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.

A Numerical Algorithm Based on Quadratic Finite Element for Two-Dimensional Nonlinear Time Fractional Thermal Diffusion Model

In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+
t2)is obtained,which is verified by the numerical results.

A Fractional Drift Diffusion Model for Organic Semiconductor Devices

Because charge carriers of many organic semiconductors(OSCs)exhibit fractional drift diffusion(Fr-DD)transport properties,the need to develop a Fr-DD model solver becomes more apparent.However,the current research on solving the governing equations of the Fr-DD model is practically nonexistent.In this paper,an iterative solver with high precision is developed to solve both the transient and steady-state Fr-DD model for organic semiconductor devices.The Fr-DD model is composed of two fractionalorder carriers(i.e.,electrons and holes)continuity equations coupled with Poisson’s equation.By treating the current density as constants within each pair of consecutive grid nodes,a linear Caputo’s fractional-order ordinary differential equation(FrODE)can be produced,and its analytic solution gives an approximation to the carrier concentration.The convergence of the solver is guaranteed by implementing a successive over-relaxation(SOR)mechanism on each loop of Gummel’s iteration.Based on our derivations,it can be shown that the Scharfetter–Gummel discretization method is essentially a special case of our scheme.In addition,the consistency and convergence of the two core algorithms are proved,with three numerical examples designed to demonstrate the accuracy and computational performance of this solver.Finally,we validate the Fr-DD model for a steady-state organic field effect transistor(OFET)by fitting the simulated transconductance and output curves to the experimental data.

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.

TendiffPure:a convolutional tensor-train denoising diffusion model for purification

Diffusion models are effective purification methods,where the noises or adversarial attacks are removed using generative approaches before pre-existing classifiers conducting classification tasks.However,the efficiency of diffusion models is still a concern,and existing solutions are based on knowledge distillation which can jeopardize the generation quality because of the small number of generation steps.Hence,we propose TendiffPure as a tensorized and compressed diffusion model for purification.Unlike the knowledge distillation methods,we directly compress U-Nets as backbones of diffusion models using tensor-train decomposition,which reduces the number of parameters and captures more spatial information in multi-dimensional data such as images.The space complexity is reduced from O(N^(2))to O(NR^(2))with R≤4 as the tensor-train rank and N as the number of channels.Experimental results show that TendiffPure can more efficiently obtain high-quality purification results and outperforms the baseline purification methods on CIFAR-10,Fashion-MNIST,and MNIST datasets for two noises and one adversarial attack.

Numerical Simulation of Diffusion Type Traffic Flow Model Using Second-Order Lax-Wendroff Scheme Based on Exponential Velocity Density Function

In order to control traffic congestion, many mathematical models have been used for several decades. In this paper, we study diffusion-type traffic flow model based on exponential velocity density relation, which provides a non-linear second-order parabolic partial differential equation. The analytical solution of the diffusion-type traffic flow model is very complicated to approximate the initial density of the Cauchy problem as a function of x from given data and it may cause a huge error. For the complexity of the analytical solution, the numerical solution is performed by implementing an explicit upwind, explicitly centered, and second-order Lax-Wendroff scheme for the numerical solution. From the comparison of relative error among these three schemes, it is observed that Lax-Wendroff scheme gives less error than the explicit upwind and explicit centered difference scheme. The numerical, analytical analysis and comparative result discussion bring out the fact that the Lax-Wendroff scheme with exponential velocity-density relation of diffusion type traffic flow model is suitable for the congested area and shows a better fit in traffic-congested regions.

An innovation diffusion model for consumer durables with three parameters

Strategic innovation diffusion converts newly created knowledge into increasing a firm’s value primarily through innovative product offerings.In this paper,we present a time-based adoption pattern with pricing and promotional expenditure as a three-dimensional innovation diffusion model(3D-IDM).In our proposed 3D-IDM,we assume that value of the product plays a crucial role of being the major driver of diffusion,and is classified into the following three main factors:(1)continuation time of the product in the market–representing goodwill of the product;(2)price of the product–indicating consumers’buying behaviour;and(3)marketing efforts of the firm.A special form of the Cobb–Douglas production function is used to design the three-dimensional framework.An empirical study is performed on number of consumer-durable sales data to validate and compare the proposed model.Various performance measures are treated uniquely using the Mahalanobis distance-based approach(DBA)to determine the relative strength of each model.

