Abstract In this work, we introduce a class of dynamic models for time series taking values on the unit interval. The proposed model follows a generalized linear model approach where the random component, conditioned on the past information, follows a beta distribution, while the conditional mean specification may include covariates and also an extra additive term given by the iteration of a map that can present chaotic behavior. The resulting model is very flexible and its systematic component can accommodate short- and long-range dependence, periodic behavior, laminar phases, etc. We derive easily verifiable conditions for the stationarity of the proposed model, as well as conditions for the law of large numbers and a Birkhoff-type theorem to hold. A Monte Carlo simulation study is performed to assess the finite sample behavior of the partial maximum likelihood approach for parameter estimation in the proposed model. Finally, an application to the proportion of stored hydroelectrical energy in Southern Brazil is presented.

Author summary Allostery in proteins is the property of highly specific responses to ligand binding at a distant site. To inform protocols of de novo drug design, it is fundamental to understand the impact of mutations on allosteric regulation and whether it can be predicted from evolutionary correlations. In this work we consider allosteric architectures artificially evolved to optimize the cooperativity of binding at allosteric and active site. We first characterize the emergent pattern of epistasis as well as the underlying mechanical phenomena, finding the four types of epistasis (Synergistic, Sign, Antagonistic, Saturation), which can be both short or long-range. The numerical evolution of these allosteric architectures allows us to benchmark Direct Coupling Analysis, a method which relies on co-evolution in sequence data to infer direct evolutionary couplings, in connection to allostery. We show that Direct Coupling Analysis predicts quantitatively point mutation costs but underestimates strong long-range epistasis. We provide an argument, based on a simplified model, illustrating the reasons for this discrepancy. Our analysis suggests neural networks as more promising tool to measure epistasis.

In the field of Statistical Process Control (SPC) there are several different approaches to deal with monitoring of batch processes. Such processes present a three-way data structure (batches × variables × time-instants), so that for each batch a multivariate time series is available. Traditional approaches do not take into account the time series nature of the data. They deal with this kind of data by applying multivariate techniques in a reduced two-way data structure, in order to capture variables dynamics in some way. Recent developments in SPC have proposed the use of the Vector Autoregressive (VAR) time series model considering the original three-way structure. However, they are restricted to control approaches focused on VAR residuals. This paper proposes a new approach to deal with batch processes using the VAR model, but focusing on coefficients instead of residuals. Through a simulated batch process, we illustrate the better performance of our approach over the residual-based control charts in both offline and online context.

In the marine realm, the interpretation of taphofacies relies heavily on how oceanographic and sedimentary conditions affect the preservation state of fossils. Several taphonomic variables either covary with depth or are directly influenced by depth. Facies-level factors rather than broad, basin-scale parameters influence the taphonomic profile of mollusc death assemblages according to actualistic and experimental evidence. To determine the possible relation between depth and the taphonomic conditions of multiple species of bivalve remains, we used seven samples gathered over a comprehensive bathymetric gradient (from 7 to 150 m below mean sea level; topmost 10- to 20-cm layer, roughly corresponding to the taphonomically active zone). We selected samples from predominantly muddy facies on the southern Brazilian shelf (SBS). The taphonomic damage profile (TDP) was measured using site samples based on a standard taphonomic analysis (categorical scoring system) of shells and fragments larger than 4 mm, to identify site damage patterns. Restricting the sedimentary grain size (samples from fine sediments) enabled the determination of the variation in damage with depth among the samples. Constrained analysis of proximities (CAP) revealed that up to 46% of the taphonomic variation observed was related to variation in depth (with approximately 28% unexplained by environmental factors). Part of the unexplained fraction was due to the effect of temporal mixing, which is predictable along large-scale patches but is inversely linked to the TDP. Our results show that taphonomic analysis, considering large spatial scales in recent environments, can explain the variations present in shell beds that formed during distinct time periods of the evolution of a Quaternary sedimentary basin. © 2018 Lethaia Foundation. Published by John Wiley & Sons Ltd