Finite reduction and Morse index estimates for mechanical systems

A simple version of exact finite dimensional reduction for the variational setting of mechanical systems is presented. It is worked out by means of a thorough global version of the implicit function theorem for monotone operators. Moreover, the Hessian of the reduced function preserves all the relevant information of the original one, by Schur's complement, which spontaneously appears in this context. Finally, the results are straightforwardly extended to the case of a Dirichlet problem on a bounded domain.Comment: 13 pages; v2: minor changes, to appear in Nonlinear Differential Equations and Application

Behavioral Characterization of the Novel GABA B Receptor- Positive Modulator GS39783 (N,NЈ-Dicyclopentyl-2- methylsulfanyl-5-nitro-pyrimidine-4,6-diamine): Anxiolytic-Like Activity without Side Effects Associated with Baclofen or Benzodiazepines

ABSTRACT The role of GABA B receptors in various behavioral processes has been largely defined using the prototypical GABA B receptor agonist baclofen. However, baclofen induces sedation, hypothermia and muscle relaxation, which may interfere with its use in behavioral paradigms. Although there is much evidence for a role of the inhibitory neurotransmitter GABA in the pathophysiology of anxiety, the role of GABA B receptors in these disorders is largely unclear. We recently identified GS39783 (N,NЈ-dicyclopentyl-2-methylsulfanyl-5-nitro-pyrimidine-4,6-diamine) as a selective allosteric positive modulator at GABA B receptors. The aim of the present study was to broadly characterize the effects of GS39783 in well-validated rodent models for motor activity, cognition, and anxiety. The following tests were included: locomotor activity in rats and mice, rotarod and traction tests (including determinations of core temperature) in mice, passive avoidance in mice and rats, elevated plus maze in rats, elevated zero maze in mice and rats, stress-induced hyperthermia in mice, and pentobarbital-and ethanol-induced sleep in mice. Unlike baclofen and/or the benzodiazepine chlordiazepoxide, GS39783 had no effect in any of the tests for locomotion, cognition, temperature, or narcosis. Most interestingly, GS39783 had anxiolytic-like effects in all the tests used. Overall, the data obtained here suggest that positive modulation of GABA B receptors may serve as a novel therapeutic strategy for the development of anxiolytics, with a superior side effect profile to both baclofen and benzodiazepines

CB1 Cannabinoid Receptor Activation Dose-Dependently Modulates Neuronal Activity within Caudal but not Rostral Song Control Regions of Adult Zebra Finch Telencephalon

CB1 cannabinoid receptors are distinctly expressed at high density within several regions of zebra finch telencephalon including those known to be involved in song learning (lMAN and Area X) and production (HVC and RA). Because: (1) exposure to cannabinoid agonists during developmental periods of auditory and sensory-motor song learning alters song patterns produced later in adulthood and; (2) densities of song region expression of CB1 waxes-and-wanes during song learning, it is becoming clear that CB1 receptor-mediated signaling is important to normal processes of vocal development. To better understand mechanisms involved in cannabinoid modulation of vocal behavior we have investigated the dose-response relationship between systemic cannabinoid exposure and changes in neuronal activity (as indicated by expression of the transcription factor, c- Fos) within telencephalic brain regions with established involvement in song learning and/or control. In adults we have found that low doses (0.1 mg/kg) of the cannabinoid agonist WIN-55212-2 decrease neuronal activity (as indicated by densities of c-fos-expressing nuclei) within vocal motor regions of caudal telencephalon (HVC and RA) while higher doses (3 mg/kg) stimulate activity. Both effects were reversed by pretreatment with the CB1-selective antagonist rimonabant. Interestingly, no effects of cannabinoid treatment were observed within the rostral song regions lMAN and Area X, despite distinct and dense CB1 receptor expression within these areas. Overall, our results demonstrate that, depending on dosage, CB1 agonism can both inhibit and stimulate neuronal activity within brain regions controlling adult vocal motor output, implicating involvement of multiple CB1-sensitive neuronal circuits. Originally published Psychopharmacology, Vol. 199, No. 2, Aug 200

