Bayesian Covariance Matrix Estimation using a Mixture of Decomposable Graphical Models

Estimating a covariance matrix efficiently and discovering its structure are important statistical problems with applications in many fields. This article takes a Bayesian approach to estimate the covariance matrix of Gaussian data. We use ideas from Gaussian graphical models and model selection to construct a prior for the covariance matrix that is a mixture over all decomposable graphs, where a graph means the configuration of nonzero offdiagonal elements in the inverse of the covariance matrix. Our prior for the covariance matrix is such that the probability of each graph size is specified by the user and graphs of equal size are assigned equal probability. Most previous approaches assume that all graphs are equally probable. We give empirical results that show the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs, both in identifying the correct decomposable graph and in more efficiently estimating the covariance matrix. The advantage is greatest when the number of observations is small relative to the dimension of the covariance matrix. The article also shows empirically that there is minimal change in statistical efficiency in using the mixture over decomposable graphs prior for estimating a general covariance compared to the Bayesian estimator by Wong et al. (2003), even when the graph of the covariance matrix is nondecomposable. However, our approach has some important advantages over that of Wong et al. (2003). Our method requires the number of decomposable graphs for each graph size. We show how to estimate these numbers using simulation and that the simulation results agree with analytic results when such results are known. We also show how to estimate the posterior distribution of the covariance matrix using Markov chain Monte Carlo with the elements of the covariance matrix integrated out and give empirical results that show the sampler is computationally efficient and converges rapidly. Finally, we note that both the prior and the simulation method to evaluate the prior apply generally to any decomposable graphical model.Covariance selection; Graphical models; Reduced conditional sampling; Variable selection

Temperature-tuning of near-infrared monodisperse quantum dot solids at 1.5 um for controllable Forster energy transfer

We present the first time-resolved cryogenic observations of Forster energy transfer in large, monodisperse lead sulphide quantum dots with ground state transitions near 1.5 um (0.83 eV), in environments from 160 K to room temperature. The observed temperature-dependent dipole-dipole transfer rate occurs in the range of (30-50 ns)^(-1), measured with our confocal single-photon counting setup at 1.5 um wavelengths. By temperature-tuning the dots, 94% efficiency of resonant energy transfer can be achieved for donor dots. The resonant transfer rates match well with proposed theoretical models

Constant Size Molecular Descriptors For Use With Machine Learning

A set of molecular descriptors whose length is independent of molecular size is developed for machine learning models that target thermodynamic and electronic properties of molecules. These features are evaluated by monitoring performance of kernel ridge regression models on well-studied data sets of small organic molecules. The features include connectivity counts, which require only the bonding pattern of the molecule, and encoded distances, which summarize distances between both bonded and non-bonded atoms and so require the full molecular geometry. In addition to having constant size, these features summarize information regarding the local environment of atoms and bonds, such that models can take advantage of similarities resulting from the presence of similar chemical fragments across molecules. Combining these two types of features leads to models whose performance is comparable to or better than the current state of the art. The features introduced here have the advantage of leading to models that may be trained on smaller molecules and then used successfully on larger molecules.Comment: 18 pages, 5 figure

Mutation of a conserved, hydrophobic, cryptic epitope improves manufacturability and immunogenicity of the SARS-CoV-2 RBD

The supply of COVID-19 vaccine doses still lags behind the global demand for first time vaccination and booster doses. Distribution of vaccine doses has been far from equitable across the world given the steep prices and logistical challenges that low- and middle-income countries face. Subunit protein vaccine candidates have now been shown to elicit protective responses against SARS-CoV-2 infection, while providing additional benefits for manufacturing capability and stability requirements compared to many currently approved vaccines. Here we report a second-generation engineered RBD sequence variant with enhanced manufacturability and immunogenicity over the wild-type ancestral RBD and a first-generation engineered variant (RBD-L452K-F490W (RBD-J)). Introducing two additional mutations, S383D and L518D, to a hydrophobic cryptic epitope in the RBD core improved expression titers and biophysical stability compared to RBD-J. These two additional mutations in RBD-S383D-L452K-F490W-L518D (RBD-J6) ablated the interaction of two neutralizing antibodies, CR3022 and EY6A, targeting the class 4 epitope on the RBD core, but the protein is still bound by human convalescent sera. Mice immunized with a Beta sequence variant of RBD-J and RBD-J6 displayed on a virus-like particle were protected against challenges with Alpha and Beta variants of SARS-CoV-2. Sera from mice immunized with three doses of a RBD-J6 β – VLP showed comparable neutralizing activity to several variants of concern compared to two doses of Comirnaty. Please click Download on the upper right corner to see the full abstract

Utilizing Social Networks in Language Classes – Perception, Production, and Interaction

