Optimal Rectangle Packing: An Absolute Placement Approach

We consider the problem of finding all enclosing rectangles of minimum area that can contain a given set of rectangles without overlap. Our rectangle packer chooses the x-coordinates of all the rectangles before any of the y-coordinates. We then transform the problem into a perfect-packing problem with no empty space by adding additional rectangles. To determine the y-coordinates, we branch on the different rectangles that can be placed in each empty position. Our packer allows us to extend the known solutions for a consecutive-square benchmark from 27 to 32 squares. We also introduce three new benchmarks, avoiding properties that make a benchmark easy, such as rectangles with shared dimensions. Our third benchmark consists of rectangles of increasingly high precision. To pack them efficiently, we limit the rectangles' coordinates and the bounding box dimensions to the set of subset sums of the rectangles' dimensions. Overall, our algorithms represent the current state-of-the-art for this problem, outperforming other algorithms by orders of magnitude, depending on the benchmark.

Satisfaction with continuous glucose monitoring in adults and youths with Type 1 diabetes

AIMS

To describe satisfaction with continuous glucose monitoring in Type 1 diabetes; to correlate continuous glucose monitoring satisfaction scores with usage; and to identify common themes in perceived benefits and barriers of monitoring reported by adults, youths and the parents of youths in the Juvenile Diabetes Research Foundation continuous glucose monitoring trials.

METHODS

The Continuous Glucose Monitoring Satisfaction Scale questionnaire was completed after 6 months of monitoring. Participants also answered open-ended queries of positive and negative attributes of continuous glucose monitoring.

RESULTS

More frequent monitoring was associated with higher satisfaction for adults (n = 224), youths (n = 208) and parents of youths (n = 192) (all P < 0.001) in both the 'benefits' and 'hassles' sub-scales of the Continuous Glucose Monitoring Satisfaction Scale, but the greatest differences between the two groups involved scores on hassle items. Common barriers to monitoring use included insertion pain, system alarms and body issues; while common benefits included glucose trend data, opportunities to self-correct out-of-range glucose levels and to detect hypoglycaemia.

CONCLUSIONS

As frequent use of continuous glucose monitoring is associated with improved glycaemic control without increased hypoglycaemia it is important to overcome barriers, reinforce benefits and set realistic expectations for this technology in order to promote its more consistent and frequent use in individuals with Type 1 diabetes.

Proliferation defects and genome instability in cells lacking Cul4A

The Cul4A gene, which encodes a core component of a cullin-based E3 ubiquitin ligase complex, is over-expressed in breast and hepatocellular cancers. In breast cancers, over-expression of Cul4A strongly correlates with poor prognosis. Also, Cul4A is required for early embryonic development. Early lethality of mouse embryos prevented a detailed analysis of the functions of Cul4A. Here, we used a strain of mice carrying floxed alleles of Cul4A to study its role in cell division, in vitro and in vivo. Embryonic fibroblasts exhibit a severe deficiency in cell proliferation following deletion of Cul4A. We observed that the Cul4A protein is abundantly expressed in brain, liver and in the mammary tissue of pregnant mice. Deletion of Cul4A in liver impairs hepatocyte proliferation during regeneration following carbon tetrachloride induced injury. The Cul4A-deleted cells are slow in entering S phase, and are deficient in progressing through early M phase. Several cell cycle regulators, including p53 and p27Kip1, are de-regulated in the Cul4A-deleted cells. Expression of a dominant negative mutant of p53 causes significant reversal of the proliferation defects in Cul4A-deleted cells. The Cul4A-deleted cells exhibit aberrant number of centrosome, multipolar spindles and micronuclei formation. Furthermore, those cells are sensitive to UV irradiation and exhibit reduced levels of unscheduled DNA synthesis. Together, our observations indicate that Cul4A is required for efficient cell proliferation, control of the centrosome amplification and genome stability.