Bifurcation and Turing Pattern Formation in a Diffusion Modified Leslie-Gower Predator-Prey Model with Crowley-Martin Functional Response

In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term. Firstly, for ODE model, the local stability of equilibrium point is given. And by using bifurcation theory and selecting suitable bifurcation parameters, we find many kinds of bifurcation phenomena, including Transcritical bifurcation and Hopf bifurcation. For the reaction-diffusion model, we find that Turing instability occurs. Besides, it is proved that Hopf bifurcation exists in the model. Finally, numerical simulations are presented to verify and illustrate the theoretical results.

A Comprehensive Survey of Recent Transformers in Image,Video and Diffusion Models

Transformer models have emerged as dominant networks for various tasks in computer vision compared to Convolutional Neural Networks(CNNs).The transformers demonstrate the ability to model long-range dependencies by utilizing a self-attention mechanism.This study aims to provide a comprehensive survey of recent transformerbased approaches in image and video applications,as well as diffusion models.We begin by discussing existing surveys of vision transformers and comparing them to this work.Then,we review the main components of a vanilla transformer network,including the self-attention mechanism,feed-forward network,position encoding,etc.In the main part of this survey,we review recent transformer-based models in three categories:Transformer for downstream tasks,Vision Transformer for Generation,and Vision Transformer for Segmentation.We also provide a comprehensive overview of recent transformer models for video tasks and diffusion models.We compare the performance of various hierarchical transformer networks for multiple tasks on popular benchmark datasets.Finally,we explore some future research directions to further improve the field.

A multilayer network diffusion-based model for reviewer recommendation

With the rapid growth of manuscript submissions,finding eligible reviewers for every submission has become a heavy task.Recommender systems are powerful tools developed in computer science and information science to deal with this problem.However,most existing approaches resort to text mining techniques to match manuscripts with potential reviewers,which require high-quality textual information to perform well.In this paper,we propose a reviewer recommendation algorithm based on a network diffusion process on a scholar-paper multilayer network,with no requirement for textual information.The network incorporates the relationship of scholar-paper pairs,the collaboration among scholars,and the bibliographic coupling among papers.Experimental results show that our proposed algorithm outperforms other state-of-the-art recommendation methods that use graph random walk and matrix factorization and methods that use machine learning and natural language processing,with improvements of over 7.62%in recall,5.66%in hit rate,and 47.53%in ranking score.Our work sheds light on the effectiveness of multilayer network diffusion-based methods in the reviewer recommendation problem,which will help to facilitate the peer-review process and promote information retrieval research in other practical scenes.

Research on Restoration of Murals Based on Diffusion Model and Transformer

Due to the limitations of a priori knowledge and convolution operation,the existing image restoration techniques cannot be directly applied to the cultural relics mural restoration,in order to more accurately restore the original appearance of the cultural relics mural images,an image restoration based on the denoising diffusion probability model(Denoising Diffusion Probability Model(DDPM))and the Transformer method.The process involves two steps:in the first step,the damaged mural image is firstly utilized as the condition to generate the noise image,using the time,condition and noise image patch as the inputs to the noise prediction network,capturing the global dependencies in the input sequence through the multi-attentionmechanismof the input sequence and feedforward neural network processing,and designing a long skip connection between the shallow and deep layers in the Transformer blocks between the shallow and deep layers using long skip connections to fuse the feature information of global and local outputs to maintain the overall consistency of the restoration results;In the second step,taking the noisy image as a condition to direct the diffusion model to back sample to generate the restored image.Experiment results show that the PSNR and SSIM of the proposedmethod are improved by 2%to 9%and 1%to 3.3%,respectively,which are compared to the comparison methods.This study proposed synthesizes the advantages of the diffusionmodel and deep learningmodel to make themural restoration results more accurate.

