Topics — What a work is about. Nucleation holds whatever reading the owner files here, whether or not an Anthology of the SOTA topic could also hold it; instruction for ML practice belongs to the anthology (ADR-048). The words are seeded from the clusters the reading-time triage of 2026-09-25 found, and grow by decision.
Network science — the structure and dynamics of networks — dimension, curvature and Ricci flow, community detection, consensus and synchronization.
67 of 2004 LIT documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| LIT-004 v2 | Community Detection on Networks with Ricci Flow | Ni et al. (2019), ARXIV-1907.03993. The paper runs Ollivier-Ricci flow w^{(k+1)}{xy} = (1 − κ^{(k)}{xy})·d^{(k)}(x,y) (= W(m_x, m_y)), then cuts edges above a weight threshold. On LFR (n = 500, avg. degree 20) this gives ARI ≈ 1 up to μ ≈ 0.6. On two-block SBM (n = 500, p_intra = 0.15) it gives ≈ 1 up to p_inter/p_intra = 0.5, but it collapses to ≈ 0.1 at 0.55, where Spinglass and Fast Greedy still score ≈ 0.9 and ≈ 0.8. Theorem 4.1 (α = p = 0, cliques G(a,b), a > b ≥ 2) proves in fact only that non-gateway intra-clique edges shrink as (1/a)ⁿ. Gateway intra-clique edges grow at the same rate λ₁ⁿ as inter-community edges, with ratio → k ∈ (0,1). | Active — read in full 2026-09-25 (NOTE-006); the source paper for Ollivier-Ricci-flow community detection and the GraphRicciCurvature package, and worth reading for the method (§3, SI §C). It should be cited for the algorithm, not for superiority. Its SBM figure shows it losing to Spinglass and Fast Greedy past p_inter/p_intra = 0.5. Its theorem is weaker than stated, and it covers a parameter setting (α = p = 0) that differs from the one used in experiments (α = ½, p = 2). |
| LIT-020 v2 | Characterizing Complex Networks with Forman-Ricci Curvature and Associated Geometric Flows | Weber et al. (2016), ARXIV-1607.08654. The paper specializes Forman’s (2003) Bochner–Weitzenböck curvature on weighted CW complexes to graphs, giving the closed-form edge curvature Ric_F(e) = ω(e)[ω(v1)/ω(e) + ω(v2)/ω(e) − Σ_{e_v1∼e, e_v2∼e}(ω(v1)/√(ω(e)ω(e_v1)) + ω(v2)/√(ω(e)ω(e_v2)))] (Eq. 11). It then proposes three uses: an EMD distance between curvature distributions, which puts Facebook, Google and BioGrid graphs at 0.050–0.060 from a Barabási–Albert model against 0.17–0.36 from Erdős–Rényi and Watts–Strogatz (Table 1); a discrete “2-D-form” Ricci flow γ̃(e) − γ(e) = −Ric_F(γ(e))·γ(e) (Eq. 36) for change detection; and a Laplacian flow ∂G/∂t = (□₁ − F)G (Eq. 45) for denoising. The authors say the flow applications are “only theoretically proposed and illustrated solely on a small example” (§5). | Active — read in full 2026-09-25 (NOTE-026); the standard early citation for Forman–Ricci curvature on networks and for the Forman–Ricci flow. Read it for §2.3 (Eqs. 11–17) and §4.1 (Eqs. 36–41), and cite it for definitions only. Its empirical and application claims are one-table or one-figure demonstrations. Several of its formulas contain sign and consistency slips, listed below, so a user should take Eq. 11 from here and check it against Sreejith et al. 2016. |
| LIT-028 v2 | Asymptotic versus mesoscopic spectral dimensions in networks and inhomogeneous structures | Grimaldi et al. (2025), ARXIV-2510.20520. The paper studies a “bundled” network, meaning a fiber graph attached at one node to every node of a base graph, with base and fiber growing with the same length L. For such a network, first-order perturbation theory (SM Eq. 10) gives the low spectrum as λ = ℓ^b/N_f, and from that the gap (“Fiedler”) dimension d_g = 2(d_f,f + d_f,b)/(d_f,f + 2d_f,b/d_g,b), while the spectral dimension stays d_s = d_s,f. The two therefore differ unless d_g,b = 2 or the fiber is finite. For example, the ring-of-rings comb has d_s = 1 but d_g = 4/3, and the 2D-base brush has d_s = 1 but d_g = 2. The rule holds only while the base-induced gap lies below the fiber’s own gap (SM Eq. 14). | Active — read in full 2026-09-25 (NOTE-005); the base-controlled gap rule and its derivation are correct and easy to check, and they are worth reading as a clean, minimal example of the density-of-states exponent and the gap exponent coming apart. Read the SM finite-size scaling forms (Eqs. 25, 29) with care: their N prefactors are wrong except when d_s,b = d_g. |
| LIT-068 v2 | How Local Separators Shape Community Structure in Large Networks | Frenkel & Carmesin (2025), ARXIV-2504.14501. This is a comparison of the authors’ local 1- and 2-separator decompositions against Infomap, Label Propagation, Leiden and Louvain (igraph) on five sparse graphs (62 to 9,133 nodes). Local separators score lower overlapping modularity than the modularity optimisers everywhere, and lower than Infomap on 3 of 5 graphs (Table 2). Their edge is confined to high density thresholds on the two road networks, where the best radius gives a handful more qualifying clusters: about 12 against about 5 at β ≥ 1.25 on Euroroads, and about 50 against about 40 for Infomap at β ≥ 1.5 on NRW (Figs. 3–4). On Netscience all methods are similar. At δ = 1 on both road networks, and at δ = 1.25 on NRW, Infomap yields more qualifying clusters than any local-separator setting. | Rejected — read in full 2026-09-25 (NOTE-085); not worth a reader’s time. Its critique of modularity (§2.4) contains two false statements. Its own “community detection problem” (§2.5) is defined but never scored. Read at the paper’s own thresholds, the figures do not support “consistently identify the densest communities”. The method itself is never defined here, so a reader wanting local separators should go to Carmesin & Frenkel, arXiv:2312.12354 (its ref. [9]). |
| LIT-069 v2 | Surface optimization governs the local design of physical networks | Meng et al. (2026), DOI-10.1038/s41586-025-09784-4. The degree counts in Fig. 1d show k = 4 nodes making up 4.6–17.7% of branch points across the six datasets. The pooled 16.6% is 96% human-neuron nodes. Bifurcation angles also fail to peak at 2π/3. From this the authors infer that local branching minimises sleeve surface area under a minimum circumference w, not wire length. For a regular tetrahedron their numerical minimiser merges two bifurcations into a trifurcation at χ = w/r ≈ 0.83, and a thin branch sprouts orthogonally below ρ = w′/w ≈ 0.6. Per-dataset empirical thresholds are ρ_th = 0.52–0.92. The “exact mapping” to string-theory worldsheets covers only the unconstrained minimal-area problem. The SI says the implemented method yields surfaces that are only locally area-minimising (§5). | Proposed — read in full 2026-09-25 (NOTE-075); a promising and cleanly falsifiable hypothesis, but the evidence does not yet separate it from simpler accounts. Three things would settle it: recomputing the empirical P(λ) without the SI’s trifurcation-merging rule, running the actual surface minimiser (rather than a sigmoid fitted to one tetrahedron) on random terminal sets, and testing the branching-to-sprouting breakpoint against a no-breakpoint null. |
| LIT-070 v2 | Dynamics of collectives with opinionated agents: The case of scrambling connectivity | Somarakis et al. (2016), DOI-10.1109/ECC.2016.7810493. For networks of agents that each have their own independently evolving opinion dynamics and communicate cooperatively with neighbours, non-negative matrix theory gives sufficient conditions for stability and convergence to a common synchronized opinion, for both identical and non-identical agents. The “scrambling” connectivity condition is presumably what the title names; I have not verified this from the full text. | Unavailable — seeded 2026-09-25 from the abstract; on 2026-10-14 a search for a lawful full text reached none, so it is not read and no NOTE is filed. OpenAlex lists it as closed with no repository copy, and Unpaywall reports no open location. arXiv has no preprint under the authors’ names or the title. Crossref’s only full-text link is IEEE’s similarity-checking PDF, not a reading copy. A web search shows a record of the paper on John Baras’s group site at the University of Maryland (baras.isr.umd.edu/node/866), described as carrying a full-text link, but the site could not be reached: HTTPS failed with a certificate that does not name the host, HTTP returned 404, a fetch returned 503, and the Internet Archive refused the lookup (429). So an author-posted copy may exist, and this failed on access, not availability. It stays Unavailable until a copy is supplied. |
| LIT-079 v2 | Causal Claims in Economics | Garg & Fetzer (2024), ARXIV-2501.06873. GPT-4o-mini is run in nine passes per paper over the first 30 pages of 44,852 NBER/CEPR working papers. Edges kept in at least 4 of 9 passes, JEL-mapped, give “claim graphs” in which the share of edges backed by DiD/IV/RCT/RDD/synthetic control rises from 7.7% (1990) to 31.7% (2020). In year-fixed-effect-only regressions, doubling causal edges is associated with +1.36 pp top-five probability and +11.2% citations, while non-causal counterparts are flat or negative. The validation checks paper-level method labels, and only weakly: RCT and field labels have precision ≤ 0.10. It never checks the edges themselves against human labels. | Proposed — read in full 2026-09-25 (NOTE-083); a promising, openly released claim-extraction infrastructure whose headline associations rest on edges never validated against human labels and on regressions with year fixed effects only. An edge-level human-annotated audit, and outcome regressions with field and method controls on a common sample, would settle it. |
| LIT-084 v2 | 3rd EEAS Report on Foreign Information Manipulation and Interference Threats: Exposing the architecture of FIMI operations | European External Action Service et al. (2025), https://www.eeas.europa.eu/sites/default/files/documents/2025/EEAS-3nd-ThreatReport-March-2025-05-Digital-HD.pdf. The EEAS classifies channels in foreign information manipulation and interference (FIMI) into four tiers by their tie to a state: official, state-controlled, state-linked (covert, attributed) and state-aligned (non-attributed). It applies the scheme to 505 incidents it detected between 4 Nov 2023 and 4 Nov 2024, involving about 38,000 channels. In a filtered co-involvement graph of 2,055 recurrent channels, 20% are Russian-attributed, 3.5% Chinese-attributed and 76.5% non-attributed. The report states that the sample is illustrative and should not be used to infer general trends. | Active — read in full 2026-09-25 (NOTE-060); worth reading as the primary statement of the EEAS’s attribution taxonomy (the Exposure Matrix) and of the covert operations it names. Its figures are counts from an avowedly non-representative monitoring sample, the network method is described only in outline, and several headline numbers need the qualifications recorded here before they are cited. |
