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The metabolism of oxygen, although central to life, produces reactive oxygen species (ROS) that have been implicated in processes as diverse as cancer, cardiovascular disease and ageing. It has recently been shown that central nervous system stem cells and haematopoietic stem cells and early progenitors contain lower levels of ROS than their more mature(More)
Cancer is often viewed as a caricature of normal developmental processes, but the extent to which its cellular heterogeneity truly recapitulates multilineage differentiation processes of normal tissues remains unknown. Here we implement single-cell PCR gene-expression analysis to dissect the cellular composition of primary human normal colon and colon(More)
A current challenge in biology is to understand the dynamics of protein circuits in living human cells. Can one define and test equations for the dynamics and variability of a protein over time? Here, we address this experimentally and theoretically, by means of accurate time-resolved measurements of endogenously tagged proteins in individual human cells.(More)
An incomplete understanding of the nature of heterogeneity within stem cell populations remains a major impediment to the development of clinically effective cell-based therapies. Transcriptional events within a single cell are inherently stochastic and can produce tremendous variability, even among genetically identical cells. It remains unclear how(More)
Biological systems often display modularity, in the sense that they can be decomposed into nearly independent subsystems. Recent studies have suggested that modular structure can spontaneously emerge if goals (environments) change over time, such that each new goal shares the same set of sub-problems with previous goals. Such modularly varying goals can(More)
Previous studies indicated that nonlinear properties of Gaussian distributed time series with long-range correlations, u(i), can be detected and quantified by studying the correlations in the magnitude series |u(i)|, the "volatility." However, the origin for this empirical observation still remains unclear and the exact relation between the correlations in(More)
We review results on the scaling of the optimal path length opt in random networks with weighted links or nodes. We refer to such networks as " weighted " or " disordered " networks. The optimal path is the path with minimum sum of the weights. In strong disorder, where the maximal weight along the path dominates the sum, we find that opt increases(More)
We study Erdös-Rényi random graphs with random weights associated with each link. We generate a "supernode network" by merging all nodes connected by links having weights below the percolation threshold (percolation clusters) into a single node. We show that this network is scale-free, i.e., the degree distribution is P(k) approximately k(-lambda) with(More)
It is known that the critical probability for the percolation transition is not a sharp threshold. Actually it is a region of nonzero width Deltap(c) for systems of finite size. Here we present evidence that for complex networks Deltap(c) approximately p(c)/l, where l approximately Nnu(opt), where is the average length of the percolation cluster, and N is(More)
We study the distribution of optimal path lengths in random graphs with random weights associated with each link ("disorder"). With each link i we associate a weight tau(i) = exp (a r(i)), where r(i) is a random number taken from a uniform distribution between 0 and 1, and the parameter a controls the strength of the disorder. We suggest, in an analogy with(More)