Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians

This paper is a sequel to ``Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey Hamiltonians at a quasi-periodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.

Simulation methods with extended stability for stiff biochemical kinetics

Background: With increasing computer power, simulating the dynamics of complex systems in chemistry and biology is becoming increasingly routine. The modelling of individual reactions in (bio)chemical systems involves a large number of random events that can be simulated by the stochastic simulation algorithm (SSA). The key quantity is the step size, or waiting time, τ, whose value inversely depends on the size of the propensities of the different channel reactions and which needs to be re-evaluated after every firing event. Such a discrete event simulation may be extremely expensive, in particular for stiff systems where τ can be very short due to the fast kinetics of some of the channel reactions. Several alternative methods have been put forward to increase the integration step size. The so-called τ-leap approach takes a larger step size by allowing all the reactions to fire, from a Poisson or Binomial distribution, within that step. Although the expected value for the different species in the reactive system is maintained with respect to more precise methods, the variance at steady state can suffer from large errors as τ grows. Results: In this paper we extend Poisson τ-leap methods to a general class of Runge-Kutta (RK) τ-leap methods. We show that with the proper selection of the coefficients, the variance of the extended τ-leap can be well-behaved, leading to significantly larger step sizes.Conclusions: The benefit of adapting the extended method to the use of RK frameworks is clear in terms of speed of calculation, as the number of evaluations of the Poisson distribution is still one set per time step, as in the original τ-leap method. The approach paves the way to explore new multiscale methods to simulate (bio)chemical systems.

Non-Quasi-Competitiveness and Stability in Cournot's Model

This paper retakes previous work of the authors, about the relationship between non-quasi-competitiveness (the increase in price caused by an increase in the number of oligopolists) and stability of the equilibrium in the classical Cournot oligopoly model. Though it has been widely accepted in the literature that the loss of quasi-competitiveness is linked, in the long run as new firms entered the market, to instability of the model, the authors in their previous work put forward a model in which a situation of monopoly changed to duopoly losing quasi-competitiveness but maintaining the stability of the equilibrium. That model could not, at the time, be extended to any number of oligopolists. The present paper exhibits such an extension. An oligopoly model is shown in which the loss of quasi-competitiveness resists the presence in the market of as many firms as one wishes and where the successive Cournot's equilibrium points are unique and asymptotically stable. In this way, for the first time, the conjecture that non-quasi- competitiveness and instability were equivalent in the long run, is proved false.

Hot vs. cold: Sequential responses and preference stability in experimental games

In experiments with two-person sequential games we analyzewhether responses to favorable and unfavorable actions dependon the elicitation procedure. In our hot treatment thesecond player responds to the first player s observed actionwhile in our cold treatment we follow the strategy method and have the second player decide on a contingent action foreach and every possible first player move, without firstobserving this move. Our analysis centers on the degree towhich subjects deviate from the maximization of their pecuniaryrewards, as a response to others actions. Our results show nodifference in behavior between the two treatments. We also findevidence of the stability of subjects preferences with respectto their behavior over time and to the consistency of theirchoices as first and second mover.

Monetary policy rules and macroeconomic stability: Evidence and some theory

We estimate a forward-looking monetary policy reaction function for thepostwar United States economy, before and after Volcker's appointmentas Fed Chairman in 1979. Our results point to substantial differencesin the estimated rule across periods. In particular, interest ratepolicy in the Volcker-Greenspan period appears to have been much moresensitive to changes in expected inflation than in the pre-Volckerperiod. We then compare some of the implications of the estimated rulesfor the equilibrium properties of inflation and output, using a simplemacroeconomic model, and show that the Volcker-Greenspan rule is stabilizing.

Adaptive learning in models with lagged variables

In this work I study the stability of the dynamics generated by adaptivelearning processes in intertemporal economies with lagged variables. Iprove that determinacy of the steady state is a necessary condition for the convergence of the learning dynamics and I show that the reciprocal is not true characterizing the economies where convergence holds. In the case of existence of cycles I show that there is not, in general, a relationship between determinacy and convergence of the learning process to the cycle. I also analyze the expectational stability of these equilibria.

Designing institutions for financial stability: Regulation and supervision by objective for the Euro area

In this paper, we discuss pros and cons ofdifferent models for financial market regulationand supervision and we present a proposal forthe re-organisation of regulatory and supervisoryagencies in the Euro Area. Our arguments areconsistent with both new theories and effectivebehaviour of financial intermediaries inindustrialized countries. Our proposed architecturefor financial market regulation is based on theassignment of different objectives or "finalities"to different authorities, both at the domesticand the European level. According to thisperspective, the three objectives of supervision- microeconomic stability, investor protectionand proper behaviour, efficiency and competition- should be assigned to three distinct Europeanauthorities, each one at the centre of a Europeansystem of financial regulators and supervisorsspecialized in overseeing the entire financialmarket with respect to a single regulatoryobjective and regardless of the subjective natureof the intermediaries. Each system should bestructured and organized similarly to the EuropeanSystem of Central Banks and work in connectionwith the central bank which would remain theinstitution responsible for price and macroeconomicstability. We suggest a plausible path to buildour 4-peak regulatory architecture in the Euro area.

