A spinlike model mimicking human behavior in groups is employed to investigate the dynamics of the decision-making process. Within the model, the temporal evolution of the state of systems is governed by a time-continuous Markov chain. The transition rates of the resulting master equation are defined in terms of the change of interaction energy between the neighboring agents (change of the level of conflict) and the change of a locally defined agent fitness. Three control parameters can be identified: (i) the social interaction strength βJ measured in units of social temperature, (ii) the level of confidence β^{'} that each individual has on his own expertise, and (iii) the level of knowledge p that identifies the expertise of each member. Based on these three parameters, the phase diagrams of the system show that a critical transition front exists where a sharp and concurrent change in fitness and consensus takes place. We show that at the critical front, the information leakage from the fitness landscape to the agents is maximized. This event triggers the emergence of the collective intelligence of the group, and in the end it leads to a dramatic improvement in the decision-making performance of the group. The effect of size M of the system is also investigated, showing that, depending on the value of the control parameters, increasing M may be either beneficial or detrimental.

A large number of optimization algorithms have been developed by researchers to solve a variety of complex problems in operations management area. We present a novel optimization algorithm belonging to the class of swarm intelligence optimization methods. The algorithm mimics the decision making process of human groups and exploits the dynamics of this process as an optimization tool for combinatorial problems. In order to achieve this aim, a continuous-time Markov process is proposed to describe the behavior of a population of socially interacting agents, modelling how humans in a group modify their opinions driven by self-interest and consensus seeking. As in the case of a collection of spins, the dynamics of such a system is characterized by a phase transition from low to high values of the overall consenus (magnetization). We recognize this phase transition as being associated with the emergence of a collective superior intelligence of the population. While this state being active, a cooling schedule is applied to make agents closer and closer to the optimal solution, while performing their random walk on the fitness landscape. A comparison with simulated annealing as well as with a multi-agent version of the simulated annealing is presented in terms of efficacy in finding good solution on a NK -Kauffman landscape. In all cases our method outperforms the others, particularly in presence of limited knowledge of the agent.

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We present a general theory of infection spreading, which directly follows from conservation laws and takes as inputs the probability density functions of latent times. The derivation of the theory substantially differs from Kermack and McKendrick (1927) argument, which instead was based on the concept of removal rates. We demonstrate the formal equivalence of the two approaches, but our theory provides a clear interpretation of the kernels of the integro-differential governing the infection spreading in terms of survival function of the latent times distributions. This aspect was never captured before. Real distributions of latent times can be, then, employed, thus overcoming the limitations of standard SIR, SEIR and other similar models, which implicitly make use of exponential or exponential-related distributions. SIR and SEIR-type models are, in fact, a subclass of the theory here presented. We show that beside the infection rate ν, the joint probability density function p_{EI}(τ,τ₁) of latent times in the exposed and infectious compartments governs the infection spreading. Assuming that the number of infected individuals is negligibile compare to the entire population, we were able to study the stability of the dynamical system and provide the general solution of equations in terms characteristic functions of the probability distribution of latent times. We present asymptotic solutions for the case R₀=1 and demostrate that the moments of the latent times distribution govern the rate of disease spreading in this case. The present theory is employed to simulate the diffusion of COVID-19 infection in Italy during the first 120 days. The estimated value of the basic reproduction number is R₀≈3.5, in very good agreement with existing data.