Biodiversity and vulnerability in a 3D mutualistic system

In this paper we study a three dimensional mutualistic model of two plants in competition and a pollinator with cooperative relation with plants. We compare the dynamical properties of this system with the associated one under absence of the pollinator. We observe how cooperation is a common fact to increase biodiversity, which it is known that, generically, holds for general mutualistic dynamical systems in Ecology as introduced in [4]. We also give mathematical evidence on how a cooperative species induces an increased biodiversity, even if the species is push to extinction. For this fact, we propose a necessary change in the model formulation which could explain this kind of phenomenon.Fondo Europeo de Desarrollo Regional MTM2011-22411Ministerio de Economía y Competitividad (España) MTM2011-22411Ministerio de Ciencia e Innovación (España) MTM2009-12367Fondo Europeo de Desarrollo Regional MTM2009-1236

An eigenvalue problem for non-bounded quasi-linear operator

In this paper we study the eigenvalues associated with a positive eigenfunction of a quasilinear elliptic problem with a not necessarily bounded operator. For that, we use the bifurcation theory and obtain the existence of positive solution for a range of values of the bifurcation parameter.Dirección General de Enseñanza Superior (Ministerio de Educación y Ciencia)Ministerio de Ciencia y Tecnologi

Characterization and Drugs Screening in Human Dermal Fibroblasts Derived From Patient With Amiotrophic Lateral Sclerosis

Motivation: Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disease caused by the loss of motor neurons. Though currently we unknow its etiology, there are several alterations related to its physiopathology, such as mutation in Superoxide dismutase-1 (SOD-1), an enzyme which prevents free radical production, and intracellular non-avaliable iron accumulation, both alterations have been observed in the patient. The mutated form of this enzyme tends to form fibrillar aggregates on the cytoplasm. In this way, the research line have two parts: the molecular characterization of the disease, and the elimination or reduction of  intracellular iron accumulation and the reestablishment of modified protein levels. Treatments screening allows to increase patient's survival due to we use commercialized compounds, with this approximation we can skip long proccess of drugs commercialization.Methods: Human Dermal Fibroblast (HDF) primary cultures with and without pathological background are used. Iron accumulation in this cultures is observed by Prussian Blue technique. Expression protein levels are measured by Western Blotting, TransferBlot, InmmunoBlot and ChemicDoc developing. Quantifications were calculated with ImageJ software.Preliminar Results: We observed differences in the expression protein levels involved in autophagy proccess (P62, LC3B), antioxidative activity (GPX, SOD1), lipid peroxidation (PLA2G6) and lisosomal dynamic (LAMP1). Drugs screening allowed to select several drugs which reduced intracellular iron levels. With this technique we did another screening combining that drugs to select the best combination

Existence and uniqueness of positive large solutions to some cooperative elliptic systems

In this work we consider positive solutions to cooperative elliptic systems of the form −∆u = λu−u2 +buv, −∆v = µv −v2 +cuv in a bounded smooth domain Ω ⊂ RN (λ, µ ∈ R, b, c > 0) which blow up on the boundary ∂Ω, that is u(x), v(x) → +∞ as dist(x, ∂Ω) → 0. We show existence and nonexistence of solutions, and give sufficient conditions for uniqueness. We also provide an exact estimate of the behaviour of the solutions near the boundary in terms of dist(x, ∂Ω).Ministerio de Ciencia y Tecnologí

Stability, instability, and bifurcation phenomena in non-autonomous differential equations

There is a vast body of literature devoted to the study of bifurcation phenomena in autonomous systems of differential equations. However, there is currently no well-developed theory that treats similar questions for the nonautonomous case. Inspired in part by the theory of pullback attractors, we discuss generalisations of various autonomous concepts of stability, instability, and invariance. Then, by means of relatively simple examples, we illustrate how the idea of a bifurcation as a change in the structure and stability of invariant sets remains a fruitful concept in the non-autonomous case.Comisión Interministerial de Ciencia y TecnologíaRoyal Society University Research Fello

