Graph Metrics for Temporal Networks

Temporal networks, i.e., networks in which the interactions among a set of elementary units change over time, can be modelled in terms of time-varying graphs, which are time-ordered sequences of graphs over a set of nodes. In such graphs, the concepts of node adjacency and reachability crucially depend on the exact temporal ordering of the links. Consequently, all the concepts and metrics proposed and used for the characterisation of static complex networks have to be redefined or appropriately extended to time-varying graphs, in order to take into account the effects of time ordering on causality. In this chapter we discuss how to represent temporal networks and we review the definitions of walks, paths, connectedness and connected components valid for graphs in which the links fluctuate over time. We then focus on temporal node-node distance, and we discuss how to characterise link persistence and the temporal small-world behaviour in this class of networks. Finally, we discuss the extension of classic centrality measures, including closeness, betweenness and spectral centrality, to the case of time-varying graphs, and we review the work on temporal motifs analysis and the definition of modularity for temporal graphs.Comment: 26 pages, 5 figures, Chapter in Temporal Networks (Petter Holme and Jari Saram\"aki editors). Springer. Berlin, Heidelberg 201

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

Emergence of scale-free close-knit friendship structure in online social networks

Despite the structural properties of online social networks have attracted much attention, the properties of the close-knit friendship structures remain an important question. Here, we mainly focus on how these mesoscale structures are affected by the local and global structural properties. Analyzing the data of four large-scale online social networks reveals several common structural properties. It is found that not only the local structures given by the indegree, outdegree, and reciprocal degree distributions follow a similar scaling behavior, the mesoscale structures represented by the distributions of close-knit friendship structures also exhibit a similar scaling law. The degree correlation is very weak over a wide range of the degrees. We propose a simple directed network model that captures the observed properties. The model incorporates two mechanisms: reciprocation and preferential attachment. Through rate equation analysis of our model, the local-scale and mesoscale structural properties are derived. In the local-scale, the same scaling behavior of indegree and outdegree distributions stems from indegree and outdegree of nodes both growing as the same function of the introduction time, and the reciprocal degree distribution also shows the same power-law due to the linear relationship between the reciprocal degree and in/outdegree of nodes. In the mesoscale, the distributions of four closed triples representing close-knit friendship structures are found to exhibit identical power-laws, a behavior attributed to the negligible degree correlations. Intriguingly, all the power-law exponents of the distributions in the local-scale and mesoscale depend only on one global parameter -- the mean in/outdegree, while both the mean in/outdegree and the reciprocity together determine the ratio of the reciprocal degree of a node to its in/outdegree.Comment: 48 pages, 34 figure

Ectonucleotidases in Müller glial cells of the rodent retina: Involvement in inhibition of osmotic cell swelling

Extracellular nucleotides mediate glia-to-neuron signalling in the retina and are implicated in the volume regulation of retinal glial (Müller) cells under osmotic stress conditions. We investigated the expression and functional role of ectonucleotidases in Müller cells of the rodent retina by cell-swelling experiments, calcium imaging, and immuno- and enzyme histochemistry. The swelling of Müller cells under hypoosmotic stress was inhibited by activation of an autocrine purinergic signalling cascade. This cascade is initiated by exogenous glutamate and involves the consecutive activation of P2Y1 and adenosine A1 receptors, the action of ectoadenosine 5′-triphosphate (ATP)ases, and a nucleoside-transporter-mediated release of adenosine. Inhibition of ectoapyrases increased the ATP-evoked calcium responses in Müller cell endfeet. Müller cells were immunoreactive for nucleoside triphosphate diphosphohydrolases (NTPDase)2 (but not NTPDase1), ecto-5′-nucleotidase, P2Y1, and A1 receptors. Enzyme histochemistry revealed that ATP but not adenosine 5′-diphosphate (ADP) is extracellularly metabolised in retinal slices of NTPDase1 knockout mice. NTPDase1 activity and protein is restricted to blood vessels, whereas activity of alkaline phosphatase is essentially absent at physiological pH. The data suggest that NTPDase2 is the major ATP-degrading ectonucleotidase of the retinal parenchyma. NTPDase2 expressed by Müller cells can be implicated in the regulation of purinergic calcium responses and cellular volume

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

Which activities threaten independent living of elderly when becoming problematic : inspiration for meaningful service robot functionality

