A prominent feature of earthquakes is their empirical laws including memory (clustering) in time and space. Several earthquake forecasting models, like the EpidemicType Aftershock Sequence (ETAS) model1,2, were develo...
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In this paper, we consider the problem of black box continuous submodular maximization where we only have access to the function values and no information about the derivatives is provided. For a monotone and continuo...
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Graphs modeling pairwise relationships between entities have become a dominant framework to study complex systems and data. Simplicial complexes extend this dyadic model of graphs to polyadic relationships and have em...
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Graphs modeling pairwise relationships between entities have become a dominant framework to study complex systems and data. Simplicial complexes extend this dyadic model of graphs to polyadic relationships and have emerged as a model for multi-node relationships occurring in many complex systems. For instance, biological interactions occur between sets of molecules, and communication systems include group messages and not only pairwise interactions. While the graph Laplacian and Laplacian dynamics have been intensely studied, corresponding notions of Laplacian dynamics beyond the node-space have so far remained largely unexplored for simplicial complexes. In particular, di usion processes such as random walks and their relationship to the graph Laplacian, that underpin many methods such as centrality measures, ow-based rankings, community detection, and contagion models, lack a proper correspondence for general simplicial complexes Focusing on the coupling between edges, here we introduce a normalized Laplacian matrix for simplicial complexes and demonstrate its relationship to a random walk model on simplicial complexes as a foundational step towards translating many Laplacian-based analytics from graphs to simplicial complexes. Our key idea is to generalize the relationship between the normalized graph Laplacian and random walks on graphs by devising an appropriate normalization for the Hodge Laplacian, the analog of the graph Laplacian for simplicial complexes. We further discuss how this Hodge Laplacian gives rise to the Hodge decomposition, a decomposition of edge ows into intuitively interpretable components that are analogous to notions such as gradient ows or rotational ows from vector calculus. We demonstrate how these results can be leveraged for data analytics that extract information about the edge-space of a simplicial complex that complements and extends graph-based analysis. To illustrate the utility of these tools we derive spectral embeddings based
Pancreatic ductal adenocarcinoma (PDAC) is characterized by a complex tumor microenvironment (TME). We utilized single cell RNA sequencing to compare the TMEs of metastatic sites and primary tumors. We detected increa...
Pancreatic ductal adenocarcinoma (PDAC) is characterized by a complex tumor microenvironment (TME). We utilized single cell RNA sequencing to compare the TMEs of metastatic sites and primary tumors. We detected increased prevalence of exhausted CD8 + T cells in metastases, as well as enrichment of complement pathway encoding genes in immunosuppressive tumor-associated macrophages, consistent with profound immunosuppression in metastatic disease. In cancer-associated fibroblasts, we identified unique upregulation of metabolic genes including UPP1 in metastasis. In cancer cells, we uncovered a specific gene signature upregulated in liver metastases; this signature was present in a proportion of primary tumors in the TCGA dataset, where it correlated with worse survival. Overall, our analysis of primary and metastatic PDAC defines a “high-risk” gene signature, metabolic reprogramming and increased immune suppression in metastasis.
In tasks involving human health condition data, feature selection is heavily affected by data types, the complexity of the condition manifestation, and the variability in physiological presentation. One type of variab...
In tasks involving human health condition data, feature selection is heavily affected by data types, the complexity of the condition manifestation, and the variability in physiological presentation. One type of variability often overlooked or oversimplified is the effect of biological sex. As females have been chronically underrepresented in clinical research, we know less about how conditions manifest in females. Innovations in wearable technology have enabled individuals to generate high temporal resolution data for extended periods of time. With millions of days of data now available, additional feature selection pipelines should be developed to systematically identify sex-dependent variability in data, along with the effects of how many per-person data are included in analysis. Here we present a set of statistical approaches as a technique for identifying sex-dependent physiological and behavioral manifestations of complex diseases starting from longitudinal data, which are evaluated on diabetes, hypertension, and their comorbidity.
Digital health technology tools (DHTTs) have the potential to transform health care delivery by enabling new forms of participatory and personalized care that fit into patients’ daily lives. However, realizing this p...
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