Maximally-fast coarsening algorithms

We present maximally-fast numerical algorithms for conserved coarsening systems that are stable and accurate with a growing natural time-step $\Delta t=A t_s^{2/3}$. For non-conserved systems, only effectively finite timesteps are accessible for similar unconditionally stable algorithms. We compare the scaling structure obtained from our maximally-fast conserved systems directly against the standard fixed-timestep Euler algorithm, and find that the error scales as $\sqrt{A}$ -- so arbitrary accuracy can be achieved.Comment: 5 pages, 3 postscript figures, Late

Dynamical network stability analysis of multiple biological ages provides a framework for understanding the aging process

Widespread interest in non-destructive biomarkers of aging has led to a curse of plenty: a multitude of biological ages that each proffers a 'true' health-adjusted age of an individual. While each measure provides salient information on the aging process, they are each univariate, in contrast to the "hallmark" and "pillar" theories of aging which are explicitly multidimensional, multicausal and multiscale. Fortunately, multiple biological ages can be systematically combined into a multidimensional network representation. The interaction network between these biological ages permits analysis of the multidimensional effects of aging, as well as quantification of causal influences during both natural aging and, potentially, after anti-aging intervention. The behaviour of the system as a whole can then be explored using dynamical network stability analysis which identifies new, efficient biomarkers that quantify long term resilience scores on the timescale between measurements (years). We demonstrate this approach using a set of 8 biological ages from the longitudinal Swedish Adoption/Twin Study of Aging (SATSA). After extracting an interaction network between these biological ages, we observed that physiological age, a proxy for cardiometabolic health, serves as a central node in the network, implicating it as a key vulnerability for slow, age-related decline. We furthermore show that while the system as a whole is stable, there is a weakly stable direction along which recovery is slow - on the timescale of a human lifespan. This slow direction provides an aging biomarker which correlates strongly with chronological age and predicts longitudinal decline in health - suggesting that it estimates an important driver of age-related changes.Comment: 65 pages including supplementa

Network dynamical stability analysis of homeostasis reveals "mallostasis": biological equilibria drifting towards worsening health with age

Using longitudinal study data, we dynamically model how aging affects homeostasis in both mice and humans. We operationalize homeostasis as a multivariate mean-reverting stochastic process. Our central hypothesis is that homeostasis causes biomarkers to have stable equilibrium values, but that deviations from equilibrium of one biomarker can affect other biomarkers through an interaction network. These interactions preclude analysis of one biomarker at a time. We therefore looked for age-related changes to homeostasis using dynamic network stability analysis (eigen-analysis), which transforms observed biomarker data into independent "natural" variables and determines their associated recovery rates. Most natural variables remained near equilibrium and were essentially constant in time. Some natural variables were unable to equilibrate due to a gradual drift with age in their homeostatic equilibrium, i.e. allostasis. This drift caused them to accumulate over the lifespan course. These accumulating variables are natural aging variables. Their rate of accumulation was correlated with risk of adverse outcomes: death or dementia onset. We call this tendency for aging organisms to drift towards an equilibrium position of ever-worsening health "mallostasis". We demonstrate that the effects of mallostasis on observed biomarkers are spread out through the interaction network. This could provide a redundancy mechanism to preserve functioning until multi-system dysfunction emerges at advanced ages.Comment: 11 pages and 5 figures + supplemental (30 pages, 2 tables and 17 figures