In the context of science, the well-known adage “a picture is worth a thousand words” might well be “a model is worth a thousand datasets.” In this manuscript we introduce the SciML software ecosystem as a tool for mixing the information of physical laws and scientific models with data-driven machine learning approaches. We describe a mathematical object, which we denote universal differential equations (UDEs), as the unifying framework connecting the ecosystem. We show how a wide variety of applications, from automatically discovering biological mechanisms to solving high-dimensional Hamilton-Jacobi-Bellman equations, can be phrased and efficiently handled through the UDE formalism and its tooling. We demonstrate the generality of the software tooling to handle stochasticity, delays, and implicit constraints. This funnels the wide variety of SciML applications into a core set of training mechanisms which are highly optimized, stabilized for stiff equations, and compatible with distributed parallelism and GPU accelerators.

Mapping individual differences in behavior is fundamental to personalized neuroscience, but quantifying complex behavior in real world settings remains a challenge. While mobility patterns captured by smartphones have increasingly been linked to a range of psychiatric symptoms, existing research has not specifically examined whether individuals have person-specific mobility patterns. We collected over 3000 days of mobility data from a sample of 41 adolescents and young adults (age 17–30 years, 28 female) with affective instability. We extracted summary mobility metrics from GPS and accelerometer data and used their covariance structures to identify individuals and calculated the individual identification accuracy—i.e., their “footprint distinctiveness”. We found that statistical patterns of smartphone-based mobility features represented unique “footprints” that allow individual identification (p < 0.001). Critically, mobility footprints exhibited varying levels of person-specific distinctiveness (4–99%), which was associated with age and sex. Furthermore, reduced individual footprint distinctiveness was associated with instability in affect (p < 0.05) and circadian patterns (p < 0.05) as measured by environmental momentary assessment. Finally, brain functional connectivity, especially those in the somatomotor network, was linked to individual differences in mobility patterns (p < 0.05). Together, these results suggest that real-world mobility patterns may provide individual-specific signatures relevant for studies of development, sleep, and psychopathology.

Ordinary differential equation (ODE) models are widely used to describe chemical or biological processes. This article considers the estimation and assessment of such models on the basis of time-course data. Due to experimental limitations, time-course data are often noisy and some components of the system may not be observed. Furthermore, the computational demands of numerical integration have hindered the widespread adoption of time-course analysis using ODEs. To address these challenges, we explore the efficacy of the recently developed MAGI (MAnifold-constrained Gaussian process Inference) method for ODE inference. First, via a range of examples we show that MAGI is capable of inferring the parameters and system trajectories, including unobserved components, with appropriate uncertainty quantification. Second, we illustrate how MAGI can be used to assess and select different ODE models with time-course data based on MAGI’s efficient computation of model predictions. Overall, we believe MAGI is a useful method for the analysis of time-course data in the context of ODE models, which bypasses the need for any numerical integration.

Complexity of the cellular organization of the tumor microenvironment as an ecosystem remains to be fully appreciated. Here, for a comprehensive investigation of tumor ecosystems across a wide variety of cancer types, we performed integrative transcriptome analyses of 4.4 million single cells from 978 tumor and 474 normal samples in combination with 9,510 TCGA and 1,339 checkpoint inhibitor-treated bulk tumors. Our analysis enabled us to define 28 different epithelial cell states, some of which had prognostic effects in cancers of relevant origin. Malignant fibroblast signatures defined according to the organ of origin demonstrated prognostic significance across diverse cancer types and revealed FN1, BGN, THBS2, and CTHRC1 as common cancer-associated fibroblast genes. Novel associations were revealed between the AKR1C1+ inflammatory fibroblast and myeloid-derived PRR-induced activation states and between the CXCL10+ fibroblast and squamous/LAMP3+ DC/SPP1+ macrophage states. We discovered tumor-specific rewiring of the tertiary lymphoid structure (TLS) network, involving previously unappreciated DC1, and pDC.. Along with other TLS component states, the tumor-associated germinal center B cell state identified from adjacent normal tissues was able to predict responses to checkpoint immunotherapy. Distinct groups of pan-cancer ecosystems were identified and characterized along the axis of immunotherapy responses. Our systematic, high-resolution dissection of tumor ecosystems provides a deeper understanding of inter- and intra-tumoral heterogeneity.