In this paper we consider an intrinsic approach for the direct computation of the fluxes for problems in potential theory. We develop a general method for the derivation of intrinsic conforming and non-conforming finite element spaces and appropriate lifting operators for the evaluation of the right-hand side from abstract theoretical principles related to the second Strang Lemma. The convergence of this intrinsic finite element method is proved.2000 Mathematics Subject Classification: 65N30
Many species used in behavioral studies are small vertebrates with high metabolic rates and potentially enhanced temporal resolution of perception. Nevertheless, the selection of an appropriate scales to evaluate behavioral dynamics has received little attention. Herein, we studied the temporal organization of behaviors at fine-grain (i.e. sampling interval ≤1s) to gain insight into dynamics and to rethink how behavioral events are defined. We statistically explored high-resolution Japanese quail (Coturnix japonica) datasets encompassing 17 defined behaviors. We show that for the majority of these behaviors, events last predominately <300ms and can be shorter than 70ms. Insufficient sampling resolution, even in the order of 1s, of behaviors that involve spatial displacement (e.g. walking) yields distorted probability distributions of event durations and overestimation of event durations. Contrarily, behaviors without spatial displacement (e.g. vigilance) maintain non-Gaussian, power-law-type distributions indicative of long-term memory, independently of the sampling resolution evaluated. Since data probability distributions reflect underlying biological processes, our results highlight the importance of quantification of behavioral dynamics based on the temporal scale pertinent to the species, and data distribution. We propose a hierarchical model that links diverse types of behavioral definitions and distributions, and paves the way towards a statistical framework for defining behaviors.
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