An algorithmic approach to the existence of ideal objects in commutative algebra

The existence of ideal objects, such as maximal ideals in nonzero rings, plays a crucial role in commutative algebra. These are typically justified using Zorn's lemma, and thus pose a challenge from a computational point of view. Giving a constructive meaning to ideal objects is a problem which dates back to Hilbert's program, and today is still a central theme in the area of dynamical algebra, which focuses on the elimination of ideal objects via syntactic methods. In this paper, we take an alternative approach based on Kreisel's no counterexample interpretation and sequential algorithms. We first give a computational interpretation to an abstract maximality principle in the countable setting via an intuitive, state based algorithm. We then carry out a concrete case study, in which we give an algorithmic account of the result that in any commutative ring, the intersection of all prime ideals is contained in its nilradical

Exploiting exciton-exciton interactions in semiconductor quantum dots for quantum-information processing

We propose an all-optical implementation of quantum-information processing in semiconductor quantum dots, where electron-hole excitations (excitons) serve as the computational degrees of freedom (qubits). We show that the strong dot confinement leads to an overall enhancement of Coulomb correlations and to a strong renormalization of the excitonic states, which can be exploited for performing conditional and unconditional qubit operations.Comment: 5 pages revtex, 2 encapsulated postscript figures. Accepted for publication in Phys. Rev. B (Rapid Communication

Adaptive Dynamics and Technological Change

This paper is about the emergence of technological variety arising from market interaction and technological innovation. Existing products in the market compete with innovative ones resulting in a slow and continuous evolution of the underlying technological characteristics of successful products. When technological evolution reaches an equilibrium, it can either be an ESS (Evolutionary Stable Strategy), where marginally innovative products do not penetrate the market, or a branching point, where new products coexist along with established ones. Thus, technological branching can give rise to product variety. In the paper we first introduce Adaptive Dynamics (AD), a recently proposed theory of evolutionary processes, aiming at modelling various features of technological change. Then, a first application of AD in economics is presented and discussed in detail. The limitations of the AD approach, as well as some promising further applications in economics and social sciences, are briefly discussed at the concluding section

Freehand-Steering Locomotion Techniques for Immersive Virtual Environments: A Comparative Evaluation

Virtual reality has achieved significant popularity in recent years, and allowing users to move freely within an immersive virtual world has become an important factor critical to realize. The user’s interactions are generally designed to increase the perceived realism, but the locomotion techniques and how these affect the user’s task performance still represent an open issue, much discussed in the literature. In this article, we evaluate the efficiency and effectiveness of, and user preferences relating to, freehand locomotion techniques designed for an immersive virtual environment performed through hand gestures tracked by a sensor placed in the egocentric position and experienced through a head-mounted display. Three freehand locomotion techniques have been implemented and compared with each other, and with a baseline technique based on a controller, through qualitative and quantitative measures. An extensive user study conducted with 60 subjects shows that the proposed methods have a performance comparable to the use of the controller, further revealing the users’ preference for decoupling the locomotion in sub-tasks, even if this means renouncing precision and adapting the interaction to the possibilities of the tracker sensor

Global relevance of marine organic aerosol as ice nucleating particles

Ice nucleating particles (INPs) increase the temperature at which supercooled droplets start to freeze. They are therefore of particular interest in mixed-phase cloud temperature regimes, where supercooled liquid droplets can persist for extended periods of time in the absence of INPs. When INPs are introduced to such an environment, the cloud can quickly glaciate following ice multiplication processes and the Wegener–Bergeron–Findeisen (WBF) process. The WBF process can also cause the ice to grow to precipitation size and precipitate out. All of these processes alter the radiative properties. Despite their potential influence on climate, the ice nucleation ability and importance of different aerosol species is still not well understood and is a field of active research. In this study, we use the aerosol–climate model ECHAM6-HAM2 to examine the global relevance of marine organic aerosol (MOA), which has drawn much interest in recent years as a potentially important INPs in remote marine regions. We address the uncertainties in emissions and ice nucleation activity of MOA with a range of reasonable set-ups and find a wide range of resulting MOA burdens. The relative importance of MOA as an INP compared to dust is investigated and found to depend strongly on the type of ice nucleation parameterisation scheme chosen. On the zonal mean, freezing due to MOA leads to relative increases in the cloud ice occurrence and in-cloud number concentration close to the surface in the polar regions during summer. Slight but consistent decreases in the in-cloud ice crystal effective radius can also be observed over the same regions during all seasons. Regardless, MOA was not found to affect the radiative balance significantly on the global scale, due to its relatively weak ice activity and a low sensitivity of cloud ice properties to heterogeneous ice nucleation in our model

A Model for Prejudiced Learning in Noisy Environments

Based on the heuristics that maintaining presumptions can be beneficial in uncertain environments, we propose a set of basic axioms for learning systems to incorporate the concept of prejudice. The simplest, memoryless model of a deterministic learning rule obeying the axioms is constructed, and shown to be equivalent to the logistic map. The system's performance is analysed in an environment in which it is subject to external randomness, weighing learning defectiveness against stability gained. The corresponding random dynamical system with inhomogeneous, additive noise is studied, and shown to exhibit the phenomena of noise induced stability and stochastic bifurcations. The overall results allow for the interpretation that prejudice in uncertain environments entails a considerable portion of stubbornness as a secondary phenomenon.Comment: 21 pages, 11 figures; reduced graphics to slash size, full version on Author's homepage. Minor revisions in text and references, identical to version to be published in Applied Mathematics and Computatio

Thermal ionization of excitons in V-shaped quantum wires

The exciton-to-free-carrier transition in GaAs and In_xGa_{1-x}As V-shaped quantum wires is revealed by means of temperature-dependent magnetoluminescence experiments. The experimental results are in excellent agreement with the diamagnetic shift obtained from a solution of the full two-dimensional Schrödinger equation for electrons and holes including magnetic-field and excitonic effects. In the GaAs wires, the exciton-to-free-carrier transition is found to occur at temperature consistent with the exciton binding energies. In the In_xGa_{1-x}As wires the diamagnetic shift of the luminescence is found to be free-carrier-like, independent of temperature, due to the weakening of the exciton binding energy induced by the internal piezoelectric field