MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS

This paper proves the multiplicity of positive solutions for the following class of quasilinear problems: {-epsilon(p)Delta(p)u+(lambda A(x) + 1)vertical bar u vertical bar(p-2)u = f(u), R(N) u(x)>0 in R(N), where Delta(p) is the p-Laplacian operator, N > p >= 2, lambda and epsilon are positive parameters, A is a nonnegative continuous function and f is a continuous function with subcritical growth. Here, we use variational methods to get multiplicity of positive solutions involving the Lusternick-Schnirelman category of intA(-1)(0) for all sufficiently large lambda and small epsilon.

Positive solutions for a fourth order equation with nonlinear boundary conditions

Existence of positive solutions for a fourth order equation with nonlinear boundary conditions, which models deformations of beams on elastic supports, is considered using fixed points theorems in cones of ordered Banach spaces. Iterative and numerical solutions are also considered. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.

Positive solutions for the p-Laplacian involving critical and supercritical nonlinearities with zeros

In this paper we show the existence of multiple solutions to a class of quasilinear elliptic equations when the continuous non-linearity has a positive zero and it satisfies a p-linear condition only at zero. In particular, our approach allows us to consider superlinear, critical and supercritical nonlinearities. (C) 2009 Elsevier Masson SAS. All rights reserved.

Positive solutions of the p-Laplacian involving a superlinear nonlinearity with zeros

Using a combination of several methods, such as variational methods. the sub and supersolutions method, comparison principles and a priori estimates. we study existence, multiplicity, and the behavior with respect to lambda of positive solutions of p-Laplace equations of the form -Delta(p)u = lambda h(x, u), where the nonlinear term has p-superlinear growth at infinity, is nonnegative, and satisfies h(x, a(x)) = 0 for a suitable positive function a. In order to manage the asymptotic behavior of the solutions we extend a result due to Redheffer and we establish a new Liouville-type theorem for the p-Laplacian operator, where the nonlinearity involved is superlinear, nonnegative, and has positive zeros. (C) 2009 Elsevier Inc. All rights reserved.

Monotone positive solutions for a fourth order equation with nonlinear boundary conditions

This work is concerned with the existence of monotone positive solutions for a class of beam equations with nonlinear boundary conditions. The results are obtained by using the monotone iteration method and they extend early works on beams with null boundary conditions. Numerical simulations are also presented. (C) 2009 Elsevier Ltd. All rights reserved.

A network of integrate and fire neurons for visual selection

Biological systems have facility to capture salient object(s) in a given scene, but it is still a difficult task to be accomplished by artificial vision systems. In this paper a visual selection mechanism based on the integrate and fire neural network is proposed. The model not only can discriminate objects in a given visual scene, but also can deliver focus of attention to the salient object. Moreover, it processes a combination of relevant features of an input scene, such as intensity, color, orientation, and the contrast of them. In comparison to other visual selection approaches, this model presents several interesting features. It is able to capture attention of objects in complex forms, including those linearly nonseparable. Moreover, computer simulations show that the model produces results similar to those observed in natural vision systems.

Single Synapse Information Coding in Intraburst Spike Patterns of Central Pattern Generator Motor Neurons

Burst firing is ubiquitous in nervous systems and has been intensively studied in central pattern generators (CPGs). Previous works have described subtle intraburst spike patterns (IBSPs) that, despite being traditionally neglected for their lack of relation to CPG motor function, were shown to be cell-type specific and sensitive to CPG connectivity. Here we address this matter by investigating how a bursting motor neuron expresses information about other neurons in the network. We performed experiments on the crustacean stomatogastric pyloric CPG, both in control conditions and interacting in real-time with computer model neurons. The sensitivity of postsynaptic to presynaptic IBSPs was inferred by computing their average mutual information along each neuron burst. We found that details of input patterns are nonlinearly and inhomogeneously coded through a single synapse into the fine IBSPs structure of the postsynaptic neuron following burst. In this way, motor neurons are able to use different time scales to convey two types of information simultaneously: muscle contraction (related to bursting rhythm) and the behavior of other CPG neurons (at a much shorter timescale by using IBSPs as information carriers). Moreover, the analysis revealed that the coding mechanism described takes part in a previously unsuspected information pathway from a CPG motor neuron to a nerve that projects to sensory brain areas, thus providing evidence of the general physiological role of information coding through IBSPs in the regulation of neuronal firing patterns in remote circuits by the CNS.

