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

Unpredictability in seasonal infectious diseases spread

In this work, we study the unpredictability of seasonal infectious diseases considering a SEIRS model with seasonal forcing. To investigate the dynamical behaviour, we compute bifurcation diagrams type hysteresis and their respective Lyapunov exponents. Our results from bifurcations and the largest Lyapunov exponent show bistable dynamics for all the parameters of the model. Choosing the inverse of latent period as control parameter, over 70% of the interval comprises the coexistence of periodic and chaotic attractors, bistable dynamics. Despite the competition between these attractors, the chaotic ones are preferred. The bistability occurs in two wide regions. One of these regions is limited by periodic attractors, while periodic and chaotic attractors bound the other. As the boundary of the second bistable region is composed of periodic and chaotic attractors, it is possible to interpret these critical points as tipping points. In other words, depending on the latent period, a periodic attractor (predictability) can evolve to a chaotic attractor (unpredictability). Therefore, we show that unpredictability is associated with bistable dynamics preferably chaotic, and, furthermore, there is a tipping point associated with unpredictable dynamics

Fractional dynamics and recurrence analysis in cancer model

In this work, we analyze the effects of fractional derivatives in the chaotic dynamics of a cancer model. We begin by studying the dynamics of a standard model, {\it i.e.}, with integer derivatives. We study the dynamical behavior by means of the bifurcation diagram, Lyapunov exponents, and recurrence quantification analysis (RQA), such as the recurrence rate (RR), the determinism (DET), and the recurrence time entropy (RTE). We find a high correlation coefficient between the Lyapunov exponents and RTE. Our simulations suggest that the tumor growth parameter ($\rho_1$) is associated with a chaotic regime. Our results suggest a high correlation between the largest Lyapunov exponents and RTE. After understanding the dynamics of the model in the standard formulation, we extend our results by considering fractional operators. We fix the parameters in the chaotic regime and investigate the effects of the fractional order. We demonstrate how fractional dynamics can be properly characterized using RQA measures, which offer the advantage of not requiring knowledge of the fractional Jacobian matrix. We find that the chaotic motion is suppressed as $\alpha$ decreases, and the system becomes periodic for $\alpha \lessapprox 0.9966$. We observe limit cycles for $\alpha \in (0.9966,0.899)$ and fixed points for $\alpha<0.899$. The fixed point is determined analytically for the considered parameters. Finally, we discover that these dynamics are separated by an exponential relationship between $\alpha$ and $\rho_1$. Also, the transition depends on a supper transient which obeys the same relationship

A model presented for classification ECG signals base on Case-Based Reasoning

Early detection of heart diseases/abnormalities can prolong life and enhance the quality of living through appropriate treatment; thus classifying cardiac signals will be helped to immediate diagnosing of heart beat type in cardiac patients. The present paper utilizes the case base reasoning (CBR) for classification of ECG signals. Four types of ECG beats (normal beat, congestive heart failure beat, ventricular tachyarrhythmia beat and atrial fibrillation beat) obtained from the PhysioBank database was classified by the proposed CBR model. The main purpose of this article is classifying heart signals and diagnosing the type of heart beat in cardiac patients that in proposed CBR (Case Base Reasoning) system, Training and testing data for diagnosing and classifying types of heart beat have been used. The evaluation results from the model are shown that the proposed model has high accuracy in classifying heart signals and helps to clinical decisions for diagnosing the type of heart beat in cardiac patients which indeed has high impact on diagnosing the type of heart beat aided computer

Anomalous Relaxation and Three-Level System: A Fractional Schrödinger Equation Approach

We investigate a three-level system in the context of the fractional Schrödinger equation by considering fractional differential operators in time and space, which promote anomalous relaxations and spreading of the wave packet. We first consider the three-level system omitting the kinetic term, i.e., taking into account only the transition among the levels, to analyze the effect of the fractional time derivative. Afterward, we incorporate a kinetic term and the fractional derivative in space to analyze simultaneous wave packet transition and spreading among the levels. For these cases, we obtain analytical and numerical solutions. Our results show a wide variety of behaviors connected to the fractional operators, such as the non-conservation of probability and the anomalous spread of the wave packet

Fractional Diffusion Equation under Singular and Non-Singular Kernel and Its Stability

The fractional reaction–diffusion equation has been used in many real-world applications in fields such as physics, biology, and chemistry. Motivated by the huge application of fractional reaction–diffusion, we propose a numerical scheme to solve the fractional reaction–diffusion equation under different kernels. Our method can be particularly employed for singular and non-singular kernels, such as the Riemann–Liouville, Caputo, Fabrizio–Caputo, and Atangana–Baleanu operators. Moreover, we obtained general inequalities that guarantee that the stability condition depends explicitly on the kernel. As an implementation of the method, we numerically solved the diffusion equation under the power-law and exponential kernels. For the power-law kernel, we solved by considering fractional time, space, and both operators. In another example, we considered the exponential kernel acting on the time derivative and compared the numerical results with the analytical ones. Our results showed that the numerical procedure developed in this work can be employed to solve fractional differential equations considering different kernels