Revisiting Complex Moments For 2D Shape Representation and Image Normalization

When comparing 2D shapes, a key issue is their normalization. Translation and scale are easily taken care of by removing the mean and normalizing the energy. However, defining and computing the orientation of a 2D shape is not so simple. In fact, although for elongated shapes the principal axis can be used to define one of two possible orientations, there is no such tool for general shapes. As we show in the paper, previous approaches fail to compute the orientation of even noiseless observations of simple shapes. We address this problem. In the paper, we show how to uniquely define the orientation of an arbitrary 2D shape, in terms of what we call its Principal Moments. We show that a small subset of these moments suffice to represent the underlying 2D shape and propose a new method to efficiently compute the shape orientation: Principal Moment Analysis. Finally, we discuss how this method can further be applied to normalize grey-level images. Besides the theoretical proof of correctness, we describe experiments demonstrating robustness to noise and illustrating the method with real images.Comment: 69 pages, 20 figure

Inline self-diffraction dispersion-scan of over octave-spanning pulses in the single-cycle regime

We present an implementation of dispersion-scan based on self-diffraction (SD d-scan) and apply it to the measurement of over octave-spanning sub-4-fs pulses. The results are compared with second-harmonic generation (SHG) d-scan. The efficiency of the SD process is derived theoretically and compared with the spectral response retrieved by the d-scan algorithm. The new SD d-scan has a robust inline setup and enables measuring pulses with over-octave spectra, single-cycle durations and wavelength ranges beyond those of SHG crystals, such as the ultraviolet and the deep-ultraviolet.Comment: 8 pages, 5 figure

Bien común y economía

This paper analyzes the meaning of the 'common good' and its impact on economics. It adopts the 'classical notion of the common good' which, conceived by Aristotle and further developed by Thomas Aquinas, has been widely used for centuries. Sections 2 and 3 introduce Aristotle's view on this notion, followed by Aquinas' developments. Section 4 addresses the different meanings of common good in the 20th century. Given that the classical version of the common good implies an anthropological position and a theory of the good, Section 5 extracts them from Aristotle's works, while Section 6 deduces policy implications from the previous definitions. Finally, Section 7 analyzes two current economic theories from the point of view of their relation with the common good: economics of happiness and the capability approach. The final section presents a brief conclusion.Este documento analiza el significado del ‘‘bien común’’ y su impacto en la Economía. Adopta la ‘‘noción clásica del bien común’’ que, concebida por Aristóteles y desarrollada posteriormente por Tomás de Aquino, ha sido ampliamente utilizada durante siglos. La segunda y tercera secciones introducen la visión aristotélica sobre esta noción, seguida de los desarrollos de Aquino. La cuarta sección aborda los diferentes significados del bien común, pertenecientes al siglo XX. Dado que la versión clásica del bien común implica una posición antropológica y una teoría del bien, la quinta sección extrae ambos conceptos de la obra de Aristóteles, mientras que la sección sexta deduce las implicaciones políticas de las definiciones anteriores. Por último, la séptima sección analiza dos teorías económicas actuales, desde el punto de vista de su relación con el bien común: la economía de la felicidad y el enfoque de las capacidades. La sección final incluye una breve conclusió

"Models as signs" as "good economic models"

This paper applies John Poinsot’s doctrine about signs to the evaluation of “good economic models”. First, a “good model” is defined. Then, Poinsot’s conceptual framework and some current ideas about models are introduced. Third, the paper shows how Poinsot’s and ideas about models can be combined. The conclusion is that a good model raises possible causes of the phenomena under examination, which should be then empirically verified.En éste trabajo se aplica la teoría de los signos de Juan Poinsot para la evaluación de un "buen modelo económico". Primero se define qué se considera un buen modelo, luego se presenta el marco conceptual de Poinsot y se presentan algunas ideas actuales acerca de modelos económicos. Luego se muestra cómo se pueden combinar las ideas de Poinsot y sobre los modelos. La conclusión es que un buen modelo señala posibles causas de los fenómenos bajo estudio las que han de verificarse empíricamente

Topological superconductivity in lead nanowires

Superconductors with an odd number of bands crossing the Fermi energy have topologically protected Andreev states at interfaces, including Majorana states in one dimensional geometries. Superconductivity, a low number of 1D channels, large spin orbit coupling, and a sizeable Zeeman energy, are present in lead nanowires produced by nanoindentation of a Pb tip on a Pb substrate, in magnetic fields higher than the Pb bulk critical field. A number of such devices have been analyzed. In some of them, the dependence of the critical current on magnetic field, and the Multiple Andreev Reflections observed at finite voltages, are compatible with the existence of topological superconductivity

Causality, teleology and explanation in social sciences

Causality and explanation are hot topics in the contemporary philosophy of natural and social sciences. The dissatisfaction with some “classical” accounts of scientific explanation (such as the deductive-nomological or covering law model, or the inductive and deductive statistical explanation) leads philosophers of science to probe the possibilities of causal explanations. However, instead of unanimous notions on causation and explanation, a plethora of concepts emerged.2 This paper argues that four analytical levels may be found in social sciences, including economics –namely, a) a statistical descriptive level, b) a causal explanatory level, c) a teleological explicative level and d) a prescriptive teleological level. Social sciences ordinarily only consider levels a) and b). The exclusion of level c) may lead to viewing behaviors that do not respect theories such as the rational choice theory or the expected utility theory –theories which adopt “instrumental rationality”— as “anomalies”. Including level c) entails factoring “practical rationality” in and makes those anomalies reasonable. Once level c) is included, level d) “automatically” applies. For reasons that will become clear as this paper unfolds, this analysis adopts Aristotle’s notions on causality, teleology and practical reason as a theoretical framework. For the sake of the proposal outlined here, it is convenient to preserve Aristotle’s notions in their original form, avoiding the changes introduced in modern times. The first section introduces the Aristotelian notions of causality and teleology, while the second section explores contemporary views on them. The third section discusses the four analytical levels of social sciences, relying on Carl Menger’s classification of economic disciplines in the case of economics