Higher geometry and trigonometry : being the third part of a series on elementary and higher geometry, trigonomentary and mensuration : containing many valuable discoveries and improvements in mathematical science, especially in relation to the quadrature of the circle, and some other curves, as well as the cubature of certain curvilinear solids : designed as a text-book for collegiate and academic instruction, and as a practical compendium of mensuration /

With: Higher geometry and mensuration / by Nathan Scholfield.

An introduction to the use of generalized coordinates in mechanics and physics,

Mode of access: Internet.

The Rab5 effector rabankyrin-5 regulates and coordinates different endocytic mechanisms

The small GTPase Rab5 is a key regulator of clathrin-mediated endocytosis. On early endosomes, within a spatially restricted domain enriched in phosphatydilinositol-3-phosphate [PI(3)P], Rab5 coordinates a complex network of effectors that functionally cooperate in membrane tethering, fusion, and organelle motility. Here we discovered a novel PI(3)P-binding Rab5 effector, Rabankyrin-5, which localises to early endosomes and stimulates their fusion activity. In addition to early endosomes, however, Rabankyrin-5 localises to large vacuolar structures that correspond to macropinosomes in epithelial cells and fibroblasts. Overexpression of Rabankyrin-5 increases the number of macropinosomes and stimulates fluid-phase uptake, whereas its downregulation inhibits these processes. In polarised epithelial cells, this function is primarily restricted to the apical membrane. Rabankyrin-5 localises to large pinocytic structures underneath the apical surface of kidney proximal tubule cells, and its overexpression in polarised Madin-Darby canine kidney cells stimulates apical but not basolateral, non-clathrin-mediated pinocytosis. in demonstrating a regulatory role in endosome fusion and (macro) pinocytosis, our studies suggest that Rab5 regulates and coordinates different endocytic mechanisms through its effector Rabankyrin-5. Furthermore, its active role in apical pinocytosis in epithelial cells suggests an important function of Rabankyrin-5 in the physiology of polarised cells.

The retromer coat complex coordinates endosomal sorting and dynein-mediated transport, with carrier recognition by the trans-Golgi network

Early endosome-to-trans-Golgi network (TGN) transport is organized by the retromer complex. Consisting of cargo-selective and membrane-bound subcomplexes, retromer coordinates sorting with membrane deformation and carrier formation. Here, we describe four mammalian retromers whose membrane-bound subcomplexes contain specific combinations of the sorting nexins (SNX), SNX1, SNX2, SNX5, and SNX6. We establish that retromer requires a dynamic spatial organization of the endosomal network, which is regulated through association of SNX5/SNX6 with the p150(glued) component of dynactin, an activator of the minus-end directed microtubule motor dynein; an association further defined through genetic studies in C. elegans. Finally, we also establish that the spatial organization of the retromer pathway is mediated through the association of SNX1 with the proposed TGN-localized tether Rab6-interacting protein-1. These interactions describe fundamental steps in retromer-mediated transport and establish that the spatial organization of the retromer network is a critical element required for efficient retromer-mediated sorting.

SNX4 coordinates endosomal sorting of TfnR with dynein-mediated transport into the endocytic recycling compartment

SNX-BAR proteins are a sub-family of sorting nexins implicated in endosomal sorting. Here, we establish that through its phox homology (PX) and Bin-Amphiphysin-Rvs (BAR) domains, sorting nexin-4 (SNX4) is associated with tubular and vesicular elements of a compartment that overlaps with peripheral early endosomes and the juxtanuclear endocytic recycling compartment (ERC). Suppression of SNX4 perturbs transport between these compartments and causes lysosomal degradation of the transferrin receptor (TfnR). Through an interaction with KIBRA, a protein previously shown to bind dynein light chain 1, we establish that SNX4 associates with the minus end-directed microtubule motor dynein. Although suppression of KIBRA and dynein perturbs early endosome-to-ERC transport, TfnR sorting is maintained. We propose that by driving membrane tubulation, SNX4 coordinates iterative, geometric-based sorting of the TfnR with the long-range transport of carriers from early endosomes to the ERC. Finally, these data suggest that by associating with molecular motors, SNX-BAR proteins may coordinate sorting with carrier transport between donor and recipient membranes.

Computation of some Differential Operators in Toric Coordinates

Toric coordinates and toric vector field have been introduced in [2]. Let A be an arbitrary vector field. We obtain formulae for the divA, rotA and the Laplace operator in toric coordinates.

Verification of the indoor GPS system, by comparison with calibrated coordinates and by angular reference

This paper details work carried out to verify the dimensional measurement performance of the Indoor GPS (iGPS) system; a network of Rotary-Laser Automatic Theodolites (R-LATs). Initially tests were carried out to determine the angular uncertainties on an individual R-LAT transmitter-receiver pair. A method is presented of determining the uncertainty of dimensional measurement for a three dimensional coordinate measurement machine. An experimental procedure was developed to compare three dimensional coordinate measurements with calibrated reference points. The reference standard used to calibrate these reference points was a fringe counting interferometer with the multilateration technique employed to establish three dimensional coordinates. This is an extension of the established technique of comparing measured lengths with calibrated lengths. The method was found to be practical and able to establish that the expanded uncertainty of the basic iGPS system was approximately 1 mm at a 95% confidence level. Further tests carried out on a highly optimized version of the iGPS system have shown that the coordinate uncertainty can be reduced to 0.25 mm at a 95% confidence level.

