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Numerous physiological processes are cyclical, but sampling these processes densely enough to perform frequency decomposition and subsequent analyses can be challenging. Mathematical approaches for decomposition and reconstruction of sparsely and irregularly sampled signals are well established but have been under-utilized in physiological applications. We developed a basis pursuit denoising with polynomial detrending (BPWP) model that recovers oscillations and trends from sparse and irregularly sampled timeseries. We validated this model on a unique dataset of long-term inter-ictal epileptiform discharge (IED) rates from human hippocampus recorded with a novel investigational device with continuous local field potential sensing. IED rates have well established circadian and multiday cycles related to sleep, wakefulness, and seizure clusters. Given sparse and irregular samples of IED rates from multi-month intracranial EEG recordings from ambulatory humans, we used BPWP to compute narrowband spectral power and polynomial trend coefficients and identify IED rate cycles in three subjects. In select cases, we propose that random and irregular sampling may be leveraged for frequency decomposition of physiological signals. Trial Registration: NCT03946618.

The heterotrophic flagellate Percolomonas cosmopolitus (Heterolobosea) is often observed in saline habitats worldwide, from coastal waters to saturated brines. However, only two cultures assigned to this morphospecies have been examined using molecular methods, and their 18S rRNA gene sequences are extremely different. Further the salinity tolerances of individual strains are unknown. Thus, our knowledge on the autecology and diversity in this morphospecies is deficient. Here, we report 18S rRNA gene data on seven strains similar to P. cosmopolitus from seven geographically remote locations (New Zealand, Kenya, Korea, Poland, Russia, Spain, and the USA) with sample salinities ranging from 4‰ to 280‰, and compare morphology and salinity tolerance of the nine available strains. Percolomonas cosmopolitus-like strains show few-to-no consistent morphological differences, and form six clades separated by often extremely large 18S rRNA gene divergences (up to 42.4%). Some strains grow best at salinities from 75 to 125‰ and represent halophiles. All but one of these belong to two geographically heterogeneous clusters that form a robust monophyletic group in phylogenetic trees; this likely represents an ecologically specialized subclade of halophiles. Our results suggest that P. cosmopolitus is a cluster of several cryptic species (at least), which are unlikely to be distinguished by geography. Interestingly, the 9 Percolomonas strains formed a clade in 18S rRNA gene phylogenies, unlike most previous analyses based on two sequences.