Fitting Linear Mixed-Effects Models using lme4

Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.Comment: 51 pages, including R code, and an appendi

Causal Inference Using Graphical Models with the R Package pcalg

The pcalg package for R can be used for the following two purposes: Causal structure learning and estimation of causal effects from observational data. In this document, we give a brief overview of the methodology, and demonstrate the package’s functionality in both toy examples and applications

Baseline oxygen consumption decreases with cortical depth

The cerebral cortex is organized in cortical layers that differ in their cellular density, composition, and wiring. Cortical laminar architecture is also readily revealed by staining for cytochrome oxidase—the last enzyme in the respiratory electron transport chain located in the inner mitochondrial membrane. It has been hypothesized that a high-density band of cytochrome oxidase in cortical layer IV reflects higher oxygen consumption under baseline (unstimulated) conditions. Here, we tested the above hypothesis using direct measurements of the partial pressure of O2 (pO2) in cortical tissue by means of 2-photon phosphorescence lifetime microscopy (2PLM). We revisited our previously developed method for extraction of the cerebral metabolic rate of O2 (CMRO2) based on 2-photon pO2 measurements around diving arterioles and applied this method to estimate baseline CMRO2 in awake mice across cortical layers. To our surprise, our results revealed a decrease in baseline CMRO2 from layer I to layer IV. This decrease of CMRO2 with cortical depth was paralleled by an increase in tissue oxygenation. Higher baseline oxygenation and cytochrome density in layer IV may serve as an O2 reserve during surges of neuronal activity or certain metabolically active brain states rather than reflecting baseline energy needs. Our study provides to our knowledge the first quantification of microscopically resolved CMRO2 across cortical layers as a step towards better understanding of brain energy metabolism.publishedVersio

Sodium signaling and astrocyte energy metabolism.

The Na(+) gradient across the plasma membrane is constantly exploited by astrocytes as a secondary energy source to regulate the intracellular and extracellular milieu, and discard waste products. One of the most prominent roles of astrocytes in the brain is the Na(+) -dependent clearance of glutamate released by neurons during synaptic transmission. The intracellular Na(+) load collectively generated by these processes converges at the Na,K-ATPase pump, responsible for Na(+) extrusion from the cell, which is achieved at the expense of cellular ATP. These processes represent pivotal mechanisms enabling astrocytes to increase the local availability of metabolic substrates in response to neuronal activity. This review presents basic principles linking the intracellular handling of Na(+) following activity-related transmembrane fluxes in astrocytes and the energy metabolic pathways involved. We propose a role of Na(+) as an energy currency and as a mediator of metabolic signals in the context of neuron-glia interactions. We further discuss the possible impact of the astrocytic syncytium for the distribution and coordination of the metabolic response, and the compartmentation of these processes in cellular microdomains and subcellular organelles. Finally, we illustrate future avenues of investigation into signaling mechanisms aimed at bridging the gap between Na(+) and the metabolic machinery. GLIA 2016;64:1667-1676

Chapter Ten - Informing marine spatial planning decisions with environmental DNA

Marine management areas provide a key tool for efforts towards sustainable development, reconciling socio-economic goals with those for biodiversity conservation. Decisions about where and when to establish spatial management areas in the oceans are currently hampered by the uncertainties of incomplete, or overly general, information about biodiversity. The analysis of environmental DNA (eDNA) provides a potentially powerful tool to overcome this lack of data in the future. Here we present directions to develop robust approaches to integrate eDNA and spatial planning processes, aiming to provide guidance to underpin tool development. The potential of eDNA use in conservation is widely recognised, although direct applications almost exclusively focus on detection of invasive or threatened species and not spatial management decisions. The implementation of broader interaction between the fields of conservation science and eDNA analysis could create substantial benefits to biodiversity conservation and management. In particular, eDNA analysis can provide information on biodiversity over spatial-temporal scales that are currently prohibitive in spatial planning studies. Here, we provide an overview of how eDNA is currently used in conservation practice, in addition to understanding its limitations and benefits within the context of spatial planning. With the goal to harness rapid technological developments in both molecular and conservation sciences, we provide a horizon scan of the future of eDNA analysis and its application to inform biodiversity conservation in a rapidly changing world

Very Smooth Nonparametric Curve Estimation by Penalizing Change of Curvature

Usual non-parametric regression estimators such as smoothing splines or kernel estimators are good tools for optimal mean squared error approximation of many smooth functions. However, they often show many little wiggles which do not appear to be necessary for a good description of the data. The new "Wp" smoother is a Maximum Penalized Likelihood estimate with a novel roughness penalty. It penalizes a relative change of curvature. This leads to disjoint classes of functions, each with a given number, nw , of inflection points. For a "Wp" estimate, f 00 (x) = \Sigma(x \Gamma w 1 ) \Delta \Delta \Delta (x \Gamma wnw ) \Delta exp h f (x), which is semi-parametric with parameters w j and nonparametric part h f (\Delta). For a very general class of M.P.L. estimators, a convenient form of the characterizing differential equation is derived. If the main smoothing parameter nw is specified correctly, this approach yields very smooth functions (including derivatives) while apparently not suff..