A nullstellensatz for sequences over F_p

Let p be a prime and let A=(a_1,...,a_l) be a sequence of nonzero elements in F_p. In this paper, we study the set of all 0-1 solutions to the equation a_1 x_1 + ... + a_l x_l = 0. We prove that whenever l >= p, this set actually characterizes A up to a nonzero multiplicative constant, which is no longer true for l < p. The critical case l=p is of particular interest. In this context, we prove that whenever l=p and A is nonconstant, the above equation has at least p-1 minimal 0-1 solutions, thus refining a theorem of Olson. The subcritical case l=p-1 is studied in detail also. Our approach is algebraic in nature and relies on the Combinatorial Nullstellensatz as well as on a Vosper type theorem.Comment: 23 page

The peroxisome proliferator activated receptor δ is required for the differentiation of THP-1 monocytic cells by phorbol ester

BACKGROUND: PPARδ (NR1C2) promotes lipid accumulation in human macrophages in vitro and has been implicated in the response of macrophages to vLDL. We have investigated the role of PPARδ in PMA-stimulated macrophage differentiation. The THP-1 monocytic cell line which displays macrophage like differentiation in response to phorbol esters was used as a model system. We manipulated the response to PMA using a potent synthetic agonist of PPARδ , compound F. THP-1 sub-lines that either over-expressed PPARδ protein, or expressed PPARδ anti-sense RNA were generated. We then explored the effects of these genetic modulations on the differentiation process. RESULTS: The PPARδ agonist, compound F, stimulated differentiation in the presence of sub-nanomolar concentrations of phorbol ester. Several markers of differentiation were induced by compound F in a synergistic fashion with phorbol ester, including CD68 and IL8. Over-expression of PPARδ also sensitised THP-1 cells to phorbol ester and correspondingly, inhibition of PPARδ by anti-sense RNA completely abolished this response. CONCLUSIONS: These data collectively demonstrate that PPARδ plays a fundamental role in mediating a subset of cellular effects of phorbol ester and supports observations from mouse knockout models that PPARδ is involved in macrophage-mediated inflammatory responses

Airborne Measurements of Gravity Wave Breaking at the Tropopause

2000 FLORIDA AVE NW, WASHINGTON, DC, 2000

Sensitivity of resolved and parameterized surface drag to changes in resolution and parameterization

The relative contribution of resolved and parameterized surface drag towards balancing the atmospheric angular momentum flux convergence (AMFC), and their sensitivity to horizontal resolution and parameterization, are investigated in an atmospheric model. This sensitivity can be difficult to elucidate in free-running climate models, in which the AMFC varies with changing climatologies and, as a result, the relative contributions of surface terms balancing the AMFC also vary. While the sensitivity question has previously been addressed using short-range forecasts, we demonstrate that a nudging framework is an effective method for constraining the AMFC. The Met Office Unified Model is integrated at three horizontal resolutions ranging from 130 km (N96) to 25 km (N512) while relaxing the model’s wind and temperature fields towards the ERAinterim reanalysis within the altitude regions of maximum AMFC. This method is validated against short range forecasts and good agreement is found. These experiments are then used to assess the fidelity of the exchange between parameterized and resolved orographic torques with changes in horizontal resolution. Although the parameterized orographic torque reduces substantially with increasing horizontal resolution, there is little change in resolved orographic torque over 20N to 50N. The tendencies produced by the nudging routine indicate that the additional drag at lower horizontal resolution is excessive. When parameterized orographic blocking is removed at the coarsest of these resolutions, there is a lack of compensation, and even compensation of the opposite sense, by the boundary layer and resolved torques which is particularly pronounced over 20N to 50N. This study demonstrates that there is strong sensitivity in the behaviour of the resolved and parameterized surface drag over this region

A boundary layer scaling technique for estimating near-surface wind energy using numerical weather prediction and wind map data

