complex-systems.
160 of 1538 NOTE documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| NOTE-007 v2 | From the origin of life to pandemics | An editorial review with no new result. Its one formal item (§4, Eq. 4.1: x(t+1) = f[x(t)], x(0) = x₀) sorts phenomena three ways. Non-emergent: local rules plus initial conditions let you deduce the “expected” high-level pattern. Weakly emergent: they let you deduce an “unexpected” one by computation. Strongly emergent: no deduction is possible even in principle. “Unexpected” is never defined. The rest is a cross-domain survey (§3), a 16-paper map of the theme issue (§5), and an outlook (§6). | Read |
| NOTE-010 v5 | Greater than the parts | A review, with no new theorem, of the ΦID theory of causal emergence. A supervenient feature V_t is k-th-order causally emergent iff Un⁽ᵏ⁾(V_t; X_t′ | X_t) > 0. A system hosts such features iff Syn⁽ᵏ⁾(X_t; X_t′) > 0 (cited as Rosas et al. 2020, Theorem 1), and Syn⁽ᵏ⁾ = D⁽ᵏ⁾ + G⁽ᵏ⁾ (downward causation plus causal decoupling). The review’s own additions are interpretive: the formalism is neutral between Granger and Pearl, coordinate dependence is defended as a feature, and it rebuts the charge that the theory makes no macro-versus-micro comparison. | Read |
| NOTE-020 v4 | Emergence as the conversion of information | Varley and Hoel apply a PID, with the Williams–Beer I_min redundancy, to past→future mutual information and summarise it with a new layer-weighted “synergy bias” B_syn ∈ [0,1]. Coarse-graining can raise B_syn at the macroscale. A macroscale XOR reaches 0.833, against 0.52 for its NAND/AND/OR implementation. In 200 random 3-node “Gaussian” TPMs expanded into equivalence-class micro/mesoscales with identical MI, every macroscale had higher B_syn, by ≈ 0.01–0.07 (r = 0.819 against macroscale B_syn). In 185 near-deterministic systems the change was mostly negative, down to ≈ −0.1. | Read |
| NOTE-027 | Adding causality to individuality | Of Krakauer et al.’s (2020) three mutual-information “individuality” terms (A* = I(S_{t+1}; S_t), A = I(S_{t+1}; S_t | E_t), nC = I(S_{t+1}; E_t | S_t)), Bourrat argues that nC and A* are not individuality measures. He then proposes the interventional  = I(S_{t+1}; Ŝ_t) (Eq. 6) and two ETI criteria: C1, a normalised Â_{S2}/H(Ŝ2) ≥ Â_{S1}/H(Ŝ1)|θ₀, and C2, low Var(Â_{S2} | Ê2 = ê2k). None of these is computed on any system. The paper’s claim that  ≡ I(S_{t+1}; S_t | E_t) = A in Krakauer’s model is false in general. | Read |
| NOTE-040 v2 | Dreyer et al. 2024, ants vs humans on a piano-movers puzzle | On one T-shaped piano-movers puzzle, the CDF of solved attempts against normalized path length shows large ant groups (≈80 carriers, n=28) well ahead of small groups (≈7, n=48) and a 3-run composite single-ant series. An agent-based model with group-size-independent rules reproduces the difference. Human groups of 6–26 barred from talking or gesturing needed more attempted state transitions than single people (−32% relative to the individuals’ median; n=48 groups vs 61 individuals), and talking groups were only slightly better (+7%). No significance test is reported anywhere: “significantly” rests on overlapping-or-not ±1 SE bands. | Read |
| NOTE-045 v2 | Gutknecht et al. 2025, Shannon invariants | For any set of quantities Π(α) satisfying the PID consistency equation (A7), whatever the redundancy measure, two averages are fixed by Shannon quantities alone. They are the average degree of redundancy, r̄ = Σᵢ I(Xᵢ;Y)/I(X;Y) (Prop. 1), and the average degree of vulnerability, v̄ = Σⱼ I(Xⱼ;Y|X₋ⱼ)/I(X;Y) (Prop. 2). Two identities follow: RSI = (r̄ − 1)·I(X;Y) (Cor. 1), and a new “dual” index DRSI = I(X;Y) − Σⱼ I(Xⱼ;Y|X₋ⱼ) = (1 − v̄)·I(X;Y) (Prop. 4, Cor. 2). In small, stochastically quantised (8-level) networks analysed on their own training set, r̄ about the label rises with depth and v̄ falls with depth and training. In a face autoencoder, decoder layers are more redundant than size-matched encoder layers, and r̄ rises with bottleneck width. | Read |
| NOTE-054 v2 | Brain states across spacetime via whole-brain models | This is a narrative review with no new data, model or quantitative synthesis. It argues that healthy waking brain dynamics sit in a metastable regime near criticality, which whole-brain models (connectome-coupled Hopf oscillators, weakly coupled, at the edge of instability) reproduce. On its “activity landscape” picture, depression deepens particular attractors and psychedelics flatten the landscape. The depression side rests on three cited fMRI studies, one of them in remitted patients, and the review itself says “further studies will be required”. | Read |
| NOTE-055 v2 | Pilgrim et al. 2025, foundations of collective intelligence | A conceptual framework, with no model, data or derivation. It sets out individual and collective computational resources in four dimensions: sensing ΣI_i, states S_c × ∏S_i, processes F_c + ΣF_i, and actions ∏A_i (Table 1). It then maps the collective’s surplus onto familiar mechanisms (aggregation with noise σ_i²/n, distributional beliefs P(H), memory persistence T_c, division of labour). Coordination and cooperation are given as the constraints that make the trade-off, and three animal case studies are retold in these terms. | Read |
| NOTE-057 v2 | Networks beyond pairwise interactions (review) | The review sets out the representation hierarchy for group interactions (graph and clique complex, bipartite graph, motifs, simplicial complex, hypergraph) with their operators (incidence, adjacency tensor, boundary B_k, Hodge Laplacian L_k = B_kᵀB_k + B_{k+1}B_{k+1}ᵀ with ker L_k ≅ H_k). It surveys the random models and the dynamics built on them. Its own §V makes the key qualification: linear diffusion with three-body terms “can always be reduced to” a weighted pairwise Laplacian (Eq. 35). A random walk with edge-independent vertex weights is equivalent to one on a weighted projected graph (Chitra–Raphael). Qualitatively new node-level behaviour needs nonlinear group coupling or edge-dependent weights. With those, it reports explosive or abrupt transitions and bistability: Kuramoto with triadic coupling, simplicial SIS with a discontinuous transition, and higher-order ecological models that stabilise coexistence. | Read |
| NOTE-059 v2 | Peters & Adamou 2022, the ergodicity solution of cooperation | If N entities’ resources follow GBM (drift μ, volatility σ, independent noise), then pooling and sharing equally every step leaves the drift at μ, cuts the volatility to σ/√N (Eq. 3.9), and raises each member’s time-average growth rate from μ − σ²/2 to μ − σ²/(2N) (Eq. 4.1). The premium is (σ²/2)(1 − 1/N) (Eq. 4.2). With pairwise correlation ρ the effective volatility is σ√((1 + (N−1)ρ)/N), and the large-N limit is μ − σ²ρ/2 (Eqs. 5.12–5.13). | Read |
| NOTE-061 v2 | Saeedian et al. 2021, delay in generalized Lotka–Volterra | The paper studies random delayed generalized Lotka–Volterra dynamics, ẋ_i = x_i(r_i + Σ_j b_ij x_j(t−τ)), with instantaneous interactions switched off (A = 0) in every delay result. A feasible, stable equilibrium loses stability by a Hopf bifurcation at τ_c = min over eig(J) of (1/|j|) arctan(Re j/Im j) (Eq. 14), where J = diag(−B⁻¹r)B, and this matches simulation (Fig. 5b; S = 100 is stable at τ = 12 and oscillates at τ = 18). In the oscillatory regime, at τ = 20 and 22 for S ≲ 70, community-level CV falls with S while mean species-level CV rises (Fig. 6). The paper reads this as a positive diversity–stability relation but tests it against no averaging null. | Read |
| NOTE-064 v2 | Bourrat 2023, a coarse-graining account of individuality | Bourrat proposes that a partition of particles into collectives defines individuals when the “projected” prediction (coarse-grain at t1, then evolve the coarse-grained state) differs from the “truthful” one (evolve at the fine grain, then coarse-grain at t2) by δC = C_T − C_P < θ, across many traits (Eqs. 1–2). He argues that, because measurement and computation are finite, coarse-graining can be the only way to predict at all: in his example, 100 operations predict 10 entities for 10 timesteps or 2 collectives for 50. That indispensability is his whole case for the “quasi-ontological” status of collectives at Godfrey-Smith and Kerr’s fifth stage. Nothing is computed on any model. | Read |
| NOTE-079 v2 | Ouazan-Reboul et al. 2023, non-reciprocal metabolic cycles | For M chemotactic catalyst species in a closed cycle, where species m converts chemical m into chemical m+1, the linearised long-wavelength interaction matrix is circulant, so its eigenvalues are Re λ_ℓ = −(αρ0/D)(μ(p)−μ(s))[1−cos(2πℓ/M)] and Im λ_ℓ = (αρ0/D)(μ(s)+μ(p)) sin(2πℓ/M) (Eq. 5). The homogeneous state is unstable exactly when the species are self-attracting, μ(p) − μ(s) < 0 (Eq. 6). For even M the leading mode is real, with stoichiometry (1,−1,1,…), so same-parity species co-aggregate. For odd M the leading mode is a complex pair, and with chasing interactions this gives persistent “invasion–explosion” oscillations. The nonlinear phases were checked by Brownian dynamics at M = 5 and M = 6 only. | Read |
| NOTE-124 v3 | McKenzie — Emergence from physics to computer science | Sole-authored survey by a condensed-matter physicist. It takes novelty (a property the parts lack) as the defining mark of emergence and sets it against twelve other characteristics in §2. The six “objective” ones are discontinuities, order, modification of parts, universality, diversity and mesoscale modularity. The six “subjective” ones are self-organisation, unpredictability, irreducibility, contextuality/downward causation, complexity and intra-stratum closure. Case studies from the Ising model to Schelling segregation and LLMs show that each can come apart from novelty: novelty without discontinuity (Kondo, Fermi liquids, spin ice), without unpredictability (BKT, spin ice), and with reduction (Butterfield). §22 sides with weak emergence and argues that strong-emergence claims from molecular structure are weak. | Read |
| NOTE-153 v2 | Rizi — What is emergence, after all? | A perspective, not an argument with results. Rizi proposes that emergence is present when a many-to-one coarse-graining F (Eq. 1, N′ < N) keeps the macro description predictive after most micro detail is discarded. He says the onset of emergence is located by order parameters, diverging susceptibility and correlation length, and RG fixed points, and that dualities show macro behaviour is not dictated by micro “stuff”. Herd immunity on networks (percolation, the S–R interface density ρ_SR) is offered as a social case. The paper then asserts that science needs only weak emergence, and that invoking strong emergence “steps outside the scope of scientific method”. | Read |
| NOTE-191 | Patterns All the Way Up | Ladyman restates the Ladyman–Ross metaphysics as fifteen theses drawn from scientific practice. The existence criterion is “to be is to be a real pattern”, a pattern that “indispensibly figures in projectible generalisations” (p. 2). Realism is realism about natural modal structure, which is “absolute” in formal mode but “domain and scale-dependent” in material mode (thesis 4). There is no single hierarchy of levels and no assumed fundamental level (theses 10–11, fn. 9). Ontology is effective and scale-relative (thesis 12). Scientific real patterns are lossy compressions, unlike the Game of Life’s; the ideal gas laws use 3 degrees of freedom for ~10²³ (thesis 14). He quotes ETMG’s Principle of Naturalistic Closure verbatim and calls it “problematic” because it refers to fundamental physics (p. 8). | Read |
| NOTE-339 v2 | Examining the Society of Mind | An exposition, read in full. Singh dates the Society of Mind to Minsky and Papert’s early-1970s robot work, finds its agent in the procedure-bearing frame of 1974, and quotes the unpublished 1976 book drafts. He sorts the 1986 book’s mechanisms into agents, simplest agents, agency construction, problem solving, communication and growth. Agents need no shared code: K-lines, randomly wired buses and paranomes stand in for messages. He finds near-relatives in Bayes nets, case-based reasoning, blackboards, Cyc and Soar, and concludes that the theory has never been implemented. Its claims of lineage are asserted, not shown. | Read |
| NOTE-341 | The Computational Boundary of a “Self” | A hypothesis essay. A Self is the set of parts that pursue goals together, and its boundary is the farthest region of space and time it can measure and act on, its “cognitive light cone”. Selves grow from homeostatic loops by adding memory, anticipation and networks, and cells form larger Selves by sharing bioelectric state through gap junctions. Every level that has its own goal is a Self, so living systems hold many nested Selves at once; the paper says this against IIT in one bracket. It has no model, no measurement of the light cone and no new data, and it confines claims about experience to a closing speculation. | Read |
