Detection of ‘Candidatus Liberibacter asiaticus’ represents one of the most difficult, yet critical, steps of controlling Huanglongbing disease. Efficient detection relies on understanding the underlying distribution of bacteria within trees. To that end, we studied the distribution of ‘Ca. L. asiaticus’ in leaves of ‘Rio Red’ grapefruit trees and in roots of ‘Valencia’ sweet orange trees grafted onto sour orange rootstock. We performed two sets of leaf collection on grapefruit trees; the first a selective sampling targeting symptomatic leaves and their neighbors and the second a systematic collection disregarding symptomology. From uprooted orange trees, we exhaustively sampled fibrous roots. In this study, the presence of ‘Ca. L. asiaticus’ was detected in leaves using real-time polymerase chain reaction (PCR) targeting the 16S ribosomal gene and in roots using the rpIJ/rpIL ribosomal protein genes and was confirmed with conventional PCR and sequencing of the rpIJ/rpIL gene in both tissues. Among randomly collected leaves, ‘Ca. L. asiaticus’ was distributed in a patchy fashion. Detection of ‘Ca. L. asiaticus’ varied with leaf symptomology with symptomatic leaves showing the highest frequency (74%) followed by their neighboring asymptomatic leaves (30%), while randomly distributed asymptomatic leaves had the lowest frequency (20%). Among symptomatic leaves, we found statistically significant differences in mean number of bacterial cells with respect to both increasing distance of the leaf from the trunk and cardinal direction. The titer of ‘Ca. L. asiaticus’ cells was significantly greater on the north side of trees than on the south and west sides. Moreover, these directions showed different spatial distributions of ‘Ca. L. asiaticus’ with higher titers near the trunk on the south and west sides as opposed to further from the trunk on the north side. Similarly, we found spatial variation in ‘Ca. L. asiaticus’ distribution among root samples. ‘Ca. L. asiaticus’ was detected more frequently and bacterial abundances were higher among horizontally growing roots just under the soil surface (96%) than among deeper vertically growing roots (78%). Bacterial abundance declined slightly with distance from the trunk. These results point to paths of research that will likely prove useful to combating this devastating disease.

The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the following converse result is true. If for some $n\ge 2$, $X_1,X_2,\dots ,X_n$ are independent copies of a random variable X with unknown distribution F and a specific linear combination of $X_j$’s has hypoexponential distribution, then F is exponential. Thus, we obtain new characterizations of the exponential distribution. As corollaries of the main results, we extend some previous characterizations established recently by Arnold and Villaseñor (2013) for a particular convolution of two random variables.

Background/Aims: Is cholecalciferol (D₃) superior to ergocalciferol (D₂) in treating nutritional vitamin D deficiency in chronic kidney disease (CKD)? The answer to this question has not been fully explored. Methods: A retrospective analysis of 57 patients with non-dialysis-requiring CKD was conducted to assess the relative effectiveness of D₂ versus D₃ replacement on circulating 25(OH)D levels. Levels of 25(OH) D were assessed at baseline, after attempted repletion with D₂, and then after attempted repletion with D₃. The relative paired differences of the drug treatment effects were tested using t-tests. Multiple regression modeling was used to determine the factors significantly associated with differential responsiveness to the drugs. Results: The mean (SEM) age was 66.4 ± 1.4 and mean eGFR was 40.5 ± 2.2 ml/min/1.73 m². The baseline 25(OH)D level was 15.3 ± 0.8 ng/ml. After standardizing to 100,000 units of drug, increases after cholecalciferol (2.7 ± 0.3 ng/ml) were more than twice as great as those from ergocalciferol (1.1 ± 0.3 ng/ml) (p < 0.0001). A sensitivity analysis, which pooled the results of an additional 109 individuals treated with ergocalciferol alone, revealed similar findings (standardized change 2.7 ± 0.3 vs. 1.6 ± 0.3 ng/ml, p = 0.0025). Factors associated with a superior response to cholecalciferol were lower baseline 25(OH) D level at the start of therapy (p = 0.015) and the interaction of sex and age (p = 0.0048), with younger females tending to benefit relatively more from cholecalciferol than older males did. Conclusion: Cholecalciferol may be superior to ergocalciferol in treating nutritional vitamin D deficiency in non-dialysis CKD.

In our pilot studies, we found that many introductory physics textbook illustrations with supporting text for sound standing waves of air columns in open-open, open-closed, and closed-closed pipes inhibit student understanding of sound standing wave phenomena due to student misunderstanding of how air molecules move within these pipes. Based on the construct of meaningful learning from cognitive psychology and semiotics, a quasiexperimental study was conducted to investigate the comparative effectiveness of two alternative approaches to student understanding: a traditional textbook illustration approach versus a newly designed air molecule motion illustration approach. Thirty volunteer students from introductory physics classes were randomly assigned to two groups of 15 each. Both groups were administered a presurvey. Then, group A read the air molecule motion illustration handout, and group B read a traditional textbook illustration handout; both groups were administered postsurveys. Subsequently, the procedure was reversed: group B read the air molecule motion illustration handout and group A read the traditional textbook illustration handout. This was followed by a second postsurvey along with an exit research questionnaire. The study found that the majority of students experienced meaningful learning and stated that they understood sound standing wave phenomena significantly better using the air molecule motion illustration approach. This finding provides a method for physics education researchers to design illustrations for abstract sound standing wave concepts, for publishers to improve their illustrations with supporting text, and for instructors to facilitate deeper learning in their students on sound standing waves.

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