On the Tomography of Networks and Multicast Trees

In this paper we model the tomography of scale free networks by studying the structure of layers around an arbitrary network node. We find, both analytically and empirically, that the distance distribution of all nodes from a specific network node consists of two regimes. The first is characterized by rapid growth, and the second decays exponentially. We also show that the nodes degree distribution at each layer is a power law with an exponential cut-off. We obtain similar results for the layers surrounding the root of multicast trees cut from such networks, as well as the Internet. All of our results were obtained both analytically and on empirical Interenet data

Localization transition on complex networks via spectral statistics

The spectral statistics of complex networks are numerically studied. The features of the Anderson metal-insulator transition are found to be similar for a wide range of different networks. A metal-insulator transition as a function of the disorder can be observed for different classes of complex networks for which the average connectivity is small. The critical index of the transition corresponds to the mean field expectation. When the connectivity is higher, the amount of disorder needed to reach a certain degree of localization is proportional to the average connectivity, though a precise transition cannot be identified. The absence of a clear transition at high connectivity is probably due to the very compact structure of the highly connected networks, resulting in a small diameter even for a large number of sites.Comment: 6 pages, expanded introduction and referencess (to appear in PRE

Stromal Gli2 activity coordinates a niche signaling program for mammary epithelial stem cells

The stem cell niche is a complex local signaling microenvironment that sustains stem cell activity during organ maintenance and regeneration. The mammary gland niche must support its associated stem cells while also responding to systemic hormonal regulation that triggers pubertal changes. We find that Gli2, the major Hedgehog pathway transcriptional effector, acts within mouse mammary stromal cells to direct a hormoneresponsive niche signaling program by activating expression of factors that regulate epithelial stem cells as well as receptors for the mammatrophic hormones estrogen and growth hormone.Whereas prior studies implicate stem cell defects in human disease, this work shows that niche dysfunction may also cause disease, with possible relevance for human disorders and in particular the breast growth pathogenesis associated with combined pituitary hormone deficiency. Copyright 2016 by the American Association for the Advancement of Science, all rights reserved.116Ysciescopu

Scale-Free Networks Emerging from Weighted Random Graphs

We study Erd\"{o}s-R\'enyi random graphs with random weights associated with each link. We generate a new ``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 $P(k)\sim k^{-\lambda}$ with $\lambda=2.5$. Our results imply that the minimum spanning tree (MST) in random graphs is composed of percolation clusters, which are interconnected by a set of links that create a scale-free tree with $\lambda=2.5$. We show that optimization causes the percolation threshold to emerge spontaneously, thus creating naturally a scale-free ``supernode network''. We discuss the possibility that this phenomenon is related to the evolution of several real world scale-free networks

Surface superconductivity in multilayered rhombohedral graphene: Supercurrent

The supercurrent for the surface superconductivity of a flat-band multilayered rhombohedral graphene is calculated. Despite the absence of dispersion of the excitation spectrum, the supercurrent is finite. The critical current is proportional to the zero-temperature superconducting gap, i.e., to the superconducting critical temperature and to the size of the flat band in the momentum space

Optimal Path and Minimal Spanning Trees in Random Weighted Networks

We review results on the scaling of the optimal path length in random networks with weighted links or nodes. In strong disorder we find that the length of the optimal path increases dramatically compared to the known small world result for the minimum distance. For Erd\H{o}s-R\'enyi (ER) and scale free networks (SF), with parameter $\lambda$ ($\lambda >3$), we find that the small-world nature is destroyed. We also find numerically that for weak disorder the length of the optimal path scales logaritmically with the size of the networks studied. We also review the transition between the strong and weak disorder regimes in the scaling properties of the length of the optimal path for ER and SF networks and for a general distribution of weights, and suggest that for any distribution of weigths, the distribution of optimal path lengths has a universal form which is controlled by the scaling parameter $Z=\ell_{\infty}/A$ where $A$ plays the role of the disorder strength, and $\ell_{\infty}$ is the length of the optimal path in strong disorder. The relation for $A$ is derived analytically and supported by numerical simulations. We then study the minimum spanning tree (MST) and show that it is composed of percolation clusters, which we regard as "super-nodes", connected by a scale-free tree. We furthermore show that the MST can be partitioned into two distinct components. One component the {\it superhighways}, for which the nodes with high centrality dominate, corresponds to the largest cluster at the percolation threshold which is a subset of the MST. In the other component, {\it roads}, low centrality nodes dominate. We demonstrate the significance identifying the superhighways by showing that one can improve significantly the global transport by improving a very small fraction of the network.Comment: review, accepted at IJB