| NOTE-344 | Plain Talk About Neurodevelopmental Epistemology | The first worked mechanism of the society-of-agents view, then “The Society of Minds”. Agents too simple for language exchange no messages: each argument sits at a fixed location on shared channels (c-lines), and the agents themselves are short-term memory. A specificity gradient makes low-level communities local, persistence-memory and a case-shift handle interruptions without a stack, and the infant’s internal “cognitive cases” are conjectured to precede and shape linguistic cases. Speculation throughout; the author says so. | Read |
| NOTE-351 | Intelligence without representation | A methodological manifesto with working robots behind it. Brooks argues that AI should build complete autonomous Creatures incrementally and test them in the real world, and that intelligence should be decomposed into parallel activity-producing layers, each running from sensing to action, not into perception, central reasoning and action. His robots have no central representation or control, and their coherence exists “in the eye of an observer”, as in Minsky’s account of human behaviour. The evidence is three layers on one robot, described, not measured, and the broad hypothesis about representation is flagged as a hypothesis. | Read |
| NOTE-352 | K-Lines: A Theory of Memory | Memory as reinstatement: a K-line, attached on a memorable event to the agents then active, later re-imposes that partial mental state. The level-band principle limits it to an intermediate band of levels, so the present is seen as an instance of the past without re-imposing the old answer. K-lines build on earlier K-lines into a K-pyramid against the perceptual P-pyramid; cross-exclusion makes conflicting details cancel into abstraction; learning needs a third, goal-holding net. A programme statement: no simulation, and the P→K link is left unspecified. | Read |
| NOTE-359 | High-level perception, representation, and analogy: A critique of artificial intelligence methodology | Traditional AI models of discovery and analogy (BACON, the Structure-Mapping Engine, ACME) start from representations built by people who already know the answer, and so skip high-level perception, where most of the difficulty lies. Two informal arguments say the gap cannot be closed later by a separate representation module: analogy shapes perception, and the right representation depends on the task. Copycat is described as an architecture that builds representations and mappings together. Argued well; nothing is measured in the paper. | Read |
| NOTE-360 | Selfridge — Pandemonium | A proposal, with a preliminary Morse-code trial, for pattern recognition by a hierarchy of parallel “demons”. Data demons hold the input, subdemons compute features, cognitive demons shout weighted sums, and a decision demon takes the loudest. It adapts by hill-climbing on the weights, by culling and breeding subdemons through mutation and “conjugation”, and in principle by adapting its own control demons. The only result is reported in the discussion: hill-climbing “does work”, subdemon selection “did not do what we hoped”, and the best single subdemon was right 90% of the time. | Read |
| NOTE-375 | Burns — Fluid Concepts and Creative Analogies: A Review | A three-page review of Hofstadter and FARG’s collection. It explains the parallel terraced scan and “cognition is recognition” clearly, then asks why the work has had little impact on AI: microdomains with possibly hidden assumptions, and critiques of rivals that rest on analogy and intuition and are not turned on Copycat. Its sharpest point is that the symbol-grounding charge against SME applies to Copycat too. | Read |
| NOTE-409 | Five Rules for the Evolution of Cooperation | A four-page review. Five mechanisms, each with a b/c threshold derived from a 2×2 game: kin selection r > c/b, direct reciprocity w > c/b, indirect reciprocity q > c/b, network reciprocity b/c > k, group selection b/c > 1 + n/m. For kin, network and group mechanisms the same condition makes cooperators ESS, risk-dominant and advantageous; for the reciprocities RD and AD need more. Derivations are in the unread supplement; the review itself proves nothing. | Read |
| NOTE-410 | The Genetical Evolution of Social Behaviour. II | Generalizes Part I into two principles (value neighbours by relatedness; discriminate so relatedness is determinate) and applies them qualitatively. Haplodiploid sisters (r = 3/4) favour worker altruism, weakened by multiple mating (eight drones give about 0.31); sibs fight to the death only for a gain above 50%; clonal colonies cooperate and sexual aggregates do not fuse. Evidence is anecdotal, partly contrary (Australian halictines), and anomalies are put down to error or misinterpretation. | Read |
| NOTE-411 | The Evolution of Cooperation | TIT FOR TAT won Axelrod’s two tournaments (14 entries plus random, 200 moves; 62 entries, expected 200 moves) and went to fixation in an ecological replay. Against it, only ALL D or alternation need be checked, so no strategy does better iff w ≥ (T−R)/(T−P) and w ≥ (T−R)/(R−S). ALL D is stable for all w; kinship or a cluster with enough in-cluster interactions lets reciprocity in, and a nice stable strategy resists clusters. ALL C ties with TIT FOR TAT, so stability is neutral, not strict. | Read |
| NOTE-414 | Belousov-Zhabotinsky reaction | An authoritative short review. BZ: bromate oxidizes an organic reductant, catalysed by Ce, Fe(phen)₃ or other metal ions. Oscillation is a relaxation cycle: autocatalytic HBrO₂ oxidizes the catalyst, Br⁻ (made when Ce⁴⁺ oxidizes bromomalonic acid) shuts the autocatalysis off. Phase resetting by Br⁻, Ag⁺ and Ce⁴⁺ confirms it. Closed: up to several thousand cycles. CSTR: indefinite oscillation, bursting, chaos. Unstirred: trigger waves, targets, spirals, scrolls; in microemulsion, Turing structures. The Oregonator is qualitative only. | Read |
| NOTE-415 | Life as a manifestation of the second law of thermodynamics | Proposes a “restated second law” (systems pushed from equilibrium resist the applied gradients by every available means) and reads Bénard cells, vortices, life and ecosystem succession as successive gradient destroyers, with the second law “necessary but not sufficient” for life. The law is asserted, not derived. The physics examples show organized structures raising dissipation, not that they must. The ecological evidence is one unreplicated marsh comparison and thermal-scanner and satellite correlations, one of whose tables is internally inconsistent. | Read |
| NOTE-416 | Statistical Physics of Adaptation | A macrostate fluctuation relation for driven systems, rearranged as an internal-entropy term, a reversal term and Ψ − Φ = −ln⟨e^{−βΔQ}⟩. It is read as a tendency of driven matter towards states formed by reliable work absorption and dissipation, “adaptation” without replication. The relation is exact. The tendency needs the other two terms held fixed, which the paper arranges only in contrived one-particle landscapes; the many-body claim and the “adaptive resonance” simulation are argued and reported, not shown. | Read |
| NOTE-418 | Pattern formation outside of equilibrium | Read for the record’s question only. Patterns away from equilibrium are classified by the linear instability of a uniform state (type I_s, III_o, I_o) and described near onset by universal amplitude equations. There is in general no free energy or Lyapunov functional selecting them. Bénard’s own 1900 hexagons were surface-tension-driven, not Rayleigh’s buoyancy convection. Closed chemical systems must reach equilibrium, so their patterns are transients or need pumping. No global minimization principle exists beyond a perturbative one near threshold. | Skimmed |
| NOTE-419 | Statistical physics of self-replication | A coarse-grained second law, β⟨ΔQ⟩ + ln π(II→I) + ΔS_int ≥ 0, applied to self-replication: the heat a replicator releases per copy is bounded below by the log-odds against its copy falling apart within one generation, so durable, fast copies cost more heat. The general bound is sound. The E. coli and RNA numbers rest on an upper bound on the reverse probability that is argued from biology, not derived, and one printed logarithm has its argument inverted. | Read |
| NOTE-421 | Life as we know it | The flow of internal and active states in an ergodic system with a Markov blanket, written in Helmholtz form, can be redescribed as gradient descent on a variational free energy once the variational density is set equal to the posterior over external states. On that redescription such systems “appear” to infer and to bound their own entropy, which the paper calls the marks of life. One simulated soup shows a blanket-enclosed cluster that predicts external motion and falls apart under lesions. The free energy is variational, not thermodynamic. The candle flame is excluded by a one-sentence assertion. The paper’s own reported p-value is not reproduced by the null it describes. | Read |
| NOTE-422 | Comments on a derivation and application of the ‘maximum entropy production’ principle | Two corrections to Dewar. First, Dewar 2005 derives MaxEP far from equilibrium from a fluctuation theorem plus a quadratic approximation to the flux distribution, used as if valid for all f. Both can hold together only for small F, where A(F) = ∂λ/∂F is constant: the linear regime. So the orthogonality condition ∂D/∂F = 4λ, which yields both maximum and minimum dissipation, fails for nonlinear constitutive relations, as an exactly solvable spin chain shows. Second, Dewar 2003’s SOC divergence disappears once the quartic term is kept. | Read |
| NOTE-423 | Nonequilibrium thermodynamics and maximum entropy production in the Earth system | A review by MEP’s leading Earth-system advocate. MEP: given enough degrees of freedom, a system adopts the steady state of maximum entropy production. It is distinguished from Prigogine’s minimum principle, which describes relaxation toward a steady state and does not select among several. Two-box models show MEP arising from a flux–force trade-off. The Earth’s entropy budget is estimated and dominated by absorption of sunlight. MEP fits are surveyed from Paltridge’s climate model to sediment ecology, and life is argued to push the planet toward MEP. The author concedes MEP is not established. | Read |
| NOTE-424 v2 | Time, Structure and Fluctuations | Prigogine’s Nobel statement. Near equilibrium δ²S < 0 with ½∂δ²S/∂t = P > 0 makes δ²S a Lyapounov function, and in the strictly linear regime (constant L_ρρ′) the steady state minimizes entropy production. Far from equilibrium ½∂δ²S/∂t = ΣδJ_ρδX_ρ has no fixed sign, and ΣδJδX ≥ 0 is offered only as a sufficient stability condition. The Brusselator goes unstable at B > 1 + A². Dissipative structures are instabilities of the thermodynamic branch, triggered by fluctuations and sustained by exchange with the outside. The microscopic §§6–7 is a programme, linked to macroscopic thermodynamics only “in the linear region”. | Read |
| NOTE-425 | Energy flow and the organization of life | An essay arguing that life, beginning with the reductive citric-acid cycle, was forced into existence as a channel relieving geochemical free-energy stresses, like lightning or a hurricane. The framework is Jaynesian entropy maximization over states that include currents, not entropy-production principles. The emergence of life is a phase-transition “collapse” of a metastable abiotic earth. The structure of core metabolism is the only evidence. The authors state that the thesis is not quantitatively demonstrated. | Read |
| NOTE-426 | Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states | Jaynes’s maximum-entropy inference, applied to microscopic paths of an open stationary system, gives p_Γ = exp(A_Γ)/Z. The action is a symmetric end-point term plus τσ_Γ/2k_B. A fluctuation theorem p(σ) = e^{τσ/k_B} p(−σ) and ⟨σ⟩ ≥ 0 follow exactly. Maximum entropy production follows only in a mean-field approximation, and only if the number of paths increases with their irreversible action, which is assumed. The self-organized-criticality corollary is a mean-field divergence. As Grinstein and Linsker showed, it does not survive keeping the quartic term. | Read |
| NOTE-427 | The Chemical Basis of Morphogenesis | Turing’s reaction–diffusion theory of pattern. Linearize about a homogeneous steady state of M morphogens on a ring of N cells: each Fourier mode grows or decays independently, and the fastest-growing one sets the pattern. Six forms of onset are possible. For two morphogens, stationary waves of finite wave-length need bc < 0 and 4√(μ′ν′)/(μ′+ν′) < (d−a)/√(−bc) < (μ′+ν′)/√(μ′ν′) (9.4a), with instability if d√(μ′/ν′)/√(−bc) − a√(ν′/μ′)/√(−bc) > 2 (9.4b). These cannot both hold when μ′ = ν′. A computed 20-cell ring gives three lobes. | Read |