| LIT-091 v2 | Networks beyond pairwise interactions: Structure and dynamics | Battiston et al. (2020), ARXIV-2006.01764. 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. | Active — read in full 2026-09-25 (NOTE-057); the standard entry point to higher-order network science, worth reading for §II–§III (definitions and operators) and as a map of the 2020 literature. Read it for definitions and pointers, not as evidence: the dynamical claims are one-paper summaries, several formulas carry typos (listed below), and the conclusion’s “profoundly change” list includes linear cases that §V itself shows reduce to pairwise. |
| LIT-150 v3 | What is emergence, after all? | Rizi (2025), ARXIV-2507.04951. 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”. | Active — read in full 2026-09-26 (NOTE-153); worth reading as a compact, well-referenced statement of the physicist’s weak-emergence view and a reading list into it (Carroll & Parola, Hoel, Rosas, Witten, De Haro & Butterfield, Dennett). Its framework is stated, not developed: no distortion measure is given for F, and “predictive” is never quantified. |
| LIT-547 | A Network Theory of Mental Disorders | Borsboom (2017), World Psychiatry 16(1):5–13. Mental disorders are not common causes of their symptoms but states of networks of symptoms that cause one another, through “myriads of biological, psychological and societal mechanisms”. Five principles; the dynamic one is hysteresis: a strongly connected network, once activated by an external trigger, can sustain itself after the trigger is gone. Disorder is an alternative stable state of a strongly connected network, mental health the stable state of a weakly connected one. Comorbidity follows from bridge symptoms. Treatments are symptom, external-field or network interventions. | Active — read in full 2026-10-03 (NOTE-435); worth reading as the short, citable statement of the network theory of mental disorders by its main author. Five principles: disorders are complex systems of interacting components, the components are the symptoms of the diagnostic manuals, the network comes from direct causal connections between symptoms, disorders are the tightly connected clusters, and disorders arise through hysteresis, so a strongly connected network can stay “stuck” after its trigger is gone. Mental health, disorder, resilience and vulnerability are redefined as stable states and dispositions of weakly or strongly connected networks. Its evidence is indirect and it says so: the theory is offered as an “organizing framework” and a deliberate simplification, and the strict symptom-component correspondence of principle 2 is its own flagged weak point. |
| LIT-633 | Cross-region neuron co-firing mediated by ripple oscillations supports distributed working memory representations | Verzhbinsky, Daume, Cheng, Rutishauser & Halgren (2026), Nature Neuroscience 29:2566–2577. In 1,373 single units from hippocampus, amygdala, vmPFC, ACC and preSMA of 35 epilepsy patients doing a Sternberg task, ripples (70–100 Hz) co-occur between bundles up to about 220 mm apart with no decline beyond the local bundle, and cross-region unit co-firing rises about 30% during co-ripples. That rise exceeds a rate-only null (STTC 117% higher), grows with memory load, and co-ripples hold more repetitions of a stimulus’s encoding co-firing at retrieval, more on fast trials. | Active — read in full 2026-10-03 (NOTE-494); worth reading as single-unit evidence that brief co-occurring ~90 Hz ripples in distant human forebrain sites (up to about 220 mm, across hemispheres) mark windows of raised cross-region co-firing, about 30% above no-ripple periods and beyond what firing rates alone predict, that this scales with working-memory load, and that stimulus-specific co-firing from encoding recurs more often inside co-ripples at retrieval, most of all on fast trials. One reanalysed open dataset (35 patients, one Sternberg task, load 1 versus 3), clinically placed electrodes, and correlational throughout: nothing perturbs the ripples. |
| LIT-676 | Unveiling Mode Connectivity in Graph Neural Networks | Li, Chen, Han, Zeng, Liu & Tang (2025), preprint. GCN solutions for node classification from different seeds are connected by quadratic Bezier curves but often separated on the straight line, more so on co-authorship and heterophilous graphs than on citation graphs. GNN variants (GCN, GraphSAGE, GAT) give similar barriers, MLPs different ones. On CSBM graphs, barriers fall with density and feature separability and are highest at middling homophily. The authors bound the barrier through the spectral gap, bound the generalisation gap by the barrier, and propose a Wasserstein distance between graphs’ interpolation-loss curves that correlates with transfer gaps. | Proposed — read in full 2026-10-03 (NOTE-529); watching, as the first study of mode connectivity in graph neural networks. Two GCNs trained on the same graph with different seeds are usually joined by a low-loss quadratic Bezier curve but often not by a straight line, and the barrier depends on the graph more than on the GNN variant: it falls with density, with feature separability, and with homophily far from one half, in synthetic CSBM graphs and, by the authors’ reading, in 12 real ones. A loss-barrier bound, a generalisation bound in terms of the barrier, and a barrier-based distance between graphs are stated, but the appendix that should hold the proofs does not; the v1 text still carries an editor’s placeholder. What would settle it: the proofs, and numbers for the barriers the figures show. |
| LIT-716 | Network Epistemology: Communication in Epistemic Communities | Zollman (2013), Philosophy Compass 8:15–27. A survey of how communication structure affects group learning. No structure is best for all problems. With costly lossless transmission, minimally connected networks are optimal; with lossy transmission, stars. When agents average opinions, regular networks are best and denser is faster. In bandit problems minimally connected networks are best even when communication is free. Optimal networks may not be reached by individuals’ choices. | Active — read 2026-10-05 (NOTE-567): read in full from the author’s posted manuscript. Worth reading as the short survey of network epistemology up to 2012. Its main lesson is that the best communication structure depends on the learning problem. Pooling estimates favours dense, regular networks. Costly transmission favours sparse ones, often a star. Active learning in bandit problems favours minimally connected ones. Intuitions about “too little” or “too centralized” communication are often wrong. A survey, weighed as one. |
| LIT-724 | The Communication Structure of Epistemic Communities | Zollman (2007), Philosophy of Science 74:574–587. Simulating Bala and Goyal’s model, in which scientists learn only about the method they pursue, small communities connected in a cycle chose the better method more often than wheels or complete graphs, and took longer to do so. Over all networks of up to six agents, density predicted failure, and hub centrality did not. Misleading early results spread through dense networks before diversity could correct them. | Active — read 2026-10-05 (NOTE-583): read in full from the author’s posted copy. Worth reading as the origin of the “Zollman effect”. In a Bala–Goyal bandit model, where agents learn only about the method they pursue, simulated communities with fewer communication links converged on the better method more often and more slowly than fully connected ones. The cause was density, not the centrality of a hub. A simulation study of small networks (3–10 agents) at one payoff gap. LIT-733 shows the effect is confined to hard inquiry. |
| LIT-733 | In Epistemic Networks, Is Less Really More? | Rosenstock, Bruner & O’Connor (2017), Philosophy of Science 84:234–252. Replicating Zollman’s models over wider parameters, the advantage of cycles over complete networks vanishes once the better action is slightly better (pB ≥ 0.525 at size 10), groups are larger, or agents gather more data per round. It persists only where inquiry is hard. Kummerfeld and Zollman’s results behave the same way. Transient diversity is the robust lesson. | Active — read 2026-10-05 (NOTE-559): read in full from the copy on Cailin O’Connor’s website. Worth reading as the robustness check on the Zollman effect. Over a wider parameter space, sparse networks beat dense ones only where inquiry is hard: small groups, small batches of data, and nearly indistinguishable alternatives. Elsewhere sparsity only slows learning. The authors keep Zollman’s transient-diversity point as robust and read these models as “how-potentially” stories. |
| LIT-735 | The Epistemic Benefit of Transient Diversity | Zollman (2010), Erkenntnis 72:17–35. In a richer bandit model with beta priors, sparse networks again beat dense ones. Making priors extreme reverses the order: dogmatic agents in a complete network do best. Both limited information and dogmatism keep diversity alive. Together they keep it alive too long, and agents fail to converge. The epistemic good is diversity that is transient. | Active — read 2026-10-05 (NOTE-564): read in full from the author’s posted manuscript (dated 29 September 2009). Worth reading for its conclusion, which Rosenstock et al. (LIT-733) single out as the robust result of this literature: what a community needs is transient diversity, long enough to keep a theory from being dropped too soon and short enough to allow convergence. Sparse communication and stubborn priors each supply it, and together they make diversity too stable and learning fails. The peptic-ulcer history is the motivating case. |
| LIT-744 | Experimentation by Industrial Selection | Holman & Bruner (2017), Philosophy of Science 84:1008–1019. Industry can bias a scientific community without corrupting anyone, by funding researchers whose methods already favour its product, so that they are more productive and train more newcomers. Shown in a bandit-model simulation with methodological diversity and turnover, after the antiarrhythmic drug case. An independent funder helps only if it discounts industry-funded work. | Active — read 2026-10-05 (NOTE-574): in full, from the publisher’s PDF in ANU Open Research, the co-author’s institutional repository, marked open access. Worth reading for a mechanism by which an outside funder biases a scientific community without corrupting anyone: given methodological diversity, a merit-based system and turnover, funding researchers whose methods already favour a product makes them more productive and more likely to train newcomers. An independent funder helps only if it discounts industry-funded work; funding on merit alone makes things worse. Limits: one historical case and a 20-agent simulation at a few parameter settings; run counts and network are not reported, and robustness to network structure rests on a footnote. |
