Showing papers on "Antisymmetry published in 1993"
TL;DR: It is shown that both antisymmetry and directional asymmetry can arise from symmetry-breaking phase transitions in the morphogen, and the implications for researchers using fluctuating asymmetry as an indicator of stress are discussed.
Abstract: Fluctuating asymmetry is the most commonly used measure of developmental instability. Some authors have claimed that antisymmetry and directional asymmetry may have a significant genetic basis, thereby rendering these forms of asymmetry useless for studies of developmental instability. Using a modified Rashevsky-Turing reaction-diffusion model of morphogenesis, we show that both antisymmetry and directional asymmetry can arise from symmetry-breaking phase transitions. Concentrations of morphogen on right and left sides can be induced to undergo transitions from phase-locked periodicity, to phase-lagged periodicity, to chaos, by simply changing the levels of feedback and inhibition in the model. The chaotic attractor has two basins of attraction-right sidedominance and left side dominance. With minor disturbance, a developmental trajectory settles into one basin or the other. With increasing disturbance, the trajectory can jump from basin to basin. The changes that lead to phase transitions and chaos are thoseexpected to occur with either genetic change or stress. If we assume that the morphogen influences the behavior of cell populations, then a transition from phase-locked periodicity to chaos in the morphogen produces a corresponding transition from fluctuating asymmetry to antisymmetry in both morphogen concentrations and cell populations. Directional asymmetry is easily modeled by introducing a bias in the conditions of the simulation. We discuss the implications of this model for researchers using fluctuating asymmetry as an indicator of stress.
269 citations
TL;DR: In this paper, the diffusion Monte Carlo method for the solution of the Schrodinger equation for atomic and molecular systems is extended to incorporate the antisymmetry constraint, where the sign problem is treated constraining the diffusion process of signed walkers within the fluctuating nodes of a function A, defined as sum of Gaussians centered on the psips.
Abstract: The diffusion Monte Carlo method for the solution of the Schrodinger equation for atomic and molecular systems is extended to incorporate the antisymmetry constraint. The sign problem is treated constraining the diffusion process of signed walkers within the fluctuating nodes of a function A, defined as sum of Gaussians centered on the psips. The function A is able to build up the full nodal surface in the 3N dimensional space. The algorithm is shown to scale as Nα3+Nβ3 where Nα and Nβ are the number of α and β electrons. Results are given for the b 3Σu+ and c 3Πu states of H2 and the 1 3S state of He.
12 citations
TL;DR: In this paper, the antisymmetric characteristic method was used to derive three-dimensional space groups G3l,p′ (p = 3, 4, 6), where p = 3.
Abstract: By use of the antisymmetric characteristic method, Pawley multiple antisymmetry three-dimensional space groups G3l,p′ (p = 3, 4, 6) are derived.
8 citations