Aging in transport processes on networks with stochastic cumulative damage

Antifragility of stochastic transport on networks with damage

A system is called antifragile when damage acts as a constructive element improving the performance of a global function. In this paper, we analyze the emergence of antifragility in the movement of random walkers on networks with modular structures or communities. The random walker hops considering the capacity of transport of each link, whereas the links are susceptible to random damage that accumulates over time. We show that in networks with communities and high modularity, the localization of damage in specific groups of nodes leads to a global antifragile response of the system improving the capacity of stochastic transport to more easily reach the nodes of a network. Our findings give evidence of the mechanisms behind antifragile response in complex systems and pave the way for their quantitative exploration in different fields.

Nutrition and stem cell integrity in aging

Adult stem cells (SCs) represent the regenerative capacity of organisms throughout their lifespan. The maintenance of robust SC populations capable of renewing organs and physiological systems is one hallmark of healthy aging. The local environment of SCs, referred to as the niche, includes the nutritional milieu, which is essential to maintain the quantity and quality of SCs available for renewal and regeneration. There is increased recognition that SCs have unique metabolism and conditional nutrient needs compared to fully differentiated cells. However, the contribution of SC nutrition to overall human nutritional requirements is an understudied and underappreciated area of investigation. Nutrient needs vary across the lifespan and are modified by many factors including individual health, disease, physiological states including pregnancy, age, sex, and during recovery from injury. Although current nutrition guidance is generally derived for apparently healthy populations and to prevent nutritional deficiency diseases, there are increased efforts to establish nutrient-based and food-based recommendations based on reducing chronic disease. Understanding the dynamics of SC nutritional needs throughout the life span, including the role of nutrition in extending biological age by blunting biological systems decay, is fundamental to establishing food and nutrient guidance for chronic disease reduction and health maintenance. This review summarizes a 3-day symposium of the Marabou Foundation (www.marabousymposium.org) held to examine the metabolic properties and unique nutritional needs of adult SCs and their role in healthy aging and age-related chronic disease.

Optimal exploration of random walks with local bias on networks

We propose local-biased random walks on general networks where a Markovian walker is defined by different types of biases in each node to establish transitions to its neighbors depending on their degrees. For this ergodic dynamics, we explore the capacity of the random walker to visit all the nodes characterized by a global mean first passage time. This quantity is calculated using eigenvalues and eigenvectors of the transition matrix that defines the dynamics. In the first part, we illustrate how our framework leads to optimal exploration for small-size graphs through the analysis of all the possible bias configurations. In the second part, we study the most favorable configurations in each node by using simulated annealing. This heuristic algorithm allows obtaining approximate solutions of the optimal bias in different types of networks. The results show how the local bias can optimize the exploration of the network in comparison with the unbiased random walk. The methods implemented in this research are general and open the doors to a broad spectrum of tools applicable to different random walk strategies and dynamical processes on networks.

Biased Continuous-Time Random Walks with Mittag-Leffler Jumps

We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with biased walks on digraphs. Within this framework, we introduce a space-time generalization of the Poisson process as a strictly increasing walk with discrete Mittag-Leffler jumps time-changed with an independent (continuous-time) fractional Poisson process. We call this process ‘space-time Mittag-Leffler process’. We derive explicit formulae for the state probabilities which solve a Cauchy problem with a Kolmogorov-Feller (forward) difference-differential equation of general fractional type. We analyze a “well-scaled” diffusion limit and obtain a Cauchy problem with a space-time convolution equation involving Mittag-Leffler densities. We deduce in this limit the ‘state density kernel’ solving this Cauchy problem. It turns out that the diffusion limit exhibits connections to Prabhakar general fractional calculus. We also analyze in this way a generalization of the space-time Mittag-Leffler process. The approach of constructing good Laplacian generator functions has a large potential in applications of space-time generalizations of the Poisson process and in the field of continuous-time random walks on digraphs.

Nonlocal biased random walks and fractional transport on directed networks

In this paper, we study nonlocal random walk strategies generated with the fractional Laplacian matrix of directed networks. We present a general approach to analyzing these strategies by defining the dynamics as a discrete-time Markovian process with transition probabilities between nodes expressed in terms of powers of the Laplacian matrix. We analyze the elements of the transition matrices and their respective eigenvalues and eigenvectors, the mean first passage times and global times to characterize the random walk strategies. We apply this approach to the study of particular local and nonlocal ergodic random walks on different directed networks; we explore circulant networks, the biased transport on rings and the dynamics on random networks. We study the efficiency of a fractional random walker with bias on these structures. Effects of ergodicity loss which occur when a directed network is not any more strongly connected are also discussed.