Estimations of expectedness and potential surprise in possibility theory

This note investigates how various ideas of 'expectedness' can be captured in the framework of possibility theory. Particularly, we are interested in trying to introduce estimates of the kind of lack of surprise expressed by people when saying 'I would not be surprised that...' before an event takes place, or by saying 'I knew it' after its realization. In possibility theory, a possibility distribution is supposed to model the relative levels of mutually exclusive alternatives in a set, or equivalently, the alternatives are assumed to be rank-ordered according to their level of possibility to take place. Four basic set-functions associated with a possibility distribution, including standard possibility and necessity measures, are discussed from the point of view of what they estimate when applied to potential events. Extensions of these estimates based on the notions of Q-projection or OWA operators are proposed when only significant parts of the possibility distribution are retained in the evaluation. The case of partially-known possibility distributions is also considered. Some potential applications are outlined

Variational charge renormalization in charged systems

We apply general variational techniques to the problem of the counterion distribution around highly charged objects where strong condensation of counterions takes place. Within a field-theoretic formulation using a fluctuating electrostatic potential, the concept of surface-charge renormalization is recovered within a simple one-parameter variational procedure. As a test, we reproduce the Poisson-Boltzmann surface potential for a single charge planar surface both in the weak-charge and strong-charge regime. We then apply our techniques to non-planar geometries where closed-form solutions of the non-linear Poisson-Boltzmann equation are not available. In the cylindrical case, the Manning charge renormalization result is obtained in the limit of vanishing salt concentration. However, for intermediate salt concentrations a slow crossover to the non-charge-renormalized regime (at high salt) is found with a quasi-power-law behavior which helps to understand conflicting experimental and theoretical results for the electrostatic persistence length of polyelectrolytes. In the spherical geometry charge renormalization is only found at intermediate salt concentrations

Beyond Poisson-Boltzmann: Fluctuations and Correlations

We formulate the non-linear field theory for a fluctuating counter-ion distribution in the presence of a fixed, arbitrary charge distribution. The Poisson-Boltzmann equation is obtained as the saddle-point, and the effects of fluctuations and correlations are included by a loop-wise expansion around this saddle point. We show that the Poisson equation is obeyed at each order in the loop expansion and explicitly give the expansion of the Gibbs potential up to two loops. We then apply our formalism to the case of an impenetrable, charged wall, and obtain the fluctuation corrections to the electrostatic potential and counter-ion density to one-loop order without further approximations. The relative importance of fluctuation corrections is controlled by a single parameter, which is proportional to the cube of the counter-ion valency and to the surface charge density. We also calculate effective interactions between charged particles, which reflect counter-ion correlation effects.Comment: 12 pages, 8 postscript figure

Secondary structure formation of homopolymeric single-stranded nucleic acids including force and loop entropy: implications for DNA hybridization

Loops are essential secondary structure elements in folded DNA and RNA molecules and proliferate close to the melting transition. Using a theory for nucleic acid secondary structures that accounts for the logarithmic entropy c ln m for a loop of length m, we study homopolymeric single-stranded nucleic acid chains under external force and varying temperature. In the thermodynamic limit of a long strand, the chain displays a phase transition between a low temperature / low force compact (folded) structure and a high temperature / high force molten (unfolded) structure. The influence of c on phase diagrams, critical exponents, melting, and force extension curves is derived analytically. For vanishing pulling force, only for the limited range of loop exponents 2 < c < 2.479 a melting transition is possible; for c <= 2 the chain is always in the folded phase and for 2.479 < c always in the unfolded phase. A force induced melting transition with singular behavior is possible for all loop exponents c < 2.479 and can be observed experimentally by single molecule force spectroscopy. These findings have implications for the hybridization or denaturation of double stranded nucleic acids. The Poland-Scheraga model for nucleic acid duplex melting does not allow base pairing between nucleotides on the same strand in denatured regions of the double strand. If the sequence allows these intra-strand base pairs, we show that for a realistic loop exponent c ~ 2.1 pronounced secondary structures appear inside the single strands. This leads to a lower melting temperature of the duplex than predicted by the Poland-Scheraga model. Further, these secondary structures renormalize the effective loop exponent c^, which characterizes the weight of a denatured region of the double strand, and thus affect universal aspects of the duplex melting transition.Comment: 19 pages, 14 figures, supplementary materia

Low-Skilled Unemployment, Biased Technological Shocks and Job Competition

The unempoyment rise in Eu countries has been particularly strong for low-skilled workers. This observation has often been explained in terms of biased technical change and relative wage rigidities. More attention has been paid recently to an alternative mechanism, the crowding-out of low-skiled workers by over-qualified workers. The objective of this paper is both methodological and empirical. We construct a dynamic general equilibrium model with two types of jobs and two types of workers and with search unemployment. The model is calibrated and simulated to examine the interactions between the “skill bias” and “crowding-out” mechanisms. When such interactions are accounted for, the model reproduces quite well the observed unemployment changes.skill bias; equilibrium search unemployment; ladder effect; crowding out; overeducation

Aggregation in Models with Quantity Constraints: The CES Aggregation Function

This paper is devoted to the problem of aggregation in models with quantity constraints. The focus is on quantity rationing macroeconomic (QRM) models where the micromarket outcome can be written as the minimum of several variables and where the diversity of situations across micromarkets is explicitly recognized. The aggregation result given in this paper generalizes that of Lambert (1988) to employment functions with more than two components, and leads to approximate aggregate functions of the CES variety. The approximation used can accomodate general variance-covariance structures. Simulation experiments show that the approximation error remains within reasonable bounds (1-4%). It thus seems that the CES formulation can accomodate a large variety of situations. It remains in particular valid when the (restrictive) conditions required to obtain the CES function as an exact result (independently identically distributed Weibull variables) are not satisfied.Macroeconomics; smoothing-by-aggregation; mismatch; approximation

Selective Reductions in Labour Taxation: Labour Market Adjustments and Macroeconomic Performance

Significant differences in unemployment incidence in Europe have been observed across skill groups, with the least skilled suffering the highest and most persistent unemployment rates. To identify policies alleviating this problem, we study the impact of reductions in employer social security contributions. We construct a general equilibrium model with three types of heterogeneous workers and firms, matching frictions, wage bargaining and a rigid minimum wage. We find evidence in favour of narrow tax cuts targeted at the minimum wage but we argue that it is most important to account for the effects of such reductions on both job creation and job destruction. The failure to do so may explain the gap between macro- and microeconometric evaluations of such policies in France and Belgium. Policy impact on welfare and inefficiencies induced by job competition, ladder effects and on-the-job search are discussed.Skill Bias, Minimum Wage, Job Creation, Job Destruction, Job Competition, Search Unemployment, Taxation

Selective Reductions in Labour Taxation : Labour Market Adjustments and Macroeconomic Performance

Significant differences in unemployment in Europe have been observed across skill groups, with the least skilled suffering the highest and most persistent unemployment rates. To identify policies alleviating this problem, we study the impact of reductions in employer social security contributions. We construct a general equilibrium model with three types of workers and firms, matching frictions, wage bargaining and a rigid minimum wage. We find evidence in favour of narrow tax cuts targeted at the minimum wage, but we argue that it is most important to account for the effects of such reductions on both job creation and job destruction. The failure to do so may explain the gap between macro- and microeconometric evaluations of such policies in France and Belgium. Policy impact on welfare and inefficiencies induced by job competition, ladder effects and on-th-job search are quantified and discussed.Minimum Wage, Job Creation, Job Destruction, Job Competition, Search Unemployment, Taxation, Computable General Equilibrium Models