Mathematical Biosciences and Engineering最新文献

Models intended to describe the time evolution of a gene network must somehow include transcription, the DNA-templated synthesis of RNA, and translation, the RNA-templated synthesis of proteins. In eukaryotes, the DNA template for transcription can be very long, often consisting of tens of thousands of nucleotides, and lengthy pauses may punctuate this process. Accordingly, transcription can last for many minutes, in some cases hours. There is a long history of introducing delays in gene expression models to take the transcription and translation times into account. Here we study a family of detailed transcription models that includes initiation, elongation, and termination reactions. We establish a framework for computing the distribution of transcription times, and work out these distributions for some typical cases. For elongation, a fixed delay is a good model provided elongation is fast compared to initiation and termination, and there are no sites where long pauses occur. The initiation and termination phases of the model then generate a nontrivial delay distribution, and elongation shifts this distribution by an amount corresponding to the elongation delay. When initiation and termination are relatively fast, the distribution of elongation times can be approximated by a Gaussian. A convolution of this Gaussian with the initiation and termination time distributions gives another analytic approximation to the transcription time distribution. If there are long pauses during elongation, because of the modularity of the family of models considered, the elongation phase can be partitioned into reactions generating a simple delay (elongation through regions where there are no long pauses), and reactions whose distribution of waiting times must be considered explicitly (initiation, termination, and motion through regions where long pauses are likely). In these cases, the distribution of transcription times again involves a nontrivial part and a shift due to fast elongation processes.

This paper focuses on the feedback global stabilization and observer construction for a sterile insect technique model. The sterile insect technique (SIT) is one of the most ecological methods for controlling insect pests responsible for worldwide crop destruction and disease transmission. In this work, we construct a feedback law that globally asymptotically stabilizes an SIT model at extinction equilibrium. Since the application of this type of control requires the measurement of different states of the target insect population, and, in practice, some states are more difficult or more expensive to measure than others, it is important to know how to construct a state estimator, which from a few well-chosen measured states, estimates the other ones, as the one we build in the second part of our work. In the last part of our work, we show that we can apply the feedback control with estimated states to stabilize the full system.

In recent years, deep learning (DL) techniques have achieved remarkable success in various fields of computer vision. This progress was attributed to the vast amounts of data utilized to train these models, as they facilitated the learning of more intricate and detailed feature information about target objects, leading to improved model performance. However, in most real-world tasks, it was challenging to gather sufficient data for model training. Insufficient datasets often resulted in models prone to overfitting. To address this issue and enhance model performance, generalization ability, and mitigate overfitting in data-limited scenarios, image data augmentation methods have been proposed. These methods generated synthetic samples to augment the original dataset, emerging as a preferred strategy to boost model performance when data was scarce. This review first introduced commonly used and highly effective image data augmentation techniques, along with a detailed analysis of their advantages and disadvantages. Second, this review presented several datasets frequently employed for evaluating the performance of image data augmentation methods and examined how advanced augmentation techniques can enhance model performance. Third, this review discussed the applications and performance of data augmentation techniques in various computer vision domains. Finally, this review provided an outlook on potential future research directions for image data augmentation methods.

Many current electronic medical record (EMR) sharing schemes that use proxy re-encryption and blockchain do not fully consider the potential threat of malicious node impersonation attacks. This oversight could lead to data leakage as attackers masquerade as legitimate users or proxy nodes during the sharing process. To deal with this problem, we propose an EMR sharing scheme based on proxy re-encryption and blockchain to protect against impersonation attacks. First, we prevent the potential threat of impersonation attacks by generating a shared temporary key and assigning tasks to multiple proxy nodes. Second, we use a random function to ensure that the selection of encrypted proxy nodes is fair. Third, we use a combination of blockchain and the InterPlanetary File System to solve the problem of insufficient storage capacity of shared processes and ensure the storage security of EMRs. Through the security proof, our scheme guarantees anti-impersonation, anti-collusion, and anti-chosen plaintext attack capability in the sharing process of EMRs. Additionally, experiments on the blockchain platform, namely Chain33, show that our scheme significantly increases efficiency.

COVID-19 is caused by the SARS-CoV-2 virus, which has produced variants and increasing concerns about a potential resurgence since the pandemic outbreak in 2019. Predicting infectious disease outbreaks is crucial for effective prevention and control. This study aims to predict the transmission patterns of COVID-19 using machine learning, such as support vector machine, random forest, and XGBoost, using confirmed cases, death cases, and imported cases, respectively. The study categorizes the transmission trends into the three groups: L0 (decrease), L1 (maintain), and L2 (increase). We develop the risk index function to quantify changes in the transmission trends, which is applied to the classification of machine learning. A high accuracy is achieved when estimating the transmission trends for the confirmed cases (91.5-95.5%), death cases (85.6-91.8%), and imported cases (77.7-89.4%). Notably, the confirmed cases exhibit a higher level of accuracy compared to the data on the deaths and imported cases. L2 predictions outperformed L0 and L1 in all cases. Predicting L2 is important because it can lead to new outbreaks. Thus, this robust L2 prediction is crucial for the timely implementation of control policies for the management of transmission dynamics.

