Evolution by alternating dominance

Dominance and Its Evolution

Clonal competition with alternating dominance in multiple myeloma.

Emerging evidence indicates that tumors can follow several evolutionary paths over a patient's disease course. With the use of serial genomic analysis of samples collected at different points during the disease course of 28 patients with multiple myeloma, we found that the genomes of standard-risk patients show few changes over time, whereas those of cytogenetically high-risk patients show sign...

The Evolution of Social Dominance

A difference in dominance rank is an often-usedcue to resolve con icts between two animals without escalated Ž ghts. At the group level, adherence to a dominance convention efŽ ciently reduces the costs associatedwith con icts, but from an individual’s point of view, it is difŽ cult to explainwhy a low ranking individualshould accept its subordinatestatus. This is especially true if, as sugge...

Alternating Evolution Schemes for Hyperbolic Conservation Laws

The alternating evolution (AE) system of Liu [25] ∂tu +∇x · f(v) = 1 2 (v − u), ∂tv +∇x · f(u) = 1 2 (u− v) serves as a refined description of systems of hyperbolic conservation laws ∂tφ +∇x · f(φ) = 0, φ(x, 0) = φ0(x). The solution of conservation laws is precisely captured when two components take the same initial value as φ0, or approached by two components exponentially fast when 2 ↓ 0 if t...

Alternating Evolution Schemes for Hamilton-Jacobi Equations

In this work, we propose a high-resolution alternating evolution (AE) scheme to solve Hamilton–Jacobi equations. The construction of the AE scheme is based on an alternating evolution system of the Hamilton–Jacobi equation, following the idea previously developed for hyperbolic conservation laws. A semidiscrete scheme derives directly from a sampling of this system on alternating grids. Higher ...