Computing with and without arbitrary large numbers

In the study of random access machines (RAMs) it has been shown that the availability of an extra input integer, having no special properties other than being sufficiently large, is enough to reduce the computational complexity of some problems. However, this has only been shown so far for specific problems. We provide a characterization of the power of such extra inputs for general problems. To do so, we first correct a classical result by Simon and Szegedy (1992) as well as one by Simon (1981). In the former we show mistakes in the proof and correct these by an entirely new construction, with no great change to the results. In the latter, the original proof direction stands with only minor modifications, but the new results are far stronger than those of Simon (1981). In both cases, the new constructions provide the theoretical tools required to characterize the power of arbitrary large numbers.Comment: 12 pages (main text) + 30 pages (appendices), 1 figure. Extended abstract. The full paper was presented at TAMC 2013. (Reference given is for the paper version, as it appears in the proceedings.

Self-gravitating Newtonian disks revisited

Recent analytic results concerning stationary, self-gravitating fluids in Newtonian theory are discussed. We give a theorem that forbids infinitely extended fluids, depending on the assumed equation of state and the rotation law. This part extends previous results that have been obtained for static configurations. The second part discusses a Sobolev bound on the mass of the fluid and a rigorous Jeans-type inequality that is valid in the stationary case.Comment: A talk given at the Spanish Relativity Meeting in Portugal 2012. To appear in Progress in Mathematical Relativity, Gravitation and Cosmology, Proceedings of the Spanish Relativity Meeting ERE2012, University of Minho, Guimaraes, Portugal, 3-7 September 2012, Springer Proceedings in Mathematics & Statistics, Vol. 6

80-Gb/s OTDM system analysis of a vertical microcavity-based saturable absorber for the enhancement of pulse pedestal suppression

In future high-speed optical time-division-multiplexed (OTDM) systems, an important factor that needs to be considered for optical pulse generation schemes is the impact of pulse pedestals on the overall system performance. The results presented in this letter are two-fold; first, the impact due to the height of pulse pedestals in an 80-Gb/s OTDM system are established. Second, a solution is provided to overcome these high pedestal levels through the use of a vertical microcavity saturable absorber, which can significantly reduce the pulse pedestal level and give enhanced system performanc

Structure–property insights into nanostructured electrodes for Li-ion batteries from local structural and diffusional probes

Microwave heating presents a faster, lower energy synthetic methodology for the realization of functional materials. Here, we demonstrate for the first time that employing this method also leads to a decrease in the occurrence of defects in olivine structured LiFe1−xMnxPO4. For example, the presence of antisite defects in this structure precludes Li+ diffusion along the b-axis leading to a significant decrease in reversible capacities. Total scattering measurements, in combination with Li+ diffusion studies using muon spin relaxation (μ+SR) spectroscopy, reveal that this synthetic method generates fewer defects in the nanostructures compared to traditional solvothermal routes. Our interest in developing these routes to mixed-metal phosphate LiFe1−xMnxPO4 olivines is due to the higher Mn2+/3+ redox potential in comparison to the Fe2+/3+ pair. Here, single-phase LiFe1−xMnxPO4 (x = 0, 0.25, 0.5, 0.75 and 1) olivines have been prepared following a microwave-assisted approach which allows for up to 4 times faster reaction times compared to traditional solvothermal methods. Interestingly, the resulting particle morphology is dependent on the Mn content. We also examine their electrochemical performance as active electrodes in Li-ion batteries. These results present microwave routes as highly attractive for reproducible, gram-scale syntheses of high quality nanostructured electrodes which display close to theoretical capacity for the full iron phase

First evidence of cryptotephra in palaeoenvironmental records associated with Norse occupation sites in Greenland

