Let T be a general complex tensor of format (n 1,…, nd). When the fraction∏ ini/[1+∑ i (ni-1)]
is an integer, and a natural inequality (called balancedness) is satisfied, it is expected that T …

We consider a free boundary tumor model with vasculature which supply nutrients to the
tumor, so that∂ σ∂ n+ β (σ− σ¯)= 0 holds on the boundary, where a positive constant β is …

Large number of papers have been devoted to the study of tumor models. Wellpostedness
as well as properties of solutions are systematically studied [1],[2],[3],[5],[6],[7],[8],[9],[10],[11] …

In this paper, we rigorously analyze a free boundary model of plaque growth under the
influence of reverse cholesterol transport (RCT). We will analyze a model with a highly …

Discretizing systems of nonlinear algebraic differential equations yields polynomial systems.
When using a fine discretization, the resulting polynomial system is often too large to solve …

In this paper, we present an adaptive step-size homotopy tracking method for computing
bifurcation points of nonlinear systems. There are four components in this new method:(1) …

A considerable number of research works has been devoted to the study of tumor models.
Several biophysical factors, such as cell proliferation, apoptosis, chemotaxis, angiogenesis …

Atherosclerosis, hardening of the arteries, originates from small plaques in the arteries; it is a
major cause of disability and premature death in the United States and worldwide. In this …

In this paper, we develop a sharp interface tumor growth model in two dimensions to study
the effect of both the intratumoral structure using a controlled necrotic core and the …

In this paper, we present a homotopy training algorithm (HTA) to solve optimization
problems arising from fully connected neural networks with complicated structures. The HTA …