arXiv subjects

M. Piacquadio

Publications and source records attributed to M. Piacquadio.

4 recordsLinked to original sources

arXiv2009

Multifractal analysis and instability index of prior-to-crash market situations

We take prior-to-crash market prices (NASDAQ, Dow Jones Industrial Average) as a signal, a function of time, we project these discrete values onto a vertical axis, thus obtaining a Cantordust. We study said cantordust with the tools of multifractal analysis, obtaining spectra by definition and by lagrangian coordinates. These spectra have properties that typify the prior-to-crash market situation. Any of these spectra entail elaborate processing of the raw signal data. With the unprocessed raw data we obtain an instability index, also with properties that typify the prior-to-crisis market situation. Both spectra and the instability index agree in characterizing such crashes, and in giving an early warning of them.

q-fin.ST↗

arXiv2009

Mendes France and thermodynamical spectra: a comparative study of contractive and expansive fractal processes

This paper presents a comparative study of two families of curves in R(n). The first ones comprise self-similar bounded fractals obtained by contractive processes, and have a non-integer Hausdorff dimension. The second ones are unbounded, locally rectifiable, locally smooth, obtained by expansive processes, and characterized by a fractional dimension defined by M. Mendes France. We present a way to relate the two types of curves and their respective non-integer dimensions. Thus, to one fractal bounded curve we associate, at first, a finite range of Mendes France dimensions, identifying the minimal and the maximal ones. Later, we show that this discrete spectrum can be made continuous, allowing it to be compared with some other multifractal spectra encountered in the literature. We discuss the corresponding physical interpretations.

math-ph↗

arXiv2008

Multifractal analysis of a road-to-crisis in a Faraday experiment

A thin layer of liquid in a horizontal cell is subjected to a periodic vertical force with two control parameters: acceleration and frequency. The influence of the rheological behavior of the fluid was considered over the empirically obtained results, which were subjected to a multfractal spectrum process. As control parameters varied, so did the corresponding spectra, according to theoretical models; each change of state was visually detected, which permitted interpreting the corresponding spectral changes.

math-ph↗

arXiv2000

The dimensions of Hausdorff and Mendes France. A comparative study

This paper contains a comparative study of two families of simple curves drawn in the plane. On the one hand, we have the fractal curves on the unit interval, with self-similar structure, which have associated a Hausdorff dimension. On the other hand, we have the opposite: a class of locally rectifiable unbounded curves, which have another "fractional dimension" defined by M. Mendes France. We propose a geometrical constructive process that will allow us to obtain - as the limit of a sequence of polygonal curves - one curve of the first family, by contractive transformations; and another of the second family, by expansive transformations. Thanks to this process of linking curves from both families, we are able to compare their dimensions - our aim in this work -, and to obtain interesting results such as the equality of the latter in the case of strict self-similarity.

math.CA↗