In this paper, we investigate an optimal harvesting problem of a spatially explicit fishery model that was previously analyzed. On the surface, this problem looks innocent, but if parameters are set to where a singular arc occurs, two complex questions arise. The first question pertains to Fuller's phenomenon (or chattering), a phenomenon in which the optimal control possesses a singular arc that cannot be concatenated with the bang-bang arcs without prompting infinite oscillations over a finite region. 1) How do we numerically assess whether or not a problem chatters in cases when we cannot analytically prove such a phenomenon? The second question focuses on implementation of an optimal control. 2) When an optimal control has regions that are difficult to implement, how can we find alternative strategies that are both suboptimal and realistic to use? Although the former question does not apply to all optimal harvesting problems, most fishery managers should be concerned about the latter. Interestingly, for this specific problem, our techniques for answering the first question results in an answer to the the second. Our methods involve using an extended version of the switch point algorithm (SPA), which handles control problems having initial and terminal conditions on the states. In our numerical experiments, we obtain strong empirical evidence that the harvesting problem chatters, and we find three alternative harvesting strategies with fewer switches that are realistic to implement and near optimal.

In this work, we investigated the finite-time passivity problem of neutral-type complex-valued neural networks with time-varying delays. On the basis of the Lyapunov functional, Wirtinger-type inequality technique, and linear matrix inequalities (LMIs) approach, new sufficient conditions were derived to ensure the finite-time boundedness (FTB) and finite-time passivity (FTP) of the concerned network model. At last, two numerical examples with simulations were presented to demonstrate the validity of our criteria.

Due to the complexity of the driving environment and the dynamics of the behavior of traffic participants, self-driving in dense traffic flow is very challenging. Traditional methods usually rely on predefined rules, which are difficult to adapt to various driving scenarios. Deep reinforcement learning (DRL) shows advantages over rule-based methods in complex self-driving environments, demonstrating the great potential of intelligent decision-making. However, one of the problems of DRL is the inefficiency of exploration; typically, it requires a lot of trial and error to learn the optimal policy, which leads to its slow learning rate and makes it difficult for the agent to learn well-performing decision-making policies in self-driving scenarios. Inspired by the outstanding performance of supervised learning in classification tasks, we propose a self-driving intelligent control method that combines human driving experience and adaptive sampling supervised actor-critic algorithm. Unlike traditional DRL, we modified the learning process of the policy network by combining supervised learning and DRL and adding human driving experience to the learning samples to better guide the self-driving vehicle to learn the optimal policy through human driving experience and real-time human guidance. In addition, in order to make the agent learn more efficiently, we introduced real-time human guidance in its learning process, and an adaptive balanced sampling method was designed for improving the sampling performance. We also designed the reward function in detail for different evaluation indexes such as traffic efficiency, which further guides the agent to learn the self-driving intelligent control policy in a better way. The experimental results show that the method is able to control vehicles in complex traffic environments for self-driving tasks and exhibits better performance than other DRL methods.

This study investigated how permanent charges influence the dynamics of ionic channels. Using a quasi-one-dimensional classical Poisson-Nernst-Planck (PNP) model, we investigated the behavior of two distinct ion species-one positively charged and the other negatively charged. The spatial distribution of permanent charges was characterized by zero values at the channel ends and a constant charge $ Q_0 $ within the central region. By treating the classical PNP model as a boundary value problem (BVP) for a singularly perturbed system, the singular orbit of the BVP depended on $ Q_0 $ in a regular way. We therefore explored the solution space in the presence of a small permanent charge, uncovering a systematic dependence on this parameter. Our analysis employed a rigorous perturbation approach to reveal higher-order effects originating from the permanent charges. Through this investigation, we shed light on the intricate interplay among boundary conditions and permanent charges, providing insights into their impact on the behavior of ionic current, fluxes, and flux ratios. We derived the quadratic solutions in terms of permanent charge, which were notably more intricate compared to the linear solutions. Through computational tools, we investigated the impact of these quadratic solutions on fluxes, current-voltage relations, and flux ratios, conducting a thorough analysis of the results. These novel findings contributed to a deeper comprehension of ionic flow dynamics and hold potential implications for enhancing the design and optimization of ion channel-based technologies.

This article considered the sampled-data control issue for a dynamic positioning ship (DPS) with the Takagi-Sugeno (T-S) fuzzy model. By introducing new useful terms such as second-order term of time, an improved Lyapunov-Krasovskii function (LKF) was constructed. Additionally, the reciprocally convex method is introduced to bound the derivative of LKF. According to the constructed LKF, the sampling information during the whole sampling period was fully utilized, and less conservatism was obtained. Then, the stability condition, robust performance, mode uncertainty and sampled-data controller design were analyzed by means of the linear matrix inequality (LMI). Finally, an example was given to demonstrate the effectiveness of the proposed method.