Anomalous Diffusion Models Involving Regularized General Fractional Derivatives with Sonin Kernels by Maryam Alkandari, Dimitri Loutchko, Yuri Luchko

“…Next, we derive a fractional diffusion equation involving regularized general fractional derivatives with Sonin kernels from the continuous time random walk model in the asymptotical sense of long times and large distances. …”
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Toward Artificial General Intelligence in Hydrogeological Modeling With an Integrated Latent Diffusion Framework by Chuanjun Zhan, Zhenxue Dai, Jiu Jimmy Jiao, Mohamad Reza Soltanian, Huichao Yin, Kenneth C. Carroll

“…Its generalization across diverse objectives underscores its potential as a cornerstone for advancing Artificial General Intelligence in hydrogeological modeling.…”
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Dynamics of a Diffusive Predator-Prey Model with General Nonlinear Functional Response by Wensheng Yang

“…We study a diffusive predator-prey model with nonconstant death rate and general nonlinear functional response. …”
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The Diffusion-Driven Instability for a General Time-Space Discrete Host-Parasitoid Model by Xuetian Zhang, Chunrui Zhang

“…In this paper, we consider a general time-space discrete host-parasitoid model with the periodic boundary conditions. …”
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The Diffusive Stresses Arising from A Locally Generalized Advection-Diffusion Process by Derya Avcı

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BCDDM: Branch Correction Denoising Diffusion Model for Black Hole Image Generation by Ao Liu, Zelin Zhang, Songbai Chen, Cuihong Wen, Jieci Wang

“…This paper introduces the Branch Correction Denoising Diffusion Model (BCDDM), a deep learning framework that synthesizes black hole images directly from physical parameters. …”
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An advection–diffusion equation with a generalized advection term: Well-posedness analysis and examples by Tetyana Malysheva, Luther W. White

“…We consider a Cauchy–Dirichlet problem for a semilinear advection–diffusion equation with a generalized advection term. …”
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Traveling waves in a delayed reaction-diffusion SVIR epidemic model with generalized incidence function and imperfect vaccination by Rassim Darazirar

“…This paper is concerned with traveling wave solutions for a delayed reaction-diffusion SVIR epidemic model that includes both general incidence function and imperfect vaccination. …”
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Information-Theoretic Security of RIS-Aided MISO System Under <i>N</i>-Wave with Diffuse Power Fading Model by José David Vega-Sánchez, Ana Zambrano, Ricardo Mena, José Oscullo

“…This general framework allows us to accurately approximate key practical factors in RIS’s channel modeling, such as generalized fading conditions, spatial correlation, discrete phase shift, beamforming, and the presence of direct and indirect links. …”
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Three-Phase-Lag Effect on Rayleigh Waves in a Generalized Thermoelastic Diffusion Medium with Modified Couple Stress by Emad K. Jaradat, Sayed M. Abo-Dahab, Rajneesh Kumar, Eslam S. Elidy

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A spatio-temporal infection epidemic model with fractional order, general incidence, and vaccination analysis by Sara Soulaimani, Abdelilah Kaddar, Fathalla A. Rihan

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Revisiting the Group Classification of the General Nonlinear Heat Equation <i>u_t</i> = (<i>K</i>(<i>u</i>)<i>u_x</i>)<i>_x</i> by Winter Sinkala

“…Group classification is a powerful tool for identifying and selecting the free elements—functions or parameters—in partial differential equations (PDEs) that maximize the symmetry properties of the model. In this paper, we revisit the group classification of the general nonlinear heat (or diffusion) equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>u</mi><mi>t</mi></msub><mo>=</mo><msub><mfenced separators="" open="(" close=")"><mi>K</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mspace width="0.166667em"></mspace><msub><mi>u</mi><mi>x</mi></msub></mfenced><mi>x</mi></msub><mo>,</mo></mrow></semantics></math></inline-formula> where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><mo>(</mo><mi>u</mi><mo>)</mo></mrow></semantics></math></inline-formula> is a non-constant function of the dependent variable. …”
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Improving AI models for rare thyroid cancer subtype by text guided diffusion models by Fang Dai, Siqiong Yao, Min Wang, Yicheng Zhu, Xiangjun Qiu, Peng Sun, Cheng Qiu, Jisheng Yin, Guangtai Shen, Jingjing Sun, Maofeng Wang, Yun Wang, Zheyu Yang, Jianfeng Sang, Xiaolei Wang, Fenyong Sun, Wei Cai, Xingcai Zhang, Hui Lu

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On the solutions of generalized Cauchy differential equations and diffusion equations with k-Hilfer-Prabhakar derivative by Ved Prakash Dubey, Jagdev Singh, Sarvesh Dubey, Dumitru Baleanu, Devendra Kumar

“…Our new generalized solutions of k-HPFD type Cauchy problems and diffusion models may be used to explore fluid mechanics, ocean engineering, and wave phenomena and so on. …”
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The general intelligence of GPT–4, its knowledge diffusive and societal influences, and its governance by Mohammad Mahdi Jahani Yekta

“…This paper explores this AGI, its knowledge diffusive and societal influences, and its governance. …”
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DIFshilling: A Diffusion Model for Shilling Attacks by Weizhi Chen, Xingkong Ma, Bo Liu

“…Many current approaches either fail to capture the natural distribution of real user data or are highly tailored to specific RS algorithms, limiting their general applicability and effectiveness. To overcome these limitations, we propose DIFshilling, a novel diffusion-based model for shilling attacks. …”
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Comparison of DKRZ Database and LARS-WG Model in Three Parameters of Minimum Temperature, Maximum Temperature and Precipitation (Case study: Qazvin plain) by Fatemeh Borzoo, Hadi Ramezani Etedali, Abbas Kaviani

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A survey of emerging applications of diffusion probabilistic models in MRI by Yuheng Fan, Hanxi Liao, Shiqi Huang, Yimin Luo, Huazhu Fu, Haikun Qi

“…Diffusion probabilistic models (DPMs) which employ explicit likelihood characterization and a gradual sampling process to synthesize data, have gained increasing research interest. …”
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Automatic Generation of Standard Nursing Unit Floor Plan in General Hospital Based on Stable Diffusion by Zhuo Han, Yongquan Chen

“…It includes dataset processing, model training, model testing and generation. It enables the generation of well-organized, clear, and readable functional block floor plans with strong generalization capabilities by inputting the boundaries of the nursing unit’s floor plan. …”
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Stability and Bifurcation Analysis for a Class of Generalized Reaction-Diffusion Neural Networks with Time Delay by Tianshi Lv, Qintao Gan, Qikai Zhu

“…Considering the fact that results for static neural networks are much more scare than results for local field neural networks and our purpose letting the problem researched be more general in many aspects, in this paper, a generalized neural networks model which includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks is built and the stability and bifurcation problems for it are investigated under Neumann boundary conditions. …”
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