Weakly coupled two slow- two fast systems, folded node and mixed mode oscillationsM

We study Mixed Mode Oscillations (MMOs) in systems of two weakly coupled slow/fast oscillators. We focus on the existence and properties of a folded singularity called FSN II that allows the emergence of MMOs in the presence of a suitable global return mechanism. As FSN II corresponds to a transcritical bifurcation for a desingularized reduced system, we prove that, under certain non-degeneracy conditions, such a transcritical bifurcation exists. We then apply this result to the case of two coupled systems of FitzHugh- Nagumo type. This leads to a non trivial condition on the coupling that enables the existence of MMOs

Activité de la phosphatase alcaline bactérienne à l'interface eau-sédiment au sein du réservoir Sahela (Maroc)

Les variations temporelles des concentrations en phosphore, celles des abondances bactériennes et de l'activité de la phosphatase alcaline (APA) ont été estimées in situ en chambre benthique placée en deux points du réservoir Sahela (Maroc) durant les mois de septembre et octobre 98. En période de faible oxygénation, nous avons enregistré des élévations relativement faibles des concentrations en orthophosphates (de 0,020 à 0,035 mg. l-1 au point 1 et 0,015 à 0,025 mg. l-1 au point 2) par rapport au phosphore total (0,080 à 0,100 mg. l-1 au point 1 et de 0,035 à 0,040 mg. l-1 au point 2). À cette période, les abondances bactériennes et l'APA montrent des valeurs maximales (8. 106 bact. ml-1 et 0,323 mmol.PNP l-1.h-1 au point 1 et 6.106 bact. ml-1 et 0,438 mmol.PNP l-1.h-1 au point 2 respectivement). L'apparition des conditions anoxiques et la diminution du pH favorisaient la dissolution du phosphore particulaire et la libération du phosphore réactif soluble. Cette libération s'accompagne d'une élévation des abondances de bactéries anaérobies (de 5.106 à 9,2. 106 bact. ml-1 au point 1 et de 3,8.106 à 7,2. 106 bact. ml-1 au point 2) et une diminution progressive d'APA (de 0,200 à 0,025 mmol.PNP l-1.h-1 au point 1 et de 0,125 à 0,077 mmol.PNP l-1.h-1 au point 2). Ce relargage du phosphore à partir du sédiment est accentué par les rejets domestiques et industriels de la ville de Taounate, ce qui accélère le processus d'eutrophisation de ce réservoir.Temporal variations of phosphorus concentrations, bacterial abundance and alkaline phosphatase activity (APA) were estimated in situ in a benthic chamber. The chamber used has a surface of 0.4m2 and a volume of 90 l ; it resembles those used in oceanography, with a tube connecting the interior of the chamber to the lake surface. The water in the chamber was permanently mixed by an electric agitation system. The chamber was placed at two points in the Sahela reservoir (Morocco). Point 1 was located near Guelta El Haila, a site that receives both domestic and industrial effluent, and point 2 was located in the centre of the reservoir. During the two incubations, eight samples were taken over 24 d in September and October 1998 from point 1, and seven samples were taken from point 2 over 29 d in October. After each sampling, an equal volume of water was injected into the chamber to avoid bubble formation.Under low dissolved oxygen concentrations in the benthic chamber, we noticed a relatively small elevation in orthophosphate concentrations (from 0.020 to 0.035 mg×L-1 at point 1 and from 0.015 to 0.025 mg×L-1 at point 2) in relation to total phosphorus (from 0.080 to 0.100 mg×L-1 and from 0.035 to 0.040 mg×L-1 at points 1 and 2 respectively). The low residual oxygenation of hypolimnic layer allowed the oxidation of iron, manganese and led to their binding to phosphorus released from the interstitial water. Dissociation of calcium-phosphorus complexes as a result of a pH decrease may have contributed to phosphorus release. The orthophosphate concentrations were relatively low, a situation that favours the synthesis of alkaline phosphatase by aerobic bacteria and facultative aerobic bacteria. In this period, the bacterial abundance and APA were comparable and showed the maximal values (8. 106 bact. ml-1 and 0.323 mmol. PNP l-1.h-1 (phosphate nitrophenol) in point 1 and 6. 106 bact. ml-1and 0.438 mmol. PNP l-1.h-1 in point 2 respectively). The lack of a significant correlation between total APA and bacterial abundance at the two sampling points is probably due to the decrease of aerobic bacteria followed by a repopulation with anaerobic bacteria. However, the relative contribution of two bacterial populations that have different sizes, as at points 1 and 2, showed that the majority of total APA was produced by bacteria that are attached to organic matter. Therefore we suggest that attached bacteria contribute more than free bacteria to APA production.The beginning of anoxic conditions and the decrease in pH favored the dissolution of particulate phosphorus and the liberation of reactive phosphorus. We noted an elevation in orthophosphate concentrations (from 0.035 to 0.050 mg×L-1 at point 1 and stabilised at 0.025 mg×L-1 at point 2) and total phosphorus (from 0.100 to 0.150 mg×L-1 at point 1 and from 0.040 to 0.050 mg×L-1 at point 2). This liberation followed an increase in anaerobic bacterial abundance (from 5×106 to 9.2×106 bact×mL-1 at point 1 and from 3.8×106 to 7.2×106 bact×mL-1 at point 2) and the progressive decrease in APA (from 0.200 to 0.025 mmol PNP L-1 ×h-1 at point 1 and from 0.125 to 0.077 mmol PNP L-1 ×h-1 at point 2). The anaerobic bacteria did not activate their alkaline phosphatase and the synthesis of their enzyme was progressively inhibited by a de-repression phenomenon caused by high phosphorus concentrations.We conclude that low oxygen and a decrease in pH favoured the release of phosphorus by dissolution of chemical complexes: calcium-phosphorus, iron-phosphorus, manganese-phosphorus and aluminium-phosphorus. This release is also the result of bacterial phosphatase activity to which fixed bacteria contributed the most. The release of phosphorus from water-sediment interface is further amplified by phosphate import from domestic and industrial waste waters originating from Taounate, which accelerates the eutrophication process in this reservoir

