Vision depends on the delivery of vitamin A (retinol) to the retina. Retinol in blood is bound to retinol‐binding protein (RBP). Retinal pigment epithelia (RPE) cells express the RBP receptor, STRA6, ...that facilitates uptake of retinol. The retinol is then converted to retinyl esters by the enzyme lecithin:retinol acyltransferase. The esters are the substrate for RPE65, an enzyme that produces 11‐cis retinol, which is converted to 11‐cis retinaldehyde for transport to the photoreceptors to form rhodopsin. The dietary xanthophylls, lutein (LUT) and zeaxanthin (ZEA), accumulate in the macula of the eye, providing protection against age‐related macular degeneration. To reach the macula, carotenoids cross the RPE. In blood, xanthophylls and β‐carotene mostly associate with high‐density lipoprotein (HDL) and low‐density lipoprotein (LDL), respectively. Studies using a human RPE cell model evaluate the kinetics of cell uptake when carotenoids are delivered in LDL or HDL. For LUT and β‐carotene, LDL delivery result in the highest rate of uptake. HDL is more effective in delivering ZEA (and meso‐ZEA). This selective HDL‐mediated uptake of ZEA, via a scavenger receptor and LDL‐mediated uptake of LUT and β‐carotene provides a mechanism for the selective accumulation of ZEA > LUT and xanthophylls over β‐carotene in the macula.
Lutein (LUT) is delivered in low‐density lipoprotein (LDL) via the LDL receptor, which binds apolipoprotein B. Zeaxanthin is delivered in high‐density lipoprotein via scavenger receptor B1 that binds apolipoprotein A1. They bind to xanthophyll‐binding proteins. LUT is converted to meso‐zeaxanthin by the enzyme RPE65. The xanthophylls move to the interphotoreceptor matrix (IPM). Retinal pigment epithelium can assemble and secrete apoB lipoproteins into the blood.
Vitamin A is an essential nutrient for humans and is converted to the visual chromophore, 11-cis-retinal, and to the hormone, retinoic acid. Vitamin A in animal-derived foods is found as long chain ...acyl esters of retinol and these are digested to free fatty acids and retinol before uptake by the intestinal mucosal cell. The retinol is then reesterified to retinyl esters for incorporation into chlylomicrons and absorbed via the lymphatics or effluxed into the portal circulation facilitated by the lipid transporter, ABCA1. Provitamin A carotenoids such as β-carotene are found in plant-derived foods. These and other carotenoids are transported into the mucosal cell by scavenger receptor class B type I (SR-BI). Provitamin A carotenoids are partly converted to retinol by oxygenase and reductase enzymes and the retinol so produced is available for absorption via the two pathways described above. The efficiency of vitamin A and carotenoid intestinal absorption is determined by the regulation of a number of proteins involved in the process. Polymorphisms in genes for these proteins lead to individual variability in the metabolism and transport of vitamin A and carotenoids. This article is part of a Special Issue entitled Retinoid and Lipid Metabolism.
► Molecular mechanisms of dietary retinyl ester digestion are reviewed. ► Mechanisms of intestinal absorption of carotenoids and vitamin A are reviewed. ► A number of proteins regulate intestinal absorption of vitamin A and carotenoids.
RATE-OPTIMAL GRAPHON ESTIMATION Gao, Chao; Lu, Yu; Zhou, Harrison H.
The Annals of statistics,
12/2015, Letnik:
43, Številka:
6
Journal Article
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Network analysis is becoming one of the most active research areas in statistics. Significant advances have been made recently on developing theories, methodologies and algorithms for analyzing ...networks. However, there has been little fundamental study on optimal estimation. In this paper, we establish optimal rate of convergence for graphon estimation. For the stochastic block model with k clusters, we show that the optimal rate under the mean squared error is n⁻¹ log k + k²/n². The minimax upper bound improves the existing results in literature through a technique of solving a quadratic equation. When $k\, \leqslant \,\sqrt {n\,\log \,n} $, as the number of the cluster k grows, the minimax rate grows slowly with only a logarithmic order n⁻¹ log k. A key step to establish the lower bound is to construct a novel subset of the parameter space and then apply Fano's lemma, from which we see a clear distinction of the non-parametric graphon estimation problem from classical nonparametric regression, due to the lack of identifiability of the order of nodes in exchangeable random graph models. As an immediate application, we consider nonparametric graphon estimation in a Holder class with smoothness α. When the smoothness α ≥ 1, the optimal rate of convergence is n⁻¹ log n, independent of α, while for α ∈ (0, 1), the rate is n-2α/(α+1), which is, to our surprise, identical to the classical nonparametric rate.
