Modern developments in single cell sequencing technologies enable broad insights into cellular state. Single cell RNA sequencing (scRNA-seq) can be used to explore cell types, states, and developmental trajectories to broaden understanding of cell heterogeneity in tissues and organs. Analysis of these sparse, high-dimensional experimental results requires dimension reduction. Several methods have been developed to estimate low-dimensional embeddings for filtered and normalized single cell data. However, methods have yet to be developed for unfiltered and unnormalized count data. We present a nonlinear latent variable model with robust, heavy-tailed error and adaptive kernel learning to estimate low-dimensional nonlinear structure in scRNA-seq data. Gene expression in a single cell is modeled as a noisy draw from a Gaussian process in high dimensions from low-dimensional latent positions. This model is called the Gaussian process latent variable model (GPLVM). We model residual errors with a heavy-tailed Student's t-distribution to estimate a manifold that is robust to technical and biological noise. We compare our approach to common dimension reduction tools to highlight our model's ability to enable important downstream tasks, including clustering and inferring cell developmental trajectories, on available experimental data. We show that our robust nonlinear manifold is well suited for raw, unfiltered gene counts from high throughput sequencing technologies for visualization and exploration of cell states. 62 factor analysis (ZIFA) (Pierson and Yau), t-SNE (Van Der Maaten and Hinton) (perplex-63 ity set to default 30), and PCA (Hotelling, 1933) were tested as comparison methods. To 64 evaluate the robust adaptations of the tGPLVM model, we fit tGPLVM with only an SE 65 kernel or SE and Matérn 1/2 kernel as well as tGPLVM with normally distributed error. 66 Trajectory building with minimum spanning trees 67 tGPLVM was used to fit a two dimensional latent mappings for the Lonnberg (Lönnberg 68 et al., 2017) developmental data. The minimum spanning tree was found on Euclidean 69 distance matrix of the posterior means of the low dimensional embedding and compared 70 to sequencing time to verify correct ordering. The same analysis was performed with 71 ZIFA (Pierson and Yau), t-SNE (Van Der Maaten and Hinton) (perplexity set to default 72 30), and PCA (Hotelling, 1933). 73 Visualization of sparse, raw count matrices 74 tGPLVM was used to fit a three-dimensional mapping for the two 10x data sets, CD34+ 75 cells and mice brain cells. Pearson correlation between latent position posterior mean and 76 expression counts was used to identify genes associated with latent dimensions. ZIFA (Pier-77 son and Yau), t-SNE (Van Der Maaten and Hinton) (perplexity set to default 30), and 78 PCA (truncated SVD (Halko et al.)) were also fit to the CD34+ cell data to compare 79 computational time.

Background: Modern developments in single-cell sequencing technologies enable broad insights into cellular state. Single-cell RNA sequencing (scRNA-seq) can be used to explore cell types, states, and developmental trajectories to broaden our understanding of cellular heterogeneity in tissues and organs. Analysis of these sparse, high-dimensional experimental results requires dimension reduction. Several methods have been developed to estimate low-dimensional embeddings for filtered and normalized single-cell data. However, methods have yet to be developed for unfiltered and unnormalized count data that estimate uncertainty in the low-dimensional space. We present a nonlinear latent variable model with robust, heavy-tailed error and adaptive kernel learning to estimate low-dimensional nonlinear structure in scRNA-seq data. Results: Gene expression in a single cell is modeled as a noisy draw from a Gaussian process in high dimensions from low-dimensional latent positions. This model is called the Gaussian process latent variable model (GPLVM). We model residual errors with a heavy-tailed Student's t-distribution to estimate a manifold that is robust to technical and biological noise found in normalized scRNA-seq data. We compare our approach to common dimension reduction tools across a diverse set of scRNA-seq data sets to highlight our model's ability to enable important downstream tasks such as clustering, inferring cell developmental trajectories, and visualizing high throughput experiments on available experimental data. Conclusion: We show that our adaptive robust statistical approach to estimate a nonlinear manifold is well suited for raw, unfiltered gene counts from high-throughput sequencing technologies for visualization, exploration, and uncertainty estimation of cell states.

Multicellular organisms rely on spatial signaling among cells to drive their organization, development, and response to stimuli. Several models have been proposed to capture the behavior of spatial signaling in multicellular systems, but existing approaches fail to capture both the autonomous behavior of single cells and the interactions of a cell with its neighbors simultaneously. We propose a spatiotemporal model of dynamic cell signaling based on Hawkes processes—self-exciting point processes—that model the signaling processes within a cell and spatial couplings between cells. With this cellular point process (CPP), we capture both the single-cell pathway activation rate and the magnitude and duration of signaling between cells relative to their spatial location. Furthermore, our model captures tissues composed of heterogeneous cell types with different bursting rates and signaling behaviors across multiple signaling proteins. We apply our model to epithelial cell systems that exhibit a range of autonomous and spatial signaling behaviors basally and under pharmacological exposure. Our model identifies known drug-induced signaling deficits, characterizes signaling changes across a wound front, and generalizes to multichannel observations.

No abstract

A major concern in coalition peace-support operations is the incidence of terrorist activity. In this paper, we propose a generative model for the occurrence of the terrorist incidents, and illustrate that an increase in diversity, as measured by the number of different social groups to which that an individual belongs, is inversely correlated with the likelihood of a terrorist incident in the society. A generative model is one that can predict the likelihood of events in new contexts, as opposed to statistical models which are used to predict the future incidents based on the history of the incidents in an existing context. Generative models can be useful in planning for persistent Information Surveillance and Reconnaissance (ISR) since they allow an estimation of regions in the theater of operation where terrorist incidents may arise, and thus can be used to better allocate the assignment and deployment of ISR assets. In this paper, we present a taxonomy of terrorist incidents, identify factors related to occurrence of terrorist incidents, and provide a mathematical analysis calculating the likelihood of occurrence of terrorist incidents in three common real-life scenarios arising in peacekeeping operations.