The ubiquitous presence of social network sites (SNSs) offers both promises and problems for language teaching and learning today. Between 2009 and 2016 the authors incorporated Facebook into their Chinese curricula in three higher education institutions and subsequently analyzed its affordances and implications. Based on student surveys and language data collected from these pedagogical experiments, this action research paper explores three aspects of the findings: students’ perception, language production, and language interaction. The discussion focuses on not only the utilization of SNSs as educational tools to engage Chinese learners in innovative and collaborative ways but also helpful suggestions for teachers to enhance instructional outcomes through SNSs. Specific attention is given to create a pedagogically effective, privacy-ensured, and userfriendly social network project with Facebook, which is applicable to other SNSs and similar digital platforms

Angiogenesis in Paget's Disease of the Vulva and the Breast: Correlation with Microvessel Density

Our understanding of the pathogenesis of Paget's disease of the vulva and the breast remains limited. Current evidence supports the fact that angiogenesis plays an important role in the pathogenesis of several diseases. Therefore, we sought to define its role, as correlated with microvessel density, in Paget's disease of the vulva and the breast. Microvessels were analysed using anti-von Willebrand factor antibody in 105 cases of Paget's disease of the vulva and the breast comprising 71 cases of Paget's disease of the vulva, including 8 cases with invasive disease, and 34 cases of Paget's disease of the breast. The latter included 12 cases with DCIS, 5 cases with both DCIS and invasive carcinoma, and 6 with carcinoma alone. Eleven cases had no underlying tumour identified. Increased microvessel density was demonstrated in Paget's disease of the breast with DCIS and with carcinoma alone compared to Paget's disease of the breast alone, P < 0.08 and P < 0.013, respectively. There were no significant differences in microvessel density in the vulval cases. Neovascularisation is an important process in the development of Paget's disease of the breast. Other biological and molecular processes are more involved in the pathogenesis of Paget's disease of the vulva

Regulation of Star Formation Rates in Multiphase Galactic Disks: a Thermal/Dynamical Equilibrium Model

We develop a model for regulation of galactic star formation rates Sigma_SFR in disk galaxies, in which ISM heating by stellar UV plays a key role. By requiring simultaneous thermal and (vertical) dynamical equilibrium in the diffuse gas, and star formation at a rate proportional to the mass of the self-gravitating component, we obtain a prediction for Sigma_SFR as a function of the total gaseous surface density Sigma and the density of stars + dark matter, rho_sd. The physical basis of this relationship is that thermal pressure in the diffuse ISM, which is proportional to the UV heating rate and therefore to Sigma_SFR, must adjust to match the midplane pressure set by the vertical gravitational field. Our model applies to regions where Sigma < 100 Msun/pc^2. In low-Sigma_SFR (outer-galaxy) regions where diffuse gas dominates, the theory predicts Sigma_SFR \propto Sigma (rho_sd)^1/2. The decrease of thermal equilibrium pressure when Sigma_SFR is low implies, consistent with observations, that star formation can extend (with declining efficiency) to large radii in galaxies, rather than having a sharp cutoff. The main parameters entering our model are the ratio of thermal pressure to total pressure in the diffuse ISM, the fraction of diffuse gas that is in the warm phase, and the star formation timescale in self-gravitating clouds; all of these are (in principle) direct observables. At low surface density, our model depends on the ratio of the mean midplane FUV intensity (or thermal pressure in the diffuse gas) to the star formation rate, which we set based on Solar neighborhood values. We compare our results to recent observations, showing good agreement overall for azimuthally-averaged data in a set of spiral galaxies. For the large flocculent spiral galaxies NGC 7331 and NGC 5055, the correspondence between theory and observation is remarkably close.Comment: 49 pages, 7 figures; accepted by the Ap.

Depressive symptoms and social context modulate oxytocin’s effect on negative memory recall

Oxytocin promotes social affiliation across various species, in part by altering social cognition to facilitate approach behaviour. However, the effects of intranasal oxytocin on human social cognition are mixed, perhaps because its effects are context-dependent and subject to inter-individual differences. Few studies have included explicit manipulations of social context to test this supposition. We examined oxytocin’s effects on autobiographical memory recall in two contexts, with and without social contact, and evaluated whether these effects were moderated by depressive symptoms. Two non-clinical samples (Study 1 N = 48; Study 2 N = 63) completed randomised, placebo-controlled, within-subject experiments. We assessed autobiographical memory recall across two sessions (intranasal oxytocin or placebo) and two contexts (memories elicited by an experimenter or by computer). Overall, intranasal oxytocin increased ratings of vividness of recalled memories during the social context only. Individuals with elevated depressive symptoms also recalled memories that were more negative following oxytocin relative to placebo only in the non-social context across the two studies. Findings highlight the negative consequences of increasing oxytocin bioavailability in vulnerable persons in the absence of social contact. Contextual factors such as social isolation among depressed populations may complicate the clinical use of oxytocin