Purpose: In light of the increasing elderly population and the growing demand for home care, the potential of robot support is given increasing attention. In this paper, an inventory of activities was made that threaten independent living of elderly when becoming problematic. Results will guide the further development of an existing service robot, the Care-O-bot®. Method: A systematic literature search of PubMed was performed, focused on the risk factors for institutionalization. Additionally, focus group sessions were conducted in the Netherlands, United Kingdom and France. In these focus group sessions, problematic activities threatening the independence of elderly people were discussed. Three separate target groups were included in the focus group sessions: (1) elderly persons (n = 41), (2) formal caregivers (n = 40) and (3) informal caregivers (n = 32). Results: Activities within the International Classification of Functioning domains mobility, self-care, and interpersonal interaction and relationships were found to be the most problematic. Conclusions: A distinct set of daily activities was identified that may threaten independent living, but no single activity could be selected as the main activity causing a loss of independence as it is often a combination of problematic activities that is person-specific. Supporting the problematic activities need not involve a robotic solution Read More: http://informahealthcare.com/doi/abs/10.3109/17483107.2013.840861Peer reviewe

Effect of correlations on network controllability

A dynamical system is controllable if by imposing appropriate external signals on a subset of its nodes, it can be driven from any initial state to any desired state in finite time. Here we study the impact of various network characteristics on the minimal number of driver nodes required to control a network. We find that clustering and modularity have no discernible impact, but the symmetries of the underlying matching problem can produce linear, quadratic or no dependence on degree correlation coefficients, depending on the nature of the underlying correlations. The results are supported by numerical simulations and help narrow the observed gap between the predicted and the observed number of driver nodes in real networks

Fluid-structure interaction in abdominal aortic aneurysms: effects of asymmetry and wall thickness

BACKGROUND: Abdominal aortic aneurysm (AAA) is a prevalent disease which is of significant concern because of the morbidity associated with the continuing expansion of the abdominal aorta and its ultimate rupture. The transient interaction between blood flow and the wall contributes to wall stress which, if it exceeds the failure strength of the dilated arterial wall, will lead to aneurysm rupture. Utilizing a computational approach, the biomechanical environment of virtual AAAs can be evaluated to study the affects of asymmetry and wall thickness on this stress, two parameters that contribute to increased risk of aneurysm rupture. METHODS: Ten virtual aneurysm models were created with five different asymmetry parameters ranging from β = 0.2 to 1.0 and either a uniform or variable wall thickness to study the flow and wall dynamics by means of fully coupled fluid-structure interaction (FSI) analyses. The AAA wall was designed to have a (i) uniform 1.5 mm thickness or (ii) variable thickness ranging from 0.5 – 1.5 mm extruded normally from the boundary surface of the lumen. These models were meshed with linear hexahedral elements, imported into a commercial finite element code and analyzed under transient flow conditions. The method proposed was then compared with traditional computational solid stress techniques on the basis of peak wall stress predictions and cost of computational effort. RESULTS: The results provide quantitative predictions of flow patterns and wall mechanics as well as the effects of aneurysm asymmetry and wall thickness heterogeneity on the estimation of peak wall stress. These parameters affect the magnitude and distribution of Von Mises stresses; varying wall thickness increases the maximum Von Mises stress by 4 times its uniform thickness counterpart. A pre-peak systole retrograde flow was observed in the AAA sac for all models, which is due to the elastic energy stored in the compliant arterial wall and the expansion force of the artery during systole. CONCLUSION: Both wall thickness and geometry asymmetry affect the stress exhibited by a virtual AAA. Our results suggest that an asymmetric AAA with regional variations in wall thickness would be exposed to higher mechanical stresses and an increased risk of rupture than a more fusiform AAA with uniform wall thickness. Therefore, it is important to accurately reproduce vessel geometry and wall thickness in computational predictions of AAA biomechanics

Centralized Modularity of N-Linked Glycosylation Pathways in Mammalian Cells

Glycosylation is a highly complex process to produce a diverse repertoire of cellular glycans that are attached to proteins and lipids. Glycans are involved in fundamental biological processes, including protein folding and clearance, cell proliferation and apoptosis, development, immune responses, and pathogenesis. One of the major types of glycans, N-linked glycans, is formed by sequential attachments of monosaccharides to proteins by a limited number of enzymes. Many of these enzymes can accept multiple N-linked glycans as substrates, thereby generating a large number of glycan intermediates and their intermingled pathways. Motivated by the quantitative methods developed in complex network research, we investigated the large-scale organization of such N-linked glycosylation pathways in mammalian cells. The N-linked glycosylation pathways are extremely modular, and are composed of cohesive topological modules that directly branch from a common upstream pathway of glycan synthesis. This unique structural property allows the glycan production between modules to be controlled by the upstream region. Although the enzymes act on multiple glycan substrates, indicating cross-talk between modules, the impact of the cross-talk on the module-specific enhancement of glycan synthesis may be confined within a moderate range by transcription-level control. The findings of the present study provide experimentally-testable predictions for glycosylation processes, and may be applicable to therapeutic glycoprotein engineering