| NOTE-432 | Explanatory Models for Psychiatric Illness | Psychiatric etiology is multilevel, non-aggregative and full of causal loops, so law-based explanation fails and so do both hard reduction and hard emergence. Mechanistic explanation proceeds by local decomposition and difficult reassembly. Following Marr, biology implements the functions psychology describes and does not replace them. The argument is philosophical, illustrated by an alcohol-dependence sketch and cited findings; it reports no data of its own. | Read |
| NOTE-435 | A Network Theory of Mental Disorders | Borsboom states the network theory as five principles: complexity, symptom-component correspondence, direct causal connections between symptoms, disorders as tightly coupled symptom clusters, and hysteresis. Disorder is an alternative stable state of a strongly connected network that outlasts its trigger; health is the stable state of a weakly connected one. Treatment is symptom, external-field or network intervention. The evidence offered is indirect, and the theory is presented as an organizing framework, not a fitted model. | Read |
| NOTE-444 | An Organizational Account of Biological Functions | Functions are contributions to a differentiated self-maintaining organization by traits that organization produces and maintains (C1–C3). Closure alone grounds teleology and normativity but is shared by flames and hurricanes; differentiation is what makes functions meaningful. The account unifies “why is T there?” and “what is T for?” in current organization, and distinguishes functional, useful, dysfunctional, primary and secondary contributions. Reproduction is left to future “second-order” self-maintaining systems. | Read |
| NOTE-450 | The Markov blanket trick: On the scope of the free energy principle and active inference | The FEP is true of things defined its way, but its scope is limited: a Markov blanket fits only some things, is placed where the model needs it, and cannot represent relational properties or a boundary the system makes. Its real job is to give any system the partition variational Bayes requires. Active-inference models smuggle perception and action into hand-built generative models. A conceptual critique; no new formal result and no data. | Read |
| NOTE-456 | Participatory sense-making: An enactive approach to social cognition | An enactive account of social cognition built on coordination dynamics. When coordination and the encounter shape each other, the interaction gains its own precarious operational closure; it is social only if the interactors stay autonomous. Coordinated sense-making then ranges from one partner’s sense-making being modulated to meanings made jointly. Conceptual throughout; evidence is illustrative (corridor, charades, mother–infant timing, perceptual crossing). | Read |
| NOTE-458 | Defining Agency: Individuality, Normativity, Asymmetry, and Spatio-temporality in Action | Minimal agency needs a self-individuated system that is the source of modulations of its coupling with the environment and regulates them by norms it generates. An autonomous organization, a precarious network of mutually enabling processes, generates all three when it adaptively modulates its coupling for its own maintenance. Life is sufficient, not necessary. The definition is a proposal: the authors say asymmetry’s formalization is incomplete and modeller-relative. | Read |
| NOTE-467 | The Haken–Kelso–Bunz (HKB) model: from matter to movement to mind | Kelso’s retrospective on HKB. The relative-phase equation dφ/dt = −a sin φ − 2b sin 2φ has stable in-phase and anti-phase states for b/a > 1/4 and only in-phase below; with noise the switch is a nonequilibrium phase transition with critical fluctuations and slowing. Symmetry breaking gives metastability (relative coordination); merged with Kuramoto it models groups. The same dynamics is reported within and between people and in brain activity. A first-person account, not a review. | Read |
| NOTE-468 | Biological organisation as closure of constraints | A constraint acts on a process while being conserved at that process’s time scale; closure is a set of constraints, each directly dependent on and generative for another, that cannot be split. This separates closure from cycles of processes, grounds functions, and gives a boundary criterion, refined by a preliminary count-based tendency to closure for symbionts and by nested separated closures for levels. Applied only to schematic examples; closure is not claimed to define organisms. | Read |
| NOTE-502 | Interacting spiral wave patterns underlie complex brain dynamics | Phase fields of 0.01–0.1 Hz HCP fMRI on the flattened cortex hold about 16 spirals per hemisphere at rest (radius 10.5 ± 4.8 mm), centred on phase singularities that move at 2.2 mm/s with superdiffusive exponent β ≈ 1.5 and sit on functional boundaries. Opposite spirals annihilate (51% fully, 46% partly), like ones repel (2.6%). Spiral centres and charges decode four language conditions at 48.3% (chance 25%, raw-amplitude decoder 30.2%), and spiral pairs act as gates and walls that route task activity flow. | Read |
| NOTE-509 | Ultraviolet Superradiance from Mega-Networks of Tryptophan in Biological Architectures | A radiative non-Hermitian Hamiltonian for N tryptophan 1La dipoles (single excitation) predicts superradiant states in microtubule architectures (max Γ/γ ≈ 4000 in a centriole, ≈ 7000 extrapolated for bundles) and a thermal quantum yield that grows with size and is insensitive to static disorder up to 200 cm⁻¹. Steady-state spectroscopy gives tryptophan QY 17.6 ± 2.1% in microtubules against 10.6 ± 0.6% in tubulin dimers. No lifetimes were measured, so the radiative rate is inferred, not observed. | Read |
| NOTE-555 | Conceptualization of the Holobiont Paradigm as It Pertains to Corals | A mini-review arguing that corals must be studied as holobionts. The holobiont is defined by location (coral plus microbiota in body, mucus and skeleton), and its membership can change. Traits belong to host–symbiont combinations: a novel anemone–alga pairing out-performed both natural ones in oxygen flux at 32–34 °C, and two octocorals lost symbionts by different routes, one per host cell and one with host cells. It asks, without answering, whether the holobiont is the unit of selection. | Read |
| NOTE-556 | Defining Coral Bleaching as a Microbial Dysbiosis within the Coral Holobiont | A review that redefines bleaching as three holobiont dysbiosis stages: microbial buffering, Symbiodiniaceae reorganisation by shuffling or switching, and traumatic dysbiosis ending in death (Figure 3). The supporting material is cited and correlational. Vibrio rose from about 0 to 30% relative abundance in bleached corals and returned in resilient ones, but the authors say cause and consequence cannot be separated. “Dysbiosis” names both the disruption and the healthy adaptive response, and the stages have no operational boundaries. | Read |
| NOTE-557 | Signaling cascades and the importance of moonlight in coral broadcast mass spawning | Two experiments at Heron Island on Acropora millepora. In 2011, colonies under ambient night light (N = 6) spawned with the reef, while colonies lit after sunset (N = 5) or kept dark (N = 5) did not spawn that night. 184 transcripts selected by variance changed around gamete release only in ambient colonies. In 2006, 90 colonies under blue, green or white nocturnal light spawned 6–8 h or two nights late, and under red light on time. The GPCR and melanopsin cascade is a model built from correlated expression. | Read |
| NOTE-558 | Phase Shifts, Herbivory, and the Resilience of Coral Reefs to Climate Change | Four roofless 25 m² cages on Orpheus Island’s reef crest kept large and medium fishes out for 30 months after the 1998 bleaching, against four partial cages and four open plots. Macroalgae averaged 56% cover in cages and 4.1% and 1.7% outside. Coral cover reached 7.7% inside against 19.2% and 20.2%. Recruitment fell to about a third (39 against 108 and 118 per 25 m²) and mortality of established colonies was 24.2% against 9.8% and 11.3%. Reopened, the cages lost their algae in 30 days. | Read |
| NOTE-571 | Catastrophic regime shifts in ecosystems: linking theory to observation | A review of how to tell whether an ecosystem has alternative stable states. Field patterns (jumps, multimodality, dual relationships) are suggestive and never conclusive, since a stepwise driver or a simple threshold produces them too. Experiments can come close to proof: initial-state dependence, lasting shifts after temporary disturbance, and hysteresis. Models show positive feedback must be strong enough. | Read |
| NOTE-572 | Resilience and Stability of Ecological Systems | Ecological theory had equated stability with behaviour near equilibrium. Holling separates stability (return to equilibrium) from resilience (the capacity to absorb change and persist, set by the domain of attraction), shows they can trade off in lakes, forests, insects and fish, and warns that managing for constant yield can erode resilience. | Read |
| NOTE-576 | The Method of Characteristics Revisited: A Viability Approach | Viability is a property of a constraint set under a dynamics: K is viable if from every state some evolution stays in K, invariant if all do. Nagumo’s theorem reduces viability to a tangency condition. When K is not viable, the viability kernel is the largest viable part of it, and everything else in K leaves in finite time. Stability in the Lyapunov sense is not discussed. | Read |
| NOTE-577 | The Viable System Model: Its Provenance, Development, Methodology and Pathology | Beer’s retrospective on the Viable System Model. Five subsystems are necessary and sufficient for any organism or organization to keep its identity independently, and the structure recurs at every level. The model is defended as a scientific model built by homomorphic mapping, testable but never proved. Pathologies are traced to failing subsystems, chiefly the collapse of Three and Five when Four is missing. Evidence is the author’s recollected consultancy. | Read |
| NOTE-584 | Risk management in a dynamic society: a modelling problem | Risk management is a control problem across a sociotechnical hierarchy. Under cost and effort gradients, activity migrates toward the boundary of acceptable performance, and redundant defences erode unobserved because breaching one shows no effect. Accidents come from the interaction of many locally reasonable decisions. The remedy is making boundaries visible, not suppressing errors. | Read |
| NOTE-655 | Irreversibility in bacterial regulatory networks | In an ensemble of sign-consistent Boolean rules on the 87-gene core of the E. coli regulatory network, 51 genes admit a transient knockout or overexpression that leaves the network in a different attractor; only genes that reach a positive circuit can, and the likelihood grows with the weighted number of paths to one. Transitions run from small basins to large. The comparison with evolved crp-knockout strains supports the network’s sign structure strongly and its irreversibility predictions only weakly; no transient perturbation was done in cells. | Read |
| NOTE-656 | A. baumannii PmrB oxidative-stress response memory | An unrefereed bioRxiv preprint arguing that the PmrA/PmrB two-component system in Acinetobacter baumannii senses sublethal oxidative stress through a periplasmic histidine box coordinating a nickel cofactor, activates iron-sulfur repair and peroxide-scavenging genes, holds a redox-gated conformational switch (from simulation), and retains a 30—90 min “response memory” that primes cross-protection against lethal peroxide and antimicrobial peptides and is required for virulence in mice and hypervirulence in a clinical isolate. | Read |
| NOTE-657 | Bhattacharyya et al. 2023, heritable iron memory in E. coli | In genetically identical E. coli, a single cell’s swarming potential is shared by its descendants for about four generations and lost by seven; it tracks the cell’s iron status as read by a Fur-repressed reporter (low iron, better swarmer), iron manipulation lengthens it, and a three-class switching model fits the lineages only if each founding cell holds its class for a fixed delay before switching. The iron link is a correlation through a promoter reporter, and the model is fitted to two time points. | Read |
| NOTE-670 | An argument for hyperbolic geometry in neural circuits | A perspective, not a result: hyperbolic geometry should suit neural circuits because it approximates trees, makes networks navigable, and shares with Zipf’s law an exponential growth of states. The Zipf link is an analogy that any power-law rank distribution, and any system with extensive entropy, would satisfy; the case for three dimensions leans on Mostow rigidity, which does not bear on noisy embeddings; and the only data shown are the olfactory embedding of Zhou, Smith & Sharpee (2018). | Read |
