Abstract. We consider (graph-)group-valued random element ξ, discuss the properties of a mean-set E(ξ), and prove the generalization of the strong law of large numbers for graphs and groups. Furthermore, we prove an analogue of the classical Chebyshev's inequality for ξ and Chernoff-like asymptotic bounds. In addition, we prove several results about configurations of mean-sets in graphs and discuss computational problems together with methods of computing mean-sets in practice and propose an algorithm for such computation.

In this paper we propose a new multi-strategy model for immersing students in STEM. Rooted in the current research and experiences, the new practices are being developed and implemented in a college-based hybrid STEM learning center that is geared to serve as a hub connecting high schools, higher education institutions, and industries bringing new and existing strategies together into one integral system with unique online features. The Hub model would serve as an educational research laboratory contributing to the knowledge base about STEM by investigating what strategies (or combination of what strategies) will best support student development for the STEM workforce. In addition, the model would illustrate the importance of interconnection between engineering education research and engineering education practice.

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We analyze the Sibert et al. group-based (Feige-Fiat-Shamir type) authentication protocol and show that the protocol is not computationally zero-knowledge. In addition, we provide experimental evidence that our approach is practical and can succeed even for groups with no efficiently computable length function such as braid groups. The novelty of this work is that we are not attacking the protocol by trying to solve an underlying complex algebraic problem, namely, the conjugacy search problem, but use a probabilistic approach, instead.