Three-state majority-vote model on small-world networks

In this work, we study the opinion dynamics of the three-state majority-vote model on small-world networks of social interactions. In the majority-vote dynamics, an individual adopts the opinion of the majority of its neighbors with probability 1-q, and a different opinion with chance q, where q stands for the noise parameter. The noise q acts as a social temperature, inducing dissent among individual opinions. With probability p, we rewire the connections of the two-dimensional square lattice network, allowing long-range interactions in the society, thus yielding the small-world property present in many different real-world systems. We investigate the degree distribution, average clustering coefficient and average shortest path length to characterize the topology of the rewired networks of social interactions. By employing Monte Carlo simulations, we investigate the second-order phase transition of the three-state majority-vote dynamics, and obtain the critical noise $$q_c$$ q c , as well as the standard critical exponents $$\beta /\nu$$ β / ν , $$\gamma /\nu$$ γ / ν , and $$1/\nu$$ 1 / ν for several values of the rewiring probability p. We conclude that the rewiring of the lattice enhances the social order in the system and drives the model to different universality classes from that of the three-state majority-vote model in two-dimensional square lattices.

Estimating Smart Wi-Fi Thermostat-Enabled Thermal Comfort Control Savings for Any Residence

Nowadays, most indoor cooling control strategies are based solely on the dry-bulb temperature, which is not close to a guarantee of thermal comfort of occupants. Prior research has shown cooling energy savings from use of a thermal comfort control methodology ranging from 10 to 85%. The present research advances prior research to enable thermal comfort control in residential buildings using a smart Wi-Fi thermostat. “Fanger’s Predicted Mean Vote model” is used to define thermal comfort. A machine learning model leveraging historical smart Wi-Fi thermostat data and outdoor temperature is trained to predict indoor temperature. A Long Short-Term-Memory neural network algorithm is employed for this purpose. The model considers solar heat input estimations to a residence as input features. The results show that this approach yields a substantially improved ability to accurately model and predict indoor temperature. Secondly, it enables a more accurate estimation of potential savings from thermal comfort control. Cooling energy savings ranging from 33 to 47% are estimated based upon real data for variable energy effectiveness and solar exposed residences.

Three-State Majority-Vote Model on Small-World Networks

In this work, we study the opinion dynamics of the three-state majority-vote model on small-world networks of social interactions. In the majority-vote dynamics, an individual adopts the opinion of the majority of its neighbors with probability 1−q, and a different opinion with chance q, where q stands for the noise parameter. The noise q acts as a social temperature, inducing the dissensus among individual opinions. With probability p, we rewire the connections of the two-dimensional square lattice network, allowing long-range interactions in the society, thus yielding the small-world property present in many different real-world systems. We employ Monte Carlo simulations to investigate the second-order phase transition of the system, and obtain the critical noise qc, as well as the standard critical exponents β/ν, γ/ν, and 1/ν for several values of the rewiring probability p. We conclude that the rewiring of the lattice enhances the social order in the system and drives the model to different universality classes from that of the three-state majority-vote model in two-dimensional square lattices.

Ferromagnetic and spin-glass-like transition in the majority vote model on complete and random graphs

Ferromagnetic and spin-glass-like transitions in nonequilibrium spin models in contact with two thermal baths with different temperatures are investigated. The models comprise the Sherrington-Kirkpatrick model and the dilute spin glass model which are the Ising models on complete and random graphs, respectively, with edges corresponding, with certain probability, to positive and negative exchange integrals. The spin flip rates are combinations of two Glauber rates at the two temperatures, and by varying the coefficients of this combination probabilities of contact of the model with each thermal bath and thus the level of thermal noise in the model are changed. Particular attention is devoted to the majority vote model in which one of the two above-mentioned temperatures is zero and the other one tends to infinity. Only in rare cases such nonequilibrium models can be mapped onto equilibrium ones at certain effective temperature. Nevertheless, Monte Carlo simulations show that transitions from the paramagnetic to the ferromagnetic and spin-glass-like phases occur in all cases under study as the level of thermal noise is varied, and the phase diagrams resemble qualitatively those for the corresponding equilibrium models obtained with varying temperature. Theoretical investigation of the model on complete and random graphs is performed using the TAP equations as well as mean-field and pair approximations, respectively. In all cases theoretical calculations yield reasonably correct predictions concerning location of the phase border between the paramagnetic and ferromagnetic phases. In the case of the spin-glass-like transition only qualitative agreement between theoretical and numerical results is achieved using the TAP equations, and the mean-field and pair approximations are not suitable for the study of this transition. The obtained results can be interesting for modeling opinion formation by means of the majority-vote and related models and suggest that in the presence of negative interactions between agents, apart from the ferromagnetic phase corresponding to consensus formation, spin-glass-like phase can occur in the society characterized by local rather than long-range ordering. Graphical abstract