| LIT-751 v3 | The Problem of Intransigently Biased Agents | Holman & Bruner (2015), Philosophy of Science 82:956–968. By its abstract, one intransigently biased agent in Zollman’s network model keeps an honest community from converging on the truth; two remedies are explored, one letting agents choose whom to trust. Unread: the authors’ 2017 paper LIT-744, read, applies the same model family to the same medical case. | Unavailable — registered 2026-10-05 from Crossref and the authors’ institutional portals, not read: the published PDF in ANU Open Research is embargoed until 31 December 2037 and was not downloaded, the journal is closed, and no author-hosted copy was found. Only the abstract was seen: one intransigently biased agent in a Zollman network keeps an honest community from ever converging on the truth, and letting agents choose whom to trust is one remedy explored. The authors’ 2017 paper “Experimentation by Industrial Selection” (LIT-744), read in full, uses the same model family on the same medical case and cites this one. Filed because it is the authors’ first model of biased agents in medical research. It stays Unavailable until a copy is supplied, not on merit. |
| LIT-854 | Irreversibility in bacterial regulatory networks | Zhao, Wytock, Reynolds and Motter (2024), Science Advances 10(35):eado3232. In Boolean models of the E. coli transcriptional regulatory network, a transient single-gene knockout or overexpression often moves the network to a different attractor, so one genotype can hold several heritable expression states without epigenetic marks. The genes able to do this are those upstream of, or inside, strongly connected components with positive circuits, and the more weighted paths to them the likelier. A prediction from a model ensemble, with no direct experiment. | Active — read 2026-10-09 (NOTE-655); worth reading as a whole-network test of whether transcriptional regulation alone can make a bacterium’s state history-dependent. In an ensemble of sign-consistent Boolean rules on the 87-gene core of the largest E. coli regulatory subnetwork (RegulonDB), 51 genes admit a transient knockout or overexpression that leaves the network in a different attractor; every such gene reaches a strongly connected component containing a positive circuit, and the probability grows roughly as a power of the weighted number of paths to one. Model only: the paper runs no transient-perturbation experiment. Its one comparison with data, against strains evolved after a permanent crp knockout, mostly tests the sign structure of the network, and its link to irreversibility is weak (P = 0.03 on small counts). |
| LIT-865 | Hyperbolic Geometry of Complex Networks | Krioukov, Papadopoulos, Kitsak, Vahdat and Boguñá (2010), Phys. Rev. E 82, 036106. Random graphs on a hyperbolic disk, with nodes joined by hyperbolic distance, have power-law degrees (γ = 2α/ζ + 1, set by node density against curvature) and strong clustering (set by a temperature, lost at a phase transition at T = 1). A circle-similarity model with power-law hidden degrees is the same ensemble once radius is taken as log degree: the paper’s “effective hyperbolic geometry”. The configuration model and Erdős–Rényi graphs are its degenerate limits, and greedy routing by the coordinates is near-optimal and robust in the model’s networks. | Active — read 2026-10-09 (NOTE-680); worth reading as the paper that put a latent hyperbolic space under complex networks. Nodes placed quasi-uniformly in a hyperbolic disk and joined when close give, in the large-disk approximation, a power-law degree distribution with exponent γ = 2α/ζ + 1 (node-density exponent over curvature), and a Fermi–Dirac connection probability with a temperature T gives clustering that falls from its maximum at T = 0 to zero at a phase transition at T = 1. Conversely, a circle-similarity model with power-law hidden degrees maps onto the hyperbolic one by taking radius as log degree: this is the paper’s “effective hyperbolic geometry”. Removing the angular term from the distance leaves the configuration model, and heating further leaves Erdős–Rényi graphs. Greedy routing by hyperbolic coordinates in the model succeeds for 99.9% of pairs at γ = 2.1 and T = 0 and survives heavy link removal. All of it is about the model: the fit to the Internet is of three summary statistics, and no real network is embedded here. |
| LIT-867 | Emergent Hyperbolic Network Geometry | Bianconi and Rahmede (2017), Scientific Reports 7, 41974. Growing simplicial complexes, made by gluing d-simplices to (d − 1)-faces with probability ∝ 1 + s n_α (flavor s = −1, 0, 1), have a tree as their dual and, drawn with equal links as ideal simplices in the Poincaré ball, fill hyperbolic d-space: the hyperbolic geometry is an outcome of a purely combinatorial rule rather than its cause. Degrees are exponential for d + s = 1 and power-law with γ = 2 + 1/(d + s − 1) ≤ 3 for d + s > 1; clustering and modularity are high for d ≥ 2. Hyperbolicity is shown by construction, conditional on equal link lengths, not proved. | Active — read 2026-10-09 (NOTE-678); worth reading as the model that turns the hidden-metric account of complex networks around: a simplicial complex grown by gluing d-simplices to (d − 1)-faces, with no geometry in the rule, comes out small-world, clustered, modular and (for d + s > 1) scale-free, with γ = 2 + 1/(d + s − 1) from a master equation. Its dual is a tree, so with every link given equal length each simplex is drawn as an ideal simplex of the Poincaré ball and each new node at the normalised sum of its parent face’s positions. That embedding, not a proof, is the paper’s case that the geometry is hyperbolic, and the authors concede it rests on the equal-length assumption (unequal lengths fit a sphere) and that the ideal-simplex distances are infinite. A fitness on faces gives a numerically observed transition in which the complex grows in one direction. |
| LIT-869 | Multiscale unfolding of real networks by geometric renormalization | García-Pérez, Boguñá and Serrano (2017; Nature Physics 14, 583–589, 2018). A geometric renormalization group for networks: merge blocks of angular neighbours on the S¹ circle into supernodes. The S¹ model maps approximately into itself under this (κ′ = (Σκ^β)^{1/β}, β fixed), so layers are self-similar with an average degree that grows or shrinks by r^ν, ν set by the degree exponent γ and the clustering parameter β. Six real networks collapse across layers and keep their communities. Applied as downscaled replicas that reproduce Ising, SIS and Kuramoto behaviour, and as multiscale greedy routing in hyperbolic space. | Active — read 2026-10-09 (NOTE-673); worth reading as the paper that defined a renormalization group for networks from a hidden metric space rather than from shortest paths. Nodes embedded on the S¹ circle are merged in blocks of r angular neighbours, supernodes linked if any of their members were, and the model maps approximately back into itself: hidden degree κ′ = (Σκ^β)^{1/β}, β unchanged, μ and R divided by r. So each layer is a smaller network of the same ensemble with a larger average degree, ⟨k⟩ growing as r^ν with ν = 2/(γ−1) − 1 or 2/β − 1, whichever dominates. Six real networks (Internet, airports, metabolism, proteome, chord transitions, word adjacency) show degree, neighbour-degree and clustering curves that collapse across layers and keep their communities, which the paper reads as evidence that hidden metric spaces underlie real networks. Pruning a layer back to the original density gives small replicas on which Ising, SIS and Kuramoto curves match the original, and greedy routing through the coarser layers raises its success rate. The renormalizability is a first-order approximation, and the collapse is shown by eye. |
| LIT-871 | Hyperbolic Representation Learning: Revisiting and Advancing | Yang, Zhou, Ying, Chen and King (2023), ICML 2023, PMLR 202. Tracks the hyperbolic distance from each node to the origin and finds that hyperbolic models trained on ordinary task losses do not by themselves place a tree’s root nearest the origin or spread its levels outward: on synthetic 3-ary trees the root sits well off the minimum and the distances are roughly bell-shaped, ordering node pairs by level only 69–75% of the time. Proposes HIE, which recentres the embedding on its hyperbolic centroid and pushes nodes outward; it improves that ordering and benchmark scores, most on the least tree-like graphs. | Active — read 2026-10-09 (NOTE-669); worth reading as an empirical check, on synthetic trees and four benchmark graphs, of the assumption that a hyperbolic model trained on an ordinary task loss lays out the data’s hierarchy by itself, root near the origin and leaves near the boundary. It does so only partly. On two 3-ary trees of 1,093 nodes, a hyperbolic graph convolutional network (HGCN) trained for link prediction or node classification puts the root nowhere near the smallest distance to the origin, and the nodes’ distances to the origin come out roughly bell-shaped rather than piling up at the leaves; read off as levels, those distances order random node pairs correctly 69–75% of the time. The proposed fix, HIE, recentres the embedding on its hyperbolic centroid and adds a loss that pushes every node outward in proportion to its current distance. It raises that ordering to 75–84% and lifts benchmark scores, most on the least tree-like graphs (Citeseer, Cora). There is no theory of why task losses fail to produce the hierarchy, and the fix itself uses no level information. |
| LIT-939 v2 | Modeling opinion misperception and the emergence of silence in online social system | Vilone and Polizzi (2024). In two agent-based models on scale-free networks with fixed private beliefs, a small hard-core minority makes expressed and perceived opinion lean far toward the minority. The first model has no voluntary silence. In the second, the majority falls silent: 55–60% of agents end silent, whatever the minority’s size or degree. The network’s direct (friendship-paradox) distortion of perception is small and of no fixed sign. Simulation only. No belief changes, and the majority is overturned in expression only above a minority of about 30%. | Active — read 2026-10-14 (NOTE-810) in full; worth reading for its separation of two sources of opinion misperception in a network: the friendship-paradox distortion of what members see, which it finds small and of no fixed sign, and a spiral of silence, which it finds large. With private beliefs held fixed, a hard-core minority drives 55–60% of agents into silence and makes expressed opinion lean far toward the minority. Read it knowing that it is simulation only, that no belief ever changes, and that the majority is overturned in expression only above a minority of about 30%. Filed for QUESTION-047; THEORY-242 holds what it shows. |