Recording from Two Neurons: Second-Order Stimulus Reconstruction from Spike Trains and Population Coding

We study the reconstruction of visual stimuli from spike trains, representing the reconstructed stimulus by a Volterra series up to second order. We illustrate this procedure in a prominent example of spiking neurons, recording simultaneously from the two H1 neurons located in the lobula plate of the fly Chrysomya megacephala. The fly views two types of stimuli, corresponding to rotational and translational displacements. Second-order reconstructions require the manipulation of potentially very large matrices, which obstructs the use of this approach when there are many neurons. We avoid the computation and inversion of these matrices using a convenient set of basis functions to expand our variables in. This requires approximating the spike train four-point functions by combinations of two-point functions similar to relations, which would be true for gaussian stochastic processes. In our test case, this approximation does not reduce the quality of the reconstruction. The overall contribution to stimulus reconstruction of the second-order kernels, measured by the mean squared error, is only about 5% of the first-order contribution. Yet at specific stimulus-dependent instants, the addition of second-order kernels represents up to 100% improvement, but only for rotational stimuli. We present a perturbative scheme to facilitate the application of our method to weakly correlated neurons.

Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

Bayesian Estimation of the Logistic Positive Exponent IRT Model

A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric ICC treats both correct and incorrect answers symmetrically, which results in a logical contradiction in ordering examinees on the ability scale. A data set corresponding to a mathematical test applied in Peruvian public schools is analyzed, where comparisons with other parametric IRT models also are conducted. Several model comparison criteria are discussed and implemented. The main conclusion is that the LPE and RLPE IRT models are easy to implement and seem to provide the best fit to the data set considered.

False-positive results of a rapid K39-based strip test and Chagas disease

Background: The definitive diagnosis of visceral. leishmaniasis (VL) requires invasive procedures with demonstration of amastigotes in tissue or promastigotes in culture. Unfortunately, these approaches require laboratory materials not available in poor countries where the disease is endemic. The correct diagnosis of VL is important, and made more difficult by the fact that several common tropical diseases such as malaria, disseminated tuberculosis, and enteric fever share the same clinical presentation. Serological tests have been developed to replace parasitological diagnosis in the field. A commercially available K39-based strip test for VL has been developed for this purpose. The endemic area of leishmaniasis in Brazil overlaps the endemic area of Chagas disease, a disease that can cause false-positive serological test results. The aim of this study was to evaluate the incidence of false-positive exams using a rapid test for VL in patients with Chagas disease. Methods: A rapid test based on the recombinant K39 antigen of Leishmania was used in: (1) 30 patients with confirmed Chagas disease, (2) 30 patients with a serological diagnosis of Chagas disease by ELISA, indirect immunofluorescence, indirect hemagglutination, and chemiluminescence, (3) 30 healthy patients from a non-endemic area as the control group, (4) 30 patients with confirmed VL, and (5) 20 patients with proved cutaneous leishmaniasis. Results: The sensitivity and specificity of the rapid strip test were 100% when compared with healthy volunteers and those with confirmed Chagas disease. One false-positive result occurred in the group with Chagas disease diagnosed by serological tests (specificity of 96%). Conclusion: The rapid test based on recombinant K39 is a useful diagnostic assay, and a false-positive result rarely occurs in patients with a serological diagnosis of Chagas disease. (C) 2008 International Society for Infectious Diseases. Published by Elsevier Ltd. All rights reserved.

Description of costandard modules for Schur superalgebra S(2 vertical bar 1) in positive characteristic

We describe the characters of simple modules and composition factors of costandard modules for S(2 vertical bar 1) in positive characteristics and verify a conjecture of La Scala-Zubkov regarding polynomial superinvariants for GL(2 vertical bar 1).