The converse of Schur's Lemma in group rings

In this paper, we study the structure of group rings by means of endomorphism rings of their modules. The main tools used here, are the subrings fixed by automorphisms and the converse of Schur's lemma. Some results are obtained on fixed subrings and on primary decomposition of group rings

Perfect rings for which the converse of Schur's lemma holds

If M is a simple module over a ring R then, by the Schur's lemma, the endomorphism ring of M is a division ring. However, the converse of this result does not hold in general, even when R is artinian. In this short note, we consider perfect rings for which the converse assertion is true, and we show that these rings are exactly the primary decomposable ones

Fence-sitters Protect Cooperation in Complex Networks

Evolutionary game theory is one of the key paradigms behind many scientific disciplines from science to engineering. In complex networks, because of the difficulty of formulating the replicator dynamics, most of previous studies are confined to a numerical level. In this paper, we introduce a vectorial formulation to derive three classes of individuals' payoff analytically. The three classes are pure cooperators, pure defectors, and fence-sitters. Here, fence-sitters are the individuals who change their strategies at least once in the strategy evolutionary process. As a general approach, our vectorial formalization can be applied to all the two-strategies games. To clarify the function of the fence-sitters, we define a parameter, payoff memory, as the number of rounds that the individuals' payoffs are aggregated. We observe that the payoff memory can control the fence-sitters' effects and the level of cooperation efficiently. Our results indicate that the fence-sitters' role is nontrivial in the complex topologies, which protects cooperation in an indirect way. Our results may provide a better understanding of the composition of cooperators in a circumstance where the temptation to defect is larger.Comment: an article with 6 pages, 3 figure

Emergence of Cooperation in Non-scale-free Networks

Evolutionary game theory is one of the key paradigms behind many scientific disciplines from science to engineering. Previous studies proposed a strategy updating mechanism, which successfully demonstrated that the scale-free network can provide a framework for the emergence of cooperation. Instead, individuals in random graphs and small-world networks do not favor cooperation under this updating rule. However, a recent empirical result shows the heterogeneous networks do not promote cooperation when humans play a Prisoner's Dilemma. In this paper, we propose a strategy updating rule with payoff memory. We observe that the random graphs and small-world networks can provide even better frameworks for cooperation than the scale-free networks in this scenario. Our observations suggest that the degree heterogeneity may be neither a sufficient condition nor a necessary condition for the widespread cooperation in complex networks. Also, the topological structures are not sufficed to determine the level of cooperation in complex networks.Comment: 6 pages, 5 figure

The presence of valine at residue 129 in human prion protein accelerates amyloid formation

The polymorphism at residue 129 of the human PRNP gene modulates disease susceptibility and the clinicopathological phenotypes in human transmissible spongiform encephalopathies. The molecular mechanisms by which the effect of this polymorphism are mediated remain unclear. It has been shown that the folding, dynamics and stability of the physiological, alpha-helix-rich form of recombinant PrP are not affected by codon 129 polymorphism. Consistent with this, we have recently shown that the kinetics of amyloid formation do not differ between protein containing methionine at codon 129 and valine at codon 129 when the reaction is initiated from the a-monomeric PrPC-like state. In contrast, we have shown that the misfolding pathway leading to the formation of beta-sheet-rich, soluble oligomer waS favoured by the presence of methionine, compared with valine, at position 129. In the present work, we examine the effect of this polymorphism on the kinetics of an alternative misfolding pathway, that of amyloid formation using partially folded PrP allelomorphs. We show that the valine 129 allelomorph forms amyloids with a considerably shorter lag phase than the methionine 129 allelomorph both under spontaneous conditions and when seeded with pre-formed amyloid fibres. Taken together, our studies demonstrate that the effect of the codon 129 polymorphism depends on the specific misfolding pathway and on the initial conformation of the protein. The inverse propensities of the two allelomorphs to misfold in vitro through the alternative oligomeric and amyloidogenic pathways could explain some aspects of prion diseases linked to this polymorphism such as age at onset and disease incubation time. (c) 2005 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved

On a coupled time-dependent SIR models fitting with New York and New-Jersey states COVID-19 data

This article describes a simple Susceptible Infected Recovered (SIR) model fitting with COVID-19 data for the month of march 2020 in New York (NY) state. The model is a classical SIR, but is non-autonomous; the rate of susceptible people becoming infected is adjusted over time in order to fit the available data. The death rate is also secondarily adjusted. Our fitting is made under the assumption that due to limiting number of tests, a large part of the infected population has not been tested positive. In the last part, we extend the model to take into account the daily fluxes between New Jersey (NJ) and NY states and fit the data for both states. Our simple model fits the available data, and illustrates typical dynamics of the disease: exponential increase, apex and decrease. The model highlights a decrease in the transmission rate over the period which gives a quantitative illustration about how lockdown policies reduce the spread of the pandemic. The coupled model with NY and NJ states shows a wave in NJ following the NY wave, illustrating the mechanism of spread from one attractive hot spot to its neighbor.