The combined effect of connectivity and dependency links on percolation of networks

Percolation theory is extensively studied in statistical physics and mathematics with applications in diverse fields. However, the research is focused on systems with only one type of links, connectivity links. We review a recently developed mathematical framework for analyzing percolation properties of realistic scenarios of networks having links of two types, connectivity and dependency links. This formalism was applied to study Erd$\ddot{o}$s-R$\acute{e}$nyi (ER) networks that include also dependency links. For an ER network with average degree $k$ that is composed of dependency clusters of size $s$, the fraction of nodes that belong to the giant component, $P_\infty$, is given by $P_\infty=p^{s-1}[1-\exp{(-kpP_\infty)}]^s$ where $1-p$ is the initial fraction of randomly removed nodes. Here, we apply the formalism to the study of random-regular (RR) networks and find a formula for the size of the giant component in the percolation process: $P_\infty=p^{s-1}(1-r^k)^s$ where $r$ is the solution of $r=p^s(r^{k-1}-1)(1-r^k)+1$. These general results coincide, for $s=1$, with the known equations for percolation in ER and RR networks respectively without dependency links. In contrast to $s=1$, where the percolation transition is second order, for $s>1$ it is of first order. Comparing the percolation behavior of ER and RR networks we find a remarkable difference regarding their resilience. We show, analytically and numerically, that in ER networks with low connectivity degree or large dependency clusters, removal of even a finite number (zero fraction) of the network nodes will trigger a cascade of failures that fragments the whole network. This result is in contrast to RR networks where such cascades and full fragmentation can be triggered only by removal of a finite fraction of nodes in the network.Comment: 11 pages, 3 figure

Identification of the prebiotic translation apparatus within the contemporary ribosome

A structural element that could have existed independently in the prebiotic era was identified at the active site of the contemporary ribosome. It is suggested to have functioned as a proto-ribosome catalyzing peptide bond formation and non-coded elongation in the same manner that contemporary ribosomes exert positional catalysis, namely by accommodating the reactants in stereochemistry favourable for inline nucleophilic attack. This simple apparatus is a dimer of self-folding RNA units that could have assembled spontaneously into a symmetrical pocket-like structure, sufficiently efficient to be preserved throughout evolution as the active site of modern ribosomes, thus presenting a conceivable starting point for translation.Here we discuss the proto-ribosome emergence hypothesis and show that the tendency for dimerization, a prerequisite for obtaining the catalytic centre, is linked to the fold of its two components, indicating functional selection at the molecular level in the prebiotic era and supporting the existence of dimeric proto-ribosome

Distributed opto-mechanical analysis of liquids outside standard fibers coated with polyimide

The analysis of surrounding media has been a long-standing challenge of optical fiber sensors. Measurements are difficult due to the confinement of light to the inner core of standard fibers. Over the last two years, new sensor concepts have enabled the analysis of liquids outside the cladding boundary, where light does not reach. Sensing is based on opto-mechanical, forward stimulated Brillouin scattering interactions between guided light and sound waves. In most previous works, however, the protective polymer coating of the fiber had to be removed first. In this work, we report the opto-mechanical analysis of liquids outside commercially available, standard single-mode fibers with polyimide coating. The polyimide layer provides mechanical protection but can also transmit acoustic waves from the fiber cladding towards outside media. Comprehensive analysis of opto-mechanical coupling in coated fibers that are immersed in liquid is provided. The model shows that forward stimulated Brillouin scattering spectra in coated fibers are more complex than those of bare fibers, and strongly depend on the exact coating diameter and the choice of acoustic mode. Nevertheless, sensing outside coated fibers is demonstrated experimentally. Integrated measurements over 100 meters of fiber clearly distinguish between air, ethanol and water outside polyimide coating. Measured spectra are in close quantitative agreement with the analytic predictions. Further, distributed opto-mechanical time-domain reflectometry mapping of water and ethanol outside coated fiber is reported, with a spatial resolution of 100 meters. The results represent a large step towards practical opto-mechanical fiber sensors

On the Origins and Control of Community Types in the Human Microbiome

Microbiome-based stratification of healthy individuals into compositional categories, referred to as "community types", holds promise for drastically improving personalized medicine. Despite this potential, the existence of community types and the degree of their distinctness have been highly debated. Here we adopted a dynamic systems approach and found that heterogeneity in the interspecific interactions or the presence of strongly interacting species is sufficient to explain community types, independent of the topology of the underlying ecological network. By controlling the presence or absence of these strongly interacting species we can steer the microbial ecosystem to any desired community type. This open-loop control strategy still holds even when the community types are not distinct but appear as dense regions within a continuous gradient. This finding can be used to develop viable therapeutic strategies for shifting the microbial composition to a healthy configurationComment: Main Text, Figures, Methods, Supplementary Figures, and Supplementary Tex

Are Glucose Readings Sufficient to Adjust Insulin Dosage?

Aims/hypothesis: Insulin therapy is effective predominantly when dosage is frequently adjusted. However, a controversy surrounds the pertinent clinical parameters required to make effective and safe frequent dosage adjustments. We hypothesize that glucose readings are sufficient to adjust insulin dosage provided that dosage is adjusted every 1-4 weeks. Methods: To test the hypothesis, we generated several algorithms implemented in software to process glucose readings and recommend insulin dosage adjustments. A post hoc analysis was made on 630 log sheets (2,520 insulin dosage adjustments) from 26 older adults with suboptimally controlled type 2 diabetes. The subjects were followed for a year and treated with intensive insulin therapy that was titrated every 1-4 weeks by a trained study team. More than 88% of subjects attained the treatment goal (hemoglobin A1c <7%) without excessive hypoglycemia. Glucose readings from each log sheet were used as an input to the software, and its recommendations for insulin dosage adjustments were compared to the original ones made by the study team. While the study team could have been exposed to multiple clinical parameters, the software relied solely on glucose readings. Results: The software recommendations for dosage adjustments were clinically equivalent to the original study team's recommendations in more than 95% of the cases, unrelated to patients' insulin sensitivity. The remaining 4.4% (n = 111) were thoroughly examined, yet we did not find any recommendations suggested by the software to be unsafe or unreasonable. Conclusions/Interpretation: Glucose readings are sufficient to effectively adjust insulin dosage provided that adjustments are made every 1-4 weeks. Therefore, dedicated software can help adjusting insulin dosage between clinic visits.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90435/1/dia-2E2010-2E0112.pd

Adaptive Search for Sparse Targets with Informative Priors

This works considers the problem of efficient energy allocation of resources in a continuous fashion in determining the location of targets in a sparse environment. We extend the work of Bashan [1] to analyze the use of non-uniform prior knowledge for the location of targets. We show that in the best-case scenario (i.e., when the known prior knowledge is also the underlying prior), then we can get significant gains (several dB) by using a two-level piecewise uniform prior over using the uniform prior that is assumed in [1]. Moreover, even when we have uncertainty in our prior knowledge, we show that we can always do at least as well as the uniform alternative in terms of worst-case and expected gains. In future work, we plan to extend our analysis to general piecewise uniform priors in order to develop multistage (i.e., greater than 2) adaptive energy allocation policies. In many situations, it might be desirable to allocate a limited amount of energy to a small region of interest (ROI) within a larger environment by using adaptive sampling techniques. For example, consider the problem of minimizing communication costs when tracking a target in a distributed sensor network. Clearly, when a node in our sensor network is far from our previous estimate of the target, we woul