Combinatorial Stokes formulas via minimal resolutions

We describe an explicit chain map from the standard resolution to the minimal resolution for the finite cyclic group Z_k of order k. We then demonstrate how such a chain map induces a "Z_k-combinatorial Stokes theorem", which in turn implies "Dold's theorem" that there is no equivariant map from an n-connected to an n-dimensional free Z_k-complex. Thus we build a combinatorial access road to problems in combinatorics and discrete geometry that have previously been treated with methods from equivariant topology. The special case k=2 for this is classical; it involves Tucker's (1949) combinatorial lemma which implies the Borsuk-Ulam theorem, its proof via chain complexes by Lefschetz (1949), the combinatorial Stokes formula of Fan (1967), and Meunier's work (2006).Comment: 18 page

Measurements and computational analysis of heat transfer and flow in a simulated turbine blade internal cooling passage

Visual and quantitative information was obtained on heat transfer and flow in a branched-duct test section that had several significant features of an internal cooling passage of a turbine blade. The objective of this study was to generate a set of experimental data that could be used to validate computer codes for internal cooling systems. Surface heat transfer coefficients and entrance flow conditions were measured at entrance Reynolds numbers of 45,000, 335,000, and 726,000. The heat transfer data were obtained using an Inconel heater sheet attached to the surface and coated with liquid crystals. Visual and quantitative flow field results using particle image velocimetry were also obtained for a plane at mid channel height for a Reynolds number of 45,000. The flow was seeded with polystyrene particles and illuminated by a laser light sheet. Computational results were determined for the same configurations and at matching Reynolds numbers; these surface heat transfer coefficients and flow velocities were computed with a commercially available code. The experimental and computational results were compared. Although some general trends did agree, there were inconsistencies in the temperature patterns as well as in the numerical results. These inconsistencies strongly suggest the need for further computational studies on complicated geometries such as the one studied

Évaluation de la capacité de rétention des métaux dissous d'un marais artificiel en utilisant le périphyton et le gastéropode Helisoma trivolvis

Le but de cette étude est de déterminer si le périphyton et le gastéropode pulmoné Helisoma trivolvis peuvent être utilisés pour évaluer la capacité de rétention des métaux dissous d'un marais construit. Cette étude a été menée dans un marais de la région d'Ottawa-Carleton (Ontario, Canada), qui a été construit en 1995 afin d'améliorer la qualité des eaux de ruissellement provenant d'un bassin versant à usage résidentiel et agricole. Au cours du mois de septembre 1999, des échantillons d'eau ont été prélevés, des escargots (H. trivolvis) ont été recoltés et un substrat artificiel a été utilisé pour faire croître du périphyton, à l'entrée et à la sortie d'eau du marais. En moyenne, les calculs de balance de masse indiquaient une rétention des formes dissoutes du Cu, Mn, Ni et Zn dans le marais. Cependant, les tendances observées pour les concentrations de métaux dissous et pour les concentrations dans les organismes différaient pour certains métaux. Les concentrations de Cd et Ni dans les tissus de H. trivolvis et le périphyton étaient significativement plus élevées à l'entrée qu'à la sortie. Cependant, les concentrations de Cr et Al dans les organismes n'étaient pas significativement différentes entre l'entrée et la sortie alors que celle de Mn était significativement plus élevée à la sortie du marais. Pour tous les métaux sauf le Cd et le Zn, les concentrations dans le périphyton étaient en moyenne plus elevées que celles dans les escargots. Le périphyton peut donc fournir une mesure plus conservatrice de la contamination du milieu pas les métaux. Cette étude montre l'importance de considérer, non-seulement les mesures chimiques, mais aussi les mesures biologiques, dans l'évaluation de l'efficacité d'un ouvrage de contrôle de pollution.Urban and agricultural development has had a significant impact on the water quality of rivers and lakes around the world. In the last few decades, constructed wetlands have been designed as wastewater treatment systems to prevent water quality deterioration in natural receiving waters. Constructed wetlands are built because they are considered sinks for many pollutants thereby protecting the water quality of downstream ecosystems. The treatment performance of these wetlands is generally assessed using mass balance calculations. However, the retention of metals by constructed wetlands is highly variable and the factors involved are still poorly understood. If wetlands are sinks for metals, the metal content of organisms should be lower downstream than upstream. In this context, organisms can be useful to assess the retention or transformation of metals by wetlands.The objective of this study was to determine whether periphyton and the gastropod Helisoma trivolvis could be used to evaluate the retention of dissolved metals in a constructed wetland. H. trivolvis is a freshwater pulmonate snail widespread in ponds across North America. It feeds mostly on periphyton and is more or less sedentary. Snails have been used as biomonitors because several species are metal tolerant. However, compared to snails, periphytic microorganisms may track more closely dissolved metal concentrations as they take up metals principally from the water column.This study was conducted at the Monahan Pond in Kanata, Ontario (Canada). This wetland was built in 1995 to treat run-off from an agricultural and residential watershed. Water chemistry samples, snails and periphyton grown on artificial substrata were collected at both the inlet and the outlet of the wetland in the fall of 1999. Tissue samples were digested with concentrated nitric acid and metal analyses were done by ICP-MS (Inductively Coupled Plasma Mass Spectrometry). During the experiment several chemical parameters differed between the inlet and the outlet. Alkalinity was significantly higher at the inflow and all major cation concentrations were higher at the inflow. The temperature was on average 3 ºC higher at the outlet. Mass balance calculations showed that the wetland was a sink for most dissolved metals. Snails and periphyton tissue metal concentrations were higher at the inflow than at the outlet for Cd and Ni. However, no significant differences were observed between inflow and outlet tissue concentrations for Cr and Al, whereas Mn was actually significantly higher at the outlet. As a result, the metal content of the organisms did not consistently reflect the dissolved metal concentrations in water. For all metals except Cd and Zn, periphyton concentrations were on average higher than snail metal concentrations. Periphyton analyses can provide a more conservative measure of metal contamination and, when artificial substrates are used, correspond to defined and known periods of exposure.This study demonstrates that constructed wetlands may lead to increased metal content of downstream organisms even if these wetlands appear to be overall sinks for dissolved metals based on mass balance calculations. It also shows the need to consider not only metal concentrations, but also biological data when assessing the performance of pollution control facilities

