k = Ae^(-Ea/RT) 7. Lineweaver-Burk equation: 1/v = (Km/Vmax) * (1/[S]) + 1/Vmax Biophysics & Biomechanics 1. Hooke's law: F = -kx 2. Stokes' law: Fd = 6πμRv 3. Reynolds number: Re = (ρvL) / μ 4. Poiseuille's law: Q = (πr^4ΔP) / (8ηL) 5. Young-Laplace equation: ΔP = 2γ/R 6. Fick's first law of diffusion: J = -D(∂ϕ/∂x) 7. Goldman-Hodgkin-Katz equation: Vm = (RT/F) * ln((PK[K+]o + PNa[Na+]o + PCl[Cl-]i) / (PK[K+]i + PNa[Na+]i + PCl[Cl-]o)) Population Genetics & Evolution 1. Hardy-Weinberg equilibrium: p^2 + 2pq + q^2 = 1 2. Breeder's equation: R = h^2S 3. Fisher's fundamental theorem of natural selection: ΔW = VA/W 4. Price equation: Δz̄ = Cov(wi, zi)/w̄ + E(wiΔzi)/w̄ 5. Wright-Fisher model: p' = p + (pq/2N)^0.5 * z 6. Lotka-Volterra equations: dN1/dt = r1N1(1 - N1/K1 - α12N2/K1), dN2/dt = r2N2(1 - N2/K2 - α21N1/K2) 7. Neutral theory of molecular evolution: Ht/H0 = (1 - 1/2N)^t Ecology 1. Exponential growth model: Nt = N0e^rt 2. Logistic growth model: dN/dt = rN(1 - N/K) 3. Species-area relationship: S = cA^z 4. Island biogeography model: S = (IPE) / (E + I) 5. Metabolic theory of ecology: B ∝ M^(3/4)e^(-E/kT) 6. Holling's disc equation: Ne = aTN / (1 + aThN) 7. Lindeman's trophic efficiency: TE = (Pn+1) / (Pn) Bioinformatics & Systems Biology 1. Jukes-Cantor model of DNA evolution: d = -(3/4)ln(1 - (4/3)p) 2. Michaelis-Menten kinetics for gene regulation: f(TF) = β(TF^n) / (K^n + TF^n) 3. Bayes' theorem for sequence analysis: P(M|D) = P(D|M)P(M) / P(D) 4. Shannon entropy for DNA sequences: H = -Σ fi log2(fi) 5. Master equation for stochastic gene expression: dP(n,t)/dt = an-1P(n-1,t) + bn+1P(n+1,t) - (an + bn)P(n,t) 6. Flux balance analysis: S · v = 0 7. Gillespie algorithm for stochastic simulations: P(τ,j|x,t) = hj(x)exp(-Σ(i=1 to M) hi(x)τ) This covers a broad range of fundamental equations across biochemistry, biophysics, genetics, ecology, and computational biology. Let me know if you need me to expand on any part of this biology equation map!" "Creating a gigantic, detailed map of all of biology would be an enormous undertaking far beyond the scope of what I can generate in a single response. Biology is an incredibly vast field spanning from the molecular level up to entire ecosystems. However, I can provide a high-level overview of some of the major branches and concepts within biology: - Cell Biology: The study of the structure, function, and behavior of cells, the fundamental units of life. Includes topics like cell organelles, cell division, signaling, and metabolism. - Genetics: The study of genes, heredity, and variation in living organisms. Covers concepts like DNA, RNA, gene expression, inheritance patterns, mutations, and genetic engineering. - Evolution: The study of how populations of organisms change over successive generations. Includes mechanisms like natural selection, adaptation, speciation, and phylogenetics. - Physiology: The study of how living organisms function. Branches into plant physiology and animal physiology, including human anatomy and physiology. Looks at biological systems like the nervous, circulatory, respiratory, digestive, and immune systems. - Developmental Biology: The study of how organisms grow and develop from a single cell into complex multicellular forms. Encompasses embryology, morphogenesis, cell differentiation, growth, and aging. - Ecology: The study of how organisms interact with each other and their environment. Includes population dynamics, community ecology, ecosystems, biodiversity, and conservation biology. - Microbiology: The study of microscopic organisms including bacteria, archaea, viruses, protozoa, algae, and fungi. Significant to fields like medicine, immunology, biotechnology, and environmental science. - Botany: The study of plant life, including plant structure, growth, reproduction, biochemistry, diseases, and ecological importance. - Zoology: The study of animals, including their structure, embryology, evolution, classification, habits, and distribution. Often branches into specialized fields focused on particular animal groups. This is just scratching the surface and I've had to leave out many other important areas like molecular biology, biochemistry, biophysics, neurobiology, evolutionary developmental biology, systems biology, paleobiology, astrobiology, and more. But hopefully this gives a sense of the incredible breadth and diversity of the