(Supplementary Material 2) Landmark coordinates of the analyzed specimens with associated metadata

The use of planktonic foraminifera in paleoceanographic studies relies on the assumption that morphospecies represent biological species with ecological preferences that are stable through time and space. However, genetic surveys unveiled a considerable level of diversity in most morphospecies of planktonic foraminifera. This diversity is significant for paleoceanographic applications because cryptic species were shown to display distinct ecological preferences that could potentially help refine paleoceanographic proxies. Subtle morphological differences between cryptic species of planktonic foraminifera have been reported, but so far their applicability within paleoceanographic studies remains largely unexplored. Here we show how information on genetic diversity can be transferred to paleoceanography using Globorotalia inflata as a case study. The two cryptic species of G. inflata are separated by the Brazil-Malvinas Confluence (BMC), a major oceanographic feature in the South Atlantic. Based on this observation, we developed a morphological model of cryptic species detection in core top material. The application of the cryptic species detection model to Holocene samples implies latitudinal oscillations in the position of the confluence that are largely consistent with reconstructions obtained from stable isotope data. We show that the occurrence of cryptic species in G. inflata, can be detected in the fossil record and used to trace the migration of the BMC. Since a similar degree of morphological separation as in G. inflata has been reported from other species of planktonic foraminifera, the approach presented in this study can potentially yield a wealth of new paleoceanographical proxies.

Seawater carbonate chemistry and morphometric coordinates and morphology of the control 8-arm pluteus of brittlestar Ophiothrix fragilis, 2008

The world's oceans are slowly becoming more acidic. In the last 150 yr, the pH of the oceans has dropped by ~0.1 units, which is equivalent to a 25% increase in acidity. Modelling predicts the pH of the oceans to fall by 0.2 to 0.4 units by the year 2100. These changes will have significant effects on marine organisms, especially those with calcareous skeletons such as echinoderms. Little is known about the possible long-term impact of predicted pH changes on marine invertebrate larval development. Here we predict the consequences of increased CO2 (corresponding to pH drops of 0.2 and 0.4 units) on the larval development of the brittlestar Ophiothrix fragilis, which is a keystone species occurring in high densities and stable populations throughout the shelf seas of northwestern Europe (eastern Atlantic). Acidification by 0.2 units induced 100% larval mortality within 8 d while control larvae showed 70% survival over the same period. Exposure to low pH also resulted in a temporal decrease in larval size as well as abnormal development and skeletogenesis (abnormalities, asymmetry, altered skeletal proportions). If oceans continue to acidify as expected, ecosystems of the Atlantic dominated by this keystone species will be seriously threatened with major changes in many key benthic and pelagic ecosystems. Thus, it may be useful to monitor O. fragilis populations and initiate conservation if needed.

Assessment of the cortisol awakening response: Real-time analysis and curvilinear effects of sample timing inaccuracy

The cortisol awakening response (CAR) is typically measured in the domestic setting. Moderate sample timing inaccuracy has been shown to result in erroneous CAR estimates and such inaccuracy has been shown partially to explain inconsistency in the CAR literature. The need for more reliable measurement of the CAR has recently been highlighted in expert consensus guidelines where it was pointed out that less than 6% of published studies provided electronic-monitoring of saliva sampling time in the post-awakening period. Analyses of a merged data-set of published studies from our laboratory are presented. To qualify for selection, both time of awakening and collection of the first sample must have been verified by electronic-monitoring and sampling commenced within 15 min of awakening. Participants (n = 128) were young (median age of 20 years) and healthy. Cortisol values were determined in the 45 min post-awakening period on 215 sampling days. On 127 days, delay between verified awakening and collection of the first sample was less than 3 min (‘no delay’ group); on 45 days there was a delay of 4–6 min (‘short delay’ group); on 43 days the delay was 7–15 min (‘moderate delay’ group). Cortisol values for verified sampling times accurately mapped on to the typical post-awakening cortisol growth curve, regardless of whether sampling deviated from desired protocol timings. This provides support for incorporating rather than excluding delayed data (up to 15 min) in CAR analyses. For this population the fitted cortisol growth curve equation predicted a mean cortisol awakening level of 6 nmols/l (±1 for 95% CI) and a mean CAR rise of 6 nmols/l (±2 for 95% CI). We also modelled the relationship between real delay and CAR magnitude, when the CAR is calculated erroneously by incorrectly assuming adherence to protocol time. Findings supported a curvilinear hypothesis in relation to effects of sample delay on the CAR. Short delays of 4–6 min between awakening and commencement of saliva sampling resulted an overestimated CAR. Moderate delays of 7–15 min were associated with an underestimated CAR. Findings emphasize the need to employ electronic-monitoring of sampling accuracy when measuring the CAR in the domestic setting.