A class of nonlinear wave equations containing the continuous Toda case

We consider a nonlinear field equation which can be derived from a binomial lattice as a continuous limit. This equation, containing a perturbative friction-like term and a free parameter $\gamma$, reproduces the Toda case (in absence of the friction-like term) and other equations of physical interest, by choosing particular values of $\gamma$. We apply the symmetry and the approximate symmetry approach, and the prolongation technique. Our main purpose is to check the limits of validity of different analytical methods in the study of nonlinear field equations. We show that the equation under investigation with the friction-like term is characterized by a finite-dimensional Lie algebra admitting a realization in terms of boson annhilation and creation operators. In absence of the friction-like term, the equation is linearized and connected with equations of the Bessel type. Examples of exact solutions are displayed, and the algebraic structure of the equation is discussed.Comment: Latex file + [equations.sty], 22 p

Properties of equations of the continuous Toda type

We study a modified version of an equation of the continuous Toda type in 1+1 dimensions. This equation contains a friction-like term which can be switched off by annihilating a free parameter \ep. We apply the prolongation method, the symmetry and the approximate symmetry approach. This strategy allows us to get insight into both the equations for \ep =0 and \ep \ne 0, whose properties arising in the above frameworks are mutually compared. For \ep =0, the related prolongation equations are solved by means of certain series expansions which lead to an infinite- dimensional Lie algebra. Furthermore, using a realization of the Lie algebra of the Euclidean group $E_{2}$, a connection is shown between the continuous Toda equation and a linear wave equation which resembles a special case of a three-dimensional wave equation that occurs in a generalized Gibbons-Hawking ansatz \cite{lebrun}. Nontrivial solutions to the wave equation expressed in terms of Bessel functions are determined. For \ep\,\ne\,0, we obtain a finite-dimensional Lie algebra with four elements. A matrix representation of this algebra yields solutions of the modified continuous Toda equation associated with a reduced form of a perturbative Liouville equation. This result coincides with that achieved in the context of the approximate symmetry approach. Example of exact solutions are also provided. In particular, the inverse of the exponential-integral function turns out to be defined by the reduced differential equation coming from a linear combination of the time and space translations. Finally, a Lie algebra characterizing the approximate symmetries is discussed.Comment: LaTex file, 27 page

Vacuum structure for expanding geometry

We consider gravitational wave modes in the FRW metrics in a de Sitter phase and show that the state space splits into many unitarily inequivalent representations of the canonical commutation relations. Non-unitary time evolution is described as a trajectory in the space of the representations. The generator of time evolution is related to the entropy operator. The thermodynamic arrow of time is shown to point in the same direction of the cosmological arrow of time. The vacuum is a two-mode SU(1,1) squeezed state of thermo field dynamics. The link between expanding geometry, squeezing and thermal properties is exhibited.Comment: Latex file, epsfig, 1 figure, 21 page

Dissipation and spontaneous symmetry breaking in brain dynamics

We compare the predictions of the dissipative quantum model of brain with neurophysiological data collected from electroencephalograms resulting from high-density arrays fixed on the surfaces of primary sensory and limbic areas of trained rabbits and cats. Functional brain imaging in relation to behavior reveals the formation of coherent domains of synchronized neuronal oscillatory activity and phase transitions predicted by the dissipative model.Comment: Restyled, slight changes in title and abstract, updated bibliography, J. Phys. A: Math. Theor. Vol. 41 (2008) in prin

Resistance and Resistance Fluctuations in Random Resistor Networks Under Biased Percolation

We consider a two-dimensional random resistor network (RRN) in the presence of two competing biased percolations consisting of the breaking and recovering of elementary resistors. These two processes are driven by the joint effects of an electrical bias and of the heat exchange with a thermal bath. The electrical bias is set up by applying a constant voltage or, alternatively, a constant current. Monte Carlo simulations are performed to analyze the network evolution in the full range of bias values. Depending on the bias strength, electrical failure or steady state are achieved. Here we investigate the steady-state of the RRN focusing on the properties of the non-Ohmic regime. In constant voltage conditions, a scaling relation is found between $/_0$ and $V/V_0$, where $$ is the average network resistance, $_0$ the linear regime resistance and $V_0$ the threshold value for the onset of nonlinearity. A similar relation is found in constant current conditions. The relative variance of resistance fluctuations also exhibits a strong nonlinearity whose properties are investigated. The power spectral density of resistance fluctuations presents a Lorentzian spectrum and the amplitude of fluctuations shows a significant non-Gaussian behavior in the pre-breakdown region. These results compare well with electrical breakdown measurements in thin films of composites and of other conducting materials.Comment: 15 figures, 23 page

Rpgrip1 is required for rod outer segment development and ciliary protein trafficking in zebrafish