A boundary layer scaling (BLS) method for predicting long-term average near-surface wind speeds and power densities was developed in this work. The method was based on the scaling of reference climatological data either from long-term average wind maps or from hourly wind speeds obtained from high-resolution Numerical Weather Prediction (NWP) models, with case study applications from Great Britain. It incorporated a more detailed parameterisation of surface aerodynamics than previous studies and the predicted wind speeds and power densities were validated against observational wind speeds from 124 sites across Great Britain. The BLS model could offer long-term average wind speed predictions using wind map data derived from long-term observational data, with a mean percentage error of 1.5 % which provided an improvement on the commonly used NOABL (Numerical Objective Analysis of Boundary Layer) wind map. The boundary layer scaling of NWP data was not, however, able to improve upon the use of raw NWP data for near surface wind speed predictions. However, the use of NWP data scaled by the BLS model could offer improved power density predictions compared to the use of the reference data sets. Using a vertical scaling of the shape factor of a Weibull distribution fitted to the BLS NWP data, power density predictions with a 1 % mean percentage error were achieved. This provided a significant improvement on the use of a fixed shape factor which must be utilised when only long-term average wind speeds are available from reference wind maps. The work therefore highlights the advantages that use of a BLS model for wind speed and NWP data for power density predictions can offer for small to medium scale wind energy resource assessments, potentially facilitating more robust annual energy production and financial assessments of prospective small and medium scale wind turbine installations

Episodic medication adherence in adolescents and young adults with perinatally acquired HIV:a within participants approach

Due to the success of antiretroviral (ART) medications, young people living with perinatally acquired HIV (PHIV+) are now surviving into adolescence and young adulthood. Understanding factors influencing ART non-adherence in this group is important in developing effective adherence interventions. Most studies of ART adherence in HIV-positive populations assess differences in adherence levels and adherence predictors between participants, over a period of time (global adherence). Many individuals living with HIV, however, including PHIV+ young people, take medication inconsistently. To investigate this pattern of adherence, a within-participants design, focussing on specific episodes of adherence and non-adherence, is suitable (episodic adherence). A within-participants design was used with 29 PHIV+ young people (17 female, median age 17 years, range 14–22 years), enrolled in the UK Adolescents and Adults Living with Perinatal HIV cohort study. Participants were eligible if they could identify one dose of medication taken and one dose they had missed in the previous two months. For each of the two episodes (one adherent, one non-adherent), behavioural factors (whom they were with, location, routine, day, reminders) and psychological factors at the time of the episode (information about medication, adherence motivation, perceived behavioural skills to adhere to medication – derived from the Information-Motivation-Behavioural Skills (IMB) Model – and affect) were assessed in a questionnaire. Non-adherence was significantly associated with weekend days (Friday to Sunday versus Monday to Thursday, p = .001), lack of routine (p = .004), and being out of the home (p = .003), but not with whom the young person was with or whether they were reminded to take medication. Non-adherence was associated with lower levels of behavioural skills (p < .001), and lower positive affect (p = .005). Non-adherence was not significantly associated with negative affect, information about ART, or ART motivation. The use of situationally specific strategies to enhance adherence in young people who take their medication inconsistently is proposed

Orographic drag associated with lee waves trapped at an inversion

The drag produced by 2D orographic gravity waves trapped at a temperature inversion and waves propagating in the stably stratified layer existing above are explicitly calculated using linear theory, for a two-layer atmosphere with neutral static stability near the surface, mimicking a well-mixed boundary layer. For realistic values of the flow parameters, trapped lee wave drag, which is given by a closed analytical expression, is comparable to propagating wave drag, especially in moderately to strongly non-hydrostatic conditions. In resonant flow, both drag components substantially exceed the single-layer hydrostatic drag estimate used in most parametrization schemes. Both drag components are optimally amplified for a relatively low-level inversion and Froude numbers Fr ≈ 1. While propagating wave drag is maximized for approximately hydrostatic flow, trapped lee wave drag is maximized for l_2 a = O(1) (where l_2 is the Scorer parameter in the stable layer and a is the mountain width). This roughly happens when the horizontal scale of trapped lee waves matches that of the mountain slope. The drag behavior as a function of Fr for l_2 H = 0.5 (where H is the inversion height) and different values of l2a shows good agreement with numerical simulations. Regions of parameter space with high trapped lee wave drag correlate reasonably well with those where lee wave rotors were found to occur in previous nonlinear numerical simulations including frictional effects. This suggests that trapped lee wave drag, besides giving a relevant contribution to low-level drag exerted on the atmosphere, may also be useful to diagnose lee rotor formation

