Encoding algebraic power series

Algebraic power series are formal power series which satisfy a univariate polynomial equation over the polynomial ring in n variables. This relation determines the series only up to conjugacy. Via the Artin-Mazur theorem and the implicit function theorem it is possible to describe algebraic series completely by a vector of polynomials in n+p variables. This vector will be the code of the series. In the paper, it is then shown how to manipulate algebraic series through their code. In particular, the Weierstrass division and the Grauert-Hironaka-Galligo division will be performed on the level of codes, thus providing a finite algorithm to compute the quotients and the remainder of the division.Comment: 35 page

Field experimental study of traffic-induced turbulence on highways

This paper is focused on traffic-induced turbulence (TIT) analysis from a field campaign performed in 2011, using ultrasonic anemometers deployed in the M-12 Highways, Madrid (Spain). The study attempts to improve knowledge about the influence of traffic-related parameters on turbulence. Linear relationships between vehicle speed and turbulent kinetic energy (TKE) values are found with coefficients of determination (R2) of 0.75 and 0.55 for the lorry and van respectively. The vehicle-induced fluctuations in the wind components (u', v' and w') showed the highest values for the longitudinal component (v) because of the wake-passing effect. In the analysis of wake produced by moving vehicles it is indicated how the turbulence dissipates in relation to a distance d and height h. The TKE values were found to be higher at the measuring points closer to the surface during the wake analysis.This work was supported by the OASIS Research Project that was co financed by CDTI (Spanish Science and Innovation Ministry) and developed with the Spanish companies: Iridium, OHL Concesiones, Abertis, Sice, Indra, Dragados, OHL, Geocisa, GMV, Asfaltos Augusta, Hidrofersa, Eipsa, PyG, CPS, AEC and Torre de Comares Arquitectos s.l and 16 research centres

Biological evolution and human cognition are analogous information processing systems

The mechanisms that govern biological evolution and human cognition are analogous, as both follow the same principles of natural information processing systems. In this article, we describe the following five principles that provide an analogy between biological evolution and human cognition: (a) Randomness as Genesis Principle and (b) Borrowing and Reorganizing Principle, which indicate how natural information processing systems obtain information; (c) Narrow Limits of Change Principle and (d) Information Store Principle, which indicate how information is processed and stored; and (e) Environmental Organizing and Linking Principle, which indicate how stored information is used to generate actions appropriate to an environment. In human cognition, these analogs only apply to cognitive processes associated with biologically secondary knowledge, the knowledge typically taught in educational institutions. Based on these five principles, cognitive load theory researchers have provided diverse prescriptions to optimize instructional activities and materials. We conclude by discussing general instructional implications and future research directions based on this analogy

Integrating cognitive load theory with other theories, within and beyond educational psychology

Background and Aims: The long-standing aim of cognitive load theory (CLT) has been to generate instructional design principles that show teachers how to instruct students effectively, based on knowledge of the intricacies of human cognitive architecture. Historically, the focus of CLT has been on identifying cognitive processes related to learning and instruction. However, the theory has become more multidisciplinary over time, drawing on theoretical perspectives both within, and beyond, educational psychology. Results: This Editorial presents a brief historical overview of key developments in CLT and seven key themes that are pertinent to research on CLT. These themes are as follows: Level of Expertise, Cognitive Load Measurement, Embodied Cognition, Self-Regulated Learning, Emotion Induction, Replenishment of Working Memory, and Two Subprocessors of Working Memory. Summaries of the nine empirical contributions to the special issue are presented and discussed in relation to how they provide insight into one or more of these themes. Conclusions: Understanding the variables that impact student learning and instruction has always represented the core aim of CLT. The growing multidisciplinary features of CLT should provide researchers and practitioners with more holistic perspectives of the factors that predict student learning and, in turn, guide instructional design

Nonextensive thermodynamic functions in the Schr\"odinger-Gibbs ensemble

Schr\"odinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum system [E. Schr\"odinger, Statistical Thermodynamics (Courier Dover, Mineola, 1967)]. Different authors have interpreted this statement by introducing density distributions on the space of quantum pure states with weights obtained as functions of the expectation value of the Hamiltonian of the system. In this work we focus on one of the best known of these distributions, and we prove that, when considered in composite quantum systems, it defines partition functions that do not factorize as products of partition functions of the noninteracting subsystems, even in the thermodynamical regime. This implies that it is not possible to define extensive thermodynamical magnitudes such as the free energy, the internal energy or the thermodynamic entropy by using these models. Therefore, we conclude that this distribution inspired by Schr\"odinger's idea can not be used to construct an appropriate quantum equilibrium thermodynamics.Comment: 32 pages, revtex 4.1 preprint style, 5 figures. Published version with several changes with respect to v2 in text and reference

Echelons of power series and Gabrielov's counterexample to nested linear Artin Approximation

Gabrielov's famous example for the failure of analytic Artin approximation in the presence of nested subring conditions is shown to be due to a growth phenomenon in standard basis computations for echelons, a generalization of the concept of ideals in power series rings.Comment: To appear in Bulletin of the London Mathematical Societ

Entropy and canonical ensemble of hybrid quantum classical systems

In this work we generalize and combine Gibbs and von Neumann approaches to build, for the first time, a rigorous definition of entropy for hybrid quantum-classical systems. The resulting function coincides with the two cases above when the suitable limits are considered. Then, we apply the MaxEnt principle for this hybrid entropy function and obtain the natural candidate for the hybrid canonical ensemble (HCE). We prove that the suitable classical and quantum limits of the HCE coincide with the usual classical and quantum canonical ensembles since the whole scheme admits both limits, thus showing that the MaxEnt principle is applicable and consistent for hybrid systems