Complexity最新文献

This paper begins by analyzing the key mathematical properties of diffusive vaccinated models, including existence, uniqueness, positivity, and boundedness. Equilibria are identified, and the basic reproductive number is calculated. The Banach contraction mapping principle is applied to rigorously establish the solution existence and uniqueness. In order to understand the disease’s time transmission, it is important to examine the global stability of the equilibrium points. Disease-free equilibrium and endemic equilibrium are the two equilibria in this model. Here, we demonstrate that the endemic equilibrium is worldwide asymptotic stable when the basic reproductive number is greater than 1, and the disease-free equilibrium is globally asymptotic stable whenever the basic reproductive number is less than 1. Moreover, based on the Caputo fractional derivative of order and the implicit Euler’s approximation, we offered an unconditionally stable numerical solution for the resultant system. This work explores the solution of some significant population models of noninteger order using an approach known as the iterative Laplace transform. The proposed methodology is developed by effectively combining Laplace transformation with an iterative procedure. A series form solution that exhibits some convergent behavior towards the precise solution can be attained. It is noted that there is a close contact between the obtained and precise solutions. Moreover, the suggested method can handle a variety of fractional order derivative problems because it involves minimal computations. This information will be helpful in further studies to determine the ideal strategy of action for preventing or stopping the spread disease transmission.

Baroreflex is critical to maintain blood pressure homeostasis, and the quantification of baroreflex regulation function (BRF) can provide guidance for disease diagnosis, treatment, and healthcare. Current quantification of BRF such as baroreflex sensitivity cannot represent BRF systematically. From the perspective of complex systems, we regard that BRF is the emergence result of fluctuate states and interactions in physiological mechanisms. Therefore, the three-layer emergence is studied in this work, which is from physiological mechanisms to physiological indexes and then to BRF. On this basis, since the entropy in statistical physics macroscopically measures the fluctuations of system’s states, in this work, the principle of maximum entropy is adopted, and a new index called PhysioEnt is proposed to quantify the fluctuations of four physiological indexes, i.e., baroreflex sensitivity, heart rate, heart rate variability, and systolic blood pressure, which aims to represent BRF in the resting condition. Further, two datasets with different subjects are analyzed, and some new findings can be obtained, such as the contributions of the physiological interactions among organs/tissues. With measurable indexes, the proposed method is expected to support individualized medicine.

Employing an improved adaptive Type-II progressively censored sample, this paper provides various point and interval estimations when the parent distribution of the population to be studied is the inverted Lomax distribution. The estimations include both the model parameters and two reliability metrics, namely, the reliability and failure rate functions. Both maximum likelihood and maximum product of spacing are studied from the conventional estimation standpoint. Along with the point estimations utilizing the two traditional approaches, the approximate confidence intervals based on both are also examined. The Bayesian point estimations with the squared error loss function and credible intervals for various parameters are investigated. Depending on the source of observed data, Bayesian estimations are obtained using two different types of posterior distributions. Numerous censoring designs are looked at in the simulation study to compare the accuracy of classical and Bayesian estimations. Using both conventional methodologies, several optimality metrics are suggested to identify the best removal design. One chemical and a pair of engineering actual data sets are examined to support the significance of the indicated methodologies. The analysis showed that the Bayesian estimation, using the likelihood function, is preferable when compared to other classical and Bayesian methods.

Social networks are important for people to obtain information, make comments, and exchange opinions. The public opinion generated in social networks has a great impact on public life and value guidance, and the effect of public opinion is worth paying attention to and analyzing. Research on the influence of hot events can help us better understand the public attention and response to an event, and help industries and social organizations to judge market trends and predict future development direction. Social phenomena and trends reflected by hot events can be used as basic data and research objects for scientific research to promote the development and progress of the discipline. Aiming at social events in social networks, this paper analyzes the relevant user behavior data such as retweets, comments, likes, topic characteristics such as event duration, and other key characteristics and proposes an influence effectiveness analysis model for events, referred to as the caloric value model. This model is based on factors such as user interactivity, event activity, duration of the event, freshness of events,media attention, and the event heat decay ratio. It evaluates event heat, calculates the influence of events, identifies hot events with a high level of discussion, selects these hot events, and validates the findings through experiments. The model proposed in this paper has a good effect on the rationality and feasibility of heat evaluation.

In recent years, the development of metrics to evaluate image aesthetics and photographic quality has proliferated. However, validating these metrics presents challenges due to the inherently subjective nature of aesthetics and photographic quality, which can be influenced by cultural contexts and individual preferences that evolve over time. This article presents a novel validation methodology utilizing a dataset assessed by individuals from two distinct nationalities: the United States and Spain. Evaluation criteria include photographic quality and aesthetic value, with the dataset comprising images previously rated on the DPChallenge photographic portal. We analyze the correlation between these values and provide the dataset for future research endeavors. Our investigation encompasses several metrics, including BRISQUE for assessing photographic quality, NIMA aesthetic and NIMA technical for evaluating both aesthetic and technical aspects, Diffusion Aesthetics (employed in Stable Diffusion), and PhotoILike for gauging the commercial appeal of real estate images. Our findings reveal a significant correlation between the Diffusion Aesthetics metric and aesthetic measures, as well as with the NIMA aesthetics metric, suggesting them as good potential candidates to capture aesthetic value.