Quantification of complementarity in multi-qubit systems

Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation between classically incompatible properties, such as visibility of interference fringes and "which-way" information, but also between purely quantum mechanical properties, such as measures of entanglement. We discuss different complementarity relations for systems of 2-, 3-, or \textit{n} qubits. Using nuclear magnetic resonance techniques, we have experimentally verified some of these complementarity relations in a two-qubit system.Comment: 12 pages, 10 figures (A display error about the figures in the previous version

The importance of ST elevation in V2–4 ECG leads in athletes

Background Early repolarization in the anterior ECG leads (ERV2–4) is considered to be a sign of right ventricular (RV) remodeling, but its etiology and importance are unclear. Methods A total of 243 top-level endurance-trained athletes (ETA; 183 men and 60 women, weekly training hours: 15–20) and 120 leisure-time athletes (LTA; 71 men and 49 women, weekly training hours: 5–6) were investigated. The ERV2–4 sign was evaluated concerning type of sport, gender, transthoracic echocardiographic parameters, and ECG changes, which can indicate elevated RV systolic pressure [left atrium enlargement (LAE), right atrium enlargement (RAE), RV conduction defect (RVcd)]. Results Stroke volume and left ventricular mass were higher in ETAs vs. LTAs in both genders (p < 0.01). Prevalence of the ERV2–4 sign was significantly higher in men than in women [p = 0.000, odds ratio (OR) = 36.4] and in ETAs than in LTAs (p = 0.000). The highest ERV2–4 prevalence appeared in the most highly trained triathlonists and canoe and kayak paddlers (OR = 13.8 and 5.2, respectively). Within the ETA group, the post-exercise LAE, RAE, and RVcd changes developed more frequently in cases with than without ERV2–4 (LAE: men: p < 0.05, females: p < 0.005; RAE: men: p < 0.05, females: p < 0.005; RVcd: N.S.). These post-exercise appearing LAE, RAE, and RVcd are associated with the ERV2–4 sign (OR = 4.0, 3.7, and 3.8, respectively). Conclusions According to these results, ERV2–4 develops mainly in male ETAs due to long-lasting and repeated endurance training. The ERV2–4 sign indicates RV’s adaptation to maintain higher compensatory pulmonary pressure and flow during exercise but its danger regarding malignant arrhythmias is unclear

Prolonged exposure of cortical neurons to oligomeric amyloid-β impairs NMDA receptor function via NADPH oxidase-mediated ROS production: protective effect of green tea (–)-epigallocatechin-3-gallate

Excessive production of Aβ (amyloid β-peptide) has been shown to play an important role in the pathogenesis of AD (Alzheimer's disease). Although not yet well understood, aggregation of Aβ is known to cause toxicity to neurons. Our recent study demonstrated the ability for oligomeric Aβ to stimulate the production of ROS (reactive oxygen species) in neurons through an NMDA (N-methyl-d-aspartate)-dependent pathway. However, whether prolonged exposure of neurons to aggregated Aβ is associated with impairment of NMDA receptor function has not been extensively investigated. In the present study, we show that prolonged exposure of primary cortical neurons to Aβ oligomers caused mitochondrial dysfunction, an attenuation of NMDA receptor-mediated Ca2+ influx and inhibition of NMDA-induced AA (arachidonic acid) release. Mitochondrial dysfunction and the decrease in NMDA receptor activity due to oligomeric Aβ are associated with an increase in ROS production. Gp91ds-tat, a specific peptide inhibitor of NADPH oxidase, and Mn(III)-tetrakis(4-benzoic acid)-porphyrin chloride, an ROS scavenger, effectively abrogated Aβ-induced ROS production. Furthermore, Aβ-induced mitochondrial dysfunction, impairment of NMDA Ca2+ influx and ROS production were prevented by pre-treatment of neurons with EGCG [(−)-epigallocatechin-3-gallate], a major polyphenolic component of green tea. Taken together, these results support a role for NADPH oxidase-mediated ROS production in the cytotoxic effects of Aβ, and demonstrate the therapeutic potential of EGCG and other dietary polyphenols in delaying onset or retarding the progression of AD