On forward induction and evolutionary and strategic stability

We analyze which normal form solution concepts capture the notion offorward induction, as defined by van Damme (JET, 1989) in the classof generic two player normal form games preceded by an outsideoption. We find that none of the known strategic stability concepts(including Mertens stable sets and hyperstable sets) captures this form of forward induction. On the other hand, we show that the evolutionary concept of EES set (Swinkels, JET, 1992) is always consistent with forward induction.

Assessing an intuitive condition for stability under a range of traffic conditions via a generalised Lu-Kumar network

We argue the importance both of developing simple sufficientconditions for the stability of general multiclass queueing networks and also of assessing such conditions under a range of assumptions on the weight of the traffic flowing between service stations. To achieve the former, we review a peak-rate stability condition and extend its range of application and for the latter, we introduce a generalisation of the Lu-Kumar network on which the stability condition may be tested for a range of traffic configurations. The peak-rate condition is close to exact when the between-station traffic is light, but degrades as this traffic increases.

Biased quantitative measurement of interval ordered homothetic preferences

We represent interval ordered homothetic preferences with a quantitative homothetic utility function and a multiplicative bias. When preferences are weakly ordered (i.e. when indifference is transitive), such a bias equals 1. When indifference is intransitive, the biasing factor is a positive function smaller than 1 and measures a threshold of indifference. We show that the bias is constant if and only if preferences are semiordered, and we identify conditions ensuring a linear utility function. We illustrate our approach with indifference sets on a two dimensional commodity space.

On the quantitative importance of wage bargaining models

Four general equilibrium search models are compared quantitatively. Thebaseline framework is a calibrated macroeconomic model of the US economydesigned for a welfare analysis of unemployment insurance policy. Theother models make three simple and natural specification changes,regarding tax incidence, monopsony power in wage determination, and therelevant threat point. These specification changes have a major impacton the equilibrium and on the welfare implications of unemploymentinsurance, partly because search externalities magnify the effects ofwage changes. The optimal level of unemployment insurance dependsstrongly on whether raising benefits has a larger impact on searcheffort or on hiring expenditure.

Quantifying quantitative literacy: Age heaping and the history of human capital

Age data frequently display excess frequencies at round or attractive ages, such as even numbers and multiples of five. This phenomenon of age heaping has been viewed as a problem in previous research, especially in demography and epidemiology. We see it as an opportunity and propose its use as a measure of human capital that can yield comparable estimates across a wide range of historical contexts. A simulation study yields methodological guidelines for measuring and interpreting differences in ageheaping, while analysis of contemporary and historical datasets demonstrates the existence of a robust correlation between age heaping and literacy at both the individual and aggregate level. To illustrate the method, we generate estimates of human capital in Europe over the very long run, which support the hypothesis of a major increase in human capital preceding the industrial revolution.

A non-quasi-competitive Cournot oligopoly with stability

This paper presents a classical Cournot oligopoly model with some peculiar features: it is non--quasi--competitive as price under N-poly is greater than monopoly price; Cournot equilibrium exists and is unique with each new entry; the successive equilibria after new entries are stable under the adjustment mechanism that assumes that actual output of each seller is adjusted proportionally to the difference between actual output and profit maximizing output. Moreover, the model tends to perfect competition as N goes to infinity, reaching the monopoly price again.

Second differential of the entropy as a criterion for the stability in low-dimensional climate models

The second differential of the entropy is used for analysing the stability of a thermodynamic climatic model. A delay time for the heat flux is introduced whereby it becomes an independent variable. Two different expressions for the second differential of the entropy are used: one follows classical irreversible thermodynamics theory; the second is related to the introduction of response time and is due to the extended irreversible thermodynamics theory. the second differential of the classical entropy leads to unstable solutions for high values of delay times. the extended expression always implies stable states for an ice-free earth. When the ice-albedo feedback is included, a discontinuous distribution of stable states is found for high response times. Following the thermodynamic analysis of the model, the maximum rates of entropy production at the steady state are obtained. A latitudinally isothermal earth produces the extremum in global entropy production. the material contribution to entropy production (by which we mean the production of entropy by material transport of heat) is a maximum when the latitudinal distribution of temperatures becomes less homogeneous than present values

PCAF regulates the stability of the transcriptional regulator and cyclin-dependent kinase inhibitor p27Kip1

P27(Kip1) (p27) is a member of the Cip/Kip family of cyclin-dependent kinase inhibitors. Recently, a new function of p27 as transcriptional regulator has been reported. It has been shown that p27 regulates the expression of target genes mostly involved in splicing, cell cycle, respiration and translation. We report here that p27 directly binds to the transcriptional coactivator PCAF by a region including amino acids 91-120. PCAF associates with p27 through its catalytic domain and acetylates p27 at lysine 100. Our data showed that overexpression of PCAF induces the degradation of p27 whereas in contrast, the knockdown of PCAF stabilizes the protein. A p27 mutant in which K100 was substituted by arginine (p27-K100R) cannot be acetylated by PCAF and has a half-life much higher than that of p27WT. Moreover, p27-K100R remains stable along cell-cycle progression. Ubiquitylation assays and the use of proteasome inhibitors indicate that PCAF induces p27 degradation via proteasome. We also observed that knockdown of skp2 did not affect the PCAF induced degradation of p27. In conclusion, our data suggest that the p27 acetylation by PCAF regulates its stability.