The Norse/Viking occupation of Greenland is part of a dispersal of communities across the North Atlantic coincident with the supposed Medieval Warm Period of the late 1st millennium AD. The abandonment of the Greenland settlements has been linked to climatic deterioration in the Little Ice Age as well as other possible explanations. There are significant dating uncertainties over the time of European abandonment of Greenland and the potential influence of climatic deterioration. Dating issues largely revolve around radiocarbon chronologies for Norse settlements and associated mire sequences close to settlement sites. Here we show the potential for moving this situation forward by a combination of palynological, radiocarbon and cryptotephra analyses of environmental records close to three ‘iconic’ Norse sites in the former Eastern Settlement of Greenland – Herjolfsnes, Hvalsey and Garðar (the modern Igaliku). While much work remains to be undertaken, our results show that palynological evidence can provide a useful marker for both the onset and end of Norse occupation in the region, while the radiocarbon chronologies for these sequences remain difficult. Significantly, we here demonstrate the potential for cryptotephra to become a useful tool in resolving the chronology of Norse occupation, when coupled with palynology. For the first time, we show that cryptotephra are present within palaeoenvironmental sequences located within or close to Norse settlement ruin-groups, with tephra horizons detected at all three sites. While shard concentrations were small at Herjolfsnes, concentrations sufficient for geochemical analyses were detected at Igaliku and Hvalsey. WDS-EPMA analyses of these tephra indicate that, unlike the predominantly Icelandic tephra sources reported in the Greenland ice core records, the tephra associated with the Norse sites correlate more closely with volcanic centres in the Aleutians and Cascades. Recent investigations of cryptotephra dispersal from North American centres, along with our new findings, point to the potential for cryptotephra to facilitate hypothesis testing, providing a key chronological tool for refining the timing of Norse activities in Greenland (e.g. abandonment) and of environmental contexts and drivers (e.g. climate forcing)

Plasma zinc concentrations are depressed during the acute phase response in children with falciparum malaria

Plasma concentrations of some micronutrients are altered in the setting of acute infectious or inflammatory stress. Previous studies have provided conflicting evidence concerning the extent and direction of changes in plasma zinc concentrations during the acute phase response. We carried out an observational cohort study in 689 children enrolled in a randomized trial of zinc supplementation during acute falciparum malaria in order to evaluate the relation between plasma zinc concentration and the acute phase response. Plasma zinc was measured by atomic absorption spectrophotometry. On admission, 70% of all subjects had low plasma zinc (\u3c9.2 μmol/L). Multivariate analysis of predictors of admission plasma zinc showed that admission C-reactive protein (CRP), parasite density, and study site were the most important predictors. Predictors of changes in plasma zinc from admission to 72 h included baseline CRP, change in CRP, treatment group, study site, and baseline zinc concentration. In children with acute malaria infection, baseline plasma zinc concentrations were very low and were inversely correlated with CRP (r = -0.24, P \u3c 0.0001) and the degree of parasitemia (r = -0.19, P \u3c 0.0001). Even when CRP and time were taken into account, zinc supplementation increased plasma zinc concentration from admission to 72 h. When available, plasma zinc concentrations should be interpreted with concurrent measures of the acute phase response such as CRP. In children whose age, diet, and/or nutritional status place them at risk of zinc deficiency, those with low plasma zinc levels should be supplemented with oral zinc and followed for clinical and/or biochemical response. © 2005 American Society for Nutritional Sciences

Using a cognitive architecture to examine what develops

Different theories of development propose alternative mechanisms by which development occurs. Cognitive architectures can be used to examine the influence of each proposed mechanism of development while keeping all other mechanisms constant. An ACT-R computational model that matched adult behavior in solving a 21-block pyramid puzzle was created. The model was modified in three ways that corresponded to mechanisms of development proposed by developmental theories. The results showed that all the modifications (two of capacity and one of strategy choice) could approximate the behavior of 7-year-old children on the task. The strategy-choice modification provided the closest match on the two central measures of task behavior (time taken per layer, r = .99, and construction attempts per layer, r = .73). Modifying cognitive architectures is a fruitful way to compare and test potential developmental mechanisms, and can therefore help in specifying “what develops.