Ric-8B interacts with G alpha olf and G gamma 13 and co-localizes with G alpha olf, G beta 1 and G gamma 13 in the cilia of olfactory sensory neurons

Olfactory sensory neurons are able to detect odorants with high sensitivity and specificity. We have demonstrated that Ric-8B, a guanine nucleotide exchange factor (GEF), interacts with G alpha olf and enhances odorant receptor signaling. Here we show that Ric-8B also interacts with G gamma 13, a divergent member of the G gamma subunit family which has been implicated in taste signal transduction, and is abundantly expressed in the cilia of olfactory sensory neurons. We show that G beta 1 is the predominant GP subunit expressed in the olfactory sensory neurons. Ric-8B and G beta 1, like G alpha olf and G gamma 13, are enriched in the cilia of olfactory sensory neurons. We also show that Ric-8B interacts with G alpha olf in a nucleotide dependent manner, consistent with the role as a GEF. Our results constitute the first example of a GEF protein that interacts with two different olfactory G protein subunits and further implicate Ric-8B as a regulator of odorant signal transduction. (C) 2008 Elsevier Inc. All rights reserved.

Evidence that OGG1 glycosylase protects neurons against oxidative DNA damage and cell death under ischemic conditions

7,8-Dihydro-8-oxoguanine DNA glycosylase (OGG1) is a major DNA glycosylase involved in base-excision repair (BER) of oxidative DNA damage to nuclear and mitochondrial DNA (mtDNA). We used OGG1-deficient (OGG1(-/-)) mice to examine the possible roles of OGG1 in the vulnerability of neurons to ischemic and oxidative stress. After exposure of cultured neurons to oxidative and metabolic stress levels of OGG1 in the nucleus were elevated and mitochondria exhibited fragmentation and increased levels of the mitochondrial fission protein dynamin-related protein 1 (Drp1) and reduced membrane potential. Cortical neurons isolated from OGG1(-/-) mice were more vulnerable to oxidative insults than were OGG1(+/+) neurons, and OGG1(-/-) mice developed larger cortical infarcts and behavioral deficits after permanent middle cerebral artery occlusion compared with OGG1(+/+) mice. Accumulations of oxidative DNA base lesions (8-oxoG, FapyAde, and FapyGua) were elevated in response to ischemia in both the ipsilateral and contralateral hemispheres, and to a greater extent in the contralateral cortex of OGG1(-/-) mice compared with OGG1(+/+) mice. Ischemia-induced elevation of 8-oxoG incision activity involved increased levels of a nuclear isoform OGG1, suggesting an adaptive response to oxidative nuclear DNA damage. Thus, OGG1 has a pivotal role in repairing oxidative damage to nuclear DNA under ischemic conditions, thereby reducing brain damage and improving functional outcome. Journal of Cerebral Blood Flow & Metabolism (2011) 31, 680-692; doi:10.1038/jcbfm.2010.147; published online 25 August 2010

Expression Profile of Rat Hippocampal Neurons Treated with the Neuroprotective Compound 2,4-Dinitrophenol: Up-Regulation of cAMP Signaling Genes

2,4-Dinitrophenol (DNP) is classically known as a mitochondrial uncoupler and, at high concentrations, is toxic to a variety of cells. However, it has recently been shown that, at subtoxic concentrations, DNP protects neurons against a variety of insults and promotes neuronal differentiation and neuritogenesis. The molecular and cellular mechanisms underlying the beneficial neuroactive properties of DNP are still largely unknown. We have now used DNA microarray analysis to investigate changes in gene expression in rat hippocampal neurons in culture treated with low micromolar concentrations of DNP. Under conditions that did not affect neuronal viability, high-energy phosphate levels or mitochondrial oxygen consumption, DNP induced up-regulation of 275 genes and down-regulation of 231 genes. Significantly, several up-regulated genes were linked to intracellular cAMP signaling, known to be involved in neurite outgrowth, synaptic plasticity, and neuronal survival. Differential expression of specific genes was validated by quantitative RT-PCR using independent samples. Results shed light on molecular mechanisms underlying neuroprotection by DNP and point to possible targets for development of novel therapeutics for neurodegenerative disorders.