Insights from a multiscale framework on metabolic rate variation driving glioblastoma multiforme growth and invasion.

Non-physiological levels of oxygen and nutrients within the tumors result in heterogeneous cell populations that exhibit distinct necrotic, hypoxic, and proliferative zones. Among these zonal cellular properties, metabolic rates strongly affect the overall growth and invasion of tumors. Here, we report on a hybrid discrete-continuum (HDC) mathematical framework that uses metabolic data from a biomimetic two-dimensional (2D) in-vitro cancer model to predict three-dimensional (3D) behaviour of in-vitro human glioblastoma (hGB).

Spectral top-down recovery of latent tree models.

Modeling the distribution of high-dimensional data by a latent tree graphical model is a prevalent approach in multiple scientific domains. A common task is to infer the underlying tree structure, given only observations of its terminal nodes. Many algorithms for tree recovery are computationally intensive, which limits their applicability to trees of moderate size.

In-silico study of asymmetric remodeling of tumors in response to external biochemical stimuli.

Among different hallmarks of cancer, understanding biomechanics of tumor growth and remodeling benefits the most from the theoretical framework of continuum mechanics. Tumor remodeling initiates when cancer cells seek new homeostasis in response to the microenvironmental stimuli. Cells within a growing tumor are capable to remodel their inter- and intra-connections and become more mobile to achieve a new homeostasis.

Orientational-induced strain hardening of axisymmetric grains.

The rheological response of oriented axisymmetric grains has additional degrees of complexity associated with their microstructure orientation. These additional kinematic degrees of freedom that give rise to complex transient macroscale rheological responses are not well understood. In this Letter, we study the rheology of axisymmetric grains subjected to transient flow.

Zero-preserving imputation of single-cell RNA-seq data.

A key challenge in analyzing single cell RNA-sequencing data is the large number of false zeros, where genes actually expressed in a given cell are incorrectly measured as unexpressed. We present a method based on low-rank matrix approximation which imputes these values while preserving biologically non-expressed genes (true biological zeros) at zero expression levels. We provide theoretical justification for this denoising approach and demonstrate its advantages relative to other methods on simulated and biological datasets.