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Abstract We fully characterize the nonasymptotic minimax separation rate for sparse signal detection in the Gaussian sequence model with $$p$$ equicorrelated observations, generalizing a result of Collier, Comminges and Tsybakov. As a consequence of the rate characterization, we find that strong correlation is a blessing, moderate correlation is a curse and weak correlation is irrelevant. Moreover, the threshold correlation level yielding a blessing exhibits phase transitions at the $$\sqrt{p}$$ and $$p-\sqrt{p}$$ sparsity levels. We also establish the emergence of new phase transitions in the minimax separation rate with a subtle dependence on the correlation level. Additionally, we study group structured correlations and derive the minimax separation rate in a model including multiple random effects. The group structure turns out to fundamentally change the detection problem from the equicorrelated case and different phenomena appear in the separation rate. 

ABSTRACT Microorganisms play a central role in sustaining soil ecosystems and agriculture, and these functions are usually associated with their complex life history. Yet, the regulation and evolution of life history have remained enigmatic and poorly understood, especially in protozoa, the third most abundant group of organisms in the soil. Here, we explore the life history of a cosmopolitan species—Colpoda steinii. Our analysis has yielded a high-quality macronuclear genome forC. steinii, with size of 155 Mbp and 37,123 protein-coding genes, as well as mean intron length of ~93 bp, longer than most other studied ciliates. Notably, we identify two possible whole-genome duplication events inC. steinii, which may account for its genome being about twice the size ofC. inflata’s, another co-existing species. We further resolve the gene expression profiles in diverse life stages ofC. steinii, which are also corroborated inC. inflata. During the resting cyst stage, genes associated with cell death and vacuole formation are upregulated, and translation-related genes are downregulated. While the translation-related genes are upregulated during the excystment of resting cysts. Reproductive cysts exhibit a significant reduction in cell adhesion. We also demonstrate that most genes expressed in specific life stages are under strong purifying selection. This study offers a deeper understanding of the life history evolution that underpins the extraordinary success and ecological functions of microorganisms in soil ecosystems.IMPORTANCEColpodaspecies, as a prominent group among the most widely distributed and abundant soil microorganisms, play a crucial role in sustaining soil ecosystems and promoting plant growth. This investigation reveals their exceptional macronuclear genomic features, including significantly large genome size, long introns, and numerous gene duplications. The gene expression profiles and the specific biological functions associated with the transitions between various life stages are also elucidated. The vast majority of genes linked to life stage transitions are subject to strong purifying selection, as inferred from multiple natural strains newly isolated and deeply sequenced. This substantiates the enduring and conservative nature ofColpoda’s life history, which has persisted throughout the extensive evolutionary history of these highly successful protozoa in soil. These findings shed light on the evolutionary dynamics of microbial eukaryotes in the ever-fluctuating soil environments. This integrative research represents a significant advancement in understanding the life histories of these understudied single-celled eukaryotes. 

Abstract The Bradley–Terry–Luce (BTL) model is a benchmark model for pairwise comparisons between individuals. Despite recent progress on the first-order asymptotics of several popular procedures, the understanding of uncertainty quantification in the BTL model remains largely incomplete, especially when the underlying comparison graph is sparse. In this paper, we fill this gap by focusing on two estimators that have received much recent attention: the maximum likelihood estimator (MLE) and the spectral estimator. Using a unified proof strategy, we derive sharp and uniform non-asymptotic expansions for both estimators in the sparsest possible regime (up to some poly-logarithmic factors) of the underlying comparison graph. These expansions allow us to obtain: (i) finite-dimensional central limit theorems for both estimators; (ii) construction of confidence intervals for individual ranks; (iii) optimal constant of $$\ell _2$$ estimation, which is achieved by the MLE but not by the spectral estimator. Our proof is based on a self-consistent equation of the second-order remainder vector and a novel leave-two-out analysis.