Beyond clustering: mean-field dynamics on networks with arbitrary subgraph composition.

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of triangles, and this has led to the principle of constructing networks from such building blocks. This approach has been generalised to networks being constructed from a set of more exotic subgraphs. As long as these are fully connected, it is then possible to derive mean-field models that approximate epidemic dynamics well. However, there are virtually no results for non-fully connected subgraphs. In this paper, we provide a general and automated approach to deriving a set of ordinary differential equations, or mean-field model, that describes, to a high degree of accuracy, the expected values of system-level quantities, such as the prevalence of infection. Our approach offers a previously unattainable degree of control over the arrangement of subgraphs and network characteristics such as classical node degree, variance and clustering. The combination of these features makes it possible to generate families of networks with different subgraph compositions while keeping classical network metrics constant. Using our approach, we show that higher-order structure realised either through the introduction of loops of different sizes or by generating networks based on different subgraphs but with identical degree distribution and clustering, leads to non-negligible differences in epidemic dynamics.

Higher-order structure and epidemic dynamics in clustered networks.

Clustering is typically measured by the ratio of triangles to all triples regardless of whether open or closed. Generating clustered networks, and how clustering affects dynamics on networks, is reasonably well understood for certain classes of networks (Volz et al., 2011; Karrer and Newman, 2010), e.g. networks composed of lines and non-overlapping triangles. In this paper we show that it is possible to generate networks which, despite having the same degree distribution and equal clustering, exhibit different higher-order structure, specifically, overlapping triangles and other order-four (a closed network motif composed of four nodes) structures. To distinguish and quantify these additional structural features, we develop a new network metric capable of measuring order-four structure which, when used alongside traditional network metrics, allows us to more accurately describe a network׳s topology. Three network generation algorithms are considered: a modified configuration model and two rewiring algorithms. By generating homogeneous networks with equal clustering we study and quantify their structural differences, and using SIS (Susceptible-Infected-Susceptible) and SIR (Susceptible-Infected-Recovered) dynamics we investigate computationally how differences in higher-order structure impact on epidemic threshold, final epidemic or prevalence levels and time evolution of epidemics. Our results suggest that characterising and measuring higher-order network structure is needed to advance our understanding of the impact of network topology on dynamics unfolding on the networks.

Prognosti implications of pigment epithelial detachment in bevacizumab (avastin)-treated eyes with age-related macular degeneration and choroidal neovascularization.

PURPOSE: To evaluate the response to primary bevacizumab treatment of eyes with age-related macular degeneration (AMD) and choroidal neovascularization (CNV) with a large pigment epithelial detachment (PED) component and to compare the increase in visual acuity and reabsorption of retinal fluid in PED eyes with eyes with CNV in AMD with a minimal to no PED component. METHODS: We reviewed 43 consecutive eyes with CNV and AMD on primary bevacizumab therapy. There were 13 eyes with a large PED component in AMD with CNV and 30 eyes with a minimal to no PED in CNV. Only patients with no previous treatment for AMD and those started on purely intravitreal bevacizumab treatment were taken in the study. Pigment epithelial detachment size, time to PED collapse, and retinal or subretinal fluid resolution were determined as was Early Treatment Diabetic Retinopathy Study vision. Time to resolution of intraretinal and subretinal fluid was compared between the PED group and the non-PED group using survival analysis. RESULTS: In AMD with CNV eyes having a large PED component, sub- and intraretinal fluid initially resolved faster than the sub-PED fluid (P = 0.03). The subretinal pigment epithelial fluid itself was highly resistant. Visual acuity improvement was similar in both groups. CONCLUSION: Despite monthly intravitreal bevacizumab injections for neovascular AMD patients with a large component PED, the majority had minimal to no response of the PED. Sub- and intraretinal fluid response was faster in neovascular AMD without large PEDs, but after 7 months, vision change and reabsorption of intra- and subretinal fluid were similar in the two groups. Sub- and intraretinal fluid response did not appear to be related to PED size. Bevacizumab was very effective in reducing more of the sub- and intraretinal fluid than the PED fluid in AMD with CNV.

76-year decline and recovery of aspen mediated by contrasting fire regimes: Long-unburned, infrequent and frequent mixed-severity wildfire.

Quaking aspen (Populus tremuloides) is a valued, minor component on northeastern California landscapes. It provides a wide range of ecosystem services and has been in decline throughout the region for the last century. This decline may be explained partially by the lack of fire on the landscape due to heavier fire suppression, as aspen benefit from fire that eliminates conifer competition and stimulates reproduction through root suckering. However, there is little known about how aspen stand area changes in response to overlapping fire. Our study area in northeastern California on the Lassen, Modoc and Plumas National Forests has experienced recent large mixed-severity wildfires where aspen was present, providing an opportunity to study the re-introduction of fire. We observed two time periods; a 52-year absence of fire from 1941 to 1993 preceding a 24-year period of wildfire activity from 1993 to 2017. We utilized aerial photos and satellite imagery to delineate aspen stands and assess conifer cover percent. We chose aspen stands in areas where wildfires overlapped (twice-burned), where only a single wildfire burned, and areas that did not burn within the recent 24-year period. We observed these same stands within the first period of fire exclusion for comparison (i.e., 1941-1993). In the absence of fire, all aspen stand areas declined and all stands experienced increases in conifer composition. After wildfire, stands that burned experienced a release from conifer competition and increased in stand area. Stands that burned twice or at high severity experienced a larger removal of conifer competition than stands that burned once at low severity, promoting expansion of aspen stand area. Stands with less edge:area ratio also expanded in area more with fire present. Across both time periods, stand movement, where aspen stand footprints were mostly in new areas compared to footprints of previous years, was highest in smaller stands. In the fire exclusion period, smaller stands exhibited greater loss of area and changes in location (movement) than in the return of fire period, highlighting their vulnerability to loss via succession to conifers in the absence of disturbances that provide adequate growing space for aspen over time.

Elementary school parents'/guardians' perceptions of school health service personnel and the services they provide.

BACKGROUND: The school nurse, the school social worker, and the school counselor play an important role in promoting the health of children. Health services in the school setting provide opportunities to appraise, protect, and promote student health. The purpose of this study was to identify parents' or caregivers' perceptions and beliefs regarding the importance of schools providing various health services to their elementary school-aged children. In addition, the study examined the levels of parental support for, perceptions of, and contact with school health service personnel. METHODS: In 2005, a nationally representative random sample of 369 (51% return rate) parents of elementary school-aged children completed the questionnaire developed for this study. RESULTS: A majority of parents/caregivers reported that their child's school had a school nurse (78.8%) and counselor (60.5%), but only 22.6% reported their school had a social worker. A majority of parents/caregivers perceived full-time school nurses (86.3%), school counselors (78.6%), and school social workers (56.3%) as important or extremely important and that schools should be held responsible for having each in their child's elementary school. A majority of parents/caregivers were willing to pay an increase in yearly tax dollars to have full-time school health personnel. CONCLUSIONS: This study established a level of parental support for, perceptions of, and contact with school health service personnel. Parents were most supportive of school nurses and should be perceived as allies in ensuring job security.