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The prediction of future outcomes of a random phenomenon is typically based on a certain number of “analogous” observations from the past. When observations are generated by multiple samples, a natural notion of analogy is partial exchangeability and the problem of prediction can be effectively addressed in a Bayesian nonparametric setting. Instead of confining ourselves to the prediction of a single future experimental outcome, as in most treatments of the subject, we aim at predicting features of an unobserved additional sample of any size. We first provide a structural property of prediction rules induced by partially exchangeable arrays, without assuming any specific nonparametric prior. Then we focus on a general class of hierarchical random probability measures and devise a simulation algorithm to forecast the outcome of m future observations, for any m ≥ 1 . The theoretical result and the algorithm are illustrated by means of a real dataset, which also highlights the “borrowing strength” behavior across samples induced by the hierarchical specification. [ABSTRACT FROM AUTHOR]

The hierarchical self-assembly properties of a dimer-forming cyclic peptide that bears a nicotinic acid moiety to form molecular pom-pom-like structures are described. This dimeric assembly self organizes into spherical structures that can encapsulate small organic molecules owing to its porosity and it can also facilitate metal deposition on its surface directed by the pyridine moiety. [ABSTRACT FROM AUTHOR]

Lepidoptera play an important role in terrestrial ecosystems as pollinators, as components of the food chain and as indicators for healthy ecosystems due to their sensitivity to change. Heterogeneous landscapes with variability of topographical features, vegetation structure combined with food sources for all life stages are the basis for successful lepidopteran oviposition. A multiple-scale analysis is proposed to understand the hierarchical relationships between selected site to plant characteristics and oviposition preferences for the dingy skipper ( Erynnis tages). To achieve this goal, factors driving oviposition at the plant and patch scale were identified and scale dependencies at the site scale were assessed. At the plant scale, tallest host plants were used for oviposition; however relative egg height upon each plant was similar in both host plant species [bird's-foot trefoil ( Lotus corniculatus) and horseshoe vetch ( Hippocrepis comosa)]. The main factors preferred by E. tages in L. corniculatus patches were sward height and percent of bare ground, and in H. comosa host plant density patches. Selected patches had slopes of greater gradients (mostly facing south) than patches with no selected host plants. At the site scale, oviposition patches were clustered at small scales and oviposition sites were dispersed at larger scales. Our study suggests that oviposition selection in E. tages is a hierarchical process varying from the site to the plant scale. Our study provides empirical evidence useful to inform landscape management strategies. These can be expanded to assess larger scale vegetation and habitat suitability beyond individual sites for systematic conservation planning. [ABSTRACT FROM AUTHOR]

Abstract: There is a growing need for statistical methods that generate an ensemble of plausible realizations of a hierarchical process from a single run or experiment. The main challenge is how to construct such an ensemble in a manner that preserves the internal dynamics (e.g. intermittency) and temporal persistency. A popular hierarchical process often used as a case study in such problems is atmospheric turbulent flow. Analogies to turbulence are often called upon when information flow from large to small scales, non Gaussian statistics, and intermittency are inherent attributes of the hierarchical process under consideration. These attributes are key defining syndromes of the turbulent cascade thereby making turbulence time series ideal for testing such ensemble generation schemes. In this study, we propose a wavelet based resampling scheme (WB) and compare it to the traditional Fourier based phase randomization bootstrap (FB) approach within the context of the turbulence energy cascade. The comparison between the two resampling methods and observed ensemble statistics constructed by clustering similar meteorological conditions demonstrate that the WB reproduces several features related to intermittency of the ensemble series when compared to FB. In particular, the WB exhibited an increase in wavelet energy activity and an increase in the wavelet flatness factor with increasing frequency consistent with the cluster of ensemble statistics. On the other hand, the FB yielded no increase in such energy activity with scale and resulted in near Gaussian wavelet coefficients at all frequencies within the inertial subrange. The scaling behavior of the longitudinal () and vertical () velocity structure functions of various order confirms that WB preserves the small scale intermittency, whereas FB completely destroys it. The extension of WB to the multivariate case is also demonstrated via the conservation of co-spectra between and time series. Because the resampling strategy proposed here is conducted in the wavelet domain, gap-infected and uneven sampled time series can be readily accommodated within the WB. Finally, recommendations about the filter and block sizes are discussed. [Copyright &y& Elsevier]

Peptide self-assembly is fast evolving into a powerful method for the development of bio-inspired nanomaterials with great potential for many applications, but it remains challenging to control the self-assembling processes and nanostrucutres because of the intricate interplay of various non-covalent interactions. A group of 28-residue α-helical peptides is designed including NN, NK, and HH that display distinct hierarchical events. The key of the design lies in the incorporation of two asparagine (Asn) or histidine (His) residues at the a positions of the second and fourth heptads, which allow one sequence to pack into homodimers with sticky ends through specific interhelical Asn-Asn or metal complexation interactions, followed by their longitudinal association into ordered nanofibers. This is in contrast to classical self-assembling helical peptide systems consisting of two complementary peptides. The collaborative roles played by the four main non-covalent interactions, including hydrogen-bonding, hydrophobic interactions, electrostatic interactions, and metal ion coordination, are well demonstrated during the hierarchical self-assembling processes of these peptides. Different nanostructures, for example, long and short nanofibers, thin and thick fibers, uniform metal ion-entrapped nanofibers, and polydisperse globular stacks, can be prepared by harnessing these interactions at different levels of hierarchy., (© 2020 Wiley-VCH GmbH.)