In this paper, we give a constructive proof that a real, piecewise continuous function can be almost uniformly approximated by single hidden-layer feedforward neural networks (SLFNNs). The construction procedure avoids the Gibbs phenomenon. Computer experiments show that the resulting approximant is much more accurate than SLFNNs trained by gradient descent.
This article discusses a theoretical construction based on the graph theory to rework the space of potential partitions in envy-free distribution. This work has the objective of applying Sperner’s lemma to the distribution of three rotating shifts for three workers who are to cover a 24 h job position in a company. As a novel feature, worker’s preferences have been modeled as functions of probability for the three shifts, according to salary offers for said shifts. Envy-free allocation was achieved, since each worker received their preferred shift without the need for negotiation between agents in conflict. Adaptation to the type of dynamic situations that arise with rotating shifts, as well as the consideration of probabilistic preferences by workers are some of the main novelties of this work.
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