Chains of large gaps between primes

Let $p_n$ denote the $n$-th prime, and for any $k \geq 1$ and sufficiently large $X$, define the quantity $$G_k(X) := \max_{p_{n+k} \leq X} \min( p_{n+1}-p_n, \dots, p_{n+k}-p_{n+k-1} ),$$ which measures the occurrence of chains of $k$ consecutive large gaps of primes. Recently, with Green and Konyagin, the authors showed that $$G_1(X) \gg \frac{\log X \log \log X\log\log\log\log X}{\log \log \log X}$$ for sufficiently large $X$. In this note, we combine the arguments in that paper with the Maier matrix method to show that $$G_k(X) \gg \frac{1}{k^2} \frac{\log X \log \log X\log\log\log\log X}{\log \log \log X}$$ for any fixed $k$ and sufficiently large $X$. The implied constant is effective and independent of $k$.Comment: 16 pages, no figure

The determinants of household water consumption: A review and assessment framework for research and practice

Achieving a thorough understanding of the determinants of household water consumption is crucial to support demand management strategies. Yet, existing research on household water consumption determinants is often limited to specific case studies, with findings that are difficult to generalize and not conclusive. Here, we first contribute an updated framework for review, classification, and analysis of the literature on the determinants of household water consumption. Our framework allows trade-off analysis of different criteria that account for the representation of a potential water consumption determinant in the literature, its impact across heterogeneous case studies, and the effort required to collect information on it. We then review a comprehensive set of 48 publications with our proposed framework. The results of our trade-off analysis show that distinct groups of determinants exist, allowing for the formulation of recommendations for practitioners and researchers on which determinants to consider in practice and prioritize in future research

The impact of low erythrocyte density in human blood on the fitness and energetic reserves of the African malaria vector Anopheles gambiae

Background Anaemia is a common health problem in the developing world. This condition is characterized by a reduction in erythrocyte density, primarily from malnutrition and/or infectious diseases such as malaria. As red blood cells are the primary source of protein for haematophagous mosquitoes, any reduction could impede the ability of mosquito vectors to transmit malaria by influencing their fitness or that of the parasites they transmit. The aim of this study was to determine the impact of differences in the density of red blood cells in human blood on malaria vector (Anopheles gambiae sensu stricto) fitness. The hypotheses tested are that mosquito vector energetic reserves and fitness are negatively influenced by reductions in the red cell density of host human blood meals commensurate with those expected from severe anaemia. Methods Mosquitoes (An. gambiae s.s.) were offered blood meals of different packed cell volume(PCV) of human blood consistent with those arising from severe anaemia (15%) and normalPCV (50%). Associations between mosquito energetic reserves (lipid, glucose and glycogen)and fitness measures (reproduction and survival) and blood meal PCV were investigated. Results The amount of protein that malaria vectors acquired from blood feeding (indexed by haematin excretion) was significantly reduced at low blood PCV. However, mosquitoes feeding on blood of low PCV had the same oviposition rates as those feeding on blood of normal PCV, and showed an increase in egg production of around 15%. The long-term survival of An. gambiae s.s was reduced after feeding on low PCV blood, but PCV had no significant impact on the proportion of mosquitoes surviving through the minimal period required to develop and transmit malaria parasites (estimated as 14 days post-blood feeding). The impact of blood PCV on the energetic reserves of mosquitoes was relatively minor. Conclusions These results suggest that feeding on human hosts whose PCV has been depleted due to severe anaemia does not significantly reduce the fitness or transmission potential of malaria vectors, and indicates that mosquitoes may be able exploit resources for reproduction more efficiently from blood of low rather than normal PCV

Two-Particle-Self-Consistent Approach for the Hubbard Model

Even at weak to intermediate coupling, the Hubbard model poses a formidable challenge. In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem. The Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem as well as particle conservation, the Pauli principle, the local moment and local charge sum rules. The self-energy formula does not assume a Migdal theorem. There is consistency between one- and two-particle quantities. Internal accuracy checks allow one to test the limits of validity of TPSC. Here I present a pedagogical review of TPSC along with a short summary of existing results and two case studies: a) the opening of a pseudogap in two dimensions when the correlation length is larger than the thermal de Broglie wavelength, and b) the conditions for the appearance of d-wave superconductivity in the two-dimensional Hubbard model.Comment: Chapter in "Theoretical methods for Strongly Correlated Systems", Edited by A. Avella and F. Mancini, Springer Verlag, (2011) 55 pages. Misprint in Eq.(23) corrected (thanks D. Bergeron

Implications of MMP9 for Blood Brain Barrier Disruption and Hemorrhagic Transformation Following Ischemic Stroke.