SeisResoDiff: Seismic resolution enhancement based on a diffusion model

High resolution of post-stack seismic data assists in better interpretation of subsurface structures as well as high accuracy of impedance inversion. Therefore, geophysicists consistently strive to acquire higher resolution seismic images in petroleum exploration. Although there have been successful applications of conventional signal processing and machine learning for post-stack seismic resolution enhancement,there is limited reference to the seismic applications of the recent emergence and rapid development of generative artificial intelligence. Hence, we propose to apply diffusion models, among the most popular generative models, to enhance seismic resolution. Specifically, we apply the classic diffusion model—denoising diffusion probabilistic model(DDPM), conditioned on the seismic data in low resolution, to reconstruct corresponding high-resolution images. Herein the entire scheme is referred to as SeisResoDiff. To provide a comprehensive and clear understanding of SeisResoDiff, we introduce the basic theories of diffusion models and detail the optimization objective's derivation with the aid of diagrams and algorithms. For implementation, we first propose a practical workflow to acquire abundant training data based on the generated pseudo-wells. Subsequently, we apply the trained model to both synthetic and field datasets, evaluating the results in three aspects: the appearance of seismic sections and slices in the time domain, frequency spectra, and comparisons with the synthetic data using real well-logging data at the well locations. The results demonstrate not only effective seismic resolution enhancement,but also additional denoising by the diffusion model. Experimental comparisons indicate that training the model on noisy data, which are more realistic, outperforms training on clean data. The proposed scheme demonstrates superiority over some conventional methods in high-resolution reconstruction and denoising ability, yielding more competitive results compared to our previous research.

Dynamics modeling and optimal control for multi-information diffusion in Social Internet of Things

As an ingenious convergence between the Internet of Things and social networks,the Social Internet of Things(SIoT)can provide effective and intelligent information services and has become one of the main platforms for people to spread and share information.Nevertheless,SIoT is characterized by high openness and autonomy,multiple kinds of information can spread rapidly,freely and cooperatively in SIoT,which makes it challenging to accurately reveal the characteristics of the information diffusion process and effectively control its diffusion.To this end,with the aim of exploring multi-information cooperative diffusion processes in SIoT,we first develop a dynamics model for multi-information cooperative diffusion based on the system dynamics theory in this paper.Subsequently,the characteristics and laws of the dynamical evolution process of multi-information cooperative diffusion are theoretically investigated,and the diffusion trend is predicted.On this basis,to further control the multi-information cooperative diffusion process efficiently,we propose two control strategies for information diffusion with control objectives,develop an optimal control system for the multi-information cooperative diffusion process,and propose the corresponding optimal control method.The optimal solution distribution of the control strategy satisfying the control system constraints and the control budget constraints is solved using the optimal control theory.Finally,extensive simulation experiments based on real dataset from Twitter validate the correctness and effectiveness of the proposed model,strategy and method.

A turbulent mass diffusivity model for analyzing the mixing characteristics in an impinging stream-rotating packed bed

In this study,the fluid flow and mixing process in an impinging stream-rotating packed bed(IS-RPB)is simulated by using a new three-dimensional computational fluid dynamics model.Specifically,the gaseliquid flow is simulated by the Euler-Euler model,the hydrodynamics of the reactor is predicted by the RNG k-εmethod,and the high-gravity environment is simulated by the sliding mesh model.The turbulent mass transfer process is characterized by the concentration variance c^(2) and its dissipation rateεc formulations,and therefore the turbulent mass diffusivity can be directly obtained.The simulated segregation index Xs is in agreement with our previous experimental results.The simulated results reveal that the fringe effect of IS can be offset by the end effect at the inner radius of RPB,so the investigation of the coupling mechanism between IS and RPB is critical to intensify the mixing process in IS-RPB.

2-D Modeling and Calculations of Stratospheric Ozone and Influences of Convection, Diffusion, and Time

An engineering system approach of 2-D cylindrical model of transient mass balance calculations of ozone and other concerned chemicals along with fourteen photolysis, ozone-generating and ozone-depleting chemical reaction equations was developed, validated, and used for studying the ozone concentrations, distribution and peak of the layer, ozone depletion and total ozone abundance in the stratosphere. The calculated ozone concentrations and profile at both the Equator and a 60˚N location were found to follow closely with the measured data. The calculated average ozone concentration was within 1% of the measured average, and the deviation of ozone profiles was within 14%. The monthly evolution of stratospheric ozone concentrations and distribution above the Equator was studied with results discussed in details. The influences of slow air movement in both altitudinal and radial directions on ozone concentrations and profile in the stratosphere were explored and discussed. Parametric studies of the influences of gas diffusivities of ozone DO3 and active atomic oxygen DO on ozone concentrations and distributions were also studied and delineated. Having both influences through physical diffusion and chemical reactions, the diffusivity (and diffusion) of atomic oxygen DO was found to be more sensitive and important than that of ozone DO3 on ozone concentrations and distribution. The 2-D ozone model present in this paper for stratospheric ozone and its layer and depletion is shown to be robust, convenient, efficient, and executable for analyzing the complex ozone phenomena in the stratosphere. .

