Efficient and exact sampling of simple graphs with given arbitrary degree sequence

Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet modeling. Existing graph sampling methods are either link-swap based (Markov-Chain Monte Carlo algorithms) or stub-matching based (the Configuration Model). Both types are ill-controlled, with typically unknown mixing times for link-swap methods and uncontrolled rejections for the Configuration Model. Here we propose an efficient, polynomial time algorithm that generates statistically independent graph samples with a given, arbitrary, degree sequence. The algorithm provides a weight associated with each sample, allowing the observable to be measured either uniformly over the graph ensemble, or, alternatively, with a desired distribution. Unlike other algorithms, this method always produces a sample, without back-tracking or rejections. Using a central limit theorem-based reasoning, we argue, that for large N, and for degree sequences admitting many realizations, the sample weights are expected to have a lognormal distribution. As examples, we apply our algorithm to generate networks with degree sequences drawn from power-law distributions and from binomial distributions.Comment: 8 pages, 3 figure

Evolving Clustered Random Networks

We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as generic models for studying the impacts of degree distributions and clustering on dynamical processes as well as null models for detecting other structural properties in empirical networks

Wormhole Cosmic Censorship

We analyze the properties of a Kerr-like wormhole supported by phantom matter, which is an exact solution of the Einstein-phantom field equations. It is shown that the solution has a naked ring singularity which is unreachable to null geodesics falling freely from the outside. Similarly to Roger Penrose's cosmic censorship, that states that all naked singularities in the Universe must be protected by event horizons, here we conjecture from our results that a naked singularity can also be fully protected by the intrinsic properties of a wormhole's throat

Derived length of solvable groups of local diffeomorphisms

Let $G$ be a solvable subgroup of the group \diff{}{n} of local complex analytic diffeomorphisms. Analogously as for groups of matrices we bound the solvable length of $G$ by a function of $n$. Moreover we provide the best possible bounds for connected, unipotent and nilpotent groups.Comment: 27 page

Structural Properties of Ego Networks

The structure of real-world social networks in large part determines the evolution of social phenomena, including opinion formation, diffusion of information and influence, and the spread of disease. Globally, network structure is characterized by features such as degree distribution, degree assortativity, and clustering coefficient. However, information about global structure is usually not available to each vertex. Instead, each vertex's knowledge is generally limited to the locally observable portion of the network consisting of the subgraph over its immediate neighbors. Such subgraphs, known as ego networks, have properties that can differ substantially from those of the global network. In this paper, we study the structural properties of ego networks and show how they relate to the global properties of networks from which they are derived. Through empirical comparisons and mathematical derivations, we show that structural features, similar to static attributes, suffer from paradoxes. We quantify the differences between global information about network structure and local estimates. This knowledge allows us to better identify and correct the biases arising from incomplete local information.Comment: Accepted by SBP 2015, to appear in the proceeding

A study on the friendship paradox – quantitative analysis and relationship with assortative mixing

The friendship paradox is the observation that friends of individuals tend to have more friends or be more popular than the individuals themselves. In this work, we first study local metrics to capture the strength of the paradox and the direction of the paradox from the perspective of individual nodes, i.e., an indication of whether the individual is more or less popular than its friends. These local metrics are aggregated, and global metrics are proposed to express the phenomenon on a network-wide level. Theoretical results show that the defined metrics are well-behaved enough to capture the friendship paradox. We also theoretically analyze the behavior of the friendship paradox for popular network models in order to understand regimes where friendship paradox occurs. These theoretical findings are complemented by experimental results on both network models and real-world networks. By conducting a correlation study between the proposed metrics and degree assortativity, we experimentally demonstrate that the phenomenon of the friendship paradox is related to the well-known phenomenon of assortative mixing

Comparison of Nitrofen Uptake via Water and Food and its Distribution in Tissue of Common Carp, Cyprinus carpio L.

