Mathematical modelling for the digital society

We argue the case for a new branch of mathematics and its applications: Mathematics for the Digital Society. There is a challenge for mathematics, a strong “pull” from new and emerging commercial and public activities; and a need to train and inspire a generation of quantitative scientists who will seek careers within the associated sectors. Although now going through an early phase of boiling up, prior to scholarly distillation, we discuss how data rich activities and applications may benefit from a wide range of continuous and discrete models, methods, analysis and inference. In ten years time such applications will be common place and associated courses may be embedded within the undergraduate curriculum.

A spirochete isolated from a case of severe virulent ovine foot disease is closely related to a Treponeme isolated from human periodontitis and bovine digital dermatitis

The isolation of spirochetes from severe ovine foot disease has been reported recently by our research group. In this study we describe the preliminary classification of this spirochete based on nucleotide sequence analysis of the PCR-amplified 16S rRNA gene. Phylogenetic analysis of this sequence in comparison with other previously reported 16S rRNA gene sequences showed that the spirochete belonged to the treponemal phylotype Treponema vincentii which has been associated with bovine digital dermatitis and human periodontal disease. Further work is required to define the common virulence determinants of these closely related treponemes in the aetiology of these tissue destructive diseases. (C) 2000 Elsevier Science B.V. All rights reserved.

Mapping power law distributions in digital health social networks: methods, interpretations, and practical implications

BACKGROUND: Social networks are common in digital health. A new stream of research is beginning to investigate the mechanisms of digital health social networks (DHSNs), how they are structured, how they function, and how their growth can be nurtured and managed. DHSNs increase in value when additional content is added, and the structure of networks may resemble the characteristics of power laws. Power laws are contrary to traditional Gaussian averages in that they demonstrate correlated phenomena. OBJECTIVES: The objective of this study is to investigate whether the distribution frequency in four DHSNs can be characterized as following a power law. A second objective is to describe the method used to determine the comparison. METHODS: Data from four DHSNs—Alcohol Help Center (AHC), Depression Center (DC), Panic Center (PC), and Stop Smoking Center (SSC)—were compared to power law distributions. To assist future researchers and managers, the 5-step methodology used to analyze and compare datasets is described. RESULTS: All four DHSNs were found to have right-skewed distributions, indicating the data were not normally distributed. When power trend lines were added to each frequency distribution, R(2) values indicated that, to a very high degree, the variance in post frequencies can be explained by actor rank (AHC .962, DC .975, PC .969, SSC .95). Spearman correlations provided further indication of the strength and statistical significance of the relationship (AHC .987. DC .967, PC .983, SSC .993, P<.001). CONCLUSIONS: This is the first study to investigate power distributions across multiple DHSNs, each addressing a unique condition. Results indicate that despite vast differences in theme, content, and length of existence, DHSNs follow properties of power laws. The structure of DHSNs is important as it gives insight to researchers and managers into the nature and mechanisms of network functionality. The 5-step process undertaken to compare actor contribution patterns can be replicated in networks that are managed by other organizations, and we conjecture that patterns observed in this study could be found in other DHSNs. Future research should analyze network growth over time and examine the characteristics and survival rates of superusers.

Targeting medication non-adherence behavior in selected autoimmune diseases: a systematic approach to digital health program development

