Volterra Integral Equations (VIEs) arise in many problems of real life, as, for example, feedback control theory, population dynamics and fluid dynamics. A reliable numerical simulation of these phenomena requires a careful analysis of the long time behavior of the numerical solution. Here we develop a numerical stability theory for Direct Quadrature (DQ) methods which applies to a quite general and representative class of problems. We obtain stability results under some conditions on the stepsize and, in particular cases, unconditional stability for DQ methods of whatever order.

We prove that on a smooth bounded set, the positive least energy solution of the Lane-Emden equation with sublinear power is isolated. As a corollary, we obtain that the first (Formula presented.) eigenvalue of the Dirichlet-Laplacian is not an accumulation point of the (Formula presented.) spectrum, on a smooth bounded set. Our results extend to a suitable class of Lipschitz domains, as well.

Starting from recent experimental observations of starlings and jackdaws, we propose a minimal agent-based mathematical model for bird flocks based on a system of second-order delayed stochastic differential equations with discontinuous (both in space and time) right-hand side. The model is specifically designed to reproduce self-organized spontaneous sudden changes of direction, not caused by external stimuli like predator's attacks. The main novelty of the model is that every bird is a potential turn initiator, thus leadership is formed in a group of indistinguishable agents.

Trust and reputation systems are decision support tools used to drive parties' interactions on the basis of parties' reputation. In such systems, parties rate with each other after each interaction.

The popularity of the cloud computing paradigm is opening new opportunities for collaborative computing. In this paper we tackle a fundamental problem in open-ended cloud-based distributed computing platforms, i.e., the quest for potential collaborators. We assume that cloud participants are willing to share their computational resources for shared distributed computing problems, but they are not willing to disclose the details of their resources. Lacking such information, we advocate to rely on reputation scores obtained by evaluating the interactions among participants.

Parties of reputation systems rate each other and use ratings to compute reputation scores that drive their interactions. When deciding which reputation model to deploy in a network environment, it is important to find the most suitable model and to determine its right initial configuration. This calls for an engineering approach for describing, implementing and evaluating reputation systems while taking into account specific aspects of both the reputation systems and the networked environment where they will run.