In silico evolution of diauxic growth

The glucose effect is a well known phenomenon whereby cells, when presented with two different nutrients, show a diauxic growth pattern, i.e. an episode of exponential growth followed by a lag phase of reduced growth followed by a second phase of exponential growth. Diauxic growth is usually thought of as a an adaptation to maximise biomass production in an environment offering two or more carbon sources. While diauxic growth has been studied widely both experimentally and theoretically, the hypothesis that diauxic growth is a strategy to increase overall growth has remained an unconfirmed conjecture. Here, we present a minimal mathematical model of a bacterial nutrient uptake system and metabolism. We subject this model to artificial evolution to test under which conditions diauxic growth evolves. As a result, we find that, indeed, sequential uptake of nutrients emerges if there is competition for nutrients and the metabolism/uptake system is capacity limited. However, we also find that diauxic growth is a secondary effect of this system and that the speed-up of nutrient uptake is a much larger effect. Notably, this speed-up of nutrient uptake coincides with an overall reduction of efficiency. Our two main conclusions are: (i) Cells competing for the same nutrients evolve rapid but inefficient growth dynamics. (ii) In the deterministic models we use here no substantial lag-phase evolves. This suggests that the lag-phase is a consequence of stochastic gene expression

Regulatory control and the costs and benefits of biochemical noise

Experiments in recent years have vividly demonstrated that gene expression can be highly stochastic. How protein concentration fluctuations affect the growth rate of a population of cells, is, however, a wide open question. We present a mathematical model that makes it possible to quantify the effect of protein concentration fluctuations on the growth rate of a population of genetically identical cells. The model predicts that the population's growth rate depends on how the growth rate of a single cell varies with protein concentration, the variance of the protein concentration fluctuations, and the correlation time of these fluctuations. The model also predicts that when the average concentration of a protein is close to the value that maximizes the growth rate, fluctuations in its concentration always reduce the growth rate. However, when the average protein concentration deviates sufficiently from the optimal level, fluctuations can enhance the growth rate of the population, even when the growth rate of a cell depends linearly on the protein concentration. The model also shows that the ensemble or population average of a quantity, such as the average protein expression level or its variance, is in general not equal to its time average as obtained from tracing a single cell and its descendants. We apply our model to perform a cost-benefit analysis of gene regulatory control. Our analysis predicts that the optimal expression level of a gene regulatory protein is determined by the trade-off between the cost of synthesizing the regulatory protein and the benefit of minimizing the fluctuations in the expression of its target gene. We discuss possible experiments that could test our predictions.Comment: Revised manuscript;35 pages, 4 figures, REVTeX4; to appear in PLoS Computational Biolog

Elliptic flow of charged pions, protons and strange particles emitted in Pb+Au collisions at top SPS energy

Differential elliptic flow spectra v2(pT) of \pi-, K0short, p, \Lambda have been measured at \sqrt(s NN)= 17.3 GeV around midrapidity by the CERN-CERES/NA45 experiment in mid-central Pb+Au collisions (10% of \sigma(geo)). The pT range extends from about 0.1 GeV/c (0.55 GeV/c for \Lambda) to more than 2 GeV/c. Protons below 0.4 GeV/c are directly identified by dE/dx. At higher pT, proton elliptic flow v2(pT) is derived as a constituent, besides \pi+ and K+, of the elliptic flow of positive pion candidates. The retrieval requires additional inputs: (i) of the particle composition, and (ii) of v2(pT) of positive pions. For (i), particle ratios obtained by NA49 were adapted to CERES conditions; for (ii), the measured v2(pT) of negative pions is substituted, assuming \pi+ and \pi- elliptic flow magnitudes to be sufficiently close. The v2(pT) spectra are compared to ideal-hydrodynamics calculations. In synopsis of the series \pi- - K0short - p - \Lambda, flow magnitudes are seen to fall with decreasing pT progressively even below hydro calculations with early kinetic freeze-out (Tf= 160 MeV) leaving not much time for hadronic evolution. The proton v2(pT) data show a downward swing towards low pT with excursions into negative v2 values. The pion-flow isospin asymmetry observed recently by STAR at RHIC, invalidating in principle our working assumption, is found in its impact on proton flow bracketed from above by the direct proton flow data, and not to alter any of our conclusions. Results are discussed in perspective of recent viscous dynamics studies which focus on late hadronic stages.Comment: 38 pages, 27 figures, 2 tables. Abstract and parts of introduction made more comprehensible; corrected typos; acknowledgement added. To appear in Nucl.Phys.

Azimuthal dependence of pion source radii in Pb+Au collisions at 158 A GeV

We present results of a two-pion correlation analysis performed with the Au+Pb collision data collected by the upgraded CERES experiment in the fall of 2000. The analysis was done in bins of the reaction centrality and the pion azimuthal emission angle with respect to the reaction plane. The pion source, deduced from the data, is slightly elongated in the direction perpendicular to the reaction plane, similarly as was observed at the AGS and at RHIC.Comment: 5 pages, 2 figure