Software reliability model for open-source software that considers the number of finite faults and dependent faults

Software has become a vital factor in the fourth industrial revolution. Owing to the increase in demand for software products in various fields (big data, artificial intelligence, the Internet of Things, etc.), the software industry has expanded more than ever before. Therefore, software reliability has become very important, and efforts are being made to increase it. One of these efforts is the development of software reliability models (SRMs). SRMs have been studied for a long time as a model that predicts software reliability by using the number of software faults. Software failures can occur for several reasons, including independent software faults such as code errors and software hangs, as well as dependent cases where code errors lead to other software faults. Recently, due to the diversity of software operating environments, software faults are more likely to occur in a dependent manner, and, for this reason, they are likely to increase rapidly from the beginning and progress slowly to the maximum number thereafter. In addition, many large companies have focused on open-source software (OSS) development, and OSS is being developed by many users. In this study, we propose a new SRM that considers the number of finite faults and dependent faults, and examine the goodness-of-fit of a new SRM and other existing non-homogeneous Poisson process models based on the OSS datasets. Through numerical examples, the proposed model demonstrated a significantly better goodness-of-fit when compared to other existing models, and it also exhibited better results on the newly proposed integrated criteria.

Data suggested hospitalization as critical indicator of the severity of the COVID-19 pandemic, even at its early stages

COVID-19 has been spreading widely since January 2020, prompting the implementation of non-pharmaceutical interventions and vaccinations to prevent overwhelming the healthcare system. Our study models four waves of the epidemic in Munich over two years using a deterministic, biology-based mathematical model of SEIR type that incorporates both non-pharmaceutical interventions and vaccinations. We analyzed incidence and hospitalization data from Munich hospitals and used a two-step approach to fit the model parameters: first, we modeled incidence without hospitalization, and then we extended the model to include hospitalization compartments using the previous estimates as a starting point. For the first two waves, changes in key parameters, such as contact reduction and increasing vaccinations, were enough to represent the data. For wave three, the introduction of vaccination compartments was essential. In wave four, reducing contacts and increasing vaccinations were critical parameters for controlling infections. The importance of hospitalization data was highlighted, as it should have been included as a crucial parameter from the outset, along with incidence, to avoid miscommunication with the public. The emergence of milder variants like Omicron and a significant proportion of vaccinated people has made this fact even more evident.

Does freelancing have a future? Mathematical analysis and modeling

During the past few years, freelancing has grown exponentially due to the pandemic and subsequent economical changes in the world. In fact, in the last ten years, a drastic increase in freelancing has been observed; people quit their jobs to be their own boss. There are various reasons for this: downsizing of employees, not having fun in their jobs, unemployment, part time work to earn more, etc. Observing this vast change, many individuals on Facebook/YouTube, NGOs, and government departments started teaching freelancing as a course; to date, thousands of youngsters have been trained to start their careers as freelancers. It has been observed that the ratio of informed freelancers is more successful than those who start their careers independently. We construct a compartmental model to explore the influence of information on the expansion of freelancing in this article, which was motivated by this surge in freelancing. Following that, the model is subjected to dynamical analysis utilizing dynamical systems and differential equation theory. To validate our analytical conclusions, we used numerical simulation.

Neural network approach to data-driven estimation of chemotactic sensitivity in the Keller-Segel model

We consider the mathematical model of chemotaxis introduced by Patlak, Keller, and Segel. Aggregation and progression waves are present everywhere in the population dynamics of chemotactic cells. Aggregation originates from the chemotaxis of mobile cells, where cells are attracted to migrate to higher concentrations of the chemical signal region produced by themselves. The neural net can be used to find the approximate solution of the PDE. We proved that the error, the difference between the actual value and the predicted value, is bound to a constant multiple of the loss we are learning. Also, the Neural Net approximation can be easily applied to the inverse problem. It was confirmed that even when the coefficient of the PDE equation was unknown, prediction with high accuracy was achieved.

Calculating all multiple parameter solutions of ODE models to avoid biological misinterpretations

Biological system's dynamics are increasingly studied with nonlinear ordinary differential equations, whose parameters are estimated from input/output experimental data. Structural identifiability analysis addresses the theoretical question whether the inverse problem of recovering the unknown parameters from noise-free data is uniquely solvable (global), or if there is a finite (local), or an infinite number (non identifiable) of parameter values that generate identical input/output trajectories. In contrast, practical identifiability analysis aims to assess whether the experimental data provide information on the parameter estimates in terms of precision and accuracy. A main difference between the two identifiability approaches is that the former is mostly carried out analytically and provides exact results at a cost of increased computational complexity, while the latter is usually numerically tested by calculating statistical confidence regions and relies on decision thresholds. Here we focus on local identifiability, a critical issue in biological modeling. This is the case when a model has multiple parameter solutions which equivalently describe the input/output data, but predict different behaviours of the unmeasured variables, often those of major interest. We present theoretical background and applications to locally identifiable ODE models described by rational functions. We show how structural identifiability analysis completes the practical identifiability results. In particular we propose an algorithmic approach, implemented with our software DAISY, to calculate all numerical parameter solutions and to predict the corresponding behaviour of the unmeasured variables, which otherwise would remain hidden. A case study of a locally identifiable HIV model shows that one should be aware of the presence of multiple parameter solutions to comprehensively describe the biological system and avoid biological misinterpretation of the results.

A genetic regulatory network based method for multi-objective sequencing problem in mixed-model assembly lines

This research proposes a genetic regulatory network based sequencing method that minimizes multiple objectives including utility work costs, production rate variation costs and setup costs in mixed-model assembly lines. After constructing mathematical model of this multi-objective sequencing problem, the proposed method generates a set of genes to represent the decision variables and develops a gene regulation equation to describe decision variable interactions composed of production constraints and some validated sequencing rules. Moreover, a gene expression procedure that determines each gene's expression state based on the gene regulation equation is designed. This enables the generation of a series of problem solutions by indicating decision variable values with related gene expression states, and realizes the minimization of weighted sum of multiple objectives by applying a regulatory parameter optimization mechanism in regulation equations. The proposed genetic regulatory network based sequencing method is validated through a series of comparative experiments, and the results demonstrate its effectiveness over other methods in terms of solution quality, especially for industrial instances collected from a diesel engine assembly line.