| LIT-955 v2 | Tangled webs: A practical investigation of graph tangles. | Salter-Duke (2024), PhD thesis, Victoria University of Wellington. Tangles (Robertson and Seymour 1991) define a cohesive region as one every low-order cut points towards. The thesis gives an exact but exponential algorithm for edge-connectivity tangles and tests them on eleven small networks and small images. Tangle communities match standard ones only where community structure is strongly delineated; three networks have no distinguishable tangles at the orders reached; tangles of one to three vertices recur; one-pixel lines cannot be distinguished. The author finds the notion “not as compelling as I had hoped”. | Active — read 2026-10-14 (NOTE-814) in full; worth reading as an early empirical test of tangles, the Robertson–Seymour notion of a region that cannot be pulled apart, as a criterion of cohesion: an exact low-order algorithm, eleven small real networks and some small images. Read it knowing that the result is mostly negative (tangle communities match standard ones only where structure is strongly delineated, tangles of one to three vertices recur, thin shapes cannot be seen), that turning a tangle into a vertex set needs the author’s assignment rule, and that only small graphs and low orders were computable. Registered for QUESTION-035; THEORY-254 is filed from it. |
| LIT-960 v2 | Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex Networks | Pecora et al. (2014). For identical units coupled through a symmetric, unweighted graph, the orbits of the graph’s symmetry group are clusters that can each be exactly synchronized. A change of coordinates built from the group’s irreducible representations block-diagonalizes the variational equations, so each cluster’s stability is computed alone. When the group is a direct product, a cluster moved by one factor can lose synchrony while the others keep it (isolated desynchronization), because the other nodes receive the same summed input from it either way. An 11-node electro-optic network showed the predicted bifurcations. Graph statistics suggest such symmetries are common. | Active — read 2026-10-14 (NOTE-775) in full; worth reading as the general account of cluster synchronization for identical units on a symmetric graph: the symmetry orbits are the clusters that can synchronize, irreducible representations separate each cluster’s stability, and a cluster moved by its own factor of the group can desynchronize alone, as an electro-optic experiment showed. Read it knowing that symmetry is sufficient, not necessary, for clusters, that nonidentical units and weighted or directed coupling are not worked through, and that it says nothing about external drive. Its use on QUESTION-063 as a coupling signature is the record’s inference, held in THEORY-276. |
| LIT-999 v2 | Naïve Learning in Social Networks and the Wisdom of Crowds | Golub and Jackson (2010). Agents with independent noisy signals of a true value repeatedly average their neighbours’ beliefs with fixed weights, ignoring repeated information. The consensus is the signals weighted by the network’s left unit eigenvector, and in a growing society it converges to the truth if and only if the largest such influence weight vanishes; with reciprocal equal weights, if and only if no degree is a non-vanishing share of all links. A finite group everyone attends to prevents it; balance and dispersion conditions ensure it. Speed of consensus is unrelated to its correctness. | Active — read 2026-10-14 (NOTE-840) in full; worth reading for QUESTION-047 as a proved case in which members share one updating rule and the network alone decides whether the group belief is right: a growing society of DeGroot averagers converges to the truth if and only if the largest influence weight vanishes. Read it knowing that its agents are naïve, not sound (they ignore repeated information), that weights are fixed and signals independent, and that the result is asymptotic and about a model, not data. |
| LIT-1098 | Efficient and Robust Approximate Nearest Neighbor Search Using Hierarchical Navigable Small World Graphs | Malkov and Yashunin (2020), IEEE TPAMI 2020. HNSW is a stack of proximity graphs on nested random subsets of the data. Each element’s top layer is drawn from a geometric distribution, and new neighbours are chosen by a pruning rule that favours diverse directions. Searching from the sparse top layer down makes per-query cost grow about logarithmically with N on uniform random data in 4 and 8 dimensions, which flat NSW graphs did not. The logarithmic bound is derived only for exact Delaunay graphs of bounded mean degree, which HNSW does not build. For the graphs it does build, logarithmic scaling is measured, at low dimension only, and on 200M SIFT vectors the paper reports the scaling “deviates from the pure logarithm”. The neighbour-selection rule is what keeps clustered data searchable: in the paper’s synthetic test with 100 isolated clusters, linking each element to its nearest neighbours fails to reach high recall. There is no worst-case or recall guarantee, no deletion, and no analysis of query distributions unlike the data. | Active — read in full 2026-10-15 from the authors’ arXiv preprint, version 4 of 14 August 2018 (arxiv.org/pdf/1603.09320v4, 13 pp., the last arXiv version, whose abstract matches the published one apart from copy-editing; the TPAMI body was not seen). Version 1 (2016) was compared: it claimed deletion, which v4 drops and lists as future work. Unpaywall and OpenAlex list no open-access copy of the TPAMI version. Worth reading as the source of the hierarchical graph index: nested proximity graphs on geometrically sampled layers, with a neighbour rule that keeps links between clusters. Its logarithmic search cost is derived only for exact Delaunay graphs of bounded degree, which it does not build, and is measured only on uniform random data in 4 and 8 dimensions; on 200M SIFT the scaling “deviates from the pure logarithm”. It gives no worst-case or recall guarantee and no deletion. For CLAIM-310 it shows, with bins replaced by graphs, that the arrangement of fixed data under a fixed distance decides cost and, on clustered data, whether items can be found at all; it narrows part 2, since the index is built without any query mix and every test drew its queries from the data. For QUESTION-114 it supplies a measured build-time against query-time curve and O(N log N) construction argued at low dimension, with insertion upkeep only. |
| LIT-1103 | The Small-World Phenomenon: An Algorithmic Perspective | Kleinberg (2000), STOC 2000. On an n × n lattice where each node also gets q long-range links drawn with probability proportional to d^(−r), short paths exist for r = 0, but no algorithm that sees only the links of nodes the message has visited finds them faster than about n^(2/3) steps in expectation. At r = 2 the greedy rule (pass to the contact nearest the target in lattice distance) delivers in O((log n)²) expected steps (proved for p = q = 1); for 0 ≤ r < 2 every such algorithm needs Ω(n^((2−r)/3)) and for r > 2 Ω(n^((r−2)/(r−1))). So efficient decentralized search depends on how the long-range links are distributed relative to the lattice, not on the links’ existence or on the graph’s diameter. The k-dimensional version (r = k) is stated without proof, and the model is a lattice with a known distance that every node can compute to the target. | Active — read in full 2026-10-15 (NOTE for LIT-1103) from the author’s own copy on Kleinberg’s Cornell page (www.cs.cornell.edu/home/kleinber/swn.pdf), a 14-page manuscript linked there under the STOC 2000 citation and footnoted as the version that is also Cornell CS Technical Report 99-1776; the ACM typeset proceedings (pp. 163–170) returned 403, and the Nature 2000 letter is a different work, not read. Worth reading as the source of the result that a network can have short paths that no searcher using local information can find: on an n × n lattice with long-range links drawn with probability proportional to d^(−r), greedy routing delivers in O((log n)²) expected steps at r = 2 (proved for one local and one long-range contact per node), every decentralized algorithm needs Ω(n^((2−r)/3)) steps for 0 ≤ r < 2 and Ω(n^((r−2)/(r−1))) for r > 2, and r = k in k dimensions is stated without proof. For CLAIM-310 it shows that findability, with nodes, lattice and link count fixed, turns on how the links are arranged relative to a distance every node can compute, which supports the claim’s “as arrangements” half; it narrows “only one distribution” to this family of inverse power laws and to polylogarithmic delivery, and it prices no cost of building the arrangement, so it adds nothing to QUESTION-114’s organizing cost. |
| LIT-1128 v2 | Nonequilibrium phase transition in the coevolution of networks and opinions | Holme & Newman (2006). Agents either rewire an edge to a random holder of their own opinion (probability φ) or adopt a neighbour’s opinion; the network always ends as disconnected one-opinion communities, and a continuous transition at a critical φ separates a regime with one giant community (low φ) from one with only small communities of mean size N/G (high φ), with non-percolation exponents and critical slowing down. | Active — read 2026-10-29 (NOTE-1385) in full, from arXiv’s own copy (v3); worth reading as perhaps the simplest model in which opinions and ties adapt to each other, rewiring to a like-minded agent with probability φ or copying a neighbour otherwise, which always freezes into like-minded components and has a continuous transition at φ_c ≈ 0.458 (k̄ = 4, γ = 10) between one giant community and only small ones, outside the percolation class. Read it knowing that it is simulation only (N ≤ 3200), that its opinions are unweighted labels with no influence or authority, that its dynamics is absorbing, and that the summary filed with it was wrong: no mixed groups form. |
| LIT-1130 v2 | Flow-based reputation with uncertainty: evidence-based subjective logic | Škorić, de Hoogh & Zannone (2016). Replaces subjective logic’s opinion discounting with an evidence-scaling discount that distributes over consensus, so reputation can be computed by a flow-based fixed point on arbitrary trust networks, loops included, without double-counting or discarding evidence, keeping referral and functional trust apart. | Active — read 2026-10-29 (NOTE-1354) in full, from arXiv’s own copy (v2); worth reading for the diagnosis that subjective logic’s discounting does not distribute over its evidence-adding consensus, which forces trust networks into canonical form and discards edges, and for the fix: discounting as scaling of evidence, x ⊡ y = g(x)·y, which distributes, so a PageRank-like fixed point handles loops without discarding information. Read it knowing that there is no ground truth and no attack model (self-promotion and Sybil attacks are left for future work), that convergence is observed and not proved, that g is left open, and that its loop example shows a referrer’s opinion can make a trust near-certain whatever the direct opinion says. |