Effects of Cannabinoids on Caffeine Contractures in Slow and Fast Skeletal Muscle Fibers of the Frog

The effect of cannabinoids on caffeine contractures was investigated in slow and fast skeletal muscle fibers using isometric tension recording. In slow muscle fibers, WIN 55,212-2 (10 and 5 μM) caused a decrease in tension. These doses reduced maximum tension to 67.43 ± 8.07% (P = 0.02, n = 5) and 79.4 ± 14.11% (P = 0.007, n = 5) compared to control, respectively. Tension-time integral was reduced to 58.37 ± 7.17% and 75.10 ± 3.60% (P = 0.002, n = 5), respectively. Using the CB1 cannabinoid receptor agonist ACPA (1 μM) reduced the maximum tension of caffeine contractures by 68.70 ± 11.63% (P = 0.01, n = 5); tension-time integral was reduced by 66.82 ± 6.89% (P = 0.02, n = 5) compared to controls. When the CB1 receptor antagonist AM281 was coapplied with ACPA, it reversed the effect of ACPA on caffeine-evoked tension. In slow and fast muscle fibers incubated with the pertussis toxin, ACPA had no effect on tension evoked by caffeine. In fast muscle fibers, ACPA (1 μM) also decreased tension; the maximum tension was reduced by 56.48 ± 3.4% (P = 0.001, n = 4), and tension-time integral was reduced by 57.81 ± 2.6% (P = 0.006, n = 4). This ACPA effect was not statistically significant with respect to the reduction in tension in slow muscle fibers. Moreover, we detected the presence of mRNA for the cannabinoid CB1 receptor on fast and slow skeletal muscle fibers, which was significantly higher in fast compared to slow muscle fiber expression. In conclusion, our results suggest that in the slow and fast muscle fibers of the frog cannabinoids diminish caffeine-evoked tension through a receptor-mediated mechanism

Geophysical monitoring and reactive transport modeling of ureolytically-driven calcium carbonate precipitation

Ureolytically-driven calcium carbonate precipitation is the basis for a promising in-situ remediation method for sequestration of divalent radionuclide and trace metal ions. It has also been proposed for use in geotechnical engineering for soil strengthening applications. Monitoring the occurrence, spatial distribution, and temporal evolution of calcium carbonate precipitation in the subsurface is critical for evaluating the performance of this technology and for developing the predictive models needed for engineering application. In this study, we conducted laboratory column experiments using natural sediment and groundwater to evaluate the utility of geophysical (complex resistivity and seismic) sensing methods, dynamic synchrotron x-ray computed tomography (micro-CT), and reactive transport modeling for tracking ureolytically-driven calcium carbonate precipitation processes under site relevant conditions. Reactive transport modeling with TOUGHREACT successfully simulated the changes of the major chemical components during urea hydrolysis. Even at the relatively low level of urea hydrolysis observed in the experiments, the simulations predicted an enhanced calcium carbonate precipitation rate that was 3-4 times greater than the baseline level. Reactive transport modeling results, geophysical monitoring data and micro-CT imaging correlated well with reaction processes validated by geochemical data. In particular, increases in ionic strength of the pore fluid during urea hydrolysis predicted by geochemical modeling were successfully captured by electrical conductivity measurements and confirmed by geochemical data. The low level of urea hydrolysis and calcium carbonate precipitation suggested by the model and geochemical data was corroborated by minor changes in seismic P-wave velocity measurements and micro-CT imaging; the latter provided direct evidence of sparsely distributed calcium carbonate precipitation. Ion exchange processes promoted through NH4+ production during urea hydrolysis were incorporated in the model and captured critical changes in the major metal species. The electrical phase increases were potentially due to ion exchange processes that modified charge structure at mineral/water interfaces. Our study revealed the potential of geophysical monitoring for geochemical changes during urea hydrolysis and the advantages of combining multiple approaches to understand complex biogeochemical processes in the subsurface