相关论文: Quasi-universality in single-cell sequencing data
The spectral properties of the adjacency matrix provide a trove of information about the structure and function of complex networks. In particular, the largest eigenvalue and its associated principal eigenvector are crucial in the…
Motivation: Modelling methods that find structure in data are necessary with the current large volumes of genomic data, and there have been various efforts to find subsets of genes exhibiting consistent patterns over subsets of treatments.…
Single-cell RNA-sequencing technologies may provide valuable insights to the understanding of the composition of different cell types and their functions within a tissue. Recent technologies such as spatial transcriptomics, enable the…
We investigate the eigenvalue density in ensembles of large sparse Bernoulli random matrices. We demonstrate that the fraction of linear subgraphs just below the percolation threshold is about 95\% of all finite subgraphs, and the…
Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…
The relationship between microscopic observations and macroscopic behavior is a fundamental open question in biophysical systems. Here, we develop a unified approach that---in contrast with existing methods---predicts cell type from…
We study a class of random matrices that appear in several communication and signal processing applications, and whose asymptotic eigenvalue distribution is closely related to the reconstruction error of an irregularly sampled bandlimited…
The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large…
We analyse the eigenvectors of the adjacency matrix of a random inhomogeneous graph constructed from a specified degree sequence. We assume that the empirical degree sequence has bounded mean and variance. We show that near the edges of the…
In increasingly many settings, data sets consist of multiple samples from a population of networks, with vertices aligned across these networks. For example, brain connectivity networks in neuroscience consist of measures of interaction…
Recent technological advances in cutting-edge ultrasensitive fluorescence microscopy have allowed single-molecule imaging experiments in living cells across all three domains of life to become commonplace. Single-molecule live-cell data is…
Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. The various proposals in the literature are usually motivated by…
One of the major challenges arising from single-cell transcriptomics experiments is the question of how to annotate the associated single-cell transcriptomic profiles. Because of the large size and the high dimensionality of the data,…
Consider $N\times N$ symmetric one-dimensional random band matrices with general distribution of the entries and band width $W \geq N^{3/4+\varepsilon}$ for any $\varepsilon>0$. In the bulk of the spectrum and in the large $N$ limit, we…
There is a growing interest in cell-type-specific analysis from bulk samples with a mixture of different cell types. A critical first step in such analyses is the accurate estimation of cell-type proportions in a bulk sample. Although many…
In recent years, the field of single-cell data analysis has seen a marked advancement in the development of clustering methods. Despite advancements, most of these algorithms still concentrate on analyzing the provided single-cell matrix…
Motivation: The discovery of relationships between gene expression measurements and phenotypic responses is hampered by both computational and statistical impediments. Conventional statistical methods are less than ideal because they either…
Single-cell trajectory analysis aims to reconstruct the biological developmental processes of cells as they evolve over time, leveraging temporal correlations in gene expression. During cellular development, gene expression patterns…
A key challenge in molecular biology is to decipher the mapping of protein sequence to function. To perform this mapping requires the identification of sequence features most informative about function. Here, we quantify the amount of…
Sparse autoencoders (SAEs) have lately been used to uncover interpretable latent features in large language models. By projecting dense embeddings into a much higher-dimensional and sparse space, learned features become disentangled and…