Arithmetical properties of Multiple Ramanujan sums

In the present paper, we introduce a multiple Ramanujan sum for arithmetic functions, which gives a multivariable extension of the generalized Ramanujan sum studied by D. R. Anderson and T. M. Apostol. We then find fundamental arithmetic properties of the multiple Ramanujan sum and study several types of Dirichlet series involving the multiple Ramanujan sum. As an application, we evaluate higher-dimensional determinants of higher-dimensional matrices, the entries of which are given by values of the multiple Ramanujan sum.Comment: 19 page

Subcortical volumes across the lifespan: data from 18,605 healthy individuals aged 3-90 years

Age has a major effect on brain volume. However, the normative studies available are constrained by small sample sizes, restricted age coverage and significant methodological variability. These limitations introduce inconsistencies and may obscure or distort the lifespan trajectories of brain morphometry. In response, we capitalized on the resources of the Enhancing Neuroimaging Genetics through Meta-Analysis (ENIGMA) Consortium to examine age-related trajectories inferred from cross-sectional measures of the ventricles, the basal ganglia (caudate, putamen, pallidum, and nucleus accumbens), the thalamus, hippocampus and amygdala using magnetic resonance imaging data obtained from 18,605 individuals aged 3-90 years. All subcortical structure volumes were at their maximum value early in life. The volume of the basal ganglia showed a monotonic negative association with age thereafter; there was no significant association between age and the volumes of the thalamus, amygdala and the hippocampus (with some degree of decline in thalamus) until the sixth decade of life after which they also showed a steep negative association with age. The lateral ventricles showed continuous enlargement throughout the lifespan. Age was positively associated with inter-individual variability in the hippocampus and amygdala and the lateral ventricles. These results were robust to potential confounders and could be used to examine the functional significance of deviations from typical age-related morphometric patterns.Education and Child Studie

Condyle-fossa modifications and muscle interactions during Herbst treatment, part 1. New technological methods

Changes in the condyle, the glenoid fossa, and the muscles of mastication were investigated in subjects undergoing continuous orthopedic advancement of the mandible with a Herbst-block appliance. The total sample consisted of 56 subjects and included 15 nonhuman primates (in the middle mixed, early permanent, and permanent dentitions), 17 human Herbst patients in the early permanent dentition, and 24 human controls from the Burlington Growth Center. The 8 nonhuman primates in the middle mixed dentition were the focus of this study. Mandibular advancement was obtained progressively in 5 animals by adding stops to the telescopic arms of fixed functional Herbst appliances with occlusal coverage; activations of 5.0 mm, 7.0 mm, and 8.0 mm were achieved. Two primates served as controls, and the third was a sham control. Two experimental animals and the 2 controls also wore surgically implanted electromyographic electrodes in the superior and inferior heads of the lateral pterygoid muscles and in the superficial masseter and anterior digastric muscles. Changes in condylar growth direction and amount were assessed with the Björk method from measurements made on serial cephalometric tracings superimposed on metallic implants. Undecalcified sections, treated with intravenous tetracycline vital staining, were viewed with fluorescence microscopy to examine histologic changes in the condyle and the glenoid fossa. New bone formation in the fossa associated with continuous mandibular protrusion was quantified by using computerized histomorphometric analysis of decalcified histological sections and polarized light. The unique combination of permanently implanted electromyographic electrodes, tetracycline vital staining, and histomorphometry represents a significant technological advancement in methods and materials. Together, they demonstrated different muscle-bone interaction results for functional appliances than those reported in previous studies. In Part 1 of this study, we describe and discuss the techniques used in this research and give a brief overview of the findings; in Part 2 (to be published next month), we offer a more in-depth discussion of the results and the implications of our findings

Condyle-fossa modifications and muscle interactions during Herbst treatment, Part 2. Results and conclusions

Herbst appliances were activated progressively in growing nonhuman primates, and the results were compared with primate and human controls. The methods and materials of this research are explained in Part 1 of this study. The results are discussed here in Part 2. All experimental subjects developed large super Class I malocclusions, the result of many factors including posterior movement of the maxilla and the maxillary teeth, an increased horizontal component of condylar growth, and anterior displacement of the mandible and the mandibular teeth. The growth modification measured in the glenoid fossa was in an inferior and anterior direction. Restriction of the downward and backward growth of the fossa observed in the control subjects might additionally contribute to the overall super Class I malocclusion. Clinically, these combined effects could be significant at the fossa. The restriction of local temporal bone (fossa) growth cannot be observed clinically; thus, these results might also clarify some Class II correction effects that cannot be explained with functional appliances. Differences in the area and maximum thickness of new bone formation in the glenoid fossa and in condylar growth were statistically significant. The bony changes in the condyle and the glenoid fossa were correlated with decreased postural electromyographic activity during the experimental period. Results from permanently implanted electromyographic sensors demonstrated that lateral pterygoid muscle hyperactivity was not associated with condyle-glenoid fossa growth modification with functional appliances, and that other factors, such as reciprocal stretch forces and subsequent transduction along the fibrocartilage between the displaced condyle and fossa, might play a more significant role in new bone formation. These results support the growth relativity concept

Dry deposition and heavy acid loading in the vicinity of Masaya volcano, a major sulfur and chlorine source in Nicaragua.

Certain volcanoes constitute the world's largest sources of SO2, HCl, and HF emissions and contribute significantly to regional acid deposition. However, the impact of volcanic acid emissions to nearby ecosystems remain poorly documented. In this paper, the spatial pattern of acid dry depositions was monitored within 44 km of Masaya Volcano, Nicaragua, with a network of sulfation plates. Measured SO2 deposition rates were <2−791 mg m-2 day-1. The plates also collected the dry deposition of HCl at rates of <1−297 mg m-2 day-1. A similar deposition velocity Vd (gas transfer) of 1.6 ± 0.8 cm/s was calculated for SO2 and HCl above the plate surfaces. Quantities of SO2 and HCl deposited daily within the area surveyed amounted to 1.5 × 108 g and 5.7 × 107 g, respectively, which correspond to about 10% of the total SO2 and HCl released by the volcano. These depositions may generate an equivalent hydrogen flux ranging from <1 to 30 mg m-2 day-1. Our results demonstrate that volcano emissions can dramatically affect acid deposition downwind and in turn cause extreme acid loading of the local ecosystems. This study opens exciting prospects for investigating the sensivity of volcanic ash soils to acid inputs