Independent Sets in Line of Sight Networks

In this thesis we study the maximum independent set problem in both 2 and higher dimensional line of sight networks. The maximum independent set problem seeks to find a largest set of pairwise disjoint vertices and we will study both the decision version and the optimisation version of the problem in this thesis. The line of sight network model was introduced to provide a model of geometric graph that incorporates both range and line of sight restrictions. A LoS network model is governed by three parameters: n-size of the underlying integer grid, d-dimension of the underlying integer grid and ω the range parameter that governs how large the communication range of each vertex is, which can range from 1 to n. We first analyse the computational complexity of the maximum independent set problem for varying classes of line of sight networks governed by the dimension and range parameters d and ω. In particular, we are interested in the cases where d ≥ 2 and ω is sublinear in the size of the integer grid and where d ≥ 3 and ω is equal to the size of the integer grid, thus maximising the communication range. This naturally leads us to the design of a number of approximation algorithms for various classes of line of sight networks where the maximum independent set problem is NP-hard. Finally we study the maximum independent set problem in a restricted 2-dimensional line of sight network model. In this model, we show that the maximum independent set problem has a connection to a scheduling application. We show how methods that we develop for solving the maximum independent set problem, can also be used to solve the scheduling problem in both an offline and semi-online setting

Development and validation of an index of musculoskeletal functional limitations

BACKGROUND: While musculoskeletal problems are leading sources of disability, there has been little research on measuring the number of functionally limiting musculoskeletal problems for use as predictor of outcome in studies of chronic disease. This paper reports on the development and preliminary validation of a self administered musculoskeletal functional limitations index. METHODS: We developed a summary musculoskeletal functional limitations index based upon a six-item self administered questionnaire in which subjects indicate whether they are limited a lot, a little or not at all because of problems in six anatomic regions (knees, hips, ankles and feet, back, neck, upper extremities). Responses are summed into an index score. The index was completed by a sample of total knee replacement recipients from four US states. Our analyses examined convergent validity at the item and at the index level as well as discriminant validity and the independence of the index from other correlates of quality of life. RESULTS: 782 subjects completed all items of the musculoskeletal functional limitations index and were included in the analyses. The mean age of the sample was 75 years and 64% were female. The index demonstrated anticipated associations with self-reported quality of life, activities of daily living, WOMAC functional status score, use of walking support, frequency of usual exercise, frequency of falls and dependence upon another person for assistance with chores. The index was strongly and independently associated with self-reported overall health. CONCLUSION: The self-reported musculoskeletal functional limitations index appears to be a valid measure of musculoskeletal functional limitations, in the aspects of validity assessed in this study. It is useful for outcome studies following TKR and shows promise as a covariate in studies of chronic disease outcomes.National Institutes of Health (NIH P60 AR 47782; NIH K24 AR 02123

Landslide Sensitivity and Response to Precipitation Changes in Wet and Dry Climates

Slow-moving landslides are hydrologically driven. Yet, landslide sensitivity to precipitation, and in particular, precipitation extremes, is difficult to constrain because landslides occur under diverse hydroclimatological conditions. Here we use standardized open-access satellite radar interferometry data to quantify the sensitivity of 38 landslides to both a record drought and extreme rainfall that occurred in California between 2015 and 2020. These landslides are hosted in similar rock types, but span more than ∼2 m/yr in mean annual rainfall. Despite the large differences in hydroclimate, we found these landslides exhibited surprisingly similar behaviors and hydrologic sensitivity, which was characterized by faster (slower) than average velocities during wetter (drier) than average years, once the impact of the drought diminished. Our findings may be representative of future landslide behaviors in California where precipitation extremes are predicted to become more frequent with climate change

Differences in limb volume trajectories after breast cancer treatment

PURPOSE: ~20% of patients develop lymphedema (LE) following breast cancer (BC) surgery. An evaluation of distinct trajectories of volume change may improve our ability to diagnose LE sooner. The purposes of this study were to identify subgroups of women with distinct trajectories of limb volume changes following BC surgery and to evaluate for phenotypic differences among these classes. METHODS: In this prospective longitudinal study, 380 women were enrolled prior to unilateral BC surgery. Upper limb bioimpedance was measured preoperatively and serially for one year postoperatively. Resistance ratios (RR) were calculated. A RR of >1 indicates affected limb volume > unaffected limb volume. Latent class growth analysis (LCGA) was used to identify classes of women with distinct postoperative RR trajectories. Differences among classes were evaluated using analyses of variance and Chi square analyses. RESULTS: Three distinct classes were identified: RR <0.95 (37.9%), RR ~1.00 (46.8%), RR >1.05 (15.3%). Patients in the RR >1.05 class were more likely to have diabetes (p=0.036); were more likely to have BC on their dominant side (P<0.001); had higher RR ratios at the preoperative and one-month assessments (P<0.001); and were more likely to be diagnosed with LE (p<0.001). CONCLUSIONS: LCGA is a useful analytic technique to identify subgroups of women who may be at higher risk for the development of LE, based on trajectories of limb volume change after BC surgery. IMPLICATIONS FOR CANCER SURVIVORS: Assessment of preoperative and one-month bioimpedance RRs may allow for the earlier identification of patients who are at higher risk for the development of LE

The association between hope, marital status, depression and persistent pain in men and women following cardiac surgery

Background Cardiac surgery is a major life event, and outcomes after surgery are associated with men’s and women’s ability to self-manage and cope with their cardiac condition in everyday life. Hope is suggested to impact cardiac health by having a positive effect on how adults cope with and adapt to illness and recommended lifestyle changes. Methods We did a secondary analysis of 416 individuals (23% women) undergoing elective coronary artery bypass graft and/or valve surgery between March 2012 and September 2013 enrolled in randomized controlled trial. Hope was assessed using The Herth Hope Index (HHI) at three, six and 12 months following cardiac surgery. Linear mixed model analyses were performed to explore associations after cardiac surgery between hope, marital status, depression, persistent pain, and surgical procedure. Results For the total sample, no statistically significant difference between global hope scores from 3 to 12 months was observed (ranging from 38.3 ± 5.1 at 3 months to 38.7 ± 5.1 at 12 months), and no differences between men and women were observed at any time points. However, 3 out of 12 individual items on the HHI were associated with significantly lower scores in women: #1) I have a positive outlook toward life, #3) I feel all alone, and #6) I feel scared about my future. Over the study period, diminished hope was associated with older age, lower education, depression prior to surgery, and persistent pain at all measurement points. Isolated valve surgery was positively associated with hope. While neither sex nor marital status, as main effects, demonstrated significant associations with hope, women who were divorced/widowed/single were significantly more likely to have lower hope scores over the study period. Conclusion Addressing pain and depression, and promoting hope, particularly for women living alone may be important targets for interventions to improve outcomes following cardiac surgery