Seasonal Stability Tests in gretl. An Application to International Tourism Data

The seasonal stability tests of Canova & Hansen (1995) (CH) provide a method complementary to that of Hylleberg et al. (1990) for testing for seasonal unit roots. But the distribution of the CH tests are unknown in small samples. We present a method to numerically compute critical values and P-values for the CH tests for any sample size and any seasonal periodicity. In fact this method is applicable to the types of seasonality which are commonly in use, but also to any other.

Self-Organized Criticality, Plasticity and Sensorimotor Coupling. Explorations with a Neurorobotic Model in a Behavioural Preference Task

During the last two decades, analysis of 1/f noise in cognitive science has led to a considerable progress in the way we understand the organization of our mental life. However, there is still a lack of specific models providing explanations of how 1/f noise is generated in coupled brain-body-environment systems, since existing models and experiments typically target either externally observable behaviour or isolated neuronal systems but do not address the interplay between neuronal mechanisms and sensorimotor dynamics. We present a conceptual model of a minimal neurorobotic agent solving a behavioural task that makes it possible to relate mechanistic (neurodynamic) and behavioural levels of description. The model consists of a simulated robot controlled by a network of Kuramoto oscillators with homeostatic plasticity and the ability to develop behavioural preferences mediated by sensorimotor patterns. With only three oscillators, this simple model displays self-organized criticality in the form of robust 1/f noise and a wide multifractal spectrum. We show that the emergence of self-organized criticality and 1/f noise in our model is the result of three simultaneous conditions: a) non-linear interaction dynamics capable of generating stable collective patterns, b) internal plastic mechanisms modulating the sensorimotor flows, and c) strong sensorimotor coupling with the environment that induces transient metastable neurodynamic regimes. We carry out a number of experiments to show that both synaptic plasticity and strong sensorimotor coupling play a necessary role, as constituents of self-organized criticality, in the generation of 1/f noise. The experiments also shown to be useful to test the robustness of 1/f scaling comparing the results of different techniques. We finally discuss the role of conceptual models as mediators between nomothetic and mechanistic models and how they can inform future experimental research where self-organized critically includes sensorimotor coupling among the essential interaction-dominant process giving rise to 1/f noise.

Helmholtz Fermi surface harmonics: an efficient approach for treating anisotropic problems involving Fermi surface integrals

We present a new efficient numerical approach for representing anisotropic physical quantities and/or matrix elements defined on the Fermi surface (FS) of metallic materials. The method introduces a set of numerically calculated generalized orthonormal functions which are the solutions of the Helmholtz equation defined on the FS. Noteworthy, many properties of our proposed basis set are also shared by the FS harmonics introduced by Philip B Allen (1976 Phys. Rev. B 13 1416), proposed to be constructed as polynomials of the cartesian components of the electronic velocity. The main motivation of both approaches is identical, to handle anisotropic problems efficiently. However, in our approach the basis set is defined as the eigenfunctions of a differential operator and several desirable properties are introduced by construction. The method is demonstrated to be very robust in handling problems with any crystal structure or topology of the FS, and the periodicity of the reciprocal space is treated as a boundary condition for our Helmholtz equation. We illustrate the method by analysing the free-electron-like lithium (Li), sodium (Na), copper (Cu), lead (Pb), tungsten (W) and magnesium diboride (MgB2)