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Abstract Increasing the number of organ donations after circulatory death (DCD) has been identified as one of the most important ways of addressing the ongoing organ shortage. While recent technological advances in organ transplantation have increased their success rate, a substantial challenge in increasing the number of DCD donations resides in the uncertainty regarding the timing of cardiac death after terminal extubation, impacting the risk of prolonged ischemic organ injury, and negatively affecting post-transplant outcomes. In this study, we trained and externally validated an ODE-RNN model, which combines recurrent neural network with neural ordinary equations and excels in processing irregularly-sampled time series data. The model is designed to predict time-to-death following terminal extubation in the intensive care unit (ICU) using the history of clinical observations. Our model was trained on a cohort of 3,238 patients from Yale New Haven Hospital, and validated on an external cohort of 1,908 patients from six hospitals across Connecticut. The model achieved accuracies of$$95.3~\pm ~1.0\%$$and$$95.4~\pm ~0.7\%$$for predicting whether death would occur in the first 30 and 60 minutes, respectively, with a calibration error of$$0.024~\pm ~0.009$$. Heart rate, respiratory rate, mean arterial blood pressure (MAP), oxygen saturation (SpO2), and Glasgow Coma Scale (GCS) scores were identified as the most important predictors. Surpassing existing clinical scores, our model sets the stage for reduced organ acquisition costs and improved post-transplant outcomes. 

Abstract In order to better understand manifold neural networks (MNNs), we introduce Manifold Filter-Combine Networks (MFCNs). Our filter-combine framework parallels the popular aggregate-combine paradigm for graph neural networks (GNNs) and naturally suggests many interesting families of MNNs which can be interpreted as manifold analogues of various popular GNNs. We propose a method for implementing MFCNs on high-dimensional point clouds that relies on approximating an underlying manifold by a sparse graph. We then prove that our method is consistent in the sense that it converges to a continuum limit as the number of data points tends to infinity, and we numerically demonstrate its effectiveness on real-world and synthetic data sets. 

apid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over SOTA in single-cell population-level trajectory inference. 

Identifying functionally important cell states and structure within heterogeneous tumors remains a significant biological and computational challenge. Current clustering or trajectory-based models are ill-equipped to address the notion that cancer cells reside along a phenotypic continuum. We present Archetypal Analysis network (AAnet), a neural network that learns archetypal states within a phenotypic continuum in single-cell data. Unlike traditional archetypal analysis, AAnet learns archetypes in simplex-shaped neural network latent space. Using pre-clinical models and clinical breast cancers, AAnet resolves distinct cell states and processes, including cell proliferation, hypoxia, metabolism and immune interactions. Primary tumor archetypes are recapitulated in matched liver, lung and lymph node metastases. Spatial transcriptomics reveal archetypal organization within the tumor, and, intra-archetypal mirroring between cancer and adjacent stromal cells. AAnet identifies GLUT3 within the hypoxic archetype that proves critical for tumor growth and metastasis. AAnet is a powerful tool, capturing complex, functional cell states from multimodal data. 

Here we consider the problem of denoising features associated to complex data, modeled as signals on a graph, via a smoothness prior. This is motivated in part by settings such as single-cell RNA where the data is very high-dimensional, but its structure can be captured via an affinity graph. This allows us to utilize ideas from graph signal processing. In particular, we present algorithms for the cases where the signal is perturbed by Gaussian noise, dropout, and uniformly distributed noise. The signals are assumed to follow a prior distribution defined in the frequency domain which favors signals which are smooth across the edges of the graph. By pairing this prior distribution with our three models of noise generation, we propose Maximum A Posteriori (M.A.P.) estimates of the true signal in the presence of noisy data and provide algorithms for computing the M.A.P. Finally, we demonstrate the algorithms’ ability to effectively restore signals from white noise on image data and from severe dropout in single-cell RNA sequence data. 

Directed graphs are a natural model for many phenomena, in particular scientific knowledge graphs such as molecular interaction or chemical reaction networks that define cellular signaling relationships. In these situations, source nodes typically have distinct biophysical properties from sinks. Due to their ordered and unidirectional relationships, many such networks also have hierarchical and multiscale structure. However, the majority of methods performing node- and edge-level tasks in machine learning do not take these properties into account, and thus have not been leveraged effectively for scientific tasks such as cellular signaling network inference. We propose a new framework called Directed Scattering Autoencoder (DSAE) which uses a directed version of a geometric scattering transform, combined with the non-linear dimensionality reduction properties of an autoencoder and the geometric properties of the hyperbolic space to learn latent hierarchies. We show this method outperforms numerous others on tasks such as embedding directed graphs and learning cellular signaling networks. 

The scattering transform is a multilayered, wavelet-based transform initially introduced as a mathematical model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks’ stability and invariance properties. In subsequent years, there has been widespread interest in extending the success of CNNs to data sets with non- Euclidean structure, such as graphs and manifolds, leading to the emerging field of geometric deep learning. In order to improve our understanding of the architectures used in this new field, several papers have proposed generalizations of the scattering transform for non-Euclidean data structures such as undirected graphs and compact Riemannian manifolds without boundary. Analogous to the original scattering transform, these works prove that these variants of the scattering transform have desirable stability and invariance properties and aim to improve our understanding of the neural networks used in geometric deep learning. In this paper, we introduce a general, unified model for geometric scattering on measure spaces. Our proposed framework includes previous work on compact Riemannian manifolds without boundary and undirected graphs as special cases but also applies to more general settings such as directed graphs, signed graphs, and manifolds with boundary. We propose a new criterion that identifies to which groups a useful representation should be invariant and show that this criterion is sufficient to guarantee that the scattering transform has desirable stability and invariance properties. Additionally, we consider finite measure spaces that are obtained from randomly sampling an unknown manifold. We propose two methods for constructing a data-driven graph on which the associated graph scattering transform approximates the scattering transform on the underlying manifold. Moreover, we use a diffusion-maps based approach to prove quantitative estimates on the rate of convergence of one of these approximations as the number of sample points tends to infinity. Lastly, we showcase the utility of our method on spherical images, a directed graph stochastic block model, and on high-dimensional single-cell data.