Natural Graph Wavelet Packet Dictionaries

We introduce a set of novel multiscale basis transforms for signals on graphs that utilize their “dual” domains by incorporating the “natural” distances between graph Laplacian eigenvectors, rather than simply using the eigenvalue ordering. These basis dictionaries can be seen as generalizations of the classical Shannon wavelet packet dictionary to arbitrary graphs, and do not rely on the frequency interpretation of Laplacian eigenvalues. We describe the algorithms (involving either vector rotations or orthogonalizations) to construct these basis dictionaries, use them to efficiently approximate graph signals through the best basis search, and demonstrate the strengths of these basis dictionaries for graph signals measured on sunflower graphs and street networks.

The Limits of Numerical Probability: Frank H. Knight and Ludwig von Mises and the Frequency Interpretation

In the following I will (1) briefly restate the principles of the fre-quency interpretation of probability as originally formulated by Richard von Mises; (2) show why Frank H. Knight and Ludwig von Mises must be considered frequency theorists; and (3) discuss and evaluate the arguments provided by F. H. Knight and L. v. Mises against the possibility of applying probability theory in the area of economic forecasting (whether on the micro or the macro level). Key words: probability theory, economic forecasting, frequency distribution. Clasificación JEL: B41, B53. Resumen: En este trabajo, 1) volveré a plantear brevemente los principios de la interpretación frecuencialista de la probabilidad tal y como fueron formulados originalmente por Richard von Mises; 2) mostraré por qué Frank H. Knight y Ludwig von Mises deben ser considerados teóricos de la interpretación frecuencialista, y 3) discutiré y evaluaré los argumentos proporcionados por F. H. Knight y L. v. Mises en contra de la posibilidad de aplicar la teoría de la probabilidad en el área de la previsión económica (ya sea a nivel microeconómico o macroeconómico). Palabras clave: teoría de la probabilidad, previsión económica, distribución de frecuencias.

John Maynard Keynes and Ludwig von Mises on Probability

The economic paradigms of Ludwig von Mises on the one hand and of John Maynard Keynes on the other have been correctly recognized as antithetical at the theoretical level, and as antagonistic with respect to their practical and public policy implications. Characteristically they have also been vindicated by opposing sides of the political spectrum. Nevertheless the respective views of these authors with respect to the meaning and interpretation of probability exhibit a closer conceptual affinity than has been acknowledged in the literature. In particular it is argued that in some relevant respects Ludwig von Mises’ interpretation of the concept of probability exhibits a closer affinity with the interpretation of probability developed by his opponent John Maynard Keynes than with the views on probability espoused by his brother Richard von Mises. Nevertheless there also exist significant differences between the views of Ludwig von Mises and those of John Maynard Keynes with respect to probability. One of these is highlighted more particularly: where John Maynard Keynes advocated a monist view of probability, Ludwig von Mises embraced a dualist view of probability, according to which the concept of probability has two different meanings each of which is valid in a particular area or context. It is concluded that both John Maynard Keynes and Ludwig von Mises presented highly nuanced views with respect to the meaning and interpretation of probability. JEL codes: B00; B40; B49; B53; C00. Key words: General Methodology; Austrian Methodology; Keynesian Methodology; Quantitative and Qualitative Probability Concepts: Meaning and Interpretation; Frequency Interpretation; Logical Interpretation; John Maynard Keynes; Ludwig von Mises; Richard von Mises. Resumen: Los paradigmas económicos de Ludwig von Mises por una parte, y de John Maynard Keynes por otra, han sido correctamente reconocidos como contradictorias a nivel teórico, y como antagonistas, con respecto a sus implicaciones políticas prácticas y públicas. Aún así, las respectivas visiones de estos autores con respecto al significado e interpretación de la probabilidad, muestra una afinidad conceptual más estrecha que los que se ha reconocido en la literatura. Se ha argumentado especialmente que en algunos aspectos importantes, la interpretación de Ludwig von Mises del concepto de probabilidad, muestra una más estrecha afinidad con la interpretación de probabilidad desarrollada por su oponente John Maynard Keynes, que con las maneras de ver la probabilidad respaldadas por su hermano Richard von Mises. Sin embargo, también existen grandes diferencias entre los puntos de vista de Ludwig von Mises y aquellos de John Maynard Keynes con respecto a la probabilidad. Uno de ellos destaca principalmente: cuando John Maynard Keynes aboga por un punto de vista monista de la probabilidad, Ludwig von Mises defiende un punto de vista dualista de la probabilidad, de acuerdo con el cual el concepto de probabilidad recibe dos significados diferentes, y en donde cada uno de ellos es válido en un área o contexto en particular. Se concluye que tanto John Maynard Keynes como Ludwig von Mises presentan puntos de vista claramente diferenciados con respecto al significado e interpretación de la probabilidad. Códigos JEL: B00; B40; B49; B53; C00. Palabras clave: Metodología General; Metodología austríaca; Metodología Keynesiana; Conceptos de probabilidad cuantitativos y cualitativos: Significado e Interpretación; Interpretación frecuencialista; Interpretación lógica; John Maynard Keynes; Ludwig von Mises; Richard von Mises.

A novel high-frequency interpretation of a general purpose Op-Amp-based negative resistance for chaotic vibrations in a simple a priori nonchaotic circuit

A novel model of general purpose operational amplifiers is made to approximate, at best, the equivalent circuit for real model at high-frequency. With this new model, it appears that certain oscillators, usually studied under ideal considerations or using many existing real models of operational amplifiers, have hidden subtle and attractive chaotic dynamics that have previously been unknown. These can now be revealed. With the new considerations, a “two-component” circuit, consisting simply of a capacitor in parallel with a nonmodified (and usually presented as a linear, negative) resistance, tends to exhibit chaotic signals. P-Spice and laboratory experimental results are in good agreement with the theoretical predictions.