High-dimensional dynamics in a single-transistor oscillator containing Feynman-Sierpiński resonators: Effect of fractal depth and irregularity

A scalable electronic analog of the Burridge-Knopoff model of earthquake faults

The Burridge-Knopoff model implements an earthquake fault as a mechanical block-spring chain. While numerical studies of the model are abundant, experimental investigations are limited to a two-blocks, analog electronic implementation that was proposed by drawing an analogy between mechanical and electrical quantities. Although elegant, this approach is not versatile, mostly because of its heavy reliance on inductors. Here, we propose an alternative, inductorless implementation of the same system. The experimental characterization of the proposed circuit shows very good agreement with theoretical predictions. Besides periodic oscillations, the circuit exhibits a chaotic regime: the corresponding markers of chaoticity, namely, the correlation dimension and the maximum Lyapunov exponent, were experimentally assessed to be consistent with those provided by numerical simulations. The improved versatility and scalability of the circuit is expected to allow for experimental implementations of the Burridge-Knopoff model with a large number of blocks. In addition, the circuit can be used as the basic element of scalable platforms to investigate the dynamics of networks of oscillators and related phenomena.

The fractal brain: scale-invariance in structure and dynamics

The past 40 years have witnessed extensive research on fractal structure and scale-free dynamics in the brain. Although considerable progress has been made, a comprehensive picture has yet to emerge, and needs further linking to a mechanistic account of brain function. Here, we review these concepts, connecting observations across different levels of organization, from both a structural and functional perspective. We argue that, paradoxically, the level of cortical circuits is the least understood from a structural point of view and perhaps the best studied from a dynamical one. We further link observations about scale-freeness and fractality with evidence that the environment provides constraints that may explain the usefulness of fractal structure and scale-free dynamics in the brain. Moreover, we discuss evidence that behavior exhibits scale-free properties, likely emerging from similarly organized brain dynamics, enabling an organism to thrive in an environment that shares the same organizational principles. Finally, we review the sparse evidence for and try to speculate on the functional consequences of fractality and scale-freeness for brain computation. These properties may endow the brain with computational capabilities that transcend current models of neural computation and could hold the key to unraveling how the brain constructs percepts and generates behavior.

Fractal Dimension Analysis of Melanocytic Nevi and Melanomas in Normal and Polarized Light-A Preliminary Report

Clinical diagnosis of pigmented lesions can be a challenge in everyday practice. Benign and dysplastic nevi and melanomas may have similar clinical presentations, but completely different prognoses. Fractal dimensions of shape and texture can describe the complexity of the pigmented lesion structure. This study aims to apply fractal dimension analysis to differentiate melanomas, dysplastic nevi, and benign nevi in polarized and non-polarized light. A total of 87 Eighty-four patients with 97 lesions were included in this study. All examined lesions were photographed under polarized and non-polarized light, surgically removed, and examined by a histopathologist to establish the correct diagnosis. The obtained images were then processed and analyzed. Area, perimeter, and fractal dimensions of shape and texture were calculated for all the lesions under polarized and non-polarized light. The fractal dimension of shape in polarized light enables differentiating melanomas, dysplastic nevi, and benign nevi. It also makes it possible to distinguish melanomas from benign and dysplastic nevi under non-polarized light. The fractal dimension of texture allows distinguishing melanomas from benign and dysplastic nevi under polarized light. All examined parameters of shape and texture can be used for developing an automatic computer-aided diagnosis system. Polarized light is superior to non-polarized light for imaging texture details.

Chasing chaos by improved identification of suitable embedding dimensions and lags

The detection of an underlying chaotic behavior in experimental recordings is a longstanding issue in the field of nonlinear time series analysis. Conventional approaches require the assessment of a suitable dimension and lag pair to embed a given input sequence and, thereupon, the estimation of dynamical invariants to characterize the underlying source. In this work, we propose an alternative approach to the problem of identifying chaos, which is built upon an improved method for optimal embedding. The core of the new approach is the analysis of an input sequence on a lattice of embedding pairs whose results provide, if any, evidence of a finite-dimensional, chaotic source generating the sequence and, if such evidence is present, yield a set of equivalently suitable embedding pairs to embed the sequence. The application of this approach to two experimental case studies, namely, an electronic circuit and magnetoencephalographic recordings of the human brain, highlights how it can make up a powerful tool to detect chaos in complex systems.

Nonclassical Systemics of Quasicoherence: From Formal Properties to Representations of Generative Mechanisms. A Conceptual Introduction to a Paradigm-Shift

In this article, we consider how formal models and properties of emergence, e.g., long-range correlations, power laws, and self-similarity are usually platonically considered to represent the essence of the phenomenon, more specifically, their acquired properties, e.g., coherence, and not their generative mechanisms. Properties are assumed to explain, rather than represent, real processes of emergence. Conversely, real phenomenological processes are intended to be approximations or degenerations of their essence. By contrast, here, we consider the essence as a simplification of the phenomenological complexity. It is assumed to be acceptable that such simplification neglects several aspects (e.g., incompleteness, inhomogeneities, instabilities, irregularities, and variations) of real phenomena in return for analytical tractability. Within this context, such a trade-off is a kind of reductionism when dealing with complex phenomena. Methodologically, we propose a paradigmatic change for systems science equivalent to the one that occurred in Physics from object to field, namely, a change from interactional entities to domains intended as extensions of fields, or multiple fields, as it were. The reason to introduce such a paradigm shift is to make nonidealist approaches suitable for dealing with more realistic quasicoherence, when the coherence does not consistently apply to all the composing entities, but rather, different forms of coherence apply. As a typical general interdisciplinary case, we focus on so-called collective behaviors. The goal of this paper is to introduce the concepts of domain and selection mechanisms which are suitable to represent the generative mechanisms of quasicoherence of collective behavior. Domains are established by self-tracking entities such as financial or are effectively GPS-detectable. Such domains allow the profiling of collective behavior. Selection mechanisms are based on learning techniques or cognitive approaches for social systems.