arXiv subjects

Ruben E. Araújo

Publications and source records attributed to Ruben E. Araújo.

3 recordsLinked to original sources

arXiv2026

Response-Aware Coarse-Graining in Summary-Mediated Opinion Dynamics

Interacting populations increasingly respond to compressed representations generated from their own collective state. We ask which information such an endogenous coarse-graining must preserve in order to reproduce the collective dynamics. The question has two complementary answers for continuous opinions with attraction, indifference, and repulsion. Inside any strict $K$-bloc response cell where every represented stance attracts every bloc, the dynamics reduce exactly to translation and disagreement. The represented distribution's shape cancels from all disagreement modes, which form a homogeneously anchored weighted signed-Laplacian system, while represented-mean error acts only on translation. This reduction yields a geometry-dependent stability boundary and shows that prevalence bias produces secular drift at marginal stability only through its projection onto the neutral eigenspace. Outside that common linear-response regime, threshold geometry makes distributional information observable. The induced force discrepancy is a behavior-defined integral probability metric; restricted force probes identify generic finite empirical discussions, and for finitely supported candidates uniform force error controls total-variation and Wasserstein error while support reduction incurs a nonzero distortion floor. A cumulative-discrepancy characterization further explains why transport-small summaries can remain behaviorally inaccurate at response thresholds. Mode-resolved integrations, projected particle simulations, finite-size ensembles, and threshold-crossing experiments test these two regimes. As a deployment consequence, broadcast summary error survives as collective noise whereas independently personalized error self-averages. The model is stylized and not empirically calibrated; generated discussion summaries motivate the general problem of endogenous, response-aware coarse-graining.

physics.soc-ph↗

arXiv2026

Radicalization Kinetics under Algorithmic Exposure in a Stochastic Multiplex Model of Opinion Dynamics

We study how physical mobility, algorithmic exposure, and repulsive social influence interact in a stochastic multiplex model of opinion dynamics. Agents diffuse in physical space while a directed digital network rewires under a conserved attention budget, so digital exposure displaces rather than supplements local interaction. With purely assimilative bounded-confidence influence, opinion-blind long-range exposure reduces locality-induced fragmentation whereas homophilic recommendation preserves echo chambers. When a contested repulsive response to sufficiently distant opinions is activated, this ordering reverses at the reference parameters: a neutral platform reaches the maximal polarization permitted by the bounded opinion space, controversy-seeking curation drives faster initial separation but slows sharply near the boundary, and homophilic curation delays radicalization by suppressing cross-bloc exposure. In a late-stage symmetric two-bloc reduction, any curation kernel maps to a state-dependent cross-bloc exposure profile $p(y)$ and an exact quadrature for the radicalization time. Pointwise-ordered profiles inherit a global kinetic ordering; crossing profiles yield target- and horizon-dependent rankings. For similarity-driven curation the quadrature has a closed form involving the exponential integral. Simulations, finite-size scans to $N=1600$, structural controls, and a well-mixed particle comparison support the mechanism. Heavy-tailed influence strengths are not required for the inversion; in the well-mixed heavy-tail regime they additionally produce a non-self-averaging stable-weighted asymptotic description. Finally, opinion-independent Brownian mobility produces no detectable geographic opinion structure in the explored regime, whereas opinion-dependent drift produces spatial domains through a Péclet-controlled crossover near $χ\ell/D \sim 1$.

physics.soc-ph↗

arXiv2024

Space-time-symmetric extension of quantum mechanics: Interpretation and arrival-time predictions

An alternative quantization rule, in which time becomes a self-adjoint operator and position is a parameter, was proposed by Dias and Parisio [Phys. Rev. A {\bf 95}, 032133 (2017)]. In this approach, the authors derive a space-time-symmetric (STS) extension of quantum mechanics (QM) where a new quantum state (intrinsic to the particle), $|ϕ(x)\rangle$, is defined at each point in space. $|ϕ(x)\rangle$ obeys a space-conditional (SC) Schrödinger equation and its projection on $|t\rangle$, $\langle t|ϕ(x)\rangle$, represents the probability amplitude of the particle's arrival time at $x$. In this work, first we provide an interpretation of the SC Schrödinger equation and the eigenstates of observables in the STS extension. Analogous to the usual QM, we propose that by knowing the "initial" state $|ϕ(x_0)\rangle$ -- which predicts any measurement on the particle performed by a detector localized at $x_0$ -- the SC Schrödinger equation provides $|ϕ(x)\rangle={\hat U}(x,x_0)|ϕ(x_0)\rangle$, enabling us to predict measurements when the detector is at $x \lessgtr x_0$. We also verify that for space-dependent potentials, momentum eigenstates in the STS extension, $|P_b(x)\rangle$, depend on position just as energy eigenstates in the usual QM depend on time for time-dependent potentials. In this context, whereas a particle in the momentum eigenstate in the standard QM, $|ψ(t)\rangle=|P\rangle|_t$, at time $t$, has momentum $P$ (and indefinite position), the same particle in the state $|ϕ(x)\rangle=|P_b(x)\rangle$ arrives at position $x$ with momentum $P_b(x)$ (and indefinite arrival time). By investigating the fact that $|ψ(t)\rangle$ and $|ϕ(x)\rangle$ describe experimental data of the same observables collected at $t$ and $x$, respectively, we conclude that they provide complementary information about the same particle...

quant-ph↗