Apocarotenoids are cleavage products of C40 isoprenoid pigments, named carotenoids, synthesized exclusively by plants and microorganisms. The colors of flowers and fruits and the photosynthetic ...process are examples of the biological properties conferred by carotenoids to these organisms. Mammals do not synthesize carotenoids but obtain them from foods of plant origin. Apocarotenoids are generated upon enzymatic and nonenzymatic cleavage of the parent compounds both in plants and in the tissues of mammals that have ingested carotenoid-containing foods. The best-characterized apocarotenoids are retinoids (vitamin A and its derivatives), generated upon central oxidative cleavage of provitamin A carotenoids, mainly β-carotene. In addition to the well-known biological actions of vitamin A, it is becoming apparent that nonretinoid apocarotenoids also have the potential to regulate a broad spectrum of critical cellular functions, thus influencing mammalian health. This review discusses the current knowledge about the generation and biological activities of nonretinoid apocarotenoids in mammals.
Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high ...dimensional setting. Optimal rates of convergence are established for a range of matrix norm losses. A fully data driven estimator based on adaptive constrained ℓ₁ minimization is proposed and its rate of convergence is obtained over a collection of parameter spaces. The estimator, called ACLIME, is easy to implement and performs well numerically. A major step in establishing the minimax rate of convergence is the derivation of a rate-sharp lower bound. A "two-directional" lower bound technique is applied to obtain the minimax lower bound. The upper and lower bounds together yield the optimal rates of convergence for sparse precision matrix estimation and show that the ACLIME estimator is adaptively minimax rate optimal for a collection of parameter spaces and a range of matrix norm losses simultaneously.
The mean field variational Bayes method is becoming increasingly popular in statistics and machine learning. Its iterative coordinate ascent variational inference algorithm has been widely applied to ...large scale Bayesian inference. See Blei et al. (2017) for a recent comprehensive review. Despite the popularity of the mean field method, there exist remarkably little fundamental theoretical justifications. To the best of our knowledge, the iterative algorithm has never been investigated for any high-dimensional and complex model. In this paper, we study the mean field method for community detection under the stochastic block model. For an iterative batch coordinate ascent variational inference algorithm, we show that it has a linear convergence rate and converges to the minimax rate within log n iterations. This complements the results of Bickel et al. (2013) which studied the global minimum of the mean field variational Bayes and obtained asymptotic normal estimation of global model parameters. In addition, we obtain similar optimality results for Gibbs sampling and an iterative procedure to calculate maximum likelihood estimation, which can be of independent interest.
Vitamin A was recognized as an essential nutrient 100 years ago. In the 1930s, it became clear that dietary β-carotene was cleaved at its central double to yield vitamin A (retinal or ...β-apo-15′-carotenal). Thus a great deal of research has focused on the central cleavage of provitamin A carotenoids to form vitamin A (retinoids). The mechanisms of formation and the physiological role(s) of noncentral (eccentric) cleavage of both provitamin A carotenoids and nonprovitamin A carotenoids has been less clear. It is becoming apparent that the apocarotenoids exert unique biological activities themselves. These compounds are found in the diet and thus may be absorbed in the intestine, or they may form from enzymatic or nonenzymatic cleavage of the parent carotenoids. The mechanism of action of apocarotenoids in mammals is not fully worked out. However, as detailed in this review, they have profound effects on gene expression and work, at least in part, through the modulation of ligand-activated nuclear receptors. Understanding the interactions of apocarotenoids with other lipid-binding proteins, chaperones, and metabolizing enzymes will undoubtedly increase our understanding of the biological roles of these carotenoid metabolites.
Canonical correlation analysis is a classical technique for exploring the relationship between two sets of variables. It has important applications in analyzing high dimensional datasets originated ...from genomics, imaging and other fields. This paper considers adaptive minimax and computationally tractable estimation of leading sparse canonical coefficient vectors in high dimensions. Under a Gaussian canonical pair model, we first establish separate minimax estimation rates for canonical coefficient vectors of each set of random variables under no structural assumption on marginal covariance matrices. Second, we propose a computationally feasible estimator to attain the optimal rates adaptively under an additional sample size condition. Finally, we show that a sample size condition of this kind is needed for any randomized polynomial-time estimator to be consistent, assuming hardness of certain instances of the planted clique detection problem. As a byproduct, we obtain the first computational lower bounds for sparse PCA under the Gaussian single spiked covariance model.
Recently, network analysis has gained more and more attention in statistics, as well as in computer science, probability and applied mathematics. Community detection for the stochastic block model ...(SBM) is probably the most studied topic in network analysis. Many methodologies have been proposed. Some beautiful and significant phase transition results are obtained in various settings. In this paper, we provide a general minimax theory for community detection. It gives minimax rates of the mis-match ratio for a wide rage of settings including homogeneous and inhomogeneous SBMs, dense and sparse networks, finite and growing number of communities. The minimax rates are exponential, different from polynomial rates we often see in statistical literature. An immediate consequence of the result is to establish threshold phenomenon for strong consistency (exact recovery) as well as weak consistency (partial recovery). We obtain the upper bound by a range of penalized likelihood-type approaches. The lower bound is achieved by a novel reduction from a global mis-match ratio to a local clustering problem for one node through an exchangeability property.
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