| NOTE-673 | Multiscale unfolding of real networks by geometric renormalization | Defines a renormalization group for networks embedded in the S¹ hidden metric space: merge blocks of angular neighbours, link supernodes if any members were linked. To first order the S¹ model maps into itself (κ′ = (Σκ^β)^{1/β}, β fixed, μ and R over r), so layers are the same ensemble with ⟨k⟩ scaled by r^ν, ν = 2/(γ−1) − 1 or 2/β − 1. Six real networks collapse across layers by eye and keep their communities; downscaled replicas reproduce three dynamics, and multiscale greedy routing succeeds more often. | Read |
| NOTE-678 | Emergent Hyperbolic Network Geometry | Shows that simplicial complexes grown by gluing d-simplices to (d − 1)-faces, by a rule with no geometry in it, have exponential or power-law degrees (γ = 2 + 1/(d + s − 1)) by a master equation, high clustering and modularity, and a tree as their dual; and draws them, with all links of equal length, as ideal simplices tiling the Poincaré ball. The hyperbolicity is that drawing, which the authors say depends on the equal-length assumption; it is not measured or proved. A fitness on faces gives a simulated transition to growth in one direction. | Read |
| NOTE-680 | Hyperbolic Geometry of Complex Networks | Shows, for a model in which nodes sit in a hyperbolic disk and connect with a Fermi–Dirac probability of their hyperbolic distance, that the degree distribution is a power law with γ = 2α/ζ + 1 and that clustering is set by a temperature, strongest at T = 0 and gone above T = 1; that a circle-similarity model with power-law hidden degrees is the same ensemble once degree is read as radial depth; and that the configuration model and Erdős–Rényi graphs are its limits with the angular, metric part of the distance removed. Greedy routing by the coordinates is near-optimal and robust in its networks. No real network is embedded. | Read |
| NOTE-704 | Simon — The Architecture of Complexity | Complexity usually takes the form of hierarchy, defined by intensity of interaction rather than subordination. Hierarchies evolve fast because stable intermediate forms survive interruption, and they are nearly decomposable: fast, nearly independent dynamics inside subsystems; slow, aggregate dynamics between them. The theorem is cited, not shown; the evolutionary numbers are illustrative; the social claims are asserted. | Read |
| NOTE-724 | Wu & Silva — How Millions Coordinate at Scale | A descriptive study of all three r/place editions plus a coalition-recovery method run on 2017. Participation stays heavy-tailed under the uniform five-minute cap; larger coalitions waste more actions and have lower median activity per member; participants concentrate into large coalitions as an event goes on; and which coalitions survive is barely predictable from their size, area, start time and colour entropy until late. Lasting artworks are those whose coalitions keep working under continual overwriting. | Read |
| NOTE-725 | Adams, Fernandez & Witkowski — Two Ways of Understanding Social Dynamics | A short, preliminary study of the 2017 canvas alone. Transitions between 10-minute snapshots are tallied as cellular-automaton-style neighbourhood rules, and a CNN predicts each pixel from its 3×3 neighbourhood. Prediction worsens with the horizon and dips in the middle of the event. Locally growing objects are predicted, and designs coordinated off the canvas are missed. There are no baselines or error bars, and participants are never modelled. | Read |
| NOTE-726 | Hoel, Albantakis & Tononi — Quantifying causal emergence shows that macro can beat micro | Effective information (EI), the mutual information between uniformly imposed interventions on a system’s states and their effects, can be higher for a coarse-grained macro description than for the micro description it supervenes on. This happens when coarse-graining makes the mechanisms more deterministic or less degenerate by more than the smaller state space costs. Four toy systems of binary logic gates give gains of 0.40 to 2.92 bits. Causal emergence is defined as that gain. The examples are computed exactly; the reading of the EI peak as the level where causation happens rests on the choice of a uniform intervention distribution at each level, which the paper adopts and does not test. | Read |
| NOTE-731 | Falmagne, Stephenson & Levin — Interpretable early warnings using machine learning in an online game-experiment | On the 2022 r/place canvas, gradient-boosted trees fed 19 composition-level time series with a 7-hour memory predict the time until a crowd-built image is abruptly overrun, far better than variance or autocorrelation trends, and still work on 2023. The precursors it relies on are many and do not reduce to critical slowing down; a large share of transitions give no warning. The interpretation of the precursors is the authors’ conjecture from SHAP curves. | Read |
| NOTE-733 | Litherland & Mørch — Instruction vs. emergence on r/place | A mixed-methods case study of one 2017 r/place artwork, the Mona Lisa, and its forum, r/monalisaclan. The design was set and revised in the forum through linked blueprints, negotiated with neighbouring communities, and carried out by tens of thousands of placers. A few central forum members could allow or stop proposals. The authors frame the outcome as two control mechanisms, top-down platform rules (“instruction”) and bottom-up emergence, and stress that quantitative traces cannot tell cooperation from conflict or reveal affiliation. | Read |
| NOTE-747 | Watson — Agency, Goal-Directed Behavior, and Part-Whole Relationships | A comparative, scale-relative notion of agency. Given a decomposition into parts with goals of their own, a whole is more agential than its parts when its organization lets them resolve more of their mutual constraints than they would at the equilibrium of the old organization. It shows this as delayed gratification. The essay argues this, and shows in cited models that unsupervised, bottom-up learning can produce such organization. It gives no threshold for an additional agent and no formula beyond comparing total frustration. | Read |
| NOTE-756 | Varley — Flickering Emergences | Information-theoretic emergence measures built on past–future mutual information are expected values, and their local (pointwise) values can be negative. In a four-node Boolean toy, a coarse-graining that is emergent on average maps about 53% of informative micro transitions to misinformative macro ones, and the whole-to-whole synergy atom is negative for 31.25% of macro transitions. In a connectome, misinformative edges fall mostly between communities. The paper argues the possibility is general to any excess-entropy measure; it shows instances, not a theorem. | Read |
| NOTE-767 | Tononi, Sporns & Edelman — A measure for brain complexity | Defines neural complexity C_N as the summed shortfall of average subset integration below a linear increase with subset size, equivalently the average mutual information across bipartitions summed over sizes. It is zero for independent parts, low for uniformly dependent ones and high when the two coexist. In simulated cortex, patchy grouped connectivity gives higher C_N than the same connections spread randomly. One number for a whole system, with no partition, threshold or penalty. | Read |
| NOTE-768 | Nowak et al. — Functional Synchronization | A programmatic proposal, offered by its authors “as a heuristic for research agendas”: functions at every level from neurons to groups are performed by functional units, which form when lower-level elements synchronize and dissolve when the task ends. Synchronization here means any binding of dynamics, including complementary roles, not convergence on one state. Group synchronization may come from mutual influence or from a common external signal, and the paper treats both alike. | Read |
| NOTE-773 | Tissot et al. — An ability to respond begins with inner alignment | In a simulated modular coordination game (30 modules of 10 bistable units, strong couplings inside modules, weak across), units that adjust only the phase of their decision cycle toward partners they currently agree with come to synchronise within modules. Each module then switches its convention as one unit in response to the others, and all 50 runs with the learned phases reach a global optimum, against none without. Global synchrony does not do this. Synchrony works by silencing the module’s internal pull at a shared moment, not by any signal passed inside it. | Read |
| NOTE-775 | Pecora et al. — Cluster synchronization and isolated desynchronization | For identical units with identical, symmetric couplings, the orbits of the coupling graph’s automorphism group are clusters that can each be exactly synchronized. An irreducible-representation change of coordinates block-diagonalizes the variational equations, so each cluster’s stability is computed separately. When the group splits as a direct product, a cluster moved by one factor can lose synchrony while the others keep it. An 11-node electro-optic network showed this as predicted. | Read |
| NOTE-791 v2 | Barnett and Seth — Dynamical independence | A coarse-graining Y = f(X) is dynamically independent when the microscopic history adds nothing to predicting Y beyond Y’s own history, given the environment: transfer entropy T(X → Y | E) = 0. The condition is transformation-invariant and transitive. For linear state-space models it has a closed form, and it is minimized numerically over the Grassmannian. Generically no coarse-graining is exactly independent for VAR order above 1. The minima are many, and the authors treat them all as the “emergence portrait”. | Read |
| NOTE-799 v2 | Luppi et al. — A synergistic workspace for human consciousness | In resting-state fMRI, regions where synergistic interactions outrank redundant ones form a “synergistic workspace”. Within it, regions whose synergistic connections spread across more resting-state networks than their redundant ones are classed as gateways (mainly default mode), and the rest as broadcasters (mainly fronto-parietal, lateral prefrontal above all). Pairwise integrated information ΦR falls between DMN gateway regions under propofol (n = 15 or 16; the paper gives both) and in 22 patients with disorders of consciousness against controls, and recovers after anaesthesia, while the original whole-minus-sum Φ shows no common decrease. The increases, near the broadcasters, are not robust. | Read |
| NOTE-819 | Hopfield — Neural networks and physical systems with emergent collective computational abilities | With symmetric couplings, asynchronous threshold updates descend an energy function, so Hebbian outer-product storage makes random patterns attractors: a cue a few bits off settles into the nearest one. In simulations at N = 30 and 100, recall degrades severely near 0.15N patterns, memories closer than about a tenth of N fuse, and overload makes every memory irretrievable unless old ones are forgotten. | Read |
| NOTE-831 | Farrell & Ioannou — Generalized Stability Theory I | For a linear system du/dt = Au with A non-normal, the eigenvalues fix only the t → ∞ behaviour. Growth over a finite time t is the largest singular value of e^{At}, bounded below by the fastest mode and at t → 0 set by the numerical abscissa, the top eigenvalue of (A + A†)/2. A system with every mode damped can amplify a perturbation a hundredfold, and its forced and stochastic responses exceed those of the normal system with the same spectrum. | Read |
| NOTE-839 | Trefethen et al. — Hydrodynamic Stability Without Eigenvalues | The linearized operators of plane Couette and Poiseuille flow are far from normal. With every eigenmode decaying, perturbations can grow transiently by O(R) and resonate by O(R²), and an operator perturbation of norm O(R⁻²) makes the flow eigenvalue-unstable, all read off the pseudospectra. That transition to turbulence then follows from linear growth plus energy-neutral nonlinear mixing is a conjecture, from a 2 × 2 model. | Read |
| NOTE-842 | Farrell & Ioannou — Generalized Stability Theory II | For du/dt = A(t)u there are no modes, but the propagator’s singular vectors and the Lyapunov exponents and vectors carry generalized stability theory over. A time-dependent operator that is stable, or neutral, at every instant can be asymptotically unstable, and only if it is non-normal. Random variation of the operator destabilizes generically, with less variation needed the more non-normal and the less damped the mean operator. | Read |
| NOTE-851 | Ashby — Design for a Brain | Adaptation is the stability of the organism–environment system in the region where the essential variables stay within limits. To find such stability in an unknown environment, a second feedback must change the parameters of the first whenever an essential variable leaves its limits: the ultrastable system, shown in the Homeostat. Its blind search takes time exponential in the number of variables unless partial adaptations are kept, and keeping them needs a system that is not fully joined, its parts separated by constancies. New learning destroys old to the degree that it uses the same parts. | Read |