The authors would like to thank the Royal Society of London, the National Eye Research Centre, the Visual Research Trust, Fight for Sight, the W.H. Ross Foundation, the Rosetrees Trust, and the Glasgow Children’s Hospital Charity for supporting this work. This work was also supported by the Deanship of Scientific Research at King Saud University for funding this research (Research Project) grant number ‘RGP – VPP – 219’.Mutations in the RPGR-interacting protein 1 (RPGRIP1) gene cause recessive Leber congenital amaurosis (LCA), juvenile retinitis pigmentosa (RP) and cone-rod dystrophy. RPGRIP1 interacts with other retinal disease-causing proteins and has been proposed to have a role in ciliary protein transport; however, its function remains elusive. Here, we describe a new zebrafish model carrying a nonsense mutation in the rpgrip1 gene. Rpgrip1homozygous mutants do not form rod outer segments and display mislocalization of rhodopsin, suggesting a role for RPGRIP1 in rhodopsin-bearing vesicle trafficking. Furthermore, Rab8, the key regulator of rhodopsin ciliary trafficking, was mislocalized in photoreceptor cells of rpgrip1 mutants. The degeneration of rod cells is early onset, followed by the death of cone cells. These phenotypes are similar to that observed in LCA and juvenile RP patients. Our data indicate RPGRIP1 is necessary for rod outer segment development through regulating ciliary protein trafficking. The rpgrip1 mutant zebrafish may provide a platform for developing therapeutic treatments for RP patients.Publisher PDFPeer reviewe

Odorant binding proteins : a biotechnological tool for odour control

The application of an odorant binding protein for odour control and fragrance delayed release from a textile surface was first explored in this work. Pig OBP-1 gene was cloned and expressed in Escherichia coli , and the purified protein was biochemically characterized. The IC50 values(concentrations of competitor that caused a decay of fluorescence to half-maximal intensity) were determined for four distinct fragrances, namely, citronellol, benzyl benzoate,citronellyl valerate and ethyl valerate. The results showed a strong binding of citronellyl valerate,citronellol and benzyl benzoate to the recombinant protein, while ethyl valerate displayed weaker binding. Cationized cotton substrates were coated with porcine odorant binding protein and tested for their capacity to retain citronellol and to mask the smell of cigarette smoke. The immobilized protein delayed the release of citronellol when compared to the untreated cotton. According to a blind evaluation of 30 assessors, the smell of cigarette smoke, trapped onto the fabrics’ surface, was successfully attenuated by porcine odorant binding protein (more than 60 % identified the weakest smell intensity after protein exposure compared to β-cyclodextrin-treated and untreated cotton fabrics). This work demonstrated that porcine odorant binding protein can be an efficient solution to prevent and/orremove unpleasant odours trapped on the large surface of textiles. Its intrinsic properties make odorant binding proteins excellent candidates for controlled release systems which constitute a new application for this class of proteins.This work was co-funded by the European Social Fund through the management authority POPH and FCT. The authors Carla Silva and Teresa Matama would like to acknowledge their post-doctoral fellowships: SFRH/BPD/46515/2008 and SFRH/BPD/47555/2008, respectively

Dysfunction of Heterotrimeric Kinesin-2 in Rod Photoreceptor Cells and the Role of Opsin Mislocalization in Rapid Cell Death

Loss of kinesin-2 function causes rapid death of rod photoreceptors. The cell death is dependent on the expression of opsin, which first accumulates along the route to the outer segment, but not on signaling by opsin-arrestin complexes or by light activation; the key element appears to be the accumulation of excessive protein in the wrong place

Neuroprotection by adenosine in the brain: From A1 receptor activation to A2A receptor blockade

Adenosine is a neuromodulator that operates via the most abundant inhibitory adenosine A1 receptors (A1Rs) and the less abundant, but widespread, facilitatory A2ARs. It is commonly assumed that A1Rs play a key role in neuroprotection since they decrease glutamate release and hyperpolarize neurons. In fact, A1R activation at the onset of neuronal injury attenuates brain damage, whereas its blockade exacerbates damage in adult animals. However, there is a down-regulation of central A1Rs in chronic noxious situations. In contrast, A2ARs are up-regulated in noxious brain conditions and their blockade confers robust brain neuroprotection in adult animals. The brain neuroprotective effect of A2AR antagonists is maintained in chronic noxious brain conditions without observable peripheral effects, thus justifying the interest of A2AR antagonists as novel protective agents in neurodegenerative diseases such as Parkinson’s and Alzheimer’s disease, ischemic brain damage and epilepsy. The greater interest of A2AR blockade compared to A1R activation does not mean that A1R activation is irrelevant for a neuroprotective strategy. In fact, it is proposed that coupling A2AR antagonists with strategies aimed at bursting the levels of extracellular adenosine (by inhibiting adenosine kinase) to activate A1Rs might constitute the more robust brain neuroprotective strategy based on the adenosine neuromodulatory system. This strategy should be useful in adult animals and especially in the elderly (where brain pathologies are prevalent) but is not valid for fetus or newborns where the impact of adenosine receptors on brain damage is different