Fractal and fractional SIS model for syphilis data.

This work studies the SIS model extended by fractional and fractal derivatives. We obtain explicit solutions for the standard and fractal formulations; for the fractional case, we study numerical solutions. As a real data example, we consider the Brazilian syphilis data from 2011 to 2021. We fit the data by considering the three variations of the model. Our fit suggests a recovery period of 11.6 days and a reproduction ratio (R0) equal to 6.5. By calculating the correlation coefficient (r) between the real data and the theoretical points, our results suggest that the fractal model presents a higher r compared to the standard or fractional case. The fractal formulation is improved when two different fractal orders with distinguishing weights are considered. This modification in the model provides a better description of the data and improves the correlation coefficient.

Analyzing bursting synchronization in structural connectivity matrix of a human brain under external pulsed currents.

Cognitive tasks in the human brain are performed by various cortical areas located in the cerebral cortex. The cerebral cortex is separated into different areas in the right and left hemispheres. We consider one human cerebral cortex according to a network composed of coupled subnetworks with small-world properties. We study the burst synchronization and desynchronization in a human neuronal network under external periodic and random pulsed currents. With and without external perturbations, the emergence of bursting synchronization is observed. Synchronization can contribute to the processing of information, however, there are evidences that it can be related to some neurological disorders. Our results show that synchronous behavior can be suppressed by means of external pulsed currents.

DeepGANnel: Synthesis of fully annotated single molecule patch-clamp data using generative adversarial networks.

Development of automated analysis tools for "single ion channel" recording is hampered by the lack of available training data. For machine learning based tools, very large training sets are necessary with sample-by-sample point labelled data (e.g., 1 sample point every 100microsecond). In an experimental context, such data are labelled with human supervision, and whilst this is feasible for simple experimental analysis, it is infeasible to generate the enormous datasets that would be necessary for a big data approach using hand crafting. In this work we aimed to develop methods to generate simulated ion channel data that is free from assumptions and prior knowledge of noise and underlying hidden Markov models. We successfully leverage generative adversarial networks (GANs) to build an end-to-end pipeline for generating an unlimited amount of labelled training data from a small, annotated ion channel "seed" record, and this needs no prior knowledge of theoretical dynamical ion channel properties. Our method utilises 2D CNNs to maintain the synchronised temporal relationship between the raw and idealised record. We demonstrate the applicability of the method with 5 different data sources and show authenticity with t-SNE and UMAP projection comparisons between real and synthetic data. The model would be easily extendable to other time series data requiring parallel labelling, such as labelled ECG signals or raw nanopore sequencing data.