BeFOI: A Novel Method Based on Conditional Diffusion Model for Medical Image Denoising

The progress in medical imaging technology highlights the importance of image quality for effective diagnosis and treatment.Yet,noise during capture and transmission can compromise image accuracy and reliability,complicating clinical decisions.The rising interest in diffusion models has led to their exploration of denoising images.We present Be-FOI(Better Fluoro Images),a weakly supervised model that uses cine images to denoise fluoroscopic images,both DR types.Trained through precise noise estimation and simulation,BeFOI employs Markov chains to denoise using only the fluoroscopic image as guidance.Our tests show that BeFOI outperforms other methods,reducing noise and enhancing clar-ity and diagnostic utility,making it an effective post-processing tool for medical images.

Diffusive modelling of glioma evolution: a review

Gliomas, the most aggressive form of brain cancer, are known for their widespread invasion into the tissue near the tumor lesion. Exponential models, which have been widely used in other types of cancers, cannot be used for the simulation of tumor growth, due to the diffusive behavior of glioma. Diffusive models that have been proposed in the last two decades seem to better approximate the expansion of gliomas. This paper covers the history of glioma diffusive modelling, starting from the simplified initial model in 90s and describing how this have been enriched to take into account heterogenous brain tissue, anisotropic migration of glioma cells and adjustable proliferation rates. Especially, adjustable proliferation rates are very important for modelling therapy plans and personalising therapy to different patients.

Existence of Forced Waves and Their Asymptotic for Leslie-Gower Prey-Predator Model with Nonlocal Effects under Shifting Environment

In this paper, we prove the existence of forced waves for Leslie-Gower prey-predator model with nonlocal effects under shifting environment. By constructing a pair of upper and lower solutions with the method of monotone iteration, we can obtain the existence of forced waves for any positive constant shifting speed. Finally, we show the asymptotical behavior of traveling wave fronts in two tails.

带有食饵避难的Leslie-Gower捕食者-食饵扩散系统的稳定性及最优税收

研究了齐次Neumann边界条件下反应扩散对一类食饵具有避难所的LeslieGower模型的影响.利用Routh-Hurwitz判别法判断平衡点的局部稳定性,通过构造合适的Lyapunov函数得到了正平衡点全局渐进稳定的充分性条件,根据Pontryagin最大值原理得到了模型的最优税收策略.

食饵有强弱之分的Leslie-Gower捕食者-食饵扩散模型的稳定性

考虑食饵有强弱之分的Leslie-Gower捕食者-食饵扩散模型(LGM)的稳定性与不稳定性.首先,通过线性化方法和构造Lyapunov函数证明仅带线性自扩散模型(LGM)的正平衡点的局部以及全局渐近稳定性;然后,给出交错扩散导致Turing不稳定的一个充分条件.

一类修正Leslie-Gower项捕食扩散系统的稳定性

研究了具有修正Leslie-Gower项和HollingⅡ类功能反应函数的捕食-食饵扩散系统的动力学性质,利用Neumann齐次边值问题和抛物型方程的比较原理,讨论了该系统存在唯一正的平衡位置的局部与全局稳定性。

Dynamic vaccine distribution model based on epidemic diffusion rule and clustering approach

Due to the fact that the emergency medicine distribution is vital to the quick response to urgent demand when an epidemic occurs, the optimal vaccine distribution approach is explored according to the epidemic diffusion rule and different urgency degrees of affected areas with the background of the epidemic outbreak in a given region. First, the SIQR （susceptible, infected, quarantined,recovered） epidemic model with pulse vaccination is introduced to describe the epidemic diffusion rule and obtain the demanded vaccine in each pulse. Based on the SIQR model, the affected areas are clustered by using the self-organizing map （SOM） neutral network to qualify the results. Then, a dynamic vaccine distribution model is formulated, incorporating the results of clustering the affected areas with the goals of both reducing the transportation cost and decreasing the unsatisfied demand for the emergency logistics network. Numerical study with twenty affected areas and four distribution centers is carried out. The corresponding numerical results indicate that the proposed approach can make an outstanding contribution to controlling the affected areas with a relatively high degree of urgency, and the comparison results prove that the performance of the clustering method is superior to that of the non-clustering method on controlling epidemic diffusion.