| LIT-1134 v3 | Persuasion Bias, Social Influence, and Unidimensional Opinions | DeMarzo, Vayanos & Zwiebel (2003). Agents who average the reports of those they listen to with fixed weights, treating every round’s report as new (persuasion bias), reach a consensus weighted by the stationary distribution of the listening matrix, so influence depends on network position as well as precision; the consensus is correct only if the network is balanced, and rational agents who know the network reach the correct beliefs in at most N² rounds. Long-run differences of opinion line up along a single axis across all issues, set by the second eigenvectors. | Active — read 2026-10-29 (NOTE-1392) in full, from the LSE Research Online copy of the authors’ version of April 2003; worth reading as the paper that reads DeGroot averaging as a bias, failing to discount repeated information, and derives from it that consensus weights are the listening matrix’s stationary distribution, correct only in balanced networks, and that long-run disagreement lines up on one axis across all issues. Read it knowing that its listening weights are fixed and reports truthful, so it gives capture without fidelity but no hysteresis or feedback from outcome to authority, that its political and marketing applications are conjecture, and that only the proofs of Theorems 2 and 3 were followed. |
| LIT-1139 v2 | Adaptive coevolutionary networks: a review | Gross & Blasius (2008). Reviews networks whose topology and node states coevolve and names four recurrent outcomes: robust self-organization toward critical states from local rules, spontaneous division of labour into distinct node classes, complex topologies, and complex system-level dynamics such as bistability and oscillation; it conjectures one mechanism, dynamics making global topology locally visible. | Active — read 2026-10-29 (NOTE-1394) in full, from arXiv’s own copy (v2, after acceptance); worth reading as the review that named adaptive networks and their four recurrent outcomes: robust self-organization to criticality by local rules, spontaneous division of labour into node classes, complex topologies, and new system-level dynamics such as bistability and oscillation in an adaptive epidemic, with a first inventory of rules and outcomes. Read it knowing that its results are reported rather than checked, that its common mechanism is conjecture, that it has no model with authority or roles, and that its summary of Holme and Newman (LIT-1128) inverts the parameter φ and its account of Bornholdt and Rohlf reverses one sentence. |
| LIT-1146 v2 | Opinion Dynamics and the Evolution of Social Power in Influence Networks | Jia, MirTabatabaei, Friedkin & Bullo (2015). In the DeGroot–Friedkin model, DeGroot averaging on each issue with self-weights set by reflected appraisal across issues, self-weights converge from every non-autocratic start to one equilibrium ordered by the eigenvector centralities of the fixed relative interpersonal weights: power accumulates at the top, is autocratic exactly for a star network (whose centre has centrality 1/2) and democratic exactly for a doubly stochastic one, and members no path of influence reaches end with none. | Active — read 2026-10-24 (NOTE-1135) from the version of record posted on the last author’s site, proofs skimmed; worth reading as the exact analysis of reflected appraisal under DeGroot dynamics. With fixed relative interpersonal weights, self-weights converge from every non-autocratic start to one equilibrium ordered by eigenvector centrality; power accumulates above a threshold, is autocratic exactly for a star and democratic exactly for a doubly stochastic network, and members no path of influence reaches end with none. Theorems about a model; the authors say its validity and robustness are not yet established. |
| LIT-1213 v2 | Knowledge and common knowledge in a distributed environment | Halpern & Moses (1990; first at PODC 1984). With knowledge defined as truth at every point a processor cannot distinguish from the present one, a guaranteed simultaneous coordinated attack makes the attack common knowledge; over a channel that can lose any message nothing becomes common knowledge that would not with no messages delivered, so no correct protocol ever attacks, and not even eventual coordination can be guaranteed. Uncertain start and delivery times alone make common knowledge unattainable; ε-, eventual and timestamped common knowledge are attainable in many systems. | Active — read 2026-10-29 (NOTE-1381) in full, from the authors’ arXiv deposit of the JACM version; worth reading as the paper that makes “knowing” precise for processors in a system of runs and proves that guaranteed coordinated action needs common knowledge, that a channel which can lose any message cannot create it, and that any uncertainty in timing already rules it out, with weaker ε-, eventual and timestamped variants that are attainable. Read it knowing that the protocols are deterministic, that several results (the S5 properties, Theorems 11–12) are proved elsewhere or left to the reader, and that it credits the coordinated attack problem to Gray (1978) without citing Akkoyunlu et al. (1975). |
| LIT-1214 v3 | Some constraints and tradeoffs in the design of network communications | Akkoyunlu, Ekanadham & Huber (1975). A design paper on interprocess communication in networks of sequential processes. Complete status of a transaction is impossible in an arbitrary distributed facility and, with time-outs, even in a reliable one; an intermediate process can be made invisible only if the system withholds status it knows. Its appendix proves, as a story of gangsters and a messenger who may be mugged, that no finite exchange over a lossy channel brings two parties to know they agree the message got through: later called the coordinated attack or two generals problem. | Active — read 2026-10-29 (NOTE-1410) in full, from a scan of the SOSP ‘75 pages on the TU Wien Distributed Systems Group’s course page (https://dsg.tuwien.ac.at/linksites/teaching/courses/AdvancedDistributedSystems/download/1975_Akkoyunlu,%20Ekanadham,%20Huber_Some%20constraints%20and%20tradeoffs%20in%20the%20design%20of%20network%20communications.pdf); worth reading as the earliest statement the record holds, with a proof, that no finite exchange over a lossy channel brings two parties to know they agree a message got through: the coordinated attack problem in substance, three years before Gray (1978). Read it knowing that the result is a one-page appendix to a design paper on interprocess communication, told as gangsters and a messenger, that its goal is mutual knowledge of delivery rather than coordinated action, and that its fuller proof is deferred to an unpublished working paper. |
| LIT-1217 v2 | Practical Byzantine Fault Tolerance | Castro & Liskov (1999), OSDI ‘99, pp. 173–186. A state-machine replication protocol that keeps safety with at most f of 3f + 1 replicas Byzantine-faulty and no timing assumption, using weak synchrony only for liveness, with MACs in place of signatures in the normal case. A Byzantine-fault-tolerant NFS on four replicas ran the Andrew benchmark 3% slower than Digital Unix’s NFS, measured without faults and with view changes not yet implemented. | Active — read 2026-10-29 (NOTE-1356) in full, from the copy MIT’s 6.824 course hosts (pdos.csail.mit.edu), the proceedings text of pp. 173–186; worth reading as the paper that made Byzantine-fault-tolerant state-machine replication practical: safety with at most f of 3f + 1 replicas faulty and no timing assumption, liveness under weak synchrony, a faulty primary replaced by rotation rather than by voting anyone out. Read it knowing that correct behaviour is defined as following the protocol, so the service’s own specification is taken as given; that its fault bound needs independent failures the paper says must be engineered; and that its measurements are of the normal case on four replicas, with view changes not implemented in the measured library. |
| LIT-1282 | Random Hyperbolic Graphs: Degree Sequence and Clustering | Gugelmann, Panagiotou and Peter (2012), ICALP. The first rigorous results for the threshold (T = 0) hyperbolic random graph of Krioukov et al., at curvature −1 with radial density exponent α > 1/2 and disk radius R = 2 log n + C: the expected average local clustering coefficient is Θ(1) and concentrated, the fraction of vertices of degree k is given exactly up to 1 + o(1) for k up to a power of n and has a power-law tail with exponent 2α + 1 up to the maximum degree, the average degree is a constant, and the maximum degree is n^(1/(2α) + o(1)). | Active |
| LIT-1283 | Clustering and the hyperbolic geometry of complex networks | Candellero and Fountoulakis (2015), Internet Mathematics. For Krioukov et al.’s hyperbolic random graph with curvature −ζ², density exponent α and 0 < ζ/α < 2, in the soft model with connection probability 1/(exp(β(ζ/2)(d − R)) + 1): when β > 1 (temperature below 1) the global clustering coefficient (three times triangles over paths of length two) converges in probability to an explicit positive constant if ζ/α < 1 and to zero if 1 ≤ ζ/α < 2; when β ≤ 1 it converges to zero. Restricted to vertices of bounded type it stays positive for every ζ/α < 2 when β > 1. | Active |
| LIT-1318 v3 | When Is Society Susceptible to Manipulation? | Mostagir, Ozdaglar & Siderius (2022). In a social-learning model a principal manipulates agents’ beliefs by using the same forces that produce the wisdom of the crowd; characterizes the social norms and network structures susceptible to such manipulation, the conditions under which a network is impervious to it, and a new centrality measure. | Unfetched — filed 2026-10-21; on 2026-10-21 a lawful full text was sought and none was reached, so no NOTE is filed. Open copies exist, so this failed on access, not availability. The authors’ working paper is in the University of Michigan’s Deep Blue repository (handle 2027.42/154046, files reputation-v11Submit.pdf and manipulation-final.pdf, by web search), but every Deep Blue URL tried (handle page, item page, bitstream and REST API) returned a Cloudflare browser check to this client, and WebFetch got HTTP 403. A copy on James Siderius’s MIT LIDS site (siderius.lids.mit.edu/wp-content/uploads/sites/36/2021/09/manipulation.pdf, by web search) failed DNS resolution from this client, and Mohamed Mostagir’s Michigan page (public.websites.umich.edu/~mosta) returned 403; mostagir.engin.umich.edu was refused by the proxy. CORE holds Deep Blue’s copy (core.ac.uk/download/287611458.pdf), which returned 403 to curl and to WebFetch, and CORE’s API withholds the full text from public users. SSRN (doi:10.2139/ssrn.3474643, which Unpaywall lists as the only open location) returned 403. Unpaywall and OpenAlex list the Management Science article as closed, Semantic Scholar had no record of its DOI, and arXiv has no copy. A copy the owner supplies would let it be read. |