Background 29 autoimmune diseases, including Rheumatoid Arthritis, gout, Crohn’s Disease, and Systematic Lupus Erythematosus affect 7.6-9.4% of the population. While effective therapy is available, many patients do not follow treatment or use medications as directed. Digital health and Web 2.0 interventions have demonstrated much promise in increasing medication and treatment adherence, but to date many Internet tools have proven disappointing. In fact, most digital interventions continue to suffer from high attrition in patient populations, are burdensome for healthcare professionals, and have relatively short life spans. Objective Digital health tools have traditionally centered on the transformation of existing interventions (such as diaries, trackers, stage-based or cognitive behavioral therapy programs, coupons, or symptom checklists) to electronic format. Advanced digital interventions have also incorporated attributes of Web 2.0 such as social networking, text messaging, and the use of video. Despite these efforts, there has not been little measurable impact in non-adherence for illnesses that require medical interventions, and research must look to other strategies or development methodologies. As a first step in investigating the feasibility of developing such a tool, the objective of the current study is to systematically rate factors of non-adherence that have been reported in past research studies. Methods Grounded Theory, recognized as a rigorous method that facilitates the emergence of new themes through systematic analysis, data collection and coding, was used to analyze quantitative, qualitative and mixed method studies addressing the following autoimmune diseases: Rheumatoid Arthritis, gout, Crohn’s Disease, Systematic Lupus Erythematosus, and inflammatory bowel disease. Studies were only included if they contained primary data addressing the relationship with non-adherence. Results Out of the 27 studies, four non-modifiable and 11 modifiable risk factors were discovered. Over one third of articles identified the following risk factors as common contributors to medication non-adherence (percent of studies reporting): patients not understanding treatment (44%), side effects (41%), age (37%), dose regimen (33%), and perceived medication ineffectiveness (33%). An unanticipated finding that emerged was the need for risk stratification tools (81%) with patient-centric approaches (67%). Conclusions This study systematically identifies and categorizes medication non-adherence risk factors in select autoimmune diseases. Findings indicate that patients understanding of their disease and the role of medication are paramount. An unexpected finding was that the majority of research articles called for the creation of tailored, patient-centric interventions that dispel personal misconceptions about disease, pharmacotherapy, and how the body responds to treatment. To our knowledge, these interventions do not yet exist in digital format. Rather than adopting a systems level approach, digital health programs should focus on cohorts with heterogeneous needs, and develop tailored interventions based on individual non-adherence patterns.

Improving the TanDEM-X Digital Elevation Model for flood modelling using flood extents from Synthetic Aperture Radar images

The topography of many floodplains in the developed world has now been surveyed with high resolution sensors such as airborne LiDAR (Light Detection and Ranging), giving accurate Digital Elevation Models (DEMs) that facilitate accurate flood inundation modelling. This is not always the case for remote rivers in developing countries. However, the accuracy of DEMs produced for modelling studies on such rivers should be enhanced in the near future by the high resolution TanDEM-X WorldDEM. In a parallel development, increasing use is now being made of flood extents derived from high resolution Synthetic Aperture Radar (SAR) images for calibrating, validating and assimilating observations into flood inundation models in order to improve these. This paper discusses an additional use of SAR flood extents, namely to improve the accuracy of the TanDEM-X DEM in the floodplain covered by the flood extents, thereby permanently improving this DEM for future flood modelling and other studies. The method is based on the fact that for larger rivers the water elevation generally changes only slowly along a reach, so that the boundary of the flood extent (the waterline) can be regarded locally as a quasi-contour. As a result, heights of adjacent pixels along a small section of waterline can be regarded as samples with a common population mean. The height of the central pixel in the section can be replaced with the average of these heights, leading to a more accurate estimate. While this will result in a reduction in the height errors along a waterline, the waterline is a linear feature in a two-dimensional space. However, improvements to the DEM heights between adjacent pairs of waterlines can also be made, because DEM heights enclosed by the higher waterline of a pair must be at least no higher than the corrected heights along the higher waterline, whereas DEM heights not enclosed by the lower waterline must in general be no lower than the corrected heights along the lower waterline. In addition, DEM heights between the higher and lower waterlines can also be assigned smaller errors because of the reduced errors on the corrected waterline heights. The method was tested on a section of the TanDEM-X Intermediate DEM (IDEM) covering an 11km reach of the Warwickshire Avon, England. Flood extents from four COSMO-SKyMed images were available at various stages of a flood in November 2012, and a LiDAR DEM was available for validation. In the area covered by the flood extents, the original IDEM heights had a mean difference from the corresponding LiDAR heights of 0.5 m with a standard deviation of 2.0 m, while the corrected heights had a mean difference of 0.3 m with standard deviation 1.2 m. These figures show that significant reductions in IDEM height bias and error can be made using the method, with the corrected error being only 60% of the original. Even if only a single SAR image obtained near the peak of the flood was used, the corrected error was only 66% of the original. The method should also be capable of improving the final TanDEM-X DEM and other DEMs, and may also be of use with data from the SWOT (Surface Water and Ocean Topography) satellite.