Abstract. The Canadian Earth System Model version 5 (CanESM5) is a global model developed to simulate historical climate change and variability, to make centennial scale projections of future climate, and to produce initialized seasonal and decadal predictions. This paper describes the model components and their coupling, as well as various aspects of model development, including tuning, optimization and a reproducibility strategy. We also document the stability of the model using a long control simulation, quantify the model's ability to reproduce large scale features of the historical climate, and evaluate the response of the model to external forcing. CanESM5 is comprised of three dimensional atmosphere (T63 spectral resolution/2.8°) and ocean (nominally 1°) general circulation models, a sea ice model, a land surface scheme, and explicit land and ocean carbon cycle models. The model features relatively coarse resolution and high throughput, which facilitates the production of large ensembles. CanESM5 has a notably higher equilibrium climate sensitivity (5.7 K) than its predecessor CanESM2 (3.8 K), which we briefly discuss, along with simulated changes over the historical period. CanESM5 simulations are contributing to the Coupled Model Intercomparison Project Phase 6 (CMIP6), and will be employed for climate science and service applications in Canada.

No abstract

Feature selection and feature transformation, the two main ways to reduce dimensionality, are often presented separately. In this paper, a feature selection method is proposed by combining the popular transformation-based dimensionality reduction method linear discriminant analysis (LDA) and sparsity regularization. We impose row sparsity on the transformation matrix of LDA through l2,1-norm regularization to achieve feature selection, and the resultant formulation optimizes for selecting the most discriminative features and removing the redundant ones simultaneously. The formulation is extended to the l2,p-norm regularized case, which is more likely to offer better sparsity when 0 < p < 1. Thus, the formulation is a better approximation to the feature selection problem. An efficient algorithm is developed to solve the l2,p-norm-based optimization problem and it is proved that the algorithm converges when 0 < p ≤ 2. Systematical experiments are conducted to understand the work of the proposed method. Promising experimental results on various types of real-world data sets demonstrate the effectiveness of our algorithm.

Spatially resolved transcriptomics involves a set of emerging technologies that enable the transcriptomic profiling of tissues with the physical location of expressions. Although a variety of methods have been developed for data integration, most of them are for single-cell RNA-seq datasets without consideration of spatial information. Thus, methods that can integrate spatial transcriptomics data from multiple tissue slides, possibly from multiple individuals, are needed. Here, we present PRECAST, a data integration method for multiple spatial transcriptomics datasets with complex batch effects and/or biological effects between slides. PRECAST unifies spatial factor analysis simultaneously with spatial clustering and embedding alignment, while requiring only partially shared cell/domain clusters across datasets. Using both simulated and four real datasets, we show improved cell/domain detection with outstanding visualization, and the estimated aligned embeddings and cell/domain labels facilitate many downstream analyses. We demonstrate that PRECAST is computationally scalable and applicable to spatial transcriptomics datasets from different platforms.

We develop a primal dual active set with continuation algorithm for solving the ℓ 0 -regularized least-squares problem that frequently arises in compressed sensing. The algorithm couples the the primal dual active set method with a continuation strategy on the regularization parameter. At each inner iteration, it first identifies the active set from both primal and dual variables, and then updates the primal variable by solving a (typically small) least-squares problem defined on the active set, from which the dual variable can be updated explicitly. Under certain conditions on the sensing matrix, i.e., mutual incoherence property or restricted isometry property, and the noise level, the finite step global convergence of the algorithm is established. Extensive numerical examples are presented to illustrate the efficiency and accuracy of the algorithm and the convergence analysis. keywords: primal dual active set method, coordinatewise minimizer, continuation strategy, global convergence.

The success of compressed sensing relies essentially on the ability to efficiently find an approximately sparse solution to an under-determined linear system. In this paper, we developed an efficient algorithm for the sparsity promoting ℓ1-regularized least squares problem by coupling the primal dual active set strategy with a continuation technique (on the regularization parameter). In the active set strategy, we first determine the active set from primal and dual variables, and then update the primal and dual variables by solving a low-dimensional least square problem on the active set, which makes the algorithm very efficient. The continuation technique globalizes the convergence of the algorithm, with provable global convergence under restricted isometry property (RIP). Further, we adopt two alternative methods, i.e., a modified discrepancy principle and a Bayesian information criterion, to choose the regularization parameter. Numerical experiments indicate that our algorithm is very competitive with state-of-the-art algorithms in terms of accuracy and efficiency.Index Terms-compressive sensing, ℓ1 regularization, primal dual active set method, continuation, modified discrepancy principle, Bayesian information criterion.

Kaczmarz method is one popular iterative method for solving inverse problems, especially in computed tomography. Recently, it was established that a randomized version of the method enjoys an exponential convergence for well-posed problems, and the convergence rate is determined by a variant of the condition number. In this work, we analyze the preasymptotic convergence behavior of the randomized Kaczmarz method, and show that the low-frequency error (with respect to the right singular vectors) decays faster during first iterations than the high-frequency error. Under the assumption that the initial error is smooth (e.g., sourcewise representation), the results allow explaining the fast empirical convergence behavior, thereby shedding new insights into the excellent performance of the randomized Kaczmarz method in practice. Further, we propose a simple strategy to stabilize the asymptotic convergence of the iteration by means of variance reduction. We provide extensive numerical experiments to confirm the analysis and to elucidate the behavior of the algorithms.

Motivation Although genome-wide association studies (GWAS) have deepened our understanding of the genetic architecture of complex traits, the mechanistic links that underlie how genetic variants cause complex traits remains elusive. To advance our understanding of the underlying mechanistic links, various consortia have collected a vast volume of genomic data that enable us to investigate the role that genetic variants play in gene expression regulation. Recently, a collaborative mixed model (CoMM) was proposed to jointly interrogate genome on complex traits by integrating both the GWAS dataset and the expression quantitative trait loci (eQTL) dataset. Although CoMM is a powerful approach that leverages regulatory information while accounting for the uncertainty in using an eQTL dataset, it requires individual-level GWAS data and cannot fully make use of widely available GWAS summary statistics. Therefore, statistically efficient methods that leverages transcriptome information using only summary statistics information from GWAS data are required. Results In this study, we propose a novel probabilistic model, CoMM-S2, to examine the mechanistic role that genetic variants play, by using only GWAS summary statistics instead of individual-level GWAS data. Similar to CoMM which uses individual-level GWAS data, CoMM-S2 combines two models: the first model examines the relationship between gene expression and genotype, while the second model examines the relationship between the phenotype and the predicted gene expression from the first model. Distinct from CoMM, CoMM-S2 requires only GWAS summary statistics. Using both simulation studies and real data analysis, we demonstrate that even though CoMM-S2 utilizes GWAS summary statistics, it has comparable performance as CoMM, which uses individual-level GWAS data. Availability and implementation The implement of CoMM-S2 is included in the CoMM package that can be downloaded from https://github.com/gordonliu810822/CoMM. Supplementary information Supplementary data are available at Bioinformatics online.