| LIT-1341 v2 | How to Beat Science and Influence People: Policymakers and Propaganda in Epistemic Networks | Weatherall, O’Connor & Bruner (2020; arXiv 2018). In network-epistemology models of scientists and policymakers, a propagandist who only selects and shares real, unbiased results that favour one side, without fabricating any, can lead policymakers to the false belief while the scientific community converges on the truth; so can one who runs honest studies and publishes only the favourable ones, best with the smallest studies; and a journalist who reports both sides equally slows policymakers’ learning. | Active — read 2026-10-21 (NOTE-1038) in full, from the authors’ arXiv manuscript (1801.01239v2); worth reading for its model of the tobacco strategy, in which selective sharing of genuine results and honest research published selectively mislead a Bayesian audience while the scientists converge on the truth (THEORY-855), for the conditions under which this works, and for the finding that ‘fair’ reporting slows the audience. Read it knowing that its policy makers update on forwarded results as if they were unselected, that every result is a simulation of a stylized bandit model averaged over runs in which the scientists reached the truth, and that why the smallest studies serve biased production best is a sufficient-statistic fact the paper does not state (THEORY-845). |
| LIT-1390 v2 | The Majority Illusion in Social Networks | Lerman, Yan and Wu (2015). Shows that in networks where well-connected nodes share an attribute, many or most nodes can see the attribute among a majority of their neighbours though it is rare overall, a local majority that is a global illusion. | Active — read in full 2026-10-22 (NOTE-1085) from the publisher’s PDF in PLOS ONE (CC BY 4.0); worth reading as the clean statement of a structural route to an apparent majority: when an attribute sits on well-connected nodes, most nodes can see it in a majority of their neighbours though few hold it, more so in disassortative and heavy-tailed networks, and a binomial model predicts how many. It shows what topology permits, not what happens: the attributes are assigned by the authors on every network, real ones included, and no person’s perception, belief or conduct is measured. Its mechanism is degree, not a loud minority, and it is not pluralistic ignorance, though it offers itself as an explanation of it. Filed as THEORY-887. |
| LIT-1401 v2 | Weaponized Interdependence: How Global Economic Networks Shape State Coercion | Farrell & Newman (2019). Global informational and financial networks grow asymmetrically, with a few highly connected hubs, many under US jurisdiction. States with jurisdiction over the hubs and suitable domestic institutions can weaponize interdependence in two ways: the “panopticon effect” (gathering strategic information) and the “chokepoint effect” (denying adversaries access). Case studies of SWIFT and the internet support the framework. | Unfetched — filed 2026-10-23, not read. A lawful free copy exists but this client could not fetch it, so no NOTE is filed. OpenAlex lists the article as hybrid open access at the publisher (doi:10.1162/isec_a_00351, MIT Press Direct, https://direct.mit.edu/isec/article/44/1/42/12237/Weaponized-Interdependence-How-Global-Economic); on 2026-10-29 the MIT Press site returned a Cloudflare 403 challenge to curl and to WebFetch, so the failure is on access, not availability. Project MUSE holds it behind a subscription. No author-posted copy was found. A browser fetch of the MIT Press copy is the cheapest way to read it. |
| LIT-1404 v2 | A Formal Theory of Reflected Appraisals in the Evolution of Power | Friedkin (2011/2012). A formal theory of how power evolves in a group’s influence network over a sequence of issues. Each issue is settled by the Friedkin–Johnsen process, with members anchored on their initial positions; by “reflected appraisal”, each member’s self-weight on the next issue is set to their share of total control over the last, with relative interpersonal weights fixed. In 50 four-person laboratory groups over five issues, prior control predicts the next self-weight. In simulations of 100,000 random networks, over 98% evolve to a single leader whose preferences control outcomes through intermediaries; the rest end with two. | Active — read 2026-10-29 (NOTE-1374) in full, from the eScholarship deposit of the OnlineFirst version of record; worth reading as the paper that formalizes reflected appraisal as an update of self-weights across issues in the Friedkin–Johnsen model, with a laboratory test of one step and a simulation in which over 98% of random groups evolve to a single leader who controls outcomes through intermediaries. Read it knowing that the end state is shown only in simulation; that the concentration depends on the Friedkin–Johnsen single-issue step, since the same rule under DeGroot consensus (LIT-1146) does not concentrate power on the same networks (re-run 2026-10-29); and that appraisals are assumed accurate. |
| LIT-1416 v2 | International Friends and Enemies | Kleinman, Liu & Redding (2024; NBER 2020). Asks whether countries that become more economically dependent on a trade partner realign politically toward it. Dependence is the elasticity of a country’s real income to the partner’s productivity, from a constant-elasticity trade model with sectors and input-output links; about 30 percent of pairs are “enemies”, with negative elasticity. Instrumented by a counterfactual Chinese productivity shock (119 countries, 1980–2010) and by the falling cost of air relative to sea transport (country pairs, 1970–2012), greater exposure raises UN voting similarity (0.094 SD per SD in the pair panel), lowers strategic rivalry except ideological rivalry, and raises formal alliances; bilateral trade does not proxy for it. | Active — read 2026-10-29 (NOTE-1403) in full, from NBER’s copy of the working paper as revised in March 2023; worth reading as a measure of economic dependence that is not bilateral trade, the general-equilibrium elasticity of one country’s real income to another’s productivity, and as a causal estimate, from two instruments, that it moves UN voting, strategic rivalry and alliances. Read it knowing that the effect in the pair panel is 0.094 SD per SD of exposure, that the China evidence is one cross-section of 119 countries, that the air-travel exclusion restriction is argued and not tested, that ideological rivalry does not respond, and that the paper’s own model of alignment is strategic. The journal version of 2024 was not seen. |
| LIT-1436 | Toward an integrative psychometric model of emotions | Lange, Dalege, Borsboom, van Kleef & Fischer (2020), Perspectives on Psychological Science 15(2):444–468. An integrative psychometric model of emotions must allow distinct emotions (affect-program theories), variation between and within persons (constructionist theories) and causal relations among components (appraisal theories). Reflective and formative latent-variable models do not; a psychometric network model, in which “the network constitutes the emotion”, does. Distinct emotions are weakly emergent small-world communities of components. Strongly connected networks sustain their own activation, which predicts hysteresis and longer emotions. | Active — read 2026-10-23 (NOTE-1098): in part, from the published version (CC BY-NC) deposited in the University of Amsterdam’s repository. Worth reading as the proposal that an emotion is a network of causally interacting components, the move Borsboom made for mental disorders (LIT-547) applied to emotion. Affect-program, constructionist and appraisal theories each demand one property: distinct emotions, variation between and within persons, and causal relations among components. Reflective and formative latent-variable models fail at least one. A network model meets all three, with a distinct emotion as a weakly emergent small-world community. Strong connectivity predicts self-sustaining activation and hysteresis, so longer emotions. The persistence it gives is a network state’s, not an ordering’s, and the model is unsigned. |
| LIT-1439 | Statistical ranking and combinatorial Hodge theory | Jiang, Lim, Yao & Ye (2011), Mathematical Programming 127:203–244. HodgeRank: an edge flow of aggregated pairwise comparisons splits orthogonally into a gradient flow, whose potential is the least-squares global ranking (a Borda count generalized to incomplete data), and a cyclic residual, which splits into curl (local) and harmonic (global) inconsistency (Theorems 4.8, 5.1). The residual’s share, the “cyclicity ratio”, certifies the ranking. | Active — read 2026-10-23 (NOTE-1099): in full, from arXiv 0811.1067v2 (42 pp.). HodgeRank. Pairwise comparisons, aggregated into a weighted edge flow on the graph of alternatives, decompose orthogonally into a gradient flow, the l2-best global ranking found by weighted least squares, and a divergence-free residual. The residual splits into curl (local, triangular inconsistency) and harmonic (global inconsistency) parts. Binary win/loss data enter as averaged signs, and on complete balanced binary data the ranking is Borda’s. The decomposition is cardinal: curl-freeness is stronger than transitivity. It is the tool for reading the record’s conflict record. |
| LIT-1442 | Flows and Decompositions of Games: Harmonic and Potential Games | Candogan, Menache, Ozdaglar & Parrilo (2011), Mathematics of Operations Research 36:474–503. The space of finite games is a direct sum P ⊕ H ⊕ N of potential, harmonic and nonstrategic subspaces (Theorem 4.1), pulled back from the Helmholtz decomposition of the game graph’s flow of unilateral payoff differences. Potential games are P ⊕ N (Theorem 5.1). Harmonic games, such as rock–paper–scissors, generically have no pure equilibrium, and the closest potential game is given in closed form under a weighted l2 norm (Theorem 6.2). | Active — read 2026-10-23 (NOTE-1116): in full, from arXiv 1005.2405v2 (45 pp.). Every finite game in strategic form splits uniquely into a potential, a harmonic and a nonstrategic component. The split pulls back the Helmholtz decomposition of the flow of unilateral payoff differences on the game graph. Potential games are exactly the games with no harmonic component. Harmonic games generically have no pure equilibrium. The nearest potential game, in a weighted l2 norm, is given in closed form. It is the paper behind the record’s measure of a potential’s share of a negotiation, and it shows that the share is cardinal. |