Forced Gravity Waves and the Tropospheric Response to Convection

We present theoretical work directed toward improving our understanding of the mesoscale influence of deep convection on its tropospheric environment through forced gravity waves. From the linear, hydrostatic, non-rotating, incompressible equations, we find a two-dimensional analytical solution to prescribed heating in a stratified atmosphere, which is upwardly radiating from the troposphere when the domain lid is sufficiently high. We interrogate the spatial and temporal sensitivity of both the vertical velocity and potential temperature to different heating functions, considering both the near-field and remote responses to steady and pulsed heating. We find that the mesoscale tropospheric response to convection is significantly dependent on the upward radiation characteristics of the gravity waves, which are in turn dependent upon the temporal and spatial structure of the source, and the assumed stratification. We find a 50% reduction in tropospherically averaged vertical velocity when moving from a trapped (i.e. low lid) to upwardly-radiating (i.e. high lid) solution, but even with maximal upward radiation, we still observe significant tropospheric vertical velocities in the far-field 4 hours after heating ends. We quantify the errors associated with coarsening a 10 km wide heating to a 100 km grid (in the way a General Circulation Model (GCM) would), observing a 20% reduction in vertical velocity. The implications of these results for the parameterisation of convection in low-resolution numerical models are quantified and it is shown that the smoothing of heating over a grid-box leads to significant in grid-box tendencies, due to the erroneous rate of transfer of compensating subsidence to neighbouring regions. Further, we explore a simple time-dependent heating parameterisation that minimises error in a parent GCM grid box, albeit at the expense of increased error in the neighbourhood

Impacts of orography on large-scale atmospheric circulation

Some of the largest and most persistent circulation errors in global numerical weather prediction and climate models are attributable to the inadequate representation of the impacts of orography on the atmospheric flow. Existing parametrization approaches attempting to account for unresolved orographic processes, such as turbulent form drag, low-level flow blocking or mountain waves, have been successful to some extent. They capture the basic impacts of the unresolved orography on atmospheric circulation in a qualitatively correct way and have led to significant progress in both numerical weather prediction and climate modelling. These approaches, however, have apparent limitations and inadequacies due to poor observational evidence, insufficient fundamental knowledge and an ambiguous separation between resolved and unresolved orographic scales and between different orographic processes. Numerical weather prediction and climate modelling has advanced to a stage where these inadequacies have become critical and hamper progress by limiting predictive skill on a wide range of spatial and temporal scales. More physically-based approaches are needed to quantify the relative importance of apparently disparate orographic processes and to account for their combined effects in a rational and accurate way in numerical models. We argue that, thanks to recent advances, significant progress can be made by combining theoretical approaches with observations, inverse modelling techniques and high-resolution and idealized numerical simulations

Pollutant dispersion in a developing valley cold-air pool

Pollutants are trapped and accumulate within cold-air pools, thereby affecting air quality. A numerical model is used to quantify the role of cold-air-pooling processes in the dispersion of air pollution in a developing cold-air pool within an alpine valley under decoupled stable conditions. Results indicate that the negatively buoyant downslope flows transport and mix pollutants into the valley to depths that depend on the temperature deficit of the flow and the ambient temperature structure inside the valley. Along the slopes, pollutants are generally entrained above the cold-air pool and detrained within the cold-air pool, largely above the ground-based inversion layer. The ability of the cold-air pool to dilute pollutants is quantified. The analysis shows that the downslope flows fill the valley with air from above, which is then largely trapped within the cold-air pool, and that dilution depends on where the pollutants are emitted with respect to the positions of the top of the ground-based inversion layer and cold-air pool, and on the slope wind speeds. Over the lower part of the slopes, the cold-air-pool-averaged concentrations are proportional to the slope wind speeds where the pollutants are emitted, and diminish as the cold-air pool deepens. Pollutants emitted within the ground-based inversion layer are largely trapped there. Pollutants emitted farther up the slopes detrain within the cold-air pool above the ground-based inversion layer, although some fraction, increasing with distance from the top of the slopes, penetrates into the ground-based inversion layer.Peer reviewe