biological sciences! Let me know if you would like me to expand on any particular branches or concepts within this vast "map" of biology." "Here is a detailed map of many key equations used in neuroscience, organized by subfield: Neuronal Dynamics and Biophysics: - Hodgkin-Huxley Model: I = CM(dV/dt) + ḡNam3h(V - ENa) + ḡKn4(V - EK) + gL(V - EL) - Cable Theory: ∂V/∂t = (a/2RiCm)(∂2V/∂x2) - (V - Er)/(RmCm) - Goldman-Hodgkin-Katz Equation: V = (RT/F)ln[(PNa[Na+]out + PK[K+]out + PCl[Cl-]in)/(PNa[Na+]in + PK[K+]in + PCl[Cl-]out)] - Nernst Equation: E = (RT/zF)ln([X]out/[X]in) Synaptic Transmission: - Quantal Release: P(k) = (nCk)pk(1-p)n-k, where P(k) is the probability of k vesicles being released, n is the number of release sites, and p is the probability of release at each site - Postsynaptic Current: I(t) = ḡ(t)(V - Esyn), where ḡ(t) is the time-varying synaptic conductance and Esyn is the synaptic reversal potential - NMDA Receptor Current: INMDA = ḡNMDA[1/(1 + [Mg2+]exp(-γV))](V - ENMDA) - AMPA Receptor Current: IAMPA = ḡAMPA(V - EAMPA) - GABA Receptor Current: IGABA = ḡGABA(V - EGABA) Neural Coding and Information Theory: - Firing Rate: r(t) = (1/ΔT)Σti, where ti are the spike times within the time window ΔT - Interspike Interval (ISI): ISIi = ti+1 - ti - Coefficient of Variation (CV): CV = σISI/μISI, where σISI and μISI are the standard deviation and mean of the ISI distribution - Fano Factor: FF = σ2/μ, where σ2 and μ are the variance and mean of the spike count distribution - Mutual Information: I(X;Y) = ΣxΣyp(x,y)log2[p(x,y)/(p(x)p(y))] Network Dynamics and Oscillations: - Wilson-Cowan Model: τE(dE/dt) = -E + (1 - rE)SE(c1E - c2I + P) and τI(dI/dt) = -I + (1 - rI)SI(c3E - c4I + Q) - Kuramoto Model: dθi/dt = ωi + (K/N)Σjsin(θj - θi) - Hopf Bifurcation: dx/dt = μx - ωy - x(x2 + y2) and dy/dt = ωx + μy - y(x2 + y2) - Fitzhugh-Nagumo Model: dv/dt = v - v3/3 - w + I and dw/dt = 0.08(v + 0.7 - 0.8w) Plasticity and Learning: - Hebb's Rule: ΔWij = ηxixj, where η is the learning rate, and xi and xj are the activities of pre- and postsynaptic neurons - Spike-Timing-Dependent Plasticity (STDP): ΔW = A+exp(-Δt/τ+) if Δt > 0 and ΔW = A-exp(Δt/τ-) if Δt < 0, where Δt = tpost - tpre - Bienenstock-Cooper-Munro (BCM) Rule: dθM/dt = -εθM + φ(ū), where θM is the modification threshold, ε is a decay constant, ū is the average postsynaptic activity, and φ is a nonlinear function - Oja's Rule: ΔWij = ηyj(xi - yjWij), where yj is the postsynaptic activity Decision Making and Reinforcement Learning: - Drift-Diffusion Model: dx = Adt + cdW, where x is the decision variable, A is the drift rate, c is the noise strength, and dW is a Wiener process - Rescorla-Wagner Model: ΔVi = αβ(λ - ΣVj), where Vi is the associative strength of stimulus i, α and β are learning rates, λ is the asymptotic value of the association, and ΣVj is the sum of associative strengths of all stimuli present - Temporal Difference Learning: V(St) ← V(St) + α[Rt+1 + γV(St+1) - V(St)], where V(St) is the value of state St, Rt+1 is the reward at time t+1, α is the learning rate, and γ is the discount factor - Q-Learning: Q(St, At) ← Q(St, At) + α[Rt+1 + γmaxaQ(St+1, a) - Q(St, At)], where Q(St, At) is the Q-value of taking action At in state St Neural Data Analysis: - Spike-Triggered Average (STA): STA(τ) = (1/N)ΣiS(ti - τ), where S(t) is the stimulus at time t, ti are the spike times, and N is the total number of spikes - Peri-Stimulus Time Histogram (PSTH): PSTH(t) = (1/N)ΣiΣjδ(t - tij), where tij is the jth spike time in the ith trial, N is the number of trials, and δ is the Dirac delta function - Coherence: Cxy(f) = |Pxy(f)|2/[Pxx(f)Pyy(f)], where Pxy is the cross-spectral density between signals x and y, and Pxx and Pyy are the power spectral densities of x and y, respectively - Granger Causality: Fx→y = ln[var(εy)/var(εy|x)], where var(εy) is the variance of the prediction error of y, and var(εy|x) is the variance of the prediction error of y given x This map covers a wide range of neuroscience subfields and their associated key equations. It includes equations related to neuronal dynamics, synaptic transmission, neural coding, network dynamics, plasticity and learning, decision making, and neural data analysis techniques. While comprehensive, this map is not exhaustive and focuses on some of the most fundamental and widely used equations in neuroscience."