Diffusion analysis and modeling of kinetic behavior for treatment of brine water using electrodialysis process

In this study,the removal of monovalent and divalent cations,Nat,Kt,Mg2t,and Ca2t,in a diluted solution from Chott-El Jerid Lake,Tunisia,was investigated with the electrodialysis technique.The process was tested using two cation-exchange membranes:sulfonated polyether sulfone cross-linked with 10%hexamethylenediamine(HEXCl)and sulfonated polyether sulfone grafted with octylamine(S-PESOS).The commercially available membrane Nafion®was used for comparison.The results showed that Nafion®and S-PESOS membranes had similar removal behaviors,and the investigated cations were ranked in the following descending order in terms of their demineralization rates:Nat>Ca2t>Mg2t>Kt.Divalent cations were more effectively removed by HEXCl than by monovalent cations.The plots based on the WebereMorris model showed a strong linearity.This reveals that intra-particle diffusion was not the removal rate-determining step,and the removal process was controlled by two or more concurrent mechanisms.The Boyd plots did not pass through their origin,and the sole controlling step was determined by film-diffusion resistance,especially after a long period of electrodialysis.Additionally,a semi-empirical model was established to simulate the temporal variation of the treatment process,and the physical significance and values of model parameters were compared for the three membranes.The findings of this study indicate that HEXCl and S-PESOS membranes can be efficiently utilized for water softening,especially when effluents are highly loaded with calcium and magnesium ions.

Convection–Diffusion Model for the Prediction of Anthropogenically-Initiated Wildfire Ignition

A spatial interaction model to predict anthropogenically-initiated accidental and incendiary wildfire ignition probability is developed using fluid flow analogies for human movement patterns. Urban areas with large populations are identified as the sites of global influencing factors, and are modeled as the gravity term. The transportation corridors are identified as local influencing factors, and are modeled using fluid flow analogy as diffusion and convection terms. The model is implemented in ArcGIS, and applied for the prediction of wildfire hazard distribution in southeastern Mississippi. The model shows87 % correlation with historic data in the winter season,whereas the previously developed gravity model shows only 75 % correlation. The normalized error for convection–diffusion model predictions is about 5 % in the winter season, whereas the gravity model shows an error of 7 %.The proposed model is robust as it couples a multi-criteria behavioral pattern within a single dynamic equation to enhance predictive capability. At the same time, the proposed model is more costly than the gravity model as it requires evaluation of distance from intermodal transportation corridors, transportation corridor density, and traffic volume maps. Nonetheless, the model is developed in a modular fashion, such that either global or local terms can be neglected if required.

A Diffusion Model for Optimal Dividend Payment and Risk Control for a Firm under Consideration of the Time Value of Ruin

In this paper,we investigate a model for an insurance company with constraint on risk control.The objective of the insurer is to find a business policy and a dividend payment scheme so as to maximize the expected discounted value of dividend payment,and the expected present value of an amount which the insurer earns until the time of ruin.By solving the constrained Hamilton-Jacobi-Bellman equation,we obtain the explicit expression for value function and the corresponding optimal strategies.

Study on Opioids Diffusion Based on Improved SIR Model

The abuse of opioids is harmful to the national economy and health.The U.S.government has spent a lot of time,energy and money to deal with this phenomenon.Based on the topic background and team discussion,we deeply excavated the data and information provided in the topic,determined the current use of opioids,and constructed an improved SIR model to determine the source of drug abuse,the mechanism of drug abuse diffusion and the origin of each state through reverse derivation,which provided guidance for the government in the context of opioid abuse.Based on the above results,we simulated and analyzed the improved SIR model and determined the accuracy and stability of the model in the data set.

Dynamics of the HBV model with diffusion and time delay

Chronic hepatitis B infection is a major health problem,with approximately 350 million virus carriers worldwide.In Africa,about 30%-60% of children and 60%-100% of adults have

Mathematical Modelling for the Diffusional Release of a Dispersed Solute from a Cylindrical Polymer Matrix into Finite External Volume

An exact solution has been obtained for the release kinetics of a solute from a cylindrical non-erodible polymeric matrix into a finite external volume when the initial solute loading is greater than the solubility limit in the matrix. The moving boundary solution is derived based on the combination of variable method. The formulas of the moving boundary and the fractional solute release are given. The moving boundary and the fractional solute release profiles have been calculated at various solute loading levels and different external volumes. The obtained results show that as the external fluid volume increases, the fractional release at any time and the maximum fractional release increase. In addition, for a given external volume, as initial drug loading increases, the fractional release at any time decreases.

Diffusionmodels for time-series applications: a survey

Diffusion models, a family of generative models based on deep learning, have become increasinglyprominent in cutting-edge machine learning research. With distinguished performance in generating samples thatresemble the observed data, diffusion models are widely used in image, video, and text synthesis nowadays. Inrecent years, the concept of diffusion has been extended to time-series applications, and many powerful models havebeen developed. Considering the deficiency of a methodical summary and discourse on these models, we providethis survey as an elementary resource for new researchers in this area and to provide inspiration to motivate futureresearch. For better understanding, we include an introduction about the basics of diffusion models. Except forthis, we primarily focus on diffusion-based methods for time-series forecasting, imputation, and generation, andpresent them, separately, in three individual sections. We also compare different methods for the same applicationand highlight their connections if applicable. Finally, we conclude with the common limitation of diffusion-basedmethods and highlight potential future research directions.