| NOTE-935 | Seth — Measuring autonomy and emergence via Granger causality | G-autonomy ga_{X|E} is the log ratio of a variable’s prediction-error variance without and with its own past, given external variables E. G-emergence ge_{M|m} = ga_{M|m}·(1/N)Σ gc_{mᵢ→M} makes a macro variable emergent to the extent that it is both autonomous from and Granger-caused by its micro variables. Validated in a predator–prey model and a boids model, where flocking shows high G-emergence and Granger causation from the flock’s centre of mass to each boid. Seth says the measures are relative to the predictor and the variables included. | Read |
| NOTE-936 | Williams and Beer — Nonnegative decomposition of multivariate information | Redundancy is I_min(S; A₁…A_k) = Σ_s p(s) min_i I(S = s; A_i), the expected minimum specific information. Restricted to antichains of sources and ordered by α ≼ β iff every source of β contains one of α, the collections form a lattice. The Möbius inverse of I_min on it gives partial-information atoms that are nonnegative (Theorem 5) and sum to I(S; R). Interaction information is synergy minus redundancy for three variables and a signed mixture for four, which explains its negativity and its +1 bit for both 3-parity and three copies. | Read |
| NOTE-937 | Bertschinger, Rauh, Olbrich, Jost and Ay — Quantifying unique information | For a target X and sources Y, Z, the unique information of Y is UĨ(X : Y \ Z) = min over Q ∈ Δ_P of MI_Q(X : Y | Z), where Δ_P is the set of joints with the same (X,Y) and (X,Z) marginals. If unique information should depend only on those marginals, this is an upper bound on any such measure, and the shared and synergistic information it implies are lower bounds. It is zero exactly when the other source is Blackwell-sufficient. The measures are non-negative, satisfy the bivariate PI axioms and the identity property, and are a convex programme, but are bivariate only. | Read |
| NOTE-940 | Schreiber — Measuring information transfer | Defines transfer entropy T_{J→I} as the Kullback entropy between I’s transition probabilities with and without J’s past, at history lengths k for I and l for J (Eq. 4), which is the conditional mutual information I(i_{n+1}; j_n^{(l)} | i_n^{(k)}). It is directional and ignores static correlation. A kernel estimator is proposed. Tent-map and Ulam-map lattices show it detecting the coupling direction where time-delayed mutual information fails; a heart–breath pair shows an asymmetry that the author says a common trigger could also explain. | Read |
| NOTE-942 | Williams and Beer — Generalized measures of information transfer | With the I_min partial information decomposition, transfer entropy T_{Y→X} = I(X_{t+1}; Y_t | X_t) is the unique information of Y_t about X_{t+1} (state-independent transfer, SITE) plus the synergy of X_t and Y_t (state-dependent transfer, SDTE). SITE alone suffices for perfect open-loop controllability (Theorem 1). Time-delayed mutual information is SITE plus redundancy. Two-source transfer splits into unique, redundant and synergistic parts. On a sleep-apnoea recording, heart→breath transfer is all SDTE. | Read |
| NOTE-943 | Lizier, Prokopenko and Zomaya — Local information transfer as a spatiotemporal filter | Transfer entropy is the expectation of a local transfer entropy, t_{Y→X}(n+1, k, l) = log p(x_{n+1} | x⁽ᵏ⁾_n, y⁽ˡ⁾n)/p(x{n+1} | x⁽ᵏ⁾_n), defined at every point and possibly negative. Apparent transfer entropy conditions on the destination’s past; complete transfer entropy also on its other causal parents. On elementary cellular automata, with k ≥ 6 (rule 110) and k = 16, local transfer entropy highlights gliders and domain walls as the dominant information-transfer structures; k = 1 and local time-lagged mutual information do not. The averages carry none of this. | Read |
| NOTE-944 v2 | Harder, Salge and Polani — A bivariate measure of redundant information | I_min gives 1 bit of redundancy to two independent bits copied into the target, because it compares amounts of specific information and not their direction in the space of distributions over the target. The paper adds an identity axiom, I∩((X,Y); X, Y) = I(X; Y), and defines a bivariate I_red: project each posterior p(z|x) onto the convex hull of the other source’s posteriors, count what survives, take the smaller direction. I_red satisfies all four axioms and gives a nonnegative PID. It agrees with I_min except where I_min overstates redundancy. | Read |
| NOTE-945 | James, Barnett and Crutchfield — Information flows? A critique of transfer entropies | Information flow from X to Y is information in Y attributable solely to X’s past. Transfer entropy is not it. For Y_t = X_{t−1} ⊕ Y_{t−1} it is 1 bit, but the bit is synergistic, carried by both pasts jointly (co-information −1). For Z_t = X_{t−1} ⊕ Y_{t−1} both transfer entropies are 0, and the causation entropies (conditional transfer entropies) are 1 bit each, again localizing a joint bit. By PID, transfer entropy is unique plus synergistic information; conditioning adds synergy, it does not only remove redundancy. | Read |
| NOTE-966 | Griffith and Koch — Quantifying synergistic mutual information | Synergy is the whole minus the union of its parts. S_VK = I(X_1…n : Y) − I_VK, where the union information I_VK is the least I*(X_1…n : Y) over joints that keep every source–target marginal. It sits between WholeMinusSum and S_max, which respectively subtract redundancy and count unique bits as synergy, and correlational importance measures something else. Versions 1–2 held that independent predictors share no information about the target; v6 withdraws it. For two predictors I_VK is Bertschinger et al.’s optimisation, so S_VK is their CI. | Read |
| NOTE-967 | Griffith, Chong, James, Ellison and Crutchfield — Intersection information based on common randomness | The redundancy is the information about the target in the Gács–Körner common random variable of the sources, I_∧ = I(X_1 ∧ … ∧ X_n : Y): the largest I(Q : Y) for Q a function of every source. It is defined for any n, satisfies target monotonicity, which no earlier measure did, and lies below I_min. But it is zero whenever the sources have full support, so it fails identity and continuity, and its synergy goes negative. A zero-error variant satisfies identity in zero-error form and goes negative too. | Read |
| NOTE-968 v2 | Ince — Measuring multivariate redundant information with pointwise common change in surprisal | I_ccs measures redundancy as the expected local co-information over only those events where each source, the joint source and the overlap change the target’s surprisal in the same direction, under the maximum-entropy joint matching source–target and joint-source marginals. Defined for any number of sources. It keeps symmetry, self-redundancy, subset equality and an independent-sources identity, and drops Harder et al.’s identity, monotonicity and non-negative atoms. A game-theoretic argument that unique information depends on the source–source marginal is offered against Bertschinger et al. | Read |
| NOTE-976 | Shalizi and Crutchfield — Information bottlenecks, causal states and statistical relevance bases | A three-page note. For memoryless transduction X → Y, the causal states are the cells of the partition of inputs by p(y|x). Among partitions that keep all information about Y, they have the least entropy. The note asserts, calling it evident, that these are what the information bottleneck delivers as β → ∞, and that Salmon’s statistical relevance basis is the same construction. It proves neither, and it says nothing about the IB solutions at finite β, nor whether they nest. The record supplies the proof of the limit and shows that every finite-β optimum is a stochastic coarsening of the causal partition (THEORY-743). | Read |
| NOTE-977 | Shpak, Stadler, Wagner and Altenberg — Simon–Ando decomposability and fitness landscapes | States Simon and Ando’s (1961) theorem for x(t+1) = (A* + εC)x, with A* block-diagonal, as existence statements: as ε → 0 the non-leading eigenvectors approach the blocks’, and times T0 < T1 < T2 < T3 exist that separate within-block relaxation, quasi-equilibrium, aggregate cross-block dynamics and global equilibrium. No rate in ε and no bound on aggregation error is given. It then applies an entrywise proxy (minimal within-class rate ≫ maximal cross-class rate) to mutation–selection on hypercubes, which low mutation rates meet trivially, and to recombination, which rarely meets it. It concludes that Simon–Ando aggregation is one source of dynamical sufficiency among several, distinct from symmetry (equitable partitions) and from linkage-equilibrium character aggregation. | Read |
| NOTE-978 | Crutchfield and Shalizi — Thermodynamic depth of causal states | The rate at which Lloyd and Pagels’ thermodynamic depth grows (the dive) is the entropy rate of whatever macrostate process it is computed over. So depth measures randomness. Lumping or splitting macrostates sets it to any value from zero up. The paper proposes the causal states as the macrostates. Among partitions of the past that predict the future as well as the past does, they are the coarsest, with the least statistical complexity and the least dive (THEORY-756). Several errors are noted. One stated entropy rate is in fact a single-symbol entropy, a footnote makes prescience vacuous, and a strict inequality fails in general. The result survives. The “objectivity” is relative to the measuring instrument, as the paper’s own logistic-map example shows. | Read |
| NOTE-979 | Shpak, Stadler, Wagner and Hermisson — Aggregation of variables and system decomposition | Separates aggregation of variables, a lower-dimensional map y = Qx whose dynamics close, from decomposition into non-interacting subsets: either can hold without the other. For a linear system the aggregate operator must satisfy ĀQ = QA. For a partition, the block sums close for every state exactly when the partition is column-equitable. Equitable partitions of mutation–selection matrices reduce single- and two-peak fitness landscapes exactly, and fail for three or more peaks unless the classes are refined to overlap classes. Simon–Ando aggregation is treated as the approximate limiting case, without error bounds. | Read |
| NOTE-987 | Rosas, Mediano et al. — Reconciling emergences | The primary paper behind LIT-025. A supervenient feature V is causally emergent of order k iff Un⁽ᵏ⁾(V_t; X_t′ | X_t) > 0; a system has one iff Syn⁽ᵏ⁾(X_t; X_t′) > 0, and the witness the proof gives is the microstate itself. Syn⁽ᵏ⁾ = D⁽ᵏ⁾ + G⁽ᵏ⁾ by definition of the ΦID atoms. The practical criteria Ψ, Δ, Γ are redundancy-free and sufficient only, and as proved they certify the system’s capacity, not the candidate feature: under the minimum-MI decomposition the parity of two independent self-copying bits has Ψ = 1 bit and no emergence. Ψ is the whole-minus-sum information about V’s next value minus V’s one-step dynamical dependence, which ties it to Barnett–Seth dynamical independence (THEORY-764). | Read |
| NOTE-1010 | Random Hyperbolic Graphs: Degree Sequence and Clustering | Proves for the threshold hyperbolic random graph (curvature −1, density exponent α > 1/2, R = 2 log n + C) that the average local clustering coefficient is Θ(1) with high probability and that the degree sequence is a power law with exponent 2α + 1 up to the maximum degree n^(1/(2α)+o(1)), with exact asymptotics for the fraction of each degree. Skimmed: the statements and the method were read, the proofs only in outline. | Skimmed |
| NOTE-1011 | Clustering and the hyperbolic geometry of complex networks | For Krioukov et al.’s hyperbolic random graph with 0 < ζ/α < 2, proves that below temperature 1 (β > 1) the global clustering coefficient converges to an explicit positive constant when ζ/α < 1 and to zero when 1 ≤ ζ/α < 2, and that at or above temperature 1 it converges to zero; clustering among vertices of bounded type stays positive for all ζ/α < 2 when β > 1. Skimmed: §1 and the theorem statements read, the proofs not. | Skimmed |
| NOTE-1018 | Machta, Chachra, Transtrum and Sethna — Parameter space compression | Two physics models are not sloppy at their microscopic scale and become so when observed coarsely. For the hopping model the Fisher eigenvalues of the density at time t scale as t^(3/2−k), proved here (THEORY-774). For a decimated critical Ising model, Monte Carlo shows the field and temperature eigenvalues staying put while the rest fall in bands drawn at b^(2y−d) per step (THEORY-777, Proposed). That rate, the source of LIT-1254’s Eq. 21, is argued by the same scaling argument, read off a figure without error bars, so THEORY-742’s scaling claim stays scaling-only. The supplement already states the d/2 line. The causal claim about emergent theories is not shown. | Read |