Bifurcation from zero of a complete trajectory for non-autonomous logistic PDEs

In this paper we extend the well-known bifurcation theory for autonomous logistic equations to the non-autonomous equation ut − ∆u = λu − b(t)u 2 with b(t) ∈ [b0, B0], 0 < b0 < B0 < 2b0. In particular, we prove the existence of a unique uniformly bounded trajectory that bifurcates from zero as λ passes through the first eigenvalue of the Laplacian, which attracts all other trajectories. Although it is this relatively simple equation that we analyse in detail, other more involved models can be treated using similar techniques.Ministerio de Educación y CienciaFondo Europeo de Desarrollo Regiona

Pullback permanence in a non-autonomous competitive Lotka-Volterra model

The goal of this work is to study in some detail the asymptotic behaviour of a non-autonomous Lotka-Volterra model, both in the conventional sense (as t → ∞) and in the “pullback” sense (starting a fixed initial condition further and further back in time). The non-autonomous terms in our model are chosen such that one species will eventually die out, ruling out any conventional type of permanence. In contrast we introduce the notion of “pullback permanence” and show that this property is enjoyed by our model. This is not just a mathematical artifice, but rather shows that if we come across an ecology that has been evolving for a very long time we still expect that both species are represented (and their numbers are bounded below), even if the final fate of one of them is less happy. The main tools in the paper are the theory of attractors for non-autonomous differential equations, the sub-supersolution method and the spectral theory for linear elliptic equations.Royal Society University Research FellowComisión Interministerial de Ciencia y Tecnologí

Bifurcations in non-autonomous scalar equations

In a previous paper we introduced various definitions of stability and instability for non-autonomous differential equations, and applied these to investigate the bifurcations in some simple models. In this paper we present a more systematic theory of local bifurcations in scalar non-autonomous equations.Royal Society University Research FellowMinisterio de Educación y Cienci

Forwards and pullback behaviour of a non-autonomous Lotka-Volterra system

Lotka-Volterra systems have been extensively studied by many authors, both in the autonomous and non-autonomous cases. In previous papers the time asymptotic behaviour as t → ∞ has been considered. In this paper we also consider the “pullback” asymptotic behaviour which roughly corresponds to observing a system “now” that has already been evolving for a long time. For a competitive system that is asymptotically autonomous both as t → −∞ and as t → +∞ we show that these two notions of asymptotic behaviour can be very different but are both important for a full understanding of the dynamics. In particular there are parameter ranges for which, although one species dies out as t → ∞, there is a distinguished time-dependent coexistent state that is attracting in the pullback sense.Ministerio de Ciencia y Tecnología (España). Dirección General de Investigación Científica y TécnicaRoyal Society University Research Fello

Improving the activity of gold nanoparticles for the water-gas shift reaction using TiO2–Y2O3: an example of catalyst design

In the last ten years, there has been an acceleration in the pace at which new catalysts for the watergas shift reaction are designed and synthesized. Pt-based catalysts remain the best solution when only activity is considered. However, cost, operation temperature, and deactivation phenomena are important variables when these catalysts are scaled in industry. Here, a new catalyst, Au/TiO2–Y2O3, is presented as an alternative to the less selective Pt/oxide systems. Experimental and theoretical techniques are combined to design, synthesize, characterize and analyze the performance of this system. The mixed oxide demonstrates a synergistic effect, improving the activity of the catalyst not only at large-to-medium temperatures but also at low temperatures. This effect is related to the homogeneous dispersion of the vacancies that act both as nucleation centers for smaller and more active gold nanoparticles and as dissociation sites for water molecules. The calculated reaction path points to carboxyl formation as the rate-limiting step with an activation energy of 6.9 kcal mol 1, which is in quantitative agreement with experimental measurements and, to the best of our knowledge, it is the lowest activation energy reported for the water-gas shift reaction. This discovery demonstrates the importance of combining experimental and theoretical techniques to model and understand catalytic processes and opens the door to new improvements to reduce the operating temperature and the deactivation of the catalyst.Ministerio de Economía y Competitividad (CTQ2015-64669-P and ENE2015-66975- C3-2-R)Junta de Andalucía (FQM-132 and TEP-106)European Union (HT-PHOTO-DB No. 752608