Carp (Cyprinus carpio L.) were exposed to nitrofen (NIP) by different routes (via water or food) to compare bioaccumulation parameters and tissue distribution. The bioconcentration factor of NIP was 5,100, and the lipid-corrected biomagnification factor was 0.137. Growth-corrected elimination half lives were 2.1–3.0 days via aqueous exposure and 2.7–2.9 days via dietary exposure. From either uptake route, the tissue distribution of NIP was highest in the head, followed by muscle, viscera, dermis, digestive tract and hepatopancreas, which was highly correlated with the tissue lipid content. We conclude that the uptake route has no influence on tissue distribution of NIP and that the accumulation potential in tissues depends on the lipid content

Mesoscopic organization reveals the constraints governing C. elegans nervous system

One of the biggest challenges in biology is to understand how activity at the cellular level of neurons, as a result of their mutual interactions, leads to the observed behavior of an organism responding to a variety of environmental stimuli. Investigating the intermediate or mesoscopic level of organization in the nervous system is a vital step towards understanding how the integration of micro-level dynamics results in macro-level functioning. In this paper, we have considered the somatic nervous system of the nematode Caenorhabditis elegans, for which the entire neuronal connectivity diagram is known. We focus on the organization of the system into modules, i.e., neuronal groups having relatively higher connection density compared to that of the overall network. We show that this mesoscopic feature cannot be explained exclusively in terms of considerations, such as optimizing for resource constraints (viz., total wiring cost) and communication efficiency (i.e., network path length). Comparison with other complex networks designed for efficient transport (of signals or resources) implies that neuronal networks form a distinct class. This suggests that the principal function of the network, viz., processing of sensory information resulting in appropriate motor response, may be playing a vital role in determining the connection topology. Using modular spectral analysis, we make explicit the intimate relation between function and structure in the nervous system. This is further brought out by identifying functionally critical neurons purely on the basis of patterns of intra- and inter-modular connections. Our study reveals how the design of the nervous system reflects several constraints, including its key functional role as a processor of information.Comment: Published version, Minor modifications, 16 pages, 9 figure

The combined diabetes and renal control trial (C-DIRECT) - a feasibility randomised controlled trial to evaluate outcomes in multi-morbid patients with diabetes and on dialysis using a mixed methods approach

Background: This cluster randomised controlled trial set out to investigate the feasibility and acceptability of the “Combined Diabetes and Renal Control Trial” (C-DIRECT) intervention, a nurse-led intervention based on motivational interviewing and self-management in patients with coexisting end stage renal diseases and diabetes mellitus (DM ESRD). Its efficacy to improve glycaemic control, as well as psychosocial and self-care outcomes were also evaluated as secondary outcomes. Methods: An assessor-blinded, clustered randomised-controlled trial was conducted with 44 haemodialysis patients with DM ESRD and ≥ 8% glycated haemoglobin (HbA1c), in dialysis centres across Singapore. Patients were randomised according to dialysis shifts. 20 patients were assigned to intervention and 24 were in usual care. The C-DIRECT intervention consisted of three weekly chair-side sessions delivered by diabetes specialist nurses. Data on recruitment, randomisation, and retention, and secondary outcomes such as clinical endpoints, emotional distress, adherence, and self-management skills measures were obtained at baseline and at 12 weeks follow-up. A qualitative evaluation using interviews was conducted at the end of the trial. Results: Of the 44 recruited at baseline, 42 patients were evaluated at follow-up. One patient died, and one discontinued the study due to deteriorating health. Recruitment, retention, and acceptability rates of C-DIRECT were generally satisfactory HbA1c levels decreased in both groups, but C-DIRECT had more participants with HbA1c < 8% at follow up compared to usual care. Significant improvements in role limitations due to physical health were noted for C-DIRECT whereas levels remained stable in usual care. No statistically significant differences between groups were observed for other clinical markers and other patient-reported outcomes. There were no adverse effects. Conclusions: The trial demonstrated satisfactory feasibility. A brief intervention delivered on bedside as part of routine dialysis care showed some benefits in glycaemic control and on QOL domain compared with usual care, although no effect was observed in other secondary outcomes. Further research is needed to design and assess interventions to promote diabetes self-management in socially vulnerable patients