| NOTE-1020 | Del Vecchio and Slotine — Contraction and singular perturbation | Contraction gives global, explicit, uniform-in-time bounds for singular perturbation: the fast state reaches an εχ_z(d + K)/λ_z neighbourhood of the slow manifold at rate λ_z/ε, and the reduced (quasi-steady-state) trajectory is O(ε)-accurate for all time. Theorem 3 as printed is false: it needs the reduced system, not f alone, to be contracting. The robustness lemma is proved for constant metrics only; the reading re-derives it for state- and time-dependent ones, and with it the two steps THEORY-771 lacked. | Read |
| NOTE-1025 | Bousquet and Slotine — Contraction and near-decomposability | Under contraction of the fast modules and of the reduced slow system, and coupling terms bounded affinely in the off-manifold state, a nearly decomposable system stays within O(ε) of its singular-perturbation reduction, uniformly in time after a transient of order (1/β_f + 1/(εβ_g)) log(1/ε), for ε below an explicit critical separation ε_c. Deterministic trajectory error only. Remark 8 prints ε_c inverted, and the slow-error bound needs an unstated d_g = 0. | Read |
| NOTE-1028 | Chorin and Lu — Discrete stochastic parametrization by NARMAX | Model reduction done wholly in discrete time: advance the resolved variables by a fixed integrator and fit the exact one-step discrepancy as a NARMAX series, so memory lives in a few lags of the discrepancy, the resolved variable and the innovations. On Lorenz 96 with ε = 0.5 one or two lags reproduce x₁’s statistics and double forecast lead time at δ = 0.05. The link to Mori–Zwanzig is analogy, not derivation; nothing is proved and no error is bounded. The record’s check: a partially observed linear Gaussian VAR(1) is exactly ARMA, with order 1 + the rank of its MZ memory kernels, so a memory non-zero at every lag is carried exactly by finitely many history-measurable coordinates. | Read |
| NOTE-1029 | Lin and Lu — Wiener projections and the Koopman–Mori–Zwanzig formalism | An exact link between Mori–Zwanzig and NARMAX, with the approximation named. For an invertible map with an invariant measure, projecting onto the whole past of chosen functions of the resolved variables removes the memory term: the reduced equation is the causal Wiener filter on the coarse variable’s own history, with a residual orthogonal to all of it. NARMAX follows only by an “uncontrolled” rational approximation of the filter; no error is bounded. The record’s checks: Mori’s kernels and the Wiener filter are both fixed by the coarse variable’s autocovariance; for a scalar coarse variable of a linear Gaussian VAR(1) both are rational with the same numerator, the rational form is exact, and the memory Hankel rank is d − 1 for any rational autocovariance of rank d. | Read |
| NOTE-1030 | Rosas et al. — Software in the natural world | Three exact closures of a coarse-graining Z of a stationary discrete process X, built from computational mechanics. Informational closure (the micro past adds nothing to predicting Z, which is Barnett–Seth dynamical independence) is proved equivalent to causal closure (Z’s ε-machine equals its υ-machine). For spatial maps it implies computational closure (Z’s ε-machine is a coarse-graining of X’s), and the converse fails. For Markov chains closure is tied to strong lumpability. The proofs of the main equivalences hold, re-derived in THEORY-820 and THEORY-822. The lattice claims are asserted and in part false. Several examples contain slips. The modular random walk closes by symmetry, not modularity. Nothing is said about approximate closure. | Read |
| NOTE-1052 | Arthur — Competing technologies and historical small events (working paper) | In a model where two types of agent arrive in random order and each adopts whichever of two technologies pays it more, with returns linear in the number of previous adopters, increasing returns make the difference in adoptions a random walk with absorbing barriers: one technology takes the market with probability one, which one is decided by the order of arrivals, it need not be the better one, and marginal subsidies cannot move it once it has locked in. Under diminishing returns the barriers reflect and the market shares predictably. | Read |
| NOTE-1076 | Pierson — Increasing returns, path dependence and the study of politics (working paper) | An argument, not a test: the conditions Arthur and North found to produce increasing returns (set-up costs, learning, coordination, adaptive expectations) are more common in politics than in markets, because politics is dense with compulsory institutions, rests on collective action and is opaque; and lock-in is more intense there, because competition and learning correct weakly, politicians’ horizons are short and institutions are built to be hard to change. Its one case is the failure of two opposite US health-care reforms in 1993–96. | Read |
| NOTE-1077 | Abbott — Linked ecologies (through its French precursor) | In the precursor, Abbott’s audiences for professional claims, above all the state, are themselves ecologies of competing actors, so every event in a profession’s history sits in two ecologies at once and succeeds only if it serves actors in both. New York’s medical licensing swung back and forth because it was a minor issue in politics and a major one in medicine; differences of tempo between the ecologies changed the doctors’ allies. “Hinges” are named and left undeveloped. The published article’s universities, avatars and English case were not reached. | Skimmed |
| NOTE-1093 | Bigand et al. — The geometry of interpersonal synchrony in human dance | In 35 dyads of untrained dancers facing each other, shared music and visual contact were varied independently. Each raised interpersonal synchrony, in different principal movements and with no interaction: lateral and hand movements synchronized through seeing the partner, anteroposterior movements such as head bobs through the shared music, and vertical bounce through both. Which factor drove a movement’s synchrony could be read from its spatial direction (100% classification) and not from its periodicity. The direction of coupling between partners was not estimated. | Read |
| NOTE-1113 | Emotions are emergent processes: they require a dynamic computational architecture | The component process model restated for computational modellers. Emotion is a bounded episode of synchronization among subsystems (appraisal, autonomic, motor, motivation, feeling), driven by appraisal checks in a fixed order and aimed at control precedence. Feeling monitors the process by representing the other components and their coherence. The degree of synchronization is hypothesised to generate consciousness. Emotions are attractor basins of coupled oscillators, with hysteresis and catastrophe jumps. No operational measure of synchronization is given. | Read |
| NOTE-1119 | Bridging emotion theory and neurobiology through dynamic systems modeling | A dynamic-systems model of appraisal and emotion. Their constituents organize one another through feedback and circular causality into one emotional interpretation (EI): triggered by a perturbation, self-amplifying until it takes over the system, then self-stabilizing as competing cues are resolved. EIs are attractors, one at a time, with abrupt transitions between them. Vertical integration gives them momentum and selects among them. Stable EIs drive learning, so real-time and developmental order are interdependent. Predicts theta-band phase synchrony as an index of emotional relevance. | Read |
| NOTE-1132 | Soma et al. — The hive mind is a single reinforcement learning agent | A short theoretical paper with simulations. In an infinite, well-mixed population, imitation of success has the expected update of Cross Learning, and the weighted voter model of the honey-bee waggle dance that of Maynard-Cross Learning, the Maynard-Smith replicator dynamic. The population’s type distribution is the policy of a stateless bandit agent, each member is one parallel sample of it, and no member learns. The authors keep the biology partial and the simulations qualitative. | Read |
| NOTE-1144 | Sato & Crutchfield — Coupled replicator equations for the dynamics of learning in multiagent systems | A four-page letter. Two agents choose by softmax over reward memories that decay at rate α; with learning slow relative to play, each agent’s choice distribution follows a replicator dynamic in the other’s play plus α Σ_j x_j log(x_j/x_i), a pull towards uniform play. Without decay the system is conservative, Hamiltonian in zero-sum games; with decay it is dissipative. Rock–scissors–paper simulations show tori, Hamiltonian chaos, heteroclinic transients, limit cycles and chaotic attractors. Derivation plus numerics, no data. | Read |
| NOTE-1145 | Shazeer et al. — Outrageously large neural networks: the sparsely-gated mixture-of-experts layer | An engineering paper with large experiments. A sparsely-gated layer of up to 131,072 experts raises capacity over 1000-fold at roughly constant computation. Read here for one observation and one fix: without constraint the gate concentrates on a few experts, which the authors call self-reinforcing, and two auxiliary losses that penalize unequal importance and load remove it, which in one ablation also improves perplexity from 39.8 to 35.6. | Read |
| NOTE-1148 | Yang et al. — Mean field multi-agent reinforcement learning | An algorithms paper with a convergence proof and three experiments. Each agent’s Q-function is approximated by its interaction with the mean action of its neighbours, which makes many-agent RL tractable for hundreds of homogeneous agents. Mean field Q-learning converges to a Nash Q-value under strong assumptions, learns Gaussian Squeeze with 500 and 1000 agents where baselines fail, matches MCMC on a 20 × 20 Ising model, and wins a 64-versus-64 battle game. | Read |
| NOTE-1153 | Wolpert & Tumer — Optimal reward functions in distributed reinforcement learning | Members of a collective each run a reinforcement learner on a private utility, and the designer wants the world utility G maximised. A private utility is factored when it orders a member’s own alternatives, others fixed, as G does; this holds exactly when it is an increasing function of G given what the member cannot affect. The Wonderful Life Utility, G minus G with the member’s effect set clamped, is factored and easier to learn than G. In a 60-agent bar problem, clamping to the average action did best, clamping to absence nearly as well, G worst. | Read |
| NOTE-1156 | Omidshafiei et al. — α-Rank: multi-agent evaluation by evolution | A methods paper with theory and applications. Agents are ranked by the stationary distribution of a finite-population, rare-mutation Fermi imitation chain on pure profiles, unique at every finite α. As α grows its transitions become those of Markov-Conley chains, the sinks of the better-response graph, which the paper ties to chain components of the replicator flow. The limit of the ranking is not characterized, and it is not invariant to copies. | Read |
| NOTE-1215 | Ashwin, Wieczorek, Vitolo & Cox — Tipping points in open systems | A classification and a criterion, not an empirical study. Tipping in an open system ẋ = f(x, λ(t)) is split into B-tipping (a bifurcation of the quasi-static attractor), N-tipping (noise carries the system out of its neighbourhood) and R-tipping, where “the system fails to track a continuously changing quasi-static attractor”. In a linear model with a fixed stable M and a tipping radius R, the attractor never changes stability, yet steady drift r tips the system when ‖M‖⁻¹|r| > R and cannot when ‖M⁻¹‖|r| < R. Three examples, one with a unique globally stable equilibrium, and a global energy balance model show each type alone. Neither N- nor R-tipping needs any change of stability, so there is no reason to expect critical-slowing warnings for them. | Read |
| NOTE-1216 | Flack — Coarse-graining as a downward causation mechanism | A conceptual paper, not a report of new data. Downward causation is made operational as components tuning their behaviour to their own estimates of coarse-grained variables that they collectively compute. In its weak, “apparent” form only one component need tune, to a variable slower than the behaviour producing it, and estimates need be neither correct nor shared. The strong, “effective” form needs the variable to be predictive (slow), robust, used nearly universally, agreed on, and gaining mutual information with the microscopic behaviour; only then does Flack speak of a new organizational level. Regeneration of the variable by its use is not among the criteria; what reinforces itself is convergence of the estimates. The macaque power distribution is the worked example, reviewed from earlier papers. | Read |
