A binary state on a graph means an assignment of binary values to its vertices. A time dependent sequence of binary states is referred to as binary dynamics. We describe a method for the classification of binary dynamics of digraphs, using particular choices of closed neighbourhoods. Our motivation and application comes from neuroscience, where a directed graph is an abstraction of neurons and their connections, and where the simplification of large amounts of data is key to any computation. We present a topological/graph theoretic method for extracting information out of binary dynamics on a graph, based on a selection of a relatively small number of vertices and their neighbourhoods. We consider existing and introduce new real-valued functions on closed neighbourhoods, comparing them by their ability to accurately classify different binary dynamics. We describe a classification algorithm that uses two parameters and sets up a machine learning pipeline. We demonstrate the effectiveness of the method on simulated activity on a digital reconstruction of cortical tissue of a rat, and on a non-biological random graph with similar density.
Animals regulate their diet in order to maximise the expression of fitness traits that often have different nutritional needs. These nutritional trade-offs have been experimentally uncovered using the Geometric framework for nutrition (GF). However, current analytical methods to measure such responses rely on either visual inspection or complex models applied to multidimensional performance landscapes, making these approaches subjective, or conceptually difficult, computationally expensive, and in some cases inaccurate. This limits our ability to understand how animal nutrition evolved to support life-histories within and between species. Here, we introduce a simple trigonometric model to measure nutritional trade-offs in multidimensional landscapes (‘Nutrigonometry’). Nutrigonometry is both conceptually and computationally easier than current approaches, as it harnesses the trigonometric relationships of right-angle triangles instead of vector calculations. Using landmark GF datasets, we first show how polynomial (Bayesian) regressions can be used for precise and accurate predictions of peaks and valleys in performance landscapes, irrespective of the underlying structure of the data (i.e., individual food intakes vs fixed diet ratios). Using trigonometric relationships, we then identified the known nutritional trade-off between lifespan and reproductive rate both in terms of nutrient balance and concentration. Nutrigonometry enables a fast, reliable and reproducible quantification of nutritional trade-offs in multidimensional performance landscapes, thereby broadening the potential for future developments in comparative research on the evolution of animal nutrition.
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