Dichotomous Hamiltonians with Unbounded Entries and Solutions of Riccati Equations

An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different indefinite inner products, we prove the existence of nonnegative and nonpositive solutions of the Riccati equation. Moreover, conditions for the boundedness and uniqueness of these solutions are established.Comment: 31 pages, 3 figures; proof of uniqueness of solutions added; to appear in Journal of Evolution Equation

Integrating science and literacy for young English learners : a pilot study.

This pilot investigated the promise of positive outcomes in literacy, science, and social behavior on K– 2 English learner (﴾EL)﴿ students after two months of implementation of the Science Inquiry Centered Argumentation Model (﴾ScICAM)﴿—a systematic teaching approach to science learning that integrates literacy instruction and argument-‐based inquiry. The sample included 17 teachers and 31 EL students. Results indicated that teacher practices (﴾proximal outcomes)﴿ aligned well with the ScICAM approach and resulted in increases in EL student learning (﴾distal outcomes)﴿. Teacher increase in the use of inquiry and writing scaffolds and student growth in the ability to express understandings through oral and written modes also suggested that ScICAM practices are supportive of key practices identified by the Next Generation Science Standards (﴾NGSS Lead States, 2013)﴿. These results highlight the merit of pursuing larger, long-‐term projects that collaborate with teachers on developing and implementing ScICAM interventions

Enhanced hydrogen peroxide generation accompanies the beneficial bioenergetic effects of methylene blue in isolated brain mitochondria

The redox dye methylene blue (MB) is proven to have beneficial effects in various models of neurodegenerative diseases. Here we investigated the effects of MB (100 nM, 300 nM, and 1 μM) on key bioenergetic parameters and on H2O2 production/elimination in isolated guinea pig brain mitochondria under normal as well as respiration-impaired conditions. As measured by high-resolution Oxygraph the rate of resting oxygen consumption was increased, but the ADP-stimulated respiration was unaffected by MB with any of the substrates (glutamate malate, succinate, or α-glycerophosphate) used for supporting mitochondrial respiration. In mitochondria treated with inhibitors of complex I or complex III MB moderately but significantly increased the rate of ATP production, restored ΔΨm, and increased the rate of Ca2+ uptake. The effects of MB are consistent with transferring electrons from upstream components of the electron transport chain to cytochrome c, which is energetically favorable when the flow of electrons in the respiratory chain is compromised. On the other hand, MB significantly increased the production of H2O2 measured by Amplex UltraRed fluorimetry under all conditions, in resting, ATP-synthesizing, and respiration-impaired mitochondria, with each substrate combination supporting respiration. Furthermore, it also decreased the elimination of H2O2. Generation of H2O2 without superoxide formation, observed in the presence of MB, is interpreted as a result of reduction of molecular oxygen to H2O2 by the reduced MB. The elevated generation and impaired elimination of H2O2 should be considered for the overall oxidative state of mitochondria treated with MB

Simplicity of extremal eigenvalues of the Klein-Gordon equation

We consider the spectral problem associated with the Klein-Gordon equation for unbounded electric potentials. If the spectrum of this problem is contained in two disjoint real intervals and the two inner boundary points are eigenvalues, we show that these extremal eigenvalues are simple and possess strictly positive eigenfunctions. Examples of electric potentials satisfying these assumptions are given

Dissipative Properties of Systems Composed of High-Loss and Lossless Components

We study here dissipative properties of systems composed of two components one of which is highly lossy and the other is lossless. A principal result of our studies is that all the eigenmodes of such a system split into two distinct classes characterized as high-loss and low-loss. Interestingly, this splitting is more pronounced the higher the loss of the lossy component. In addition, the real frequencies of the high-loss eigenmodes can become very small and even can vanish entirely, which is the case of overdamping.Comment: Revision; Improved exposition and typos corrected; 45 pages, 4 figure

A False Start in the Race Against Doping in Sport: Concerns With Cycling’s Biological Passport

Professional cycling has suffered from a number of doping scandals. The sport’s governing bodies have responded by implementing an aggressive new antidoping program known as the biological passport. Cycling’s biological passport marks a departure from traditional antidoping efforts, which have focused on directly detecting prohibited substances in a cyclist’s system. Instead, the biological passport tracks biological variables in a cyclist’s blood and urine over time, monitoring for fluctuations that are thought to indirectly reveal the effects of doping. Although this method of indirect detection is promising, it also raises serious legal and scientific concerns. Since its introduction, the cycling community has debated the reliability of indirect biological-passport evidence and the clarity, consistency, and transparency of its use in proving doping violations. Such uncertainty undermines the legitimacy of finding cyclists guilty of doping based on this indirect evidence alone. Antidoping authorities should address these important concerns before continuing to pursue doping sanctions against cyclists solely on the basis of their biological passports

Membrane potential and delta pH dependency of reverse electron transport-associated hydrogen peroxide production in brain and heart mitochondria

Succinate-driven reverse electron transport (RET) is one of the main sources of mitochondrial reactive oxygen species (mtROS) in ischemia-reperfusion injury. RET is dependent on mitochondrial membrane potential (Δψm) and transmembrane pH difference (ΔpH), components of the proton motive force (pmf); a decrease in Δψm and/or ΔpH inhibits RET. In this study we aimed to determine which component of the pmf displays the more dominant effect on RET-provoked ROS generation in isolated guinea pig brain and heart mitochondria respiring on succinate or α-glycerophosphate (α-GP). Δψm was detected via safranin fluorescence and a TPP+ electrode, the rate of H2O2 formation was measured by Amplex UltraRed, the intramitochondrial pH (pHin) was assessed via BCECF fluorescence. Ionophores were used to dissect the effects of the two components of pmf. The K+/H+ exchanger, nigericin lowered pHin and ΔpH, followed by a compensatory increase in Δψm that led to an augmented H2O2 production. Valinomycin, a K+ ionophore, at low [K+] increased ΔpH and pHin, decreased Δψm, which resulted in a decline in H2O2 formation. It was concluded that Δψm is dominant over ∆pH in modulating the succinate- and α-GP-evoked RET. The elevation of extramitochondrial pH was accompanied by an enhanced H2O2 release and a decreased ∆pH. This phenomenon reveals that from the pH component not ∆pH, but rather absolute value of pH has higher impact on the rate of mtROS formation. Minor decrease of Δψm might be applied as a therapeutic strategy to attenuate RET-driven ROS generation in ischemia-reperfusion injury

Metabolic Control Analysis in a Cellular Model of Elevated MAO-B: Relevance to Parkinson’s Disease

We previously demonstrated that spare respiratory capacity of the TCA cycle enzyme alpha-ketoglutarate dehydrogenase (KGDH) was completely abolished upon increasing levels of MAO-B activity in a dopaminergic cell model system (Kumar et al., J Biol Chem 278:46432–46439, 2003). MAO-B mediated increases in H2O2 also appeared to result in direct oxidative inhibition of both mitochondrial complex I and aconitase. In order to elucidate the contribution that each of these components exerts over metabolic respiratory control as well as the impact of MAO-B elevation on their spare respiratory capacities, we performed metabolic respiratory control analysis. In addition to KGDH, we assessed the activities and substrate-mediated respiration of complex I, pyruvate dehydrogenase (PDH), succinate dehydrogenase (SDH), and mitochondrial aconitase in the absence and presence of complex-specific inhibitors in specific and mixed substrate conditions in mitochondria from our MAO-B elevated cells versus controls. Data from this study indicates that Complex I and KGDH are the most sensitive to inhibition by MAO-B mediated H2O2 generation, and could be instrumental in determining the fate of mitochondrial metabolism in this cellular PD model system