Research on characteristics of noise-perturbed M–J sets based on equipotential point algorithm

AbstractAs the classical ones among the fractal sets, Julia set (abbreviated as J set) and Mandelbrot set (abbreviated as M set) have been explored widely in recent years. In this study, J set and M set under additive noise perturbation and multiplicative noise perturbation are created by equipotential point algorithm. Changes of the J set and M set under random noise perturbation as well as the close correlation between them are studied. Experimental results show that either additive noise perturbation or multiplicative noise perturbation may cause dramatic changes on J set. On the other hand, when the M set is perturbed by additive noise, it almost changes nothing but its position; when the M set is perturbed by multiplicative noise, its inner structures change with the stabilized areas shrinking, but it keeps the symmetry with respect to X axis. In addition, the J set and the M set still share the same stabilized periodic point in spite of noise perturbation

Biomorphs via Modified Iterations

The aim of this paper is to present some modifications of the biomorphs generation algorithm introduced by Pickover in 1986. A biomorph stands for biological morphologies. It is obtained by a modified Julia set generation algorithm. The biomorph algorithm can be used in the creation of diverse and complicated forms resembling invertebrate organisms. In this paper the modifications of the biomorph algorithm in two directions are proposed. The first one uses different types of iterations (Picard, Mann, Ishikawa). The second one uses a sequence of parameters instead of one fixed parameter used in the original biomorph algorithm. Biomorphs generated by the modified algorithm are essentially different in comparison to those obtained by the standard biomorph algorithm, i.e., the algorithm with Picard iteration and one fixed constant

A direct method to detect deterministic and stochastic properties of data

AbstractA fundamental question of data analysis is how to distinguish noise corrupted deterministic chaotic dynamics from time-(un)correlated stochastic fluctuations when just short length data is available. Despite its importance, direct tests of chaos vs stochasticity in finite time series still lack of a definitive quantification. Here we present a novel approach based on recurrence analysis, a nonlinear approach to deal with data. The main idea is the identification of how recurrence microstates and permutation patterns are affected by time reversibility of data, and how its behavior can be used to distinguish stochastic and deterministic data. We demonstrate the efficiency of the method for a bunch of paradigmatic systems under strong noise influence, as well as for real-world data, covering electronic circuit, sound vocalization and human speeches, neuronal activity, heart beat data, and geomagnetic indexes. Our results support the conclusion that the method distinguishes well deterministic from stochastic fluctuations in simulated and empirical data even under strong noise corruption, finding applications involving various areas of science and technology. In particular, for deterministic signals, the quantification of chaotic behavior may be of fundamental importance because it is believed that chaotic properties of some systems play important functional roles, opening doors to a better understanding and/or control of the physical mechanisms behind the generation of the signals.Financiadora de Estudos e Projetoshttps://doi.org/10.13039/501100004809Coordenação de Aperfeiçoamento de Pessoal de Nível Superiorhttps://doi.org/10.13039/501100002322Conselho Nacional de Desenvolvimento Científico e Tecnológicohttps://doi.org/10.13039/501100003593Peer Reviewe

Bayesian Inference of Synaptic Quantal Parameters from Correlated Vesicle Release

Synaptic transmission is both history-dependent and stochastic, resulting in varying responses to presentations of the same presynaptic stimulus. This complicates attempts to infer synaptic parameters and has led to the proposal of a number of different strategies for their quantification. Recently Bayesian approaches have been applied to make more efficient use of the data collected in paired intracellular recordings. Methods have been developed that either provide a complete model of the distribution of amplitudes for isolated responses or approximate the amplitude distributions of a train of post-synaptic potentials, with correct short-term synaptic dynamics but neglecting correlations. In both cases the methods provided significantly improved inference of model parameters as compared to existing mean-variance fitting approaches. However, for synapses with high release probability, low vesicle number or relatively low restock rate and for data in which only one or few repeats of the same pattern are available, correlations between serial events can allow for the extraction of significantly more information from experiment: a more complete Bayesian approach would take this into account also. This has not been possible previously because of the technical difficulty in calculating the likelihood of amplitudes seen in correlated post-synaptic potential trains; however, recent theoretical advances have now rendered the likelihood calculation tractable for a broad class of synaptic dynamics models. Here we present a compact mathematical form for the likelihood in terms of a matrix product and demonstrate how marginals of the posterior provide information on covariance of parameter distributions. The associated computer code for Bayesian parameter inference for a variety of models of synaptic dynamics is provided in the supplementary material allowing for quantal and dynamical parameters to be readily inferred from experimental data sets

Synthetic Gene Circuits: Design with Directed Evolution

Synthetic circuits offer great promise for generating insights into nature's underlying design principles or forward engineering novel biotechnology applications. However, construction of these circuits is not straightforward. Synthetic circuits generally consist of components optimized to function in their natural context, not in the context of the synthetic circuit. Combining mathematical modeling with directed evolution offers one promising means for addressing this problem. Modeling identifies mutational targets and limits the evolutionary search space for directed evolution, which alters circuit performance without the need for detailed biophysical information. This review examines strategies for integrating modeling and directed evolution and discusses the utility and limitations of available methods

Predicting extreme VaR: Nonparametric quantile regression with refinements from extreme value theory

This paper studies the performance of nonparametric quantile regression as a tool to predict Value at Risk (VaR). The approach is flexible as it requires no assumptions on the form of return distributions. A monotonized double kernel local linear estimator is applied to estimate moderate (1%) conditional quantiles of index return distributions. For extreme (0.1%) quantiles, where particularly few data points are available, we propose to combine nonparametric quantile regression with extreme value theory. The out-of-sample forecasting performance of our methods turns out to be clearly superior to different specifications of the Conditionally Autoregressive VaR (CAViaR) models.Value at Risk, nonparametric quantile regression, risk management, extreme value theory, monotonization, CAViaR