The enumeration of chemical graphs satisfying given constraints is one of the fundamental problems in chemoinformatics. In this paper, we consider the problem of enumerating (i.e., listing) all treelike chemical graphs from a given path frequency. We propose an exact algorithm for enumerating all solutions to this problem on the basis of the branch-and-bound method. To further improve the efficiency of the enumeration, we introduce a new variant of the compound enumeration problem by adding a specification on the number of multiple bonds to the input and design another exact enumeration algorithm. The experimental results show that our algorithms can efficiently solve instances with larger sizes that are impossible to solve by the previous methods. In particular, we apply the latter algorithm to the enumeration problem of the special treelike chemical structures-alkane isomers. The theoretical and experimental results show that our algorithm works at least as fast as the state-of-the-art algorithms specially designed for generating alkane isomers, however using much less memory space.

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Diabetic retinopathy (DR) is a leading cause of vision-loss globally among type 2 diabetes (T2DM) patients. Information on the economic burden of DR in Singapore is limited. We aim to identify the total annual direct medical costs of DR at different stages, and to examine factors influencing the costs. Four hundreds and seventy T2DM patients who attended the Diabetes Centre in a secondary hospital in Singapore in 2011–2014 were included. Digital color fundus photographs were assessed for DR in a masked fashion. Retinopathy severity was further categorized into non-proliferative DR (NPDR), including mild, moderate and severe NPDR, and proliferative DR (PDR). Medical costs were assessed using hospital administrative data. DR was diagnosed in 172 (39.5%) patients, including 51 mild, 62 moderate and 18 severe NPDR, and 41 PDR. The median cost in DR [2012.0 (1111.2–4192.3)] was significantly higher than that in non-DR patients [1158.1 (724.1–1838.9)] (p<0.001). The corresponding costs for mild, moderate, severe NPDR and PDR were [1167.1 (895.4–2012.0)], [2212.0 (1215.5–3825.5)], [2717.5 (1444.0–6310.7)], and [3594.8.1 (1978.4–8427.7)], respectively. After adjustment, the corresponding cost ratios for mild, moderate, severe NPDR, and PDR relative to non-DR were 1.1 (p = 0.827), 1.8 (p = 0.003), 2.0 (p = 0.031) and 2.3 (p<0.001), respectively. The other factors affecting the total cost include smoking (ratio = 1.7, p = 0.019), neuropathy (ratio = 1.9, p = 0.001) and chronic kidney disease (CKD) (ratio = 1.4, p = 0.019). The presence and severity of DR was associated with increased direct medical costs in T2DM. Our results suggest that preventing progression of DR may reduce the economic burden of DR.

Multidisciplinary endocrinology and nephrology care in the DKD clinic is associated with a lower risk of end-stage renal disease. These findings may inform future management strategies targeted at patients with T2DM and CKD, especially with regard to joint specialist management involving endocrinologists and nephrologists.

Summary Literature evaluating the relationship between central obesity and cognitive deficits in type 2 diabetes (T2DM) remains scarce. This cross‐sectional analysis explored the association of novel and traditional central obesity measures with cognitive performance in older (aged ≥60 years) non‐demented multi‐ethnic Asians with T2DM, including a stratified analysis by body mass index (BMI). Cognitive function was assessed using the Repeatable Battery for the Assessment of Neuropsychological Status. Central obesity measures including visceral fat area (VFA), waist circumference, waist:hip ratio, waist:height ratio, abdominal volume index, body roundness index and conicity index were measured and/or computed. In our cohort (N = 677; mean age = 67 ± 5 years, 51.7% men), VFA emerged as an associate of overall cognitive performance after covariate adjustment and Bonferroni correction (β = −.10, 95% CI = −0.18, −0.03), outperforming the other adiposity indices. Specifically, VFA was inversely associated with delayed memory and language scores. Additionally, compared with normal‐weight individuals, excess visceral obesity (VFA ≥100 cm2) was independently associated with lower cognitive scores to a greater extent in normal BMI (<23 kg/m2) adults than in those with high BMI (≥23 kg/m2). Assessment and management of visceral adiposity may help to prevent cognitive decline in older people with T2DM, and reduce the global burden of dementia in ageing populations.