Central hubs prediction for bio networks by directed hypergraph - GA with validation to COVID-19 PPI.

Network structures have attracted much interest and have been rigorously studied in the past two decades. Researchers used many mathematical tools to represent these networks, and in recent days, hypergraphs play a vital role in this analysis. This paper presents an efficient technique to find the influential nodes using centrality measure of weighted directed hypergraph. Genetic Algorithm is exploited for tuning the weights of the node in the weighted directed hypergraph through which the characterization of the strength of the nodes, such as strong and weak ties by statistical measurements (mean, standard deviation, and quartiles) is identified effectively. Also, the proposed work is applied to various biological networks for identification of influential nodes and results shows the prominence the work over the existing measures. Furthermore, the technique has been applied to COVID-19 viral protein interactions. The proposed algorithm identified some critical human proteins that belong to the enzymes TMPRSS2, ACE2, and AT-II, which have a considerable role in hosting COVID-19 viral proteins and causes for various types of diseases. Hence these proteins can be targeted in drug design for an effective therapeutic against COVID-19.

Noisy threshold in neuronal models: connections with the noisy leaky integrate-and-fire model.

Providing an analytical treatment to the stochastic feature of neurons' dynamics is one of the current biggest challenges in mathematical biology. The noisy leaky integrate-and-fire model and its associated Fokker-Planck equation are probably the most popular way to deal with neural variability. Another well-known formalism is the escape-rate model: a model giving the probability that a neuron fires at a certain time knowing the time elapsed since its last action potential. This model leads to a so-called age-structured system, a partial differential equation with non-local boundary condition famous in the field of population dynamics, where the age of a neuron is the amount of time passed by since its previous spike. In this theoretical paper, we investigate the mathematical connection between the two formalisms. We shall derive an integral transform of the solution to the age-structured model into the solution of the Fokker-Planck equation. This integral transform highlights the link between the two stochastic processes. As far as we know, an explicit mathematical correspondence between the two solutions has not been introduced until now.

Generic and specific recurrent neural network models: Applications for large and small scale biopharmaceutical upstream processes.

The calculation of temporally varying upstream process outcomes is a challenging task. Over the last years, several parametric, semi-parametric as well as non-parametric approaches were developed to provide reliable estimates for key process parameters. We present generic and product-specific recurrent neural network (RNN) models for the computation and study of growth and metabolite-related upstream process parameters as well as their temporal evolution. Our approach can be used for the control and study of single product-specific large-scale manufacturing runs as well as generic small-scale evaluations for combined processes and products at development stage. The computational results for the product titer as well as various major upstream outcomes in addition to relevant process parameters show a high degree of accuracy when compared to experimental data and, accordingly, a reasonable predictive capability of the RNN models. The calculated values for the root-mean squared errors of prediction are significantly smaller than the experimental standard deviation for the considered process run ensembles, which highlights the broad applicability of our approach. As a specific benefit for platform processes, the generic RNN model is also used to simulate process outcomes for different temperatures in good agreement with experimental results. The high level of accuracy and the straightforward usage of the approach without sophisticated parameterization and recalibration procedures highlight the benefits of the RNN models, which can be regarded as promising alternatives to existing parametric and semi-parametric methods.

Segmentation of bones in medical dual-energy computed tomography volumes using the 3D U-Net.

Deep learning algorithms have improved the speed and quality of segmentation for certain tasks in medical imaging. The aim of this work is to design and evaluate an algorithm capable of segmenting bones in dual-energy CT data sets. A convolutional neural network based on the 3D U-Net architecture was implemented and evaluated using high tube voltage images, mixed images and dual-energy images from 30 patients. The network performed well on all the data sets; the mean Dice coefficient for the test data was larger than 0.963. Of special interest is that it performed better on dual-energy CT volumes compared to mixed images that mimicked images taken at 120 kV. The corresponding increase in the Dice coefficient from 0.965 to 0.966 was small since the enhancements were mainly at the edges of the bones. The method can easily be extended to the segmentation of multi-energy CT data.

On open and closed convex codes.

Neural codes serve as a language for neurons in the brain. Open (or closed) convex codes, which arise from the pattern of intersections of collections of open (or closed) convex sets in Euclidean space, are of particular relevance to neuroscience. Not every code is open or closed convex, however, and the combinatorial properties of a code that determine its realization by such sets are still poorly understood. Here we find that a code that can be realized by a collection of open convex sets may or may not be realizable by closed convex sets, and vice versa, establishing that open convex and closed convex codes are distinct classes. We establish a non-degeneracy condition that guarantees that the corresponding code is both open convex and closed convex. We also prove that max intersection-complete codes (i.e. codes that contain all intersections of maximal codewords) are both open convex and closed convex, and provide an upper bound for their minimal embedding dimension. Finally, we show that the addition of non-maximal codewords to an open convex code preserves convexity.

An evolutionary computing approach for parameter estimation investigation of a model for cholera.

We consider the problem of using time-series data to inform a corresponding deterministic model and introduce the concept of genetic algorithms (GA) as a tool for parameter estimation, providing instructions for an implementation of the method that does not require access to special toolboxes or software. We give as an example a model for cholera, a disease for which there is much mechanistic uncertainty in the literature. We use GA to find parameter sets using available time-series data from the introduction of cholera in Haiti and we discuss the value of comparing multiple parameter sets with similar performances in describing the data.

Existence and stability of periodic solution of impulsive neural systems with complex deviating arguments.

This paper discusses a class of impulsive neural networks with the variable delay and complex deviating arguments. By using Mawhin's continuation theorem of coincidence degree and the Halanay-type inequalities, several sufficient conditions for impulsive neural networks are established for the existence and globally exponential stability of periodic solutions, respectively. Furthermore, the obtained results are applied to some typical impulsive neural network systems as special cases, with a real-life example to show feasibility of our results.