| LIT-1482 v2 | A Theory of the Evolution of Social Power: Natural Trajectories of Interpersonal Influence Systems along Issue Sequences | Friedkin, Jia & Bullo (2016). Extends the single-issue opinion dynamics of small deliberative groups to dynamics along a sequence of issues: elementary reflected-appraisal mechanisms modify the influence network and the flows of influence, and the theory predicts how influence centralities evolve from issue to issue. New experimental findings from groups discussing issue sequences show issue-sequence effects on influence-network structure consistent with the predictions. | Active — read in full 2026-10-24 (NOTE-1126) from the CC BY version of record and its online supplement; worth reading as the first experiment long enough (30 groups of four, 15 issues each) to look for social power evolving along an issue sequence. A member’s self-reported closure on the next issue rose with their prior influence, and influence networks thinned and discussions shortened, while the rate of consensus did not change. Its single-issue model is Friedkin–Johnsen, not DeGroot; closure and influence come from one self-report, and prior closure is not controlled. |
| LIT-1527 v3 | Reaching a Consensus | DeGroot (1974). Members of a group that must act together each hold a subjective probability distribution for an unknown parameter. A model describes how they might reach agreement on a common distribution by repeatedly pooling one another’s opinions; the process and the consensus it reaches are given explicitly. The model also applies when each opinion is a point estimate rather than a distribution (abstract). | Active — read 2026-10-25 (NOTE-1157) in full, from the copy the owner supplied on 2026-10-25, a JSTOR scan of the published article (the searches of the same day had found no lawful copy). Worth reading as the source of the DeGroot model: repeated averaging with fixed weights is a Markov chain on opinions, a consensus from every start is reached exactly when the chain has one closed class and it is aperiodic, and its weights are the stationary vector, zero for members outside that class (THEORY-960). Read it knowing that the theorems are cited from Markov-chain texts without proof, that the “if and only if” of §4 needs the quantifier “for every starting opinion”, that its Theorems 1 and 2 are the same condition, and that the weights are fixed and nothing tracks the truth. |
| LIT-1553 v2 | Mixed Membership Stochastic Blockmodels | Airoldi, Blei, Fienberg & Xing (2008), JMLR 9: 1981–2014. For pairwise measurements such as links between objects, where the usual exchangeability assumptions fail, mixed membership stochastic blockmodels combine global parameters for dense patches of connectivity (the blockmodel) with node-specific mixed memberships. A variational algorithm gives fast approximate inference, applied to social and protein-interaction networks. | Active — read 2026-10-26 (NOTE-1179) in full, from the typeset JMLR copy; worth reading for the mixed membership stochastic blockmodel, in which a node takes one block per interaction drawn from its own membership vector, for the variational EM that fits it, and as the relational baseline a model of members’ perspectives must beat. Read it knowing that its §5 claim that the blockmodel and the memberships do not compete is asserted and fails for the likelihood given memberships, that its sparsity parameter is confounded with the blockmodel’s scale and its printed estimator is the fraction of zeros (THEORY-993), that K is chosen by criterion, that it cannot generate hubs, and that its protein-function check is against a weak baseline (THEORY-1008, Proposed). |
| LIT-1646 v2 | Opinion Dynamics on Discourse Sheaves | Hansen & Ghrist (2020; SIAM J. Appl. Math. 2021). A discourse sheaf gives each agent a private opinion space and each edge a space of discussed topics, with a linear expression map from each agent into each edge, which may be selective, scaled or sign-reversed (“lie”). Sheaf-Laplacian diffusion converges to the projection onto the global sections: agreement in expression, not in held opinion, so stable polarized distributions exist. Stubbornness, control and observability reduce to relative cohomology. Letting the expression maps diffuse converges to the nearest sheaf of which the opinions are a section (“learning to lie”); joint diffusion is gradient descent on the discord, and a conserved quantity keeps the opinions from collapsing to zero when it starts indefinite. Bounded confidence and antagonism are nonlinear Laplacians. | Active — read in full 2026-10-27 (NOTE-1222), from the arXiv preprint; worth reading as the clearest formal case of agreement on what is expressed without identity of what is held, and of correspondence maps revised by interaction. Mathematics with toy examples, no data; its expression learning reaches coherence with nothing outside the loop to check it, which the authors call “learning to lie”. |
| LIT-1655 v2 | Angular synchronization by eigenvectors and semidefinite programming | Singer (2011). Estimates n angles, up to one common phase, from noisy measurements of their pairwise offsets when an unknown share are outliers uniform on the circle, by the top eigenvector of the Hermitian matrix of e^{iδᵢⱼ} or by a complex Goemans–Williamson SDP. A random-matrix argument puts the eigenvector’s threshold at a share p > 1/√n of good offsets on the complete graph, and simulations recover 400 angles with 85% outliers at correlation 0.97. Fano’s inequality shows no algorithm can succeed below a threshold of order √(n/m), and the eigenvector method is within a factor √((L − 1)/(2 log₂ L)) of it, where exhaustive maximum likelihood costs O(mLⁿ). Extensions to other compact groups, cryo-EM and clock synchronization are sketched. | Active — read in full 2026-10-27 (NOTE-1224), from arXiv v2; worth reading as the paper that posed angular synchronization with outliers and sketched its extension to other groups, and as a clean case that separates what pairwise evidence determines from what a cheap method can recover: an information bound that binds every algorithm, and a spectral relaxation whose threshold sits within an L-dependent factor of it. The spectral threshold is a careful heuristic confirmed by simulation, not a theorem. |
| LIT-1659 v2 | Toward a spectral theory of cellular sheaves | Hansen & Ghrist (2019), J. Appl. Comput. Topology 3. Defines the Hodge Laplacians of a cellular sheaf of inner-product spaces; by discrete Hodge theory the degree-k kernel is the cohomology H^k, in degree 0 the global sections, and the flow ẋ = −Δ^k x converges exponentially to the orthogonal projection onto it (Prop. 8.1). Lifts spectral graph theory’s basics with short proofs: harmonic extension, a bound k + 2 for normalized sheaves, interlacing, pushforward, covering and product spectra, effective resistance and spectral sparsification. The Laplacian does not determine the sheaf, Kron reduction fails in general because an interior vertex can impose a non-pairwise boundary constraint, and no Cheeger inequality is proved. Consensus, flocking, opinion dynamics, communication compression and synchronization are sketched as applications. | Active — read in full 2026-10-27 (NOTE-1233), from arXiv v2; worth reading as the standard introduction to sheaf Laplacians: the kernel is the global sections, the heat flow projects onto them, and a set of spectral graph theory’s basics lift with short proofs. Exploratory by its own account: no Cheeger inequality, and the applications are sketches. |
| LIT-1668 v2 | Cycle holonomy captures higher-order compatibility constraints in remote synchronization | Torres-Hugas et al. (2026), Communications Physics. 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; otherwise its smallest eigenvalue measures the residual incompatibility, largest on an isolated cycle 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 that 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 an exact two-group state; the branch has already lost transverse stability at αc ≃ 1.0164, so the holonomy marks geometry, not stability. | Active — read in full 2026-10-27 (NOTE-1218), from the arXiv preprint v2; worth reading for a clean statement of when edge-wise phase relations can be met around cycles, and for its own caution that the point of maximal cycle frustration is not where remote synchronization loses stability. The spectral criterion is standard mathematics; the synchronization result is one seven-node motif. |
| LIT-1674 v2 | Symmetry Groupoids and Patterns of Synchrony in Coupled Cell Networks | Stewart, Golubitsky & Pivato (2003), SIAM J. Appl. Dyn. Syst. 2(4). In a coupled cell network, a typed directed graph whose admissible dynamics give each cell an arbitrary smooth function of its input set, the same for cells with isomorphic inputs, a synchrony pattern is invariant under every admissible vector field iff its equivalence relation is balanced: equivalent cells receive the same number of inputs from each class along each arrow type (Theorem 6.5). Symmetry gives balance but is not needed, so robust synchrony occurs in networks with no symmetry and among cells with no arrows between them. The dynamics on a balanced subspace are admissible for a quotient network (Theorem 9.2), which can have symmetry the original lacks; not every quotient field lifts. The paper studies “existence, not stability”. | Active — read in full 2026-10-27 (NOTE-1217), from the accepted version in the Warwick repository; worth reading as the theorem behind robust synchrony in networks: an architecture forces a synchrony pattern for every admissible dynamics exactly when the pattern is balanced, which symmetry implies but does not exhaust, and the dynamics on it are a quotient network’s. It treats existence only, not stability. |
| LIT-1807 v2 | AvAtar: Learning to Align via Active Optimal Transport | Yu et al. (2026). Active learning for alignment by entropic optimal transport. The oracle answers one fixed question, which target matches a given source object, and an answer sets that pair’s cost to zero. AvAtar ranks source objects by the derivative of a proxy utility of the transport plan (its squared norm, entropy, or graph consistency) with respect to supervising each candidate match, averaged over matches by the current plan. The derivative is exact, from one singular positive semidefinite (n + m) linear system solved by conjugate gradients. With 20% of true pairs given and 20% more chosen in ten rounds, it beats uncertainty, centrality and matching-sampling rules on network alignment and image–text tasks by up to 2.8 MRR points, without reported variances; weighting by the current plan is essential. | Active — read in full 2026-10-29 (NOTE-1327), from the arXiv v2; worth reading as a precise case of budgeted question choice within a fixed vocabulary: which object’s correspondence to ask about, scored by an exact derivative through entropic transport of a coherence proxy, and evaluated on accuracy. |