Constitutive model for methane desorption and diffusion based on pore structure differences between soft and hard coal

This paper aims to improve the accuracy and applicability of gas diffusion mathematical models from coal particles. Firstly, a new constitutive model for gas diffusion from coal particles with tri-disperse pore structure is constructed by considering the difference in characteristics between soft coal and hard coal.The analytical solution is then derived, that is, the quantitative relationship between gas diffusion rate(Qt/Q_∞) and diffusion time(t), The pore structure parameters of soft coal and hard coal from Juji coal mine are determined. Gas diffusion rules are numerically calculated and investigated by physical simulation methods. Lastly, the applicability of this model is verified. The results show that the homogeneous model only applies to the gas diffusion process of hard coal during the initial 10 min. The calculation results from this model and the physical experimental results of soft coal and hard coal are nearly identical during the initial 30 min.

A Three-Dimensional Model of Transport and Diffusion of Seeding Agents within Stratus

It is essential to learn the temporal and spatial concentration distributions and variations of seeding agents in cloud seeding of precipitation enhancement. A three-dimensional puff trajectory model incorporating a mesoscale nonhydrostatic model has been formulated, and is applied to simulating the transporting and diffusive characteristics of multiple line sources of seeding agents within super-cooled stratus. Several important factors are taken into consideration that affect the diffusion of seeding materials such as effects of topography and vertical wind shear, temporal and spatial variation of seeding parameters and wet deposition. The particles of seeding agents are assumed to be almost inert, they have no interaction with the particles of the cloud or precipitation except that they are washed out by precipitation. The model validity is demonstrated by the analyses and comparisons of model results, and checked by the sensitivity experiments of diffusive coefficients and atmospheric stratification. The advantage of this model includes not only its exact reflection of heterogeneity and unsteadiness of background fields, but also its good simulation of transport and diffusion of multiple line sources. The horizontal diffusion rate and the horizontal transport distance have been proposed that they usually were difficult to obtain in other models. In this simulation the horizontal diffusion rate is 0.82 m s(-1) for average of one hour, and the horizontal average transport distance reaches 65 km after 1 4 which are closely related to the background Fields.

A novel diffusion model considering curvature radius at the bonding interface in a titanium/steel explosive clad plate

This article introduces an element diffusion behavior model for a titanium/steel explosive clad plate characterized by a typical curved interface during the heat-treatment process. A series of heat-treatment experiments were conducted in the temperature range from 750℃ to 950℃, and the effects of heat-treatment parameters on the microstructural evolution and diffusion behavior were investigated by optical microscopy, scanning electron microscopy, X-ray diffraction analysis, and electron-probe microanalysis. Carbon atoms within the steel matrix were observed to diffuse toward the titanium matrix and to aggregate at the bonding interface at 850℃ or lower; in contrast, when the temperature exceeded 850℃, the mutual diffusion of Ti and Fe occurred, along with the diffusion of C atoms, resulting in the for- marion of Ti-Fe intermetallics （Fe2Ti/FeTi）. The diffusion distances of C, Ti, and Fe atoms increased with increasing heating temperature and/or holding time. On the basis of this diffusion behavior, a novel diffusion model was proposed. This model considers the effects of various factors, including the curvature radius of the curved interface, the diffusion coefficient, the heating temperature, and the holding rime. The experimental results show good agreement with the calculated values. The proposed model could clearly provide a general prediction of the elements＇ diffusion at both straight and curved interfaces.

OPTIMAL HARVESTING POLICY FOR INSHORE-OFFSHORE FISHERY MODEL WITH IMPULSIVE DIFFUSION

This article studies the inshore-offshore fishery model with impulsive diffusion. The existence and global asymptotic stability of both the trivial periodic solution and the positive periodic solution are obtained. The complexity of this system is also analyzed. Moreover, the optimal harvesting policy are given for the inshore subpopulation, which includes the maximum sustainable yield and the corresponding harvesting effort.