Second cohomology groups for algebraic groups and their Frobenius kernels

Let $G$ be a simple simply connected algebraic group scheme defined over an algebraically closed field of characteristic $p > 0$. Let $T$ be a maximal split torus in $G$, $B \supset T$ be a Borel subgroup of $G$ and $U$ its unipotent radical. Let $F: G \rightarrow G$ be the Frobenius morphism. For $r \geq 1$ define the Frobenius kernel, $G_r$, to be the kernel of $F$ iterated with itself $r$ times. Define $U_r$ (respectively $B_r$) to be the kernel of the Frobenius map restricted to $U$ (respectively $B$). Let $X(T)$ be the integral weight lattice and $X(T)_+$ be the dominant integral weights. The computations of particular importance are \h^2(U_1,k), \h^2(B_r,\la) for \la \in X(T), \h^2(G_r,H^0(\la)) for \la \in X(T)_+, and \h^2(B,\la) for \la \in X(T). The above cohomology groups for the case when the field has characteristic 2 one computed in this paper. These computations complete the picture started by Bendel, Nakano, and Pillen for $p \geq 3$ \cite{BNP2}.Comment: 49 pages, 4 appendices, 6 table

Cohomology of quantum groups: An analog of Kostant's Theorem

We prove the analog of Kostant's Theorem on Lie algebra cohomology in the context of quantum groups. We prove that Kostant's cohomology formula holds for quantum groups at a generic parameter $q$, recovering an earlier result of Malikov in the case where the underlying semisimple Lie algebra $\mathfrak{g} = \mathfrak{sl}(n)$. We also show that Kostant's formula holds when $q$ is specialized to an $\ell$-th root of unity for odd $\ell \ge h-1$ (where $h$ is the Coxeter number of $\mathfrak{g}$) when the highest weight of the coefficient module lies in the lowest alcove. This can be regarded as an extension of results of Friedlander-Parshall and Polo-Tilouine on the cohomology of Lie algebras of reductive algebraic groups in prime characteristic.Comment: 12 page

Stem diameter growth rates in a fire-prone savanna correlate with photosynthetic rate and branch-scale biomass allocation, but not specific leaf area

Plant growth rates strongly determine ecosystem productivity and are a central element of plant ecological strategies. For laboratory and glasshouse‐grown seedlings, specific leaf area (SLA; ratio of leaf area to mass) is a key driver of interspecific variation in growth rate (GR). Consequently, SLA is often assumed to drive GR variation in field‐grown adult plants. However, there is an increasing evidence that this is not the general case. This suggests that GR – SLA relationships (and perhaps those for other traits) may vary depending on the age or size of the plants being studied. Here we investigated GR – trait relationships and their size dependence among 17 woody species from an open‐canopy, fire‐prone savanna in northern Australia. We tested the predictions that SLA and stem diameter growth rate would be positively correlated in saplings but unrelated in adults while, in both age classes, faster‐GR species would have higher light‐saturated photosynthetic rate (Asat), higher leaf nutrient concentrations, higher branch‐scale biomass allocation to leaf versus stem tissues and lower wood density (WD). SLA showed no relationship to stem diameter GR, even in saplings, and the same was true of leaf N and P concentrations, and WD. However, branch‐scale leaf:stem allocation was strongly related to GR in both age groups, as was Asat. Together, these two traits accounted for up to 80% of interspecific variation in adult GR, and 41% of sapling GR. Asat is rarely measured in field‐based GR studies, and this is the first report of branch‐scale leaf:stem allocation (analogous to a benefit:cost ratio) in relation to plant growth rate. Our results suggest that we may yet find general trait‐drivers of field growth rates, but SLA will not be one

Effects of heavy metals on Cyanothece sp. CCY 0110 growth, extracellular polymeric substances (EPS) production, ultrastructure and protein profiles

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Behavior problems and prevalence of asthma symptoms among Brazilian children.

OBJECTIVE: Asthma is the most common chronic disease in childhood and has been designated a public health problem due to the increase in its prevalence in recent decades, the amount of health service expenditure it absorbs and an absence of consensus about its etiology. The relationships among psychosocial factors and the occurrence, symptomatology, and severity of asthma have recently been considered. There is still controversy about the association between asthma and a child's mental health, since the pathways through which this relationship is established are complex and not well researched. This study aims to investigate whether behavior problems are associated with the prevalence of asthma symptoms in a large urban center in Latin America. METHODS: It is a cross-section study of 869 children between 6 and 12 years old, residents of Salvador, Brazil. The International Study of Allergy and Asthma in Childhood (ISAAC) instrument was used to evaluate prevalence of asthma symptoms. The Child Behavior Checklist (CBCL) was employed to evaluate behavioral problems. RESULTS: 19.26% (n=212) of the children presented symptoms of asthma. 35% were classified as having clinical behavioral problems. Poisson's robust regression model demonstrated a statistically significant association between the presence of behavioral problems and asthma symptoms occurrence (PR: 1.43; 95% CI: 1.10-1.85). CONCLUSION: These results suggest an association between behavioral problems and pediatric asthma, and support the inclusion of mental health care in the provision of services for asthma morbidity