| LIT-1811 v2 | Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs | Bodnar et al. (2022). In the time limit, diffusion with a sheaf Laplacian projects node features onto its harmonic space, and the class of restriction maps decides which labellings that space can linearly separate. Weighted graph Laplacians cannot separate the sides of a balanced bipartite graph; signed one-dimensional maps separate any two classes and no one-dimensional sheaf separates three; diagonal maps with d ≥ C stalks and orthogonal bundles with C ≤ 2d separate any number. Sheaf convolutions with non-symmetric maps can raise the Dirichlet energy that graph convolutions must lower. A model that learns the maps from node features at each layer is competitive on small heterophilic benchmarks. The separating sheaves are built from the labels, and the learned ones are inspected only on synthetic data. | Active — read in full 2026-10-29 (NOTE-1332) from arXiv v4; worth reading for the cleanest statement of what a sheaf’s restriction maps decide about diffusion: which labellings its harmonic space can separate, class by class of maps, with proofs. The separating sheaves are all built from the labels, and the orthogonal construction works at d = 8, which the paper denies. |
| LIT-1813 v2 | Optimal Transport for structured data with application on graphs | Vayer, Chapel, Flamary, Tavenard & Courty (2019). Fused Gromov–Wasserstein compares two attributed graphs with one coupling whose cost mixes, with weight α, a Wasserstein term on node features and a Gromov–Wasserstein term on structure. It tends to W as α → 0 and to GW as α → 1, and for q = 1, interior α and distance-matrix structures it is a metric that vanishes exactly when a bijection preserves weights, features and structure (a 2^{q−1}-relaxed semi-metric for q > 1). A conditional-gradient solver reaches stationary points, and a block coordinate barycenter supports graph k-means. On graph classification it is competitive with kernels and graph CNNs, though the supplement’s Wasserstein-only scores match or beat it on several datasets. | Active — read in full 2026-10-29 (NOTE-1328), from arXiv v3; worth reading for the metric and interpolation theorems of fused Gromov–Wasserstein, from which it follows that anchors as features break exactly the structural symmetries that move them. |
| LIT-1814 v2 | Hierarchical Multi-Marginal Optimal Transport for Network Alignment | Zeng et al. (2024). HOT aligns several networks with one multi-marginal fused Gromov–Wasserstein coupling tensor. A fused GW barycenter first co-clusters the networks, and nodes are then aligned jointly within aligned clusters, with a cost from random-walk-with-restart scores relative to anchor node sets and a KL proximal point solver. Under square loss the joint objective at a tensor is the sum of the pairwise objectives at its marginals, so it is never below the sum of pairwise optima. On three-network benchmarks with 10% anchors, HOT beats 13 baselines in pairwise and whole-tuple hits and scales far better than a dense tensor; the ground truth is consistent by construction, and no ablation isolates joint fitting from the new cost and the clustering. | Active — read in full 2026-10-29 (NOTE-1334), from the arXiv v2; worth reading for the identity behind joint alignment, that a multi-marginal objective is the sum of pairwise objectives at its marginals, so joint fitting buys consistency at a measurable price; its experiments do not test whether that consistency costs true local distinctions. |
| LIT-1820 | Attention as Lattice Gauge Theory: Relations Interact Only Through Wilson Loops | Sarkar, Mukherjee & Sato (2026), ARXIV-2610.37656. If every entity’s coordinate frame may be rotated independently, so that relation transports Tᵢⱼ ∈ O(d) change as gᵢTᵢⱼgⱼ⁻¹, then relations with no cycle between them cannot interact (in the pure-gauge sector), a triangle’s only invariants are class functions of its holonomy, and an equivariant edge update has the form Ψ(H)Tᵢⱼ with Ψ conjugation-equivariant. An untrained instance on S4 synchronization with outliers gains 26–45 points over a single path by composition, and 0.6–7.8 more by Wilson-loop routing; it does not beat spectral synchronization. | Active — read in full 2026-10-29 (NOTE-1331), after the owner brought it to the exchange “Paper assessment” asking whether it is “on to something or if this is AI slop nonsense”. Worth keeping for its conditional theorem, which is sound and is QUESTION-130’s construction carried further, and for its measured caution about its own experiments. Its framing outruns both. |
| LIT-1822 v2 | The Gromov–Wasserstein distance between networks and stable network invariants | Chowdhury & Mémoli (2019). Extends the Gromov–Wasserstein distance to measure networks: a Polish node set with a probability measure and any bounded, possibly asymmetric, edge-weight function. Proves it is a pseudometric whose zero set is weak isomorphism, so nodes with identical in- and out-weights can be merged or split freely. Gives in- and out-going versions of the first, second and third lower bounds and proves each equals a transport problem on the real line, so the third is computed in closed form. Adds sublevel size functions, stable in an interleaving sense, which raise the known lower bound between the circle and the 2-sphere to 0.17. Illustrates the third lower bound on simulated block-model networks and World Bank migration networks. | Active — read in full 2026-10-29 (NOTE-1330), from the arXiv v2; worth reading as the clean statement of what a Gromov–Wasserstein comparison of directed weighted networks can and cannot see: it is a pseudometric on any bounded weights, zero exactly at weak isomorphism, and its cheap invariants are lower bounds that can all vanish for networks apart. |
| LIT-1825 | Social Networks and Financial Markets | DeMarzo, Vayanos & Zwiebel (2001), working paper, MIT and Stanford. Described in their 2003 QJE paper (LIT-1134) as a model in which agents choose whom to listen to by the profits of trading on what they hear, and stable structures have everyone listening to the same experts, who need not be the best informed, so that influence can perpetuate itself apart from accuracy. Not read; that description is all the record has. | Unavailable — registered 2026-10-29, not read. A lawful full text was sought on 2026-10-29 and not reached. The paper is an unpublished working paper of 2001 (MIT and Stanford, as the QJE paper’s references give it); it has no DOI, and Crossref, OpenAlex and SSRN hold no record of it under this title. Vayanos’s research page at LSE (https://personal.lse.ac.uk/vayanos/research.html) lists “Financial Markets and Social Networks”, with DeMarzo and Zwiebel, among his working papers with no link and no file; the authors’ Stanford pages and RePEc list no copy. Web searches found only citations. It stays Unavailable until a copy is supplied. |
| LIT-1828 | Policing stabilizes construction of social niches in primates | Flack, Girvan, de Waal & Krakauer (2006), Nature 439: 426–429. By the abstract: in “knockout” experiments on a large captive group of pigtailed macaques, temporarily removing the few individuals who police conflicts left grooming, play, proximity and contact-sitting networks smaller, less diverse and less integrated (lower mean degree and reach, higher clustering and assortativity), so a rare policing function stabilizes the social networks members build. Not read. | Unavailable — filed 2026-10-29 from the triage of the day, not read. A lawful full text was sought on 2026-10-29 and not reached. The copy search engines still index, on Emory’s Living Links reprint pages (co-author de Waal’s centre), at https://www.emory.edu/LIVING_LINKS/publications/articles/Flack_etal_2006.pdf, now returns 404, as does the whole Living Links site. web.archive.org reset every connection on 2026-10-29, so whether a capture of that copy exists could not be checked; if one does, it is the quickest route. OpenAlex reports the Nature copy closed, Jessica Flack’s old SFI site is gone, and the Collective Computation Group’s publication list did not resolve for this client. No NOTE is filed. |
| LIT-1840 | Encoding Power in Communication Networks | Flack & Krakauer (2006), The American Naturalist 168: E87–E102. By the abstract: in a captive pigtailed macaque group, power is defined as the consensus among individuals about one’s capacity to use force, measured from the network of a unidirectional dominance signal; its distribution is fat-tailed and it predicts requests for support and the cost and intensity of interventions, and models show how signalling strategies keep the distribution robust to signalling errors. Not read. | Unavailable — filed 2026-10-29 from the triage of the day, not read. A lawful full text was sought on 2026-10-29 and not reached. OpenAlex reports it closed, with the University of Chicago Press DOI and PubMed as its only locations, and Semantic Scholar reports no open copy. The publisher’s page returned a 403 challenge. Searches found no copy on the authors’ pages: Jessica Flack’s old SFI site (sites.santafe.edu/~jflack/) says “This website is no longer available”, the Collective Computation Group’s publication list (c4.santafe.edu/c4pubs/) did not resolve for this client, David Krakauer’s current site lists recent papers only, and the Emory Living Links reprint directory that held the authors’ Nature paper of 2006 now returns 404. web.archive.org reset every connection, so no capture of any of these could be checked. It stays Unavailable until a copy is supplied. No NOTE is filed. |
| LIT-1842 v2 | Spontaneous structure formation in a network of chaotic units with variable connection strengths | Ito & Kaneko (PRL 2002; arXiv 2001). N = 100 logistic maps, each driven by a weighted mean of the others; each unit’s incoming weights are renormalized to sum to 1 after strengthening those from units in similar states. In the desynchronized phase with high weight turnover (a = 3.97, c = 0.12), identical units split into a core of about 14 to 16 that sends many strong connections, dense among themselves and to the periphery, and a periphery that sends almost none to the core (2 of about 1,344 possible). Membership stops changing after about 3 × 10⁶ steps. Freezing the effect of weights on states removes the structure. | Active — read 2026-10-29 (NOTE-1414) in full, from arXiv’s v1; worth reading as the minimal model in which identical units, each normalizing the weights it gives to the others and strengthening weights to units in similar states, split into a persistent core of about 14 to 16 units that is heavily attended by the rest and a periphery that the core ignores, while individual weights keep changing; an ablation shows the split needs the two-way coupling of states and weights. Read it knowing that it is a four-page letter of simulations at N = 100 with one parameter point studied in detail, that its classes are defined by a threshold on outgoing weight and an out-degree cut of 20, that nothing in it measures recovery, accuracy or perturbation of a class, and that its Table I fits a core of 16 though the text says typically 14. |