Related papers: Multifractal Analysis of the Coupling Space of Fee…
The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=\gamma N$ random input patterns. The multifractal spectrum $f(\alpha)$ can be calculated…
Random input patterns induce a partition of the coupling space of a perceptron into cells labeled by their output sequences. Learning some data with a maximal error rate leads to clusters of neighboring cells. By analyzing the internal…
We calculate the multifractal spectrum of the partition of the coupling space of a perceptron induced by random input-output pairs with non-zero mean. From the results we infer the influence of the input and output bias respectively on both…
A model for the generation of fractal growth networks in Euclidean spaces of arbitrary dimension is presented. These networks are considered as the spatial support of reaction-diffusion and pattern formation processes. The local dynamics at…
We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…
A two-state master equation based decision making model has been shown to generate phase transitions, to be topologically complex and to manifest temporal complexity through an inverse power-law probability distribution function in the…
The brain criticality hypothesis has largely only characterized brain dynamics in terms of their self-similarity, although experimental evidence suggests that the brain exhibits significant multifractality. To understand how multifractality…
A feed-forward neural network is demonstrated to efficiently unfold the energy distribution of protons and alpha particles passing through passive material. This model-independent approach works with unbinned data and does not require…
Cross-frequency coupling (CFC) has been proposed to coordinate neural dynamics across spatial and temporal scales. Despite its potential relevance for understanding healthy and pathological brain function, the standard CFC analysis and…
Identifying causal relationships is a challenging yet crucial problem in many fields of science like epidemiology, climatology, ecology, genomics, economics and neuroscience, to mention only a few. Recent studies have demonstrated that…
Two neurons coupled by unreliable synapses are modeled by leaky integrate-and-fire neurons and stochastic on-off synapses. The dynamics is mapped to an iterated function system. Numerical calculations yield a multifractal distribution of…
In the multi-cell multiuser multi-input multi-output (MU-MIMO) systems, fractional programming (FP) has demonstrated considerable effectiveness in optimizing beamforming vectors, yet it suffers from high computational complexity. Recent…
This article studies (multilayer perceptron) neural networks with an emphasis on the transformations involved --- both forward and backward --- in order to develop a semantical/logical perspective that is in line with standard program…
We study the interplay between measurement-induced dynamics and conditional unitary evolution in quantum systems. We numerically and analytically investigate commuting random measurement and feedforward (MFF) processes, and find a sharp…
Feed-forward multilayer neural networks implementing random input-output mappings develop characteristic correlations between the activity of their hidden nodes which are important for the understanding of the storage and generalization…
Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal…
The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
Many models and real complex systems possess critical thresholds at which the systems shift from one sate to another. The discovery of the early warnings of the systems in the vicinity of critical point are of great importance to estimate…
The temporal activity of many biological systems, including neural circuits, exhibits fluctuations simultaneously varying over a large range of timescales. The mechanisms leading to this temporal heterogeneity are yet unknown. Here we show…