Numerous studies have documented increases in matrix metalloproteinases (MMPs), specifically MMP-9 levels following stroke, with such perturbations associated with disruption of the blood brain barrier (BBB), increased risk of hemorrhagic complications, and worsened outcome. Despite this, controversy remains as to which cells release MMP-9 at the normal and pathological BBB, with even less clarity in the context of stroke. This may be further complicated by the influence of tissue plasminogen activator (tPA) treatment. The aim of the present review is to examine the relationship between neutrophils, MMP-9 and tPA following ischemic stroke to elucidate which cells are responsible for the increases in MMP-9 and resultant barrier changes and hemorrhage observed following stroke

Phosphoenolpyruvate carboxylase dentified as a key enzyme in erythrocytic Plasmodium falciparum carbon metabolism

Phospoenolpyruvate carboxylase (PEPC) is absent from humans but encoded in thePlasmodium falciparum genome, suggesting that PEPC has a parasite-specific function. To investigate its importance in P. falciparum, we generated a pepc null mutant (D10Δpepc), which was only achievable when malate, a reduction product of oxaloacetate, was added to the growth medium. D10Δpepc had a severe growth defect in vitro, which was partially reversed by addition of malate or fumarate, suggesting that pepc may be essential in vivo. Targeted metabolomics using 13C-U-D-glucose and 13C-bicarbonate showed that the conversion of glycolytically-derived PEP into malate, fumarate, aspartate and citrate was abolished in D10Δpepc and that pentose phosphate pathway metabolites and glycerol 3-phosphate were present at increased levels. In contrast, metabolism of the carbon skeleton of 13C,15N-U-glutamine was similar in both parasite lines, although the flux was lower in D10Δpepc; it also confirmed the operation of a complete forward TCA cycle in the wild type parasite. Overall, these data confirm the CO2 fixing activity of PEPC and suggest that it provides metabolites essential for TCA cycle anaplerosis and the maintenance of cytosolic and mitochondrial redox balance. Moreover, these findings imply that PEPC may be an exploitable target for future drug discovery

Nitrogen uptake and internal recycling in Zostera marina exposed to oyster farming: eelgrass potential as a natural biofilter

Oyster farming in estuaries and coastal lagoons frequently overlaps with the distribution of seagrass meadows, yet there are few studies on how this aquaculture practice affects seagrass physiology. We compared in situ nitrogen uptake and the productivity of Zostera marina shoots growing near off-bottom longlines and at a site not affected by oyster farming in San Quintin Bay, a coastal lagoon in Baja California, Mexico. We used benthic chambers to measure leaf NH4 (+) uptake capacities by pulse labeling with (NH4)-N-15 (+) and plant photosynthesis and respiration. The internal N-15 resorption/recycling was measured in shoots 2 weeks after incubations. The natural isotopic composition of eelgrass tissues and vegetative descriptors were also examined. Plants growing at the oyster farming site showed a higher leaf NH4 (+) uptake rate (33.1 mmol NH4 (+) m(-2) day(-1)) relative to those not exposed to oyster cultures (25.6 mmol NH4 (+) m(-2) day(-1)). We calculated that an eelgrass meadow of 15-16 ha (which represents only about 3-4 % of the subtidal eelgrass meadow cover in the western arm of the lagoon) can potentially incorporate the total amount of NH4 (+) excreted by oysters (similar to 5.2 x 10(6) mmol NH4 (+) day(-1)). This highlights the potential of eelgrass to act as a natural biofilter for the NH4 (+) produced by oyster farming. Shoots exposed to oysters were more efficient in re-utilizing the internal N-15 into the growth of new leaf tissues or to translocate it to belowground tissues. Photosynthetic rates were greater in shoots exposed to oysters, which is consistent with higher NH4 (+) uptake and less negative delta C-13 values. Vegetative production (shoot size, leaf growth) was also higher in these shoots. Aboveground/belowground biomass ratio was lower in eelgrass beds not directly influenced by oyster farms, likely related to the higher investment in belowground biomass to incorporate sedimentary nutrients

Distortions of Subjective Time Perception Within and Across Senses

Background: The ability to estimate the passage of time is of fundamental importance for perceptual and cognitive processes. One experience of time is the perception of duration, which is not isomorphic to physical duration and can be distorted by a number of factors. Yet, the critical features generating these perceptual shifts in subjective duration are not understood. Methodology/Findings: We used prospective duration judgments within and across sensory modalities to examine the effect of stimulus predictability and feature change on the perception of duration. First, we found robust distortions of perceived duration in auditory, visual and auditory-visual presentations despite the predictability of the feature changes in the stimuli. For example, a looming disc embedded in a series of steady discs led to time dilation, whereas a steady disc embedded in a series of looming discs led to time compression. Second, we addressed whether visual (auditory) inputs could alter the perception of duration of auditory (visual) inputs. When participants were presented with incongruent audio-visual stimuli, the perceived duration of auditory events could be shortened or lengthened by the presence of conflicting visual information; however, the perceived duration of visual events was seldom distorted by the presence of auditory information and was never perceived shorter than their actual durations. Conclusions/Significance: These results support the existence of multisensory interactions in the perception of duration and, importantly, suggest that vision can modify auditory temporal perception in a pure timing task. Insofar as distortions in subjective duration can neither be accounted for by the unpredictability of an auditory, visual or auditory-visual event, we propose that it is the intrinsic features of the stimulus that critically affect subjective time distortions