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In this paper, we study the flow of signals through linear paths with the nonlinear condition that a node emits a signal when it receives external stimuli or when two incoming signals from other nodes arrive coincidentally with a combined amplitude above a fixed threshold. Sets of such nodes form a polychrony group and can sometimes lead to cascades. In the context of this work, cascades are polychrony groups in which the number of nodes activated as a consequence of other nodes is greater than the number of externally activated nodes. The difference between these two numbers is the so-called profit. Given the initial conditions, we predict the conditions for a vertex to activate at a prescribed time and provide an algorithm to efficiently reconstruct a cascade. We develop a dictionary between polychrony groups and graph theory. We call the graph corresponding to a cascade a chinampa. This link leads to a topological classification of chinampas. We enumerate the chinampas of profits zero and one and the description of a family of chinampas isomorphic to a family of partially ordered sets, which implies that the enumeration problem of this family is equivalent to computing the Stanley-order polynomials of those partially ordered sets.

This research proposes a methodology with multi-objective optimization for the placement of Pumps operating As Turbines (PATs), energizing street lighting, devices for monitoring the water network, and charging stations for small electric vehicles such as bikes and scooters. This methodology helps to find the most profitable project for benefiting life quality and energy recovery through pumps operating as turbines, replacing virtual pressure reduction valves to locate the best point for decreasing pressure. PATs are selected by maximizing power recovery and minimizing pressure in the system as well as maximizing recoverable energy. Benefits analyzed include the reduction of carbon dioxide emissions and fuel use, as well as the saving of electricity consumption and benefiting socio-economic impact with street lighting, monitoring, and charging station. It was considered that each PAT proposed by the methodology will supply a street light pole, a station for monitoring the water network, and a charging station; under these established conditions, the return on investment is up to 1.07 at 12 years, with a power generation of 60 kWh per day.

We study the flow of signals through paths with the following condition: a node emits a signal if two incoming signals from other nodes arrive consecutively or if it receives an external stimuli. We apply our study to count and describe families of polychrony groups and we introduce triangular sequences.

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