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Title: Order-restricted inference in chronobiology Authors:  Yolanda Larriba - University of Valladolid (Spain) [presenting]
Cristina Rueda - University of Valladolid (Spain)
Miguel Fernandez - Universidad de Valladolid (Spain)
Abstract: Biological processes, such as cell cycle, circadian clock or blood pressure, are governed by oscillatory systems consisting of numerous components that exhibit periodic patterns over time. Modelling these rhythms is a challenge in literature since usually the sampling density and the number of periods are low, and the underlying signals adopt a wide range of temporal patterns. Several authors proposed parametric functions of time, such as the sinusoidal function, to model these signals. However, these parametric functions might be too rigid for data derived from cell-cycle or circadian clock. These signals usually have a unique peak at time point U and a unique trough at time point $L$ within each period, so that they monotonically increase up to $U$ (when $L > U$) and then decrease up to $L$; before increasing again. The shape of these signals can be entirely described in the Euclidean space by mathematical inequalities among their components. The main novelty is the definition of circular signals using restrictions to model common signal shapes in biology. We will give a definition that allows us to state equivalent signal formulations both in the euclidean and in the circular spaces. Additionally, a general methodology is proposed to analyse rhythmicity including an efficient algorithm to compute the restricted maximum likelihood estimate, rhythmicity tests or an approach to estimate sampling order. Results are given for simulations and real data bases.