| NOTE-1217 | Stewart, Golubitsky & Pivato — Symmetry groupoids and patterns of synchrony | In a coupled cell network, an equivalence relation on the cells gives a synchrony subspace invariant under every vector field the network admits if and only if it is balanced: every two equivalent cells have an input isomorphism that maps each input to an equivalent one (Theorem 6.5). Symmetry is one source of balance, not the only one, so robust synchrony occurs in networks with no symmetry. The dynamics on such a subspace are admissible for a smaller quotient network (Theorem 9.2), which can have a symmetry the original lacks. The paper treats existence only, not stability, and says so. | Read |
| NOTE-1218 | Torres-Hugas et al. — Cycle holonomy and remote synchronization | For a phase model whose edges carry antisymmetric phase lags, the twisted Laplacian Lα = δα*δα has a zero mode exactly when every cycle holonomy is 0 mod 2π, and otherwise its smallest eigenvalue measures the residual incompatibility; for an isolated ℓ-cycle that eigenvalue is largest at holonomy π. The symmetric Sakaguchi–Kuramoto model is a different model, but on cactus graphs its lag gives each ℓ-cycle a path mismatch (ℓ − 2)α, which an associated connection is built to carry as holonomy. In the triangle–pentagon remote-synchronization motif, the pentagon’s mismatch reaches π at α = π/3, where the locked branch is exactly a two-group state; but the branch has already lost transverse stability at αc ≈ 1.0164, so the holonomy marks geometry, not stability. | Read |
| NOTE-1228 | Toner & Tu — How birds fly together | A continuum theory of a flock: a coarse-grained velocity field with a convective term, a preferred speed and noise, coupled to a conserved density. Its linearized theory loses order in d ≤ 2, as the equilibrium XY model does, but the convective nonlinearity is relevant below d = 4, and in d = 2 symmetry fixes the exponents at z = 6/5, ζ = 3/5, χ = −1/5. Since χ < 0 the transverse velocity fluctuations stay bounded as the flock grows, so a flock has true long-range orientational order in two dimensions. The exactness rests on a cubic vertex staying irrelevant, which the authors “strongly suspect”; a fallback argument gives χ < 0 from z < 2, which they “expect on physical grounds”. | Read |
| NOTE-1340 | Nicholson — The organism as a system (Weiss) | Nicholson reconstructs from Paul Weiss’s writings a non-formal concept of a system: a whole that keeps its configuration while its parts vary and turn over, whose parts are produced and constrained by the network they form, and which therefore cannot be assembled stepwise or recovered from an inventory of parts. He uses it against reductionism, genocentrism, determinism and mechanicism. The critiques rest mostly on conceptual argument, analogy and Weiss’s authority; only the one against determinism leans on cited evidence, and its one formal criterion, that the whole varies far less than the summed variances of its parts, is met by any aggregate whose whole is measured as an average. | Read |
| NOTE-1351 | Flack — Multiple time-scales and the developmental dynamics of social systems | A review of the pigtailed macaque power-structure work. Fight outcomes flip; the peaceful silent bared-teeth signal that encodes a subordination contract almost never does, so the signalling network changes about two orders of magnitude more slowly and predicts fights better than any single fight. Power, read from that network, is a further slow variable. That the animals perceive and use these variables is argued from earlier studies and stated as what “the data suggest”, not shown here. | Read |
| NOTE-1352 | Marsland, Cui and Mehta — The minimum environmental perturbation principle | In niche models whose environmentally mediated interactions are symmetric, which it characterizes as impact vectors of the form q_iα = −a_i b_α ∂g_i/∂R_α, the uninvadable equilibrium minimizes a perturbation d(R0, R) of the environment from its supply point subject to no species having positive growth, with the species’ scaled abundances as KKT multipliers. MacArthur’s minimization principle is its Lagrange dual. d rises with every successful invasion. | Read |
| NOTE-1359 | Jansma and Hoel — Engineering emergence | Extends causal emergence 2.0 from one micro→macro path to the whole lattice of partitions of a Markov chain’s states: a partition’s ∆CP is its CP minus the largest CP of any finer partition, and the partitions with ∆CP > 0 form the “emergent hierarchy”. Shown on 5- and 8-state chains by enumeration and on 40-state preferential-attachment chains by a greedy sampler, where the spread of ∆CP within and across levels peaks near linear attachment; cycles let a single emergent scale be placed at any level. No theorem; the dynamical-consistency filter of CE 2.0 is dropped. | Read |
| NOTE-1366 | Blumenthal, Rocks and Mehta — Phase transition to chaos with nonreciprocal species-resource interactions | In MacArthur’s consumer–resource model with species’ benefits c and impacts e on resources correlated by ρ, the cavity method’s replica-symmetric fixed point loses stability at ρ² = (surviving species)/(non-depleted resources); below ρ simulations do not settle, their largest Lyapunov exponents are positive and the probability of reaching a steady state falls with system size. With ρ = 1 the model has an optimization principle and competitive exclusion keeps the ratio ≤ 1, so the transition never occurs. | Read |
| NOTE-1367 | Chizat and Bach — Global convergence of gradient descent for over-parameterized models using optimal transport | Training a sum of many units by gradient descent is, as the number of units grows, a Wasserstein gradient flow of a convex functional of the measure over unit parameters. A measure is a global minimizer exactly when the first variation F′(µ) is nonnegative everywhere and zero on its support. Under 2-homogeneity or partial 1-homogeneity, and an initialization whose support separates the domain, any limit of the flow is global, because mass in any region where F′ < 0 grows exponentially. The result is conditional on convergence and non-quantitative. | Read |
| NOTE-1368 | Power et al. — What can ecosystems learn? | In a competitive Lotka–Volterra community where individual selection lowers the competitive effect ω_ij of species j on species i at a rate proportional to x_i x_j, and a normalising trade-off holds each row and column sum of ω fixed, interactions change as Hebbian learning does. In simulation (400 species, symmetric ω) the community comes to hold attractors for two past forcing patterns, completes them from fragments and switches with hysteresis. The memory needs the imposed trade-off, and in the long run it degrades. | Read |
| NOTE-1372 | Shalizi and Crutchfield — Computational mechanics | For a discrete-valued, discrete-time stationary process whose joint distribution is known, the causal states (classes of pasts with the same distribution over the whole future) are as predictive as the full past, are the minimal and, up to measure zero, the unique such states, and have the least stochastic transitions; their entropy Cµ bounds the excess entropy from above. Minimality holds only for predicting the entire future: for any finite horizon a coarser state set can be as predictive and simpler. The paper proves these; it does not show how to estimate causal states from data. | Read |
| NOTE-1383 | Medrano, Friston and Zeidman — Linking fast and slow | A review for neuroimagers: multiscale time series are best tested with hierarchical generative models in which each level is a slower timescale, justified by centre-manifold and adiabatic reduction (the slaving principle) and compared by variational free energy; the worked example is adiabatic DCM of NMDA-receptor-antibody mouse LFP (Rosch et al. 2018). It states the slaving principle and the HKB model in a paragraph each, with no equations, and asserts rather than shows that the principle extends to discrete switching models such as HMMs. | Read |
| NOTE-1385 | Holme and Newman — Coevolution of networks and opinions | N agents with G = N/γ possible opinions on a random graph; at each step a random agent either moves one of its edges to a random holder of its own opinion (probability φ) or copies a random neighbour’s opinion (1 − φ). The process always ends in disconnected communities each of one opinion. For k̄ = 4 and γ = 10 a continuous transition at φ_c = 0.458 ± 0.008 separates a giant like-minded community plus small ones (φ < φ_c) from only small communities of mean size about γ (φ > φ_c), with exponents a = 0.61, b = 0.7 and z = 0.61 outside the percolation class. Simulation only. | Read |
| NOTE-1387 v2 | Hoel — Causal emergence 2.0 | Replaces CE 1.0’s single EI-maximizing macroscale with a path from the microscale up through coarse-grainings of a Markov chain, along which each step’s gain in CP (determinism minus degeneracy, both normalized, uniform interventions per scale) is that scale’s causal contribution; causal emergence is the total gain and “emergent complexity” the entropy of the gains along the path. Only dynamically consistent coarse-grains are admitted. Shown on three hand-built 8-state chains; the multi-path version is left open, and the paper’s claim to capture all macroscale causation is asserted, not proved. | Read |
| NOTE-1394 v2 | Gross and Blasius — Adaptive coevolutionary networks | Reviews models, mostly 1998–2007, in which a network’s topology and its nodes’ states change each other, and names four recurrent outcomes: robust self-organization toward critical states (Bornholdt and Rohlf’s threshold networks reach K = 2), spontaneous “division of labour” into classes of nodes (Ito and Kaneko), complex topologies from local rules, and new system-level dynamics such as bistability and oscillation in an adaptive SIS epidemic. A sketch, not a theory: the mechanisms are argued from examples, and its summary of Holme and Newman inverts the model’s parameter. | Read |
| NOTE-1397 | Bunin — Ecological communities with Lotka-Volterra dynamics | For generalized Lotka–Volterra dynamics of a community assembled from a pool of S species with random interactions of mean μ/S, variance σ²/S and symmetry γ, the cavity method gives exact large-S results in the phase with a unique uninvadable fixed point: a Gaussian truncated at zero for abundances, the fraction of surviving species, and a loss of stability at σ = √2/(1 + γ) for equal carrying capacities, independent of μ. Beyond it lies a multiple-attractor phase in which the outcome depends on history; that phase is located, not solved, and its history dependence is shown numerically. | Read |
| NOTE-1399 v2 | Zhang et al. — Dynamical reversibility and causal emergence based on SVD | Measures how close a Markov transition matrix is to a permutation by Γ_α = Σσᵢ^α of its singular values, shows log Γ_α − log N ≤ EI ≤ (2/α) log Γ_α, and defines causal emergence without a coarse-graining as the rise in the average singular value when those at or below a threshold ε are dropped. With ε = 0 it is a rank test; with ε > 0 it depends on ε, and any matrix with unequal singular values shows it for some ε. Its SVD-plus-k-means coarse-graining matches EI maximization on Hoel’s Boolean networks, but its claim that the lumping commutes with the dynamics for any grouping (Proposition 5) is false. | Read |
| NOTE-1400 | Krakauer et al. — The information theory of individuality | Splits I(S_n, E_n; S_{n+1}) two ways, into A* = I(S_{n+1}; S_n) plus nC = I(S_{n+1}; E_n | S_n), or I(S_{n+1}; E_n) plus A = I(S_{n+1}; S_n | E_n), and in the 2020 version names A* organismal, A colonial and nC environmentally determined individuality, read through a partial information decomposition left unspecified. Both A* and A can only grow as variables move from environment to system, so they cannot by themselves find a boundary; the 2020 version says a size cost is needed and does not supply one. Illustrated on one two-unit system; no algorithm and no data. | Read |
| NOTE-1411 | Seeley et al. — Stop signals provide cross inhibition in honeybee swarms | Nest-site scouts of honeybee swarms deliver stop signals, head-butts with a brief vibration, to scouts dancing for sites other than their own while the swarm is choosing (213 of 237 signals in two two-box swarms), and to all dancers once it has chosen. An ODE model, in the supplement, shows that above a critical rate of such cross inhibition a swarm facing two equal sites breaks deadlock and picks one at random, and picks the better when they differ enough. | Read |
| NOTE-1413 v2 | Eberhardt and Lee — Causal emergence: when distortions in a map obscure the territory | Under Hoel’s effective information, with uniform interventions at each level and macro interventions as uniform averages over micro states, the EI-optimal coarse-graining can merge micro states whose effects differ widely, so the macro variable has ambiguous manipulations; and the EI-optimal abstraction of a two-step matrix differs from the square of the one-step abstraction, so abstraction and marginalization do not commute. Both are traced to the maximum-entropy distribution, which the authors call extraneous to the system. The numbers check. | Read |
