We investigate opinion dynamics as a stochastic process in social networks. We introduce the stubborn agent in order to determine the impact of network structure on the emergence of consensus. Depending on the fraction of undirected long-range connections, we observe fascinatingly rich dynamical behavior and transitions from disordered to ordered states. In general, we find that the stubborn agent promotes the emergence of consensus due to the so-called “group effect” that facilitates coalescence between separated network components. Agents are also behaviorally constrained Shannon information entropy in networks. However, since agents want to evolve their opinion with Brownian motion, which may in turn impede full consensus, sufficiently frequent long-range links are in such situations crucial for the network to converge into an absorbing phase. Our experimental findings indicate that, for a large range of control parameters, our model yields stable and fluctuating polarized states.

The recommendation system serves as a pivotal component of numerous online systems, playing a crucial role in enhancing user experience. Nevertheless, the majority of these models make the assumption that the user interaction history sequence is continuous, without taking into account the event intervals between user behaviors during modeling. The combination of Long Short Term Memory (LSTM) and Hawkes process incorporating the power law decay characteristics, enables the modeling of complex temporal dynamics in sequential data. To achieve this, we leverage the capabilities of a LSTM to automatically acquire a representation of the influences derived from the behavior history. Through this hybrid model, we are able to predict the next item a user is likely to interact with, taking into consideration the temporal dimension of user-item interactions. We evaluate our model on three real-world datasets, demonstrating significant improvements in recommendation performance compared to state-of-the-art baseline methods. Additionally, the inclusion of the power-law feature within the Hawkes process provides deeper insights into the underlying temporal patterns of user behavior, which can be leveraged for more refined and timely recommendations.

Urban welfare can deteriorate over a few weeks, yet most official indicators are only updated quarterly. This mismatch in time scales leaves city administrations effectively blind to the early stages of emerging crises, especially in areas where vulnerable residents generate few administrative or digital records. We cast urban socioeconomic monitoring as a systems problem: a six-dimensional welfare state on a spatial grid, observed through sparse delayed administrative data and noisy digital traces whose reliability declines with digital exclusion. On top of this latent state, we design a four-layer cyber–physical–social (CPSS) architecture centered on a stochastic state-space model with empirically guided couplings. This is supported by a semantic sensing layer where large language models (LLMs) convert daily geo-referenced public text into noisy welfare indicators. These signals are then fused with quarterly administrative records via an extended Kalman filter (EKF). Finally, a lightweight convex post-processing layer enforces fairness, differential privacy, and minimum representation as hard constraints. A key ingredient is a state-dependent noise model in which the LLM observation variance grows exponentially with digital exclusion. Under this model, we study finite-horizon observability and obtain an exclusion threshold beyond which several welfare dimensions become effectively unobservable over 30–60 day horizons; EKF error bounds scale with the same exponent, clarifying when semantic sensing is informative and when it is not. Finally, a 100,000-agent agent-based model of a synthetic city with daily shocks suggests that, relative to a quarterly-only baseline, the LLM-augmented fusion pipeline substantially reduces detection lags and multi-dimensional cascade failures while keeping estimation error bounded and satisfying the explicit fairness and privacy constraints.