Tame Functions with strongly isolated singularities at infinity: a tame version of a Parusinski's Theorem

Let f be a definable function, enough differentiable. Under the condition of having strongly isolated singularities at infinity at a regular value c we give a sufficient condition expressed in terms of the total absolute curvature function to ensure the local triviality of the function f over a neighbourhood of c and doing so providing the tame version of Parusinski's Theorem on complex polynomials with isolated singularities at infinity.Comment: 20 page

REFLEXIONES ACERCA DEL PROBLEMA TEOLÓGICO-JURÍDICO SOBRE EL ORIGEN DEL PODER POLÍTICO EN DANTE ALIGHIERI Y MARSILIO DE PADUA

Dante Alighieri y Marsilio de Padua fueron dos pensadores involucrados en los conflictos políticos de las primeras décadas del siglo XIV entre el Papado y el Imperio. Ambos autores propusieron modelos de organización en los que buscaron asignar las atribuciones y jurisdicciones de cada investidura para poner fin a los litigios que aquejaban a las ciudades-Estado del norte de la península itálica, al reino de Francia y al Sacro Imperio Romano Germánico. Sin embargo, si bien comparten algunos aspectos de sus postulados sobre el poder político y el espiritual, Dante se inclina por el equilibrio de las investiduras donde el Dios y el derecho es fundamento del Imperio, mientras que el paduano aboga a fondo por la superioridad del Emperador sobre el Pontífice fundamentado en la comunidad como origen de la ley. 

Microbial colonization of anaerobic biofilms: a mathematical model

A 1-D mathematical model for analysis and prediction of microbial colonization of anaerobic multispecies biofilms for methane production is presented. The model combines the related processes of hydrolysis, acidogenesis, acetogenesis, methanogenesis and takes into account phenomena of substrate reaction and diffusion, biomass growth, detachment and, in particular, the colonization of new species from bulk liquid to biofilm. The colonization phenomenon is initiated by planktonic cells, present in the bulk liquid but not initially in the biofilm, which thanks to the characteristic porous structure of biofilm matrix, may enter the channels and establish where they find favorable growth conditions. The model consists of a free boundary value problem where the biofilm growth process is governed by nonlinear hyperbolic PDEs and substrate dynamics are dominated by semilinear parabolic PDEs. The transport of colonizing bacteria from the bulk liquid to the biofilm is modelled by using a diffusionreaction equation, where the reaction term represents the loss of planktonic bacteria due to their establishment within the biofilm. The method of characteristics is used for numerical purposes. The model is based on the biological framework of ADM1 and has been applied to simulate microbial competition and evaluate the influence of substrate diffusion on microbial stratification. Specific scenarios have been simulated describing the effect of colonization of motile bacteria into an established anaerobic biofilm

The Effect of Cell Death on the Stability of a Growing Biofilm

In this paper, we investigate the role of cell death in promoting pattern formation within bacterial biofilms. To do this we utilise an extension of the model proposed by Dockery and Klapper [13], and consider the effects of two distinct death rates. Equations describing the evolution of a moving biofilm interface are derived, and properties of steady state solutions are examined. In particular, a comparison of the planar behaviour of the biofilm interface in the different cases of cell death is investigated. Linear stability analysis is carried out at steady state solutions of the interface, and it is shown that, under certain conditions, instabilities may arise. Analysis determines that, while the emergence of patterns is a possibility in `deep’ biofilms, it is unlikely that pattern formation will arise in `shallow’ biofilms

Is the astronomical forcing a reliable and unique pacemaker for climate? A conceptual model study

There is evidence that ice age cycles are paced by astronomical forcing, suggesting some kind of synchronisation phenomenon. Here, we identify the type of such synchronisation and explore systematically its uniqueness and robustness using a simple paleoclimate model akin to the van der Pol relaxation oscillator and dynamical system theory. As the insolation is quite a complex quasiperiodic signal involving different frequencies, the traditional concepts used to define synchronisation to periodic forcing are no longer applicable. Instead, we explore a different concept of generalised synchronisation in terms of (coexisting) synchronised solutions for the forced system, their basins of attraction and instabilities. We propose a clustering technique to compute the number of synchronised solutions, each of which corresponds to a different paleoclimate history. In this way, we uncover multistable synchronisation (reminiscent of phase- or frequency-locking to individual periodic components of astronomical forcing) at low forcing strength, and monostable or unique synchronisation at stronger forcing. In the multistable regime, different initial conditions may lead to different paleoclimate histories. To study their robustness, we analyse Lyapunov exponents that quantify the rate of convergence towards each synchronised solution (local stability), and basins of attraction that indicate critical levels of external perturbations (global stability). We find that even though synchronised solutions are stable on a long term, there exist short episodes of desynchronisation where nearby climate trajectories diverge temporarily (for about 50 kyr). (...)Comment: 22 pages, 18 figure

The restorative role of annexin A1 at the blood–brain barrier

Annexin A1 is a potent anti-inflammatory molecule that has been extensively studied in the peripheral immune system, but has not as yet been exploited as a therapeutic target/agent. In the last decade, we have undertaken the study of this molecule in the central nervous system (CNS), focusing particularly on the primary interface between the peripheral body and CNS: the blood–brain barrier. In this review, we provide an overview of the role of this molecule in the brain, with a particular emphasis on its functions in the endothelium of the blood–brain barrier, and the protective actions the molecule may exert in neuroinflammatory, neurovascular and metabolic disease. We focus on the possible new therapeutic avenues opened up by an increased understanding of the role of annexin A1 in the CNS vasculature, and its potential for repairing blood–brain barrier damage in disease and aging

Mathematical modeling of the competition between sulfate reducing, acetoclastic and methanogenic bacteria within multispecies biofilms

Increasing anthropogenic activity has contributed to local imbalances in the natural sulfur cycle, leading to serious environmental problems. Industrial wastewater containing sulfate has contributed to this sulfur imbalance. Biological sulfate reducing processes that involve a bacterial biomass attached to media (biofilm), represent an attractive solution to the problem. The advantage of bacteria disposing in a biofilm is very important in an environmental industrial application, as the bacteria in the biofilm, different from suspended bacteria, cannot be washed out with the water flow. This allows to retain the biomass within the reactor and therefore to operate at shorter hydraulic retention time (HRT),and higher biomass concentration . Biological sulfate reduction in anaerobic fixed growth reactors has been investigated extensively at lab-scale. Under anaerobic conditions dissimilatory sulfate reducing bacteria use sulfate as a terminal electron acceptor for the degradation of organic compounds. In this anaerobic process, sulfate is reduced to sulfide by the action of sulfate reducing bacteria (SRB), which have the ability of coupling the oxidation of organic matter (electron donor) to the reduction of sulfate (electron acceptor) and depend on hydrolytic and fermentative bacteria that degrade complex organic matter. A major problem of sulfate-reducing fixed-growth reactors is the formation of undesired bacteria species which compete for space and substrate in the biofilm with SRB. This work presents a mathematical model able to simulate the physical, chemical and biological processes prevailing in a sulfate reducing biofilm under dynamic conditions. The proposed model includes sulfate reduction by complete and incomplete SRB; COD (lactate) removal by sulfate reduction and by acetogenic bacteria; acetate consumption via methanogenesis. The method of characteristics is used for the numerical resolution of the model equations. In particular the effect of the COD/SO42- ratio and the effect of different simulation times on the reactor performances in terms of bacterial species distribution and substrate diffusion trends in the biofilm have been assessed