Taking into account the most recent improvements in graph theory and algebra, we can associate graphs of some mathematical structures with certifiable, widely known applications. This paper seeks to explore the connections established through edge labeling among Latin squares derived from Moufang quasigroups, which are constructed using additive abelian and multiplicative groups, along with their substructures and complete bipartite graphs. The algebraic characteristics of quasigroups exhibiting the antiautomorphic inverse property have been extensively examined in this study. These characteristics encompass identities associated with fixed element maps. To analyze the behavior of these groups under holomorphism, we utilize similar conditions.

Normal and aberrant cognitive functions are the result of the dynamic interplay between large-scale neural circuits. Describing the nature of these interactions has been a challenging task yet important for neurodegenerative disease evolution. Fusing modern dynamic graph network theory techniques and control theory applied on complex brain networks creates a new framework for neurodegenerative disease research by determining disease evolution at the subject level, facilitating a predictive treatment response and revealing key mechanisms responsible for disease alterations. It has been shown that two types of controllability—the average and the modal controllability—are relevant for the mechanistic explanation of how the brain navigates between cognitive states. The average controllability favors highly connected areas which move the brain to easily reachable states, while the modal controllability favors weakly connected areas representative for difficult-to-reach states. We propose two different techniques to achieve these two types of controllability: a centrality measure based on a sensitivity analysis of the Laplacian matrix is employed to determine the average controllability, while graph distances form the basis of the modal controllability. The concepts of “choosing the best driver set” and “graph distances” are applied to measure the average controllability and the modal controllability, respectively. Based on these new techniques, we obtain important disease descriptors that visualize alterations in the disease trajectory by revealing densely connected hubs or sparser areas. Our results suggest that these two techniques can accurately describe the different node roles in controlling trajectories of brain networks.

We study the existence of fixed points, local stability analysis, bifurcation sets at fixed points, codimension-one and codimension-two bifurcation analysis, and chaos control in a predator-prey model with Holling types I and III functional responses. It is proven that the model has a trivial equilibrium point for all involved parameters but interior and semitrivial equilibrium solutions under certain model parameter conditions. Furthermore, local stability at trivial, semitrivial, and interior equilibria using the theory of linear stability is investigated. We have also explored the bifurcation sets for trivial, semitrivial, and interior equilibria and proved that flip bifurcation occurs at semitrivial equilibrium. Furthermore, it is also proven that Neimark–Sacker bifurcation as well as flip bifurcation occurs at an interior equilibrium solution, and in addition, at the same equilibrium solution, we also studied codimension-two 1 : 2 strong resonance bifurcation. Then, OGY and hybrid control strategies are employed to manage chaos in the model under study, which arises from Neimark–Sacker and flip bifurcations, respectively. We have also examined the preservation of the positive solution of the understudied model. Finally, numerical simulations are given to verify the theoretical results.

This paper studies the complexity of the decision system when a brand enterprise introduces new products and makes dynamic quality decisions to cope with imitation threats caused by a counterfeit enterprise. Using game theory, nonlinear system theory, and numerical simulation, the complexity characteristics of this system and consumer utility are further discussed; moreover, delay feedback control is used to restrain chaos. The conclusions are as follows: (1) The stable scope of the brand enterprise price adjustment enlarges with the increase of the adjustment parameters of new product quality and imitation price. (2) The attraction domain of the initial decisions of the counterfeit enterprise decreases when the brand enterprise makes dynamic decisions on new product quality; a higher new product quality adjustment parameter can reduce the imitation ability of the counterfeit enterprise. (3) With the growth of the degree of substitution between new products and existing products, the quality of new products is improved, the output of existing products is reduced, and the counterfeit enterprise withdraws from the market if the degree of substitution between existing products and imitations is high. (4) The dynamic system can suppress chaos and restore stability by using the delay feedback control method. Results are of great importance for managers to make reasonable decisions when dealing with imitation threats.

Infectious diseases pose a significant threat to global health, necessitating the development of effective vaccination strategies. This study examines the dynamics of viral infections and immune responses, with a particular focus on the roles of antibodies and CD8+ T cells induced by vaccination. Through a mathematical model, we explore the intricate interactions between host cells and viruses to assess the impact of vaccination on viral replication. Our findings align with experimental results, demonstrating that vaccination substantially enhances immune responses and reduces viral replication. The contributions of both antibody and CD8+ T cell responses are shown to be vital for achieving optimal vaccine efficacy. The model’s predictions, validated against experimental observations, emphasize the need to incorporate mechanisms that induce robust immune responses in vaccine design. This study underscores the critical role of mathematical modeling in understanding immune dynamics and in refining vaccination strategies to develop more effective treatments against viral infections.