Methane leak detection and sizing over long distances using dual frequency comb laser spectroscopy and a bootstrap inversion technique

Advances in natural gas extraction technology have led to increased activity in the production and transport sectors in the United States, and, as a consequence, an increased need for reliable monitoring of methane leaks to the atmosphere. We present a statistical methodology in combination with an observing system for the detection and attribution of fugitive emissions of methane from distributed potential source location landscapes such as natural gas production sites. We measure long (&gt;500 m), integrated open path concentrations of atmospheric methane using a dual frequency comb spectrometer and combine measurements with an atmospheric transport model to infer leak locations and strengths using a novel statistical method, the non-zero minimum bootstrap (NZMB). The new statistical method allows us to determine whether the empirical distribution of possible source strengths for a given location excludes zero. Using this information, we identify leaking source locations (i.e., natural gas wells) through rejection of the null hypothesis that the source is not leaking. The method is tested with a series of synthetic data inversions with varying measurement density and varying levels of model-data mismatch. It is also tested with field observations of 1) a non-leaking source location and 2) a source location where a controlled emission of 2.1 E-5 kg s-1 of methane gas is released over a period of several hours. This series of synthetic data tests and outdoor field observations using a controlled methane release demonstrate the viability of the approach for the detection and sizing of very small (&lt;2 g m-1 ) leaks of methane across large distances (4+ km2 in synthetic tests). The field tests demonstrate the ability to attribute small atmospheric enhancements of 18 ppb to the emitting source location against a background of combined atmospheric (e.g., background methane variability) and measurement uncertainty of 6 ppb (1-sigma), when measurements are averaged over 2 minutes. The results of the synthetic and field data testing show that the new observing system and statistical approach greatly decreases the incidence of false alarms (that is, wrongly identifying a well site to be leaking) compared with the same tests that don&rsquo;t use the NZMB approach, and therefore offers increased leak detection and sizing capabilities.</p

Vascular pedicle width in acute lung injury: correlation with intravascular pressures and ability to discriminate fluid status

Abstract Introduction Conservative fluid management in patients with acute lung injury (ALI) increases time alive and free from mechanical ventilation. Vascular pedicle width (VPW) is a non-invasive measurement of intravascular volume status. The VPW was studied in ALI patients to determine the correlation between VPW and intravascular pressure measurements and whether VPW could predict fluid status. Methods This retrospective cohort study involved 152 patients with ALI enrolled in the Fluid and Catheter Treatment Trial (FACTT) from five NHLBI ARDS (Acute Respiratory Distress Syndrome) Network sites. VPW and central venous pressure (CVP) or pulmonary artery occlusion pressure (PAOP) from the first four study days were correlated. The relationships between VPW, positive end-expiratory pressure (PEEP), cumulative fluid balance, and PAOP were also evaluated. Receiver operator characteristic (ROC) curves were used to determine the ability of VPW to detect PAOP &lt;8 mmHg and PAOP ≥18 mm Hg. Results A total of 71 and 152 patients provided 118 and 276 paired VPW/PAOP and VPW/CVP measurements, respectively. VPW correlated with PAOP (r = 0.41; P &lt; 0.001) and less well with CVP (r = 0.21; P = 0.001). In linear regression, VPW correlated with PAOP 1.5-fold better than cumulative fluid balance and 2.5-fold better than PEEP. VPW discriminated achievement of PAOP &lt;8 mm Hg (AUC = 0.73; P = 0.04) with VPW ≤67 mm demonstrating 71% sensitivity (95% CI 30 to 95%) and 68% specificity (95% CI 59 to 75%). For discriminating a hydrostatic component of the edema (that is, PAOP ≥18 mm Hg), VPW ≥72 mm demonstrated 61.4% sensitivity (95% CI 47 to 74%) and 61% specificity (49 to 71%) (area under the curve (AUC) 0.69; P = 0.001). Conclusions VPW correlates with PAOP better than CVP in patients with ALI. Due to its only moderate sensitivity and specificity, the ability of VPW to discriminate fluid status in patients with acute lung injury is limited and should only be considered when intravascular pressures are unavailable