A Ky Fan minimax inequality for quasiequilibria on finite dimensional spaces

Several results concerning existence of solutions of a quasiequilibrium problem defined on a finite dimensional space are established. The proof of the first result is based on a Michael selection theorem for lower semicontinuous set-valued maps which holds in finite dimensional spaces. Furthermore this result allows one to locate the position of a solution. Sufficient conditions, which are easier to verify, may be obtained by imposing restrictions either on the domain or on the bifunction. These facts make it possible to yield various existence results which reduce to the well known Ky Fan minimax inequality when the constraint map is constant and the quasiequilibrium problem coincides with an equilibrium problem. Lastly, a comparison with other results from the literature is discussed

Forecasting Long-Term Government Bond Yields: An Application of Statistical and AI Models

This paper evaluates several artificial intelligence and classical algorithms on their ability of forecasting the monthly yield of the US 10-year Treasury bonds from a set of four economic indicators. Due to the complexity of the prediction problem, the task represents a challenging test for the algorithms under evaluation. At the same time, the study is of particular significance for the important and paradigmatic role played by the US market in the world economy. Four data-driven artificial intelligence approaches are considered, namely, a manually built fuzzy logic model, a machine learned fuzzy logic model, a self-organising map model and a multi-layer perceptron model. Their performance is compared with the performance of two classical approaches, namely, a statistical ARIMA model and an econometric error correction model. The algorithms are evaluated on a complete series of end-month US 10-year Treasury bonds yields and economic indicators from 1986:1 to 2004:12. In terms of prediction accuracy and reliability of the modelling procedure, the best results are obtained by the three parametric regression algorithms, namely the econometric, the statistical and the multi-layer perceptron model. Due to the sparseness of the learning data samples, the manual and the automatic fuzzy logic approaches fail to follow with adequate precision the range of variations of the US 10-year Treasury bonds. For similar reasons, the self-organising map model gives an unsatisfactory performance. Analysis of the results indicates that the econometric model has a slight edge over the statistical and the multi-layer perceptron models. This suggests that pure data-driven induction may not fully capture the complicated mechanisms ruling the changes in interest rates. Overall, the prediction accuracy of the best models is only marginally better than the prediction accuracy of a basic one-step lag predictor. This result highlights the difficulty of the modelling task and, in general, the difficulty of building reliable predictors for financial markets.interest rates; forecasting; neural networks; fuzzy logic.

The bees algorithm: Modelling nature to solve complex optimisation problems

The Bees Algorithm models the foraging behaviour of honey bees in order to solve optimisation problems. The algorithm performs a kind of exploitative neighbourhood search combined with random explorative search. This paper describes the Bees Algorithm and presents two application examples: the training of neural networks to predict the energy efficiency of buildings, and the solution of the protein folding problem. The Bees Algorithm proved its effectiveness and speed, and obtained very competitive modelling accuracies compared with other state-of-the-art methods

A note on quantum structure constants

The Cartan-Maurer equations for any $q$-group of the $A_{n-1}, B_n, C_n, D_n$ series are given in a convenient form, which allows their direct computation and clarifies their connection with the $q=1$ case. These equations, defining the field strengths, are essential in the construction of $q$-deformed gauge theories. An explicit expression \om ^i\we \om^j= -\Z {ij}{kl}\om ^k\we \om^l for the $q$-commutations of left-invariant one-forms is found, with \Z{ij}{kl} \om^k \we \om^l \qonelim \om^j\we\om^i.Comment: 9 pp., LaTe

Metal-superconductor transition in low-dimensional superconducting clusters embedded in two-dimensional electron systems

Motivated by recent experimental data on thin film superconductors and oxide interfaces, we propose a random-resistor network apt to describe the occurrence of a metal-superconductor transition in a two-dimensional electron system with disorder on the mesoscopic scale. We consider low-dimensional (e.g. filamentary) structures of a superconducting cluster embedded in the two-dimensional network and we explore the separate effects and the interplay of the superconducting structure and of the statistical distribution of local critical temperatures. The thermal evolution of the resistivity is determined by a numerical calculation of the random-resistor network and, for comparison, a mean-field approach called effective medium theory (EMT). Our calculations reveal the relevance of the distribution of critical temperatures for clusters with low connectivity. In addition, we show that the presence of spatial correlations requires a modification of standard EMT to give qualitative agreement with the numerical results. Applying the present approach to an LaTiO3/SrTiO3 oxide interface, we find that the measured resistivity curves are compatible with a network of spatially dense but loosely connected superconducting islands

Strongly Correlated Superconductivity rising from a Pseudo-gap Metal

We solve by Dynamical Mean Field Theory a toy-model which has a phase diagram strikingly similar to that of high $T_c$ superconductors: a bell-shaped superconducting region adjacent the Mott insulator and a normal phase that evolves from a conventional Fermi liquid to a pseudogapped semi-metal as the Mott transition is approached. Guided by the physics of the impurity model that is self-consistently solved within Dynamical Mean Field Theory, we introduce an analytical ansatz to model the dynamical behavior across the various phases which fits very accurately the numerical data. The ansatz is based on the assumption that the wave-function renormalization, that is very severe especially in the pseudogap phase close to the Mott transition, is perfectly canceled by the vertex corrections in the Cooper pairing channel.A remarkable outcome is that a superconducting state can develop even from a pseudogapped normal state, in which there are no low-energy quasiparticles. The overall physical scenario that emerges, although unraveled in a specific model and in an infinite-coordination Bethe lattice, can be interpreted in terms of so general arguments to suggest that it can be realized in other correlated systems.Comment: 14 pages, 11 figure

Micro Behavioural Attitudes and Macro Technological Adaptation in Industrial Districts. An Agent-Based Prototype

Industrial Districts (IDs) are complex productive systems based on an evolutionary network of heterogeneous, functionally integrated and complementary firms, which are within the same market and geographical space. Setting up a prototype, able to reproduce an idealised ID, we model cognitive processes underlying the behaviour of ID firms. ID firms are bounded rationality agents, able to process information coming from technology and market environment and from their relational contexts. They are able to evaluate such information and to transform it into courses of action, routinising their choices, monitoring the environment, categorising, typifying and comparing information. But they have bounded cognitive resources: attention, time and memory. We test two different settings: the first one shows ID firms behaving according to a self-centred attitude, while the second one shows ID firms behaving according to a social centred attitude. We study how such a strong difference at micro-level can affect at macro-level the technological adaptation of IDs

Can European productivity make progress?

Since the Lisbon European Council in 2000, the European Union has been working to improve its industrial and innovation policy, with the aim of turning the European economy into the most competitive and dynamic knowledge-based economic system in the world. Its initiatives have been mainly driven by concern about the lower productivity of European companies in comparison with their United States competitors. Therefore, European policy makers have advised member countries to strengthen their knowledge base in order to foster productivity and support economic growth. Yet, despite the substantial shifts in policies during the last two decades, the productivity gap between European countries and the US has not been signifi cantly reduced