| NOTE-1414 | Ito and Kaneko — Spontaneous structure formation in a network of chaotic units | In a globally coupled logistic map whose units each renormalize their incoming weights after strengthening those from units in similar states, identical units split, in the desynchronized high-turnover regime, into a persistent core that the others attend to and a periphery the core ignores; the split needs states and weights to act on each other. Simulation only, N = 100, one parameter point in detail. | Read |
| NOTE-1415 | Chalupka, Eberhardt and Perona — Causal feature learning: an overview | A macro cause is a class of micro states with the same P(effect | man(state)); a macro intervention is any manipulation into the class, which is unambiguous by construction. The causal coarsening theorem makes the causal partition a coarsening of the observational one except on a null set, so one experiment per observational class finds it. No distribution over interventions enters the definitions. The example is a one-dimensional toy, and two displayed equations carry slips. | Read |
| NOTE-1416 | Comolatti and Hoel — Causal emergence is widespread across measures of causation | Writes a dozen measures of causal strength as functions of sufficiency and necessity, or of determinism and degeneracy, and finds every one showing causal emergence on a bipartite Markov chain whose macro is a deterministic NOT gate, under three intervention distributions; the system-level EI under the stationary distribution shows none, as data processing requires. The model is hand-built for a deterministic macro, so it is the kind of result THEORY-787’s promote_when says cannot settle it. | Read |
| NOTE-1420 | Chalupka, Perona and Eberhardt — Multi-level cause-effect systems | Defines the fundamental cause and effect of a confounded micro system as the partitions of causes by P(J | man(i)) and of effects by P(j | man(·)), learns both from experimental data, and proves they generically coarsen the observational partitions, so passive data plus one experiment per class find them. It assumes no distribution over interventions. Its claim that the effect partition is the minimal sufficient one fails for proportional, unequal columns. | Read |
| NOTE-1424 | Haken, Kelso & Bunz — A theoretical model of phase transitions in human hand movements | A theory paper. It takes relative phase as the order parameter of bimanual rhythmic movement and models the switch from anti-phase to in-phase at a critical frequency with φ̇ = −∂V/∂φ, V = −a cos φ − b cos 2φ, anti-phase being lost when |b| < |a|/4. It derives that equation from two self-sustained oscillators whose coupling must be nonlinear, and shows the switch and hysteresis in one simulation. The data it models are Kelso’s earlier experiments, summarized, and critical fluctuations and slowing are left to future work. | Read |
| NOTE-1433 | Kelso, Scholz & Schöner — Critical fluctuations | As bimanual wrist or finger movement is paced faster, the standard deviation of relative phase grows as the anti-phase pattern nears its switch to in-phase, peaks in the transition (about 85° mean phase, near the 90° of a uniform spread), and falls once in-phase is reached; started in-phase, the same movement shows neither a switch nor that growth. The authors take this as critical fluctuations, a mark of a nonequilibrium phase transition. Critical slowing is predicted, not measured, and the evidence is shown for a few subjects without a test. | Read |
| NOTE-1437 | Moreno & Mossio — Biological Autonomy, the Introduction | The Introduction alone. Moreno and Mossio state their programme: the organism, not natural selection, is biology’s central idea; its core is a closure of constraints, which they say fundamentally differs from the process loops and self-organisation of dissipative structures, and which grounds teleology, normativity and function. With regulation and agency, closure makes an autonomous system, an organism; ecosystems meet only closure. The arguments are announced for chapters 1–7, which this reading does not cover. | Skimmed |
| NOTE-1443 | Mossio & Bich — What makes biological organisation teleological? | Biological organisation is intrinsically teleological because it self-determines, and it self-determines only as self-constraint: closure, a set of mutually dependent constraints that channel a far-from-equilibrium flow at a second level of causation. A cycle of transformations, such as the water cycle, is not closure. Dissipative structures do not realise closure; at most, on a contested reading, they make “a single macroscopic constraint” that acts on its own boundary conditions, and so would be minimally teleological but not organised and without functions. The paper never names differentiation or time scales as a condition: it folds the “division of labour” into closure. | Read |
| NOTE-1449 | Kelso, Scholz & Schöner — Dynamics governs switching | Four people switched on cue between in-phase and anti-phase finger movement. Going from in-phase to anti-phase took about twice as long as the reverse at every frequency tested, with a longer-tailed distribution, significant for each subject. A stochastic HKB equation with the earlier experiments’ parameters plus a term pulling relative phase toward the intended pattern reproduces the asymmetry and the shapes, with one parameter set to the right order of magnitude: the less stable a pattern, the faster it is left. Loss of stability before spontaneous switches is cited, not shown. | Read |
| NOTE-1461 | Mossio, Montévil & Longo — organization as a theoretical principle | Proposes organization, understood as closure of constraints, as one of two theoretical principles for biology, the other being variation (treated in a companion paper). A principle is posited a priori, as physics posits its phase space, and it defines the domain: any system meeting both principles is biological, organisms being one class. The paper restates Montévil and Mossio’s definitions of constraint, dependence and closure, and argues without a model that closure grounds biological stability by regenerating constraints beyond their own time scales, and that it also propagates variation, so a local change can end in a new closure; rocks, flames and tables, it says, cannot do that. | Read |
| NOTE-1464 | Rao & Esposito — Thermodynamics of open chemical reaction networks | Builds the nonequilibrium thermodynamics of open, deterministic, mass-action networks of reversible elementary reactions on top of the rate equations, as stochastic thermodynamics is built on master equations. Chemostatting a species either breaks a conservation law or opens an emergent cycle; a network with no emergent affinity relaxes to a unique equilibrium, and a steady state dissipates the sum of emergent currents times emergent affinities. The minimal chemical work to hold a network away from equilibrium is a relative entropy of concentrations, a nonequilibrium Landauer principle. For complex-balanced networks the dissipation splits into a non-negative steady and a non-negative transient part. | Read |
| NOTE-1477 | Kolathaya & Ames — input-to-state safe control barrier functions | Defines input-to-state safety of a set C = {h ≥ 0}: under a bounded input disturbance d, the larger set C_d = {h + γ(‖d‖∞) ≥ 0} is forward invariant, for a class-K γ. A barrier condition with a disturbance term, ḣ ≥ −α(h) − ι(‖d‖), implies it (Theorem 1). Given an ordinary control barrier function, adding L_g hᵀ to a safeguarding controller, or the constraint term −εL_g h L_g hᵀ in a CLF–CBF quadratic program, yields such a function with ι(‖d‖) = ‖d‖²/(4ε) (Theorem 2). The enlargement is a class-K function of the disturbance bound in barrier units, quadratic in the universal construction; it is not proportional to the bound. | Read |
| NOTE-1504 | Heymann & Vanden-Eijnden — The geometric minimum action method | The Freidlin–Wentzell quasi-potential, a double minimization over paths and their duration, is rewritten as a single minimization over curves of a parametrization-free action, which has minimizers when the end points are equilibria and is computed by a string-method-like relaxation (gMAM). For a diffusion it is V = 2 inf ∫ |b| sin²(θ/2) ds. In gradient systems with identity noise the most likely transition paths are parallel to the drift; in the nongradient Maier–Stein model they depart from the heteroclinic orbit once the drift is far enough from gradient. | Skimmed |
| NOTE-1506 | Sánchez-Cañizares — Decision-making through irruption theory | Uses the Haken–Kelso–Bunz potential with parameters switched in time (no landscape, then two wells, then one) as a model of binary decisions, and compares the resulting rise and fall of the across-trial standard deviation of cos φ with trial-to-trial variability of event-related potentials in Sergent et al. 2021, Wolff et al. 2019 and 2021 and Hua et al. 2025, qualitatively only. It reinterprets Froese’s irruption as the onset of a two-attractor landscape and absorption as the passage to one (IAT*), reversing the sign of Froese 2024’s variance hypothesis. The mind’s role is to set the control parameters, “selecting the relevant physical coarse-graining”, which is not derived and is said to be underivable. Re-simulation confirms the trend, but under the stated noise the deviation settles near 0.40, not 0. | Read |
| NOTE-1521 | Froese — Irruption Theory | Froese proposes Irruption Theory, a libertarian, nonreductive account of how an agent’s motivations “as such” make a difference to behaviour. Three axioms (motivational efficacy, incomplete materiality, underdetermined materiality) and three theses (irruption, scalability, attunement). The difference motivation makes can only show up as increased material underdetermination, measurable as neural entropy. Chaos, 1/f noise and criticality are offered as what scales it up. Irruptions have no direction: they “can loosen the organization of the current behavior but cannot force the formation of the behavior that is to come” (§5.2.3). What makes behaviour adaptive is attunement, chiefly Watson et al.’s self-optimization in Hopfield networks with random resets and Hebbian learning. Conceptual throughout: no model, no data. | Read |
| NOTE-1532 | Juarrero — Context Changes Everything | Juarrero’s restatement of her 1999 constraint account as a general natural philosophy, self-described “speculative metaphysics” (p. 32). Context-independent constraints take conditions away from equiprobability, context-dependent ones away from independence (Gatlin), and enabling constraints couple separate processes into coherent “interactional types” whose constitutive constraints double as governing, “second-order” constraints that hold components to a subregion of state space, top down, “as constraints, not efficient causes” (p. 25). Levels are demarcated by rate discontinuities, wholes are slower than parts, and inter-level control is lost when the rates converge (ch. 12, from Salthe and Allen and Starr). It adopts Montévil and Mossio’s closure of constraints verbatim (pp. 93–94). It has no formal model of its own and does not discuss Kane, free will, chaos or contextual emergence. | Skimmed |
| NOTE-1534 | Yang & Abanin — Integrals of motion as slow modes | Under weak local noise an operator decays at a rate set by its size; chaotic dynamics makes generic operators grow, while small-sized integrals of motion do not, so they are the Lindbladian’s slow modes. Exact diagonalization at L ≤ 9 bears this out for Ising and Heisenberg chains and finds approximate conservation laws, including some not put in by hand. The large-L footing is a perturbative argument through a gap of order min(γL, √(v_Bγ)), which the authors say hydrodynamic modes may close. Stronger noise reorders the slow modes in favour of approximate conservation laws. | Read |
| NOTE-1536 | Scheffer et al. — Early-warning signals for critical transitions | A review of generic early-warning signals for critical transitions. At a fold bifurcation the dominant eigenvalue goes to zero, so recovery from small perturbations slows (critical slowing down). Under ongoing perturbation that shows as rising lag-1 autocorrelation and rising variance. Skewness and flickering are further signals, not caused by slowing down. Spatial systems add rising cross-correlation and specific pattern sequences. Evidence from climate, ecosystems, epilepsy, asthma and finance is reviewed. The signals mark proximity to a broad class of thresholds, not only catastrophic ones, so they do not say which kind; false positives and negatives are named. Cyclic and chaotic systems are “less well studied”. | Skimmed |