Variational calculation of static and dynamic vibrational nonlinear optical properties

The vibrational configuration interaction method used to obtain static vibrational (hyper)polarizabilities is extended to dynamic nonlinear optical properties in the infinite optical frequency approximation. Illustrative calculations are carried out on H2 O and N H3. The former molecule is weakly anharmonic while the latter contains a strongly anharmonic umbrella mode. The effect on vibrational (hyper)polarizabilities due to various truncations of the potential energy and property surfaces involved in the calculation are examined

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.

Asymptotic capacity of static multiuser channels with an unknown number of users

We examine a multiple-access communication system in which multiuser detection is performed without knowledge of the number of active interferers. Using a statistical-physics approach, we compute the single-user channel capacity and spectral efficiency in the large-system limit.

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.

Price increase and stability with new entries in Cournot markets

It is widely accepted in the literature about the classicalCournot oligopoly model that the loss of quasi competitiveness is linked,in the long run as new firms enter the market, to instability of the equilibrium. In this paper, though, we present a model in which a stableunique symmetric equilibrium is reached for any number of oligopolistsas industry price increases with each new entry. Consequently, the suspicion that non quasi competitiveness implies, in the long run, instabilityis proved false.

On the impact of fundamentals, liquidity and coordination on market stability

We develop a coordination game to model interactions betweenfundamentals and liquidity during unstable periods in financial markets.We then propose a flexible econometric framework for estimationof the model and analysis of its quantitative implications. The specificempirical application is carry trades in the yen dollar market, includingthe turmoil of 1998. We find a generally very deep market, withlow information disparities amongst agents. We observe occasionallyepisodes of market fragility, or turmoil with up by the escalator, downby the elevator patterns in prices. The key role of strategic behaviorin the econometric model is also confirmed.

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.

Measuring the stability of histogram appearance when the anchor position is changed

Although the histogram is the most widely used density estimator, itis well--known that the appearance of a constructed histogram for a given binwidth can change markedly for different choices of anchor position. In thispaper we construct a stability index $G$ that assesses the potential changesin the appearance of histograms for a given data set and bin width as theanchor position changes. If a particular bin width choice leads to an unstableappearance, the arbitrary choice of any one anchor position is dangerous, anda different bin width should be considered. The index is based on the statisticalroughness of the histogram estimate. We show via Monte Carlo simulation thatdensities with more structure are more likely to lead to histograms withunstable appearance. In addition, ignoring the precision to which the datavalues are provided when choosing the bin width leads to instability. We provideseveral real data examples to illustrate the properties of $G$. Applicationsto other binned density estimators are also discussed.

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.

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.

Systematic study of the static electrical properties of the CO molecule: influence of the basis set size and correlation energy

The influence of the basis set size and the correlation energy in the static electrical properties of the CO molecule is assessed. In particular, we have studied both the nuclear relaxation and the vibrational contributions to the static molecular electrical properties, the vibrational Stark effect (VSE) and the vibrational intensity effect (VIE). From a mathematical point of view, when a static and uniform electric field is applied to a molecule, the energy of this system can be expressed in terms of a double power series with respect to the bond length and to the field strength. From the power series expansion of the potential energy, field-dependent expressions for the equilibrium geometry, for the potential energy and for the force constant are obtained. The nuclear relaxation and vibrational contributions to the molecular electrical properties are analyzed in terms of the derivatives of the electronic molecular properties. In general, the results presented show that accurate inclusion of the correlation energy and large basis sets are needed to calculate the molecular electrical properties and their derivatives with respect to either nuclear displacements or/and field strength. With respect to experimental data, the calculated power series coefficients are overestimated by the SCF, CISD, and QCISD methods. On the contrary, perturbation methods (MP2 and MP4) tend to underestimate them. In average and using the 6-311 + G(3df) basis set and for the CO molecule, the nuclear relaxation and the vibrational contributions to the molecular electrical properties amount to 11.7%, 3.3%, and 69.7% of the purely electronic μ, α, and β values, respectively

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