1,724 research outputs found
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
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
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
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
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
Hopf Bifurcation Analysis in a Delayed Kaldor-Kalecki Model of Business Cycle
In this paper, we analyze the model of business cycle with time delay set forth by A. Krawiec and M. SzydĆowski [1]. Our goal in this model is to introduce the time delay into capital stock and gross product in capital accumulation equation. The dynamics are studied in terms of local stability and of the description of the Hopf bifurcation, that is proven to exist as the delay (taken as a parameter of bifurcation) cross some critical value. Additionally we conclude with an application
Local Hopf Birurcation and Stability of Limit Cycle in a Delayed Kaldor-Kalecki Model
We consider a delayed Kaldor-Kalecki business cycle model. We first consider the existence of local Hopf bifurcation, and we establish an explicit algorithm for determining the direction of the Hopf bifurcation and the stability or instability of the bifurcating branch of periodic solutions using the methods presented by O. Diekmann et al. in [1]. In the end, we conclude with an application
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