A rapid and accurate direct measurement method of underground coal seam gas content based on dynamic diffusion theory

Coal seam gas content is frequently measured in quantity during underground coal mining operation and coalbed methane(CBM)exploration as a significant basic parameter.Due to the calculation error of lost gas and residual gas in the direct method,the efficiency and accuracy of the current methods are not inadequate to the large area multi-point measurement of coal seam gas content.This paper firstly deduces a simplified theoretical dynamic model for calculating lost gas based on gas dynamic diffusion theory.Secondly,the effects of various factors on gas dynamic diffusion from coal particle are experimentally studied.And sampling procedure of representative coal particle is improved.Thirdly,a new estimation method of residual gas content based on excess adsorption and competitive adsorption theory is proposed.The results showed that the maximum error of calculating the losing gas content by using the new simplified model is only 4%.Considering the influence of particle size on gas diffusion law,the particle size of the collected coal sample is below 0.25 mm,which improves the measurement speed and reflects the safety representativeness of the sample.The determination time of gas content reduced from 36 to 3 h/piece.Moreover,the absolute error is 0.15–0.50 m^3/t,and the relative error is within 5%.A new engineering method for determining the coal seam gas content is developed according to the above research.

OPTIMAL CONTROL OF A POPULATION DYNAMICS MODEL WITH HYSTERESIS

This paper addresses a nonlinear partial differential control system arising in population dynamics.The system consist of three diffusion equations describing the evolutions of three biological species:prey,predator,and food for the prey or vegetation.The equation for the food density incorporates a hysteresis operator of generalized stop type accounting for underlying hysteresis effects occurring in the dynamical process.We study the problem of minimization of a given integral cost functional over solutions of the above system.The set-valued mapping defining the control constraint is state-dependent and its values are nonconvex as is the cost integrand as a function of the control variable.Some relaxationtype results for the minimization problem are obtained and the existence of a nearly optimal solution is established.

Identifying Influential Communities Using IID for a Multilayer Networks

In online social networks(OSN),they generate several specific user activities daily,corresponding to the billions of data points shared.However,although users exhibit significant interest in social media,they are uninterested in the content,discussions,or opinions available on certain sites.Therefore,this study aims to identify influential communities and understand user behavior across networks in the information diffusion process.Social media platforms,such as Facebook and Twitter,extract data to analyze the information diffusion process,based on which they cascade information among the individuals in the network.Therefore,this study proposes an influential information diffusion model that identifies influential communities across these two social media sites.More-over,it addresses site migration by visualizing a set of overlapping communities using hyper-edge detection.Thus,the overlapping community structure is used to identify similar communities with identical user interests.Furthermore,the com-munity structure helps in determining the node activation and user influence from the information cascade model.Finally,the Fraction of Intra/Inter-Layer(FIL)dif-fusion score is used to evaluate the efficiency of the influential information diffu-sion model by analyzing the trending influential communities in a multilayer network.However,from the experimental result,it observes that the FIL diffusion score for the proposed method achieves better results in terms of accuracy,preci-sion,recall and efficiency of community detection than the existing methods.

High-precision parallel computing model of solute transport based on GPU acceleration

The scenario simulation analysis of water environmental emergencies is very important for risk prevention and control,and emergency response.To quickly and accurately simulate the transport and diffusion process of high-intensity pollutants during sudden environmental water pollution events,in this study,a high-precision pollution transport and diffusion model for unstructured grids based on Compute Unified Device Architecture(CUDA)is proposed.The finite volume method of a total variation diminishing limiter with the Kong proposed r-factor is used to reduce numerical diffusion and oscillation errors in the simulation of pollutants under sharp concentration conditions,and graphics processing unit acceleration technology is used to improve computational efficiency.The advection diffusion process of the model is verified numerically using two benchmark cases,and the efficiency of the model is evaluated using an engineering example.The results demonstrate that the model perform well in the simulation of material transport in the presence of sharp concentration.Additionally,it has high computational efficiency.The acceleration ratio is 46 times the single-thread acceleration effect of the original model.The efficiency of the accelerated model meet the requirements of an engineering application,and the rapid early warning and assessment of water pollution accidents is achieved.

空心纳米柱状电极力-扩散耦合行为研究

文章以纳米尺度离子电池的电极结构为研究对象,建立可考虑表面效应的力-扩散双向耦合理论模型,对其在表面效应和外部载荷作用下的力学响应行为进行系统研究。借助建立的理论模型,研究尺寸效应、表面效应等对恒电压充电条件下空心纳米柱状电极中浓度场、应力场分布规律的影响并分析其内在机制。研究发现在该文条件下,表面效应对电极中环向和轴向应力场有压应力作用,且尺寸越小压应力作用越明显,而对径向应力场的作用则与位置有关。该研究为优化空心纳米柱状电极中的力-扩散耦合行为性能及应用拓展提供了一定的理论基础和参考依据。

Global Existence of Smooth Solutions for the Diffusion Approximation Model of General Gas in Radiation Hydrodynamics

In this paper,we consider the 3-D Cauchy problem for the diffusion approximation model in radiation hydrodynamics.The existence and uniqueness of global solutions is proved in perturbation framework,for more general gases including ideal poly tropic gas.Moreover,the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity,temperature,and radiation field.