Uniqueness and delayed blow-up of solutions for fractional stochastic differential equations with mulitiplicative noise

The solution of some deterministic equation without noise may not be unique or existential. We study a nonlinear fractional partial differential equation which is driven by multiplicative noise of the form \[D_t^\beta u = \left[ { - {{\left( { - \Delta } \right)}^s}u + \zeta \left( u \right)} \right]dt + A\sum\limits_{m \in Z_0^d} {\sum\limits_{j = 1}^{d - 1} {{\theta_m}{\sigma_{m,j}}\left( x \right)} } \circ dW_t^{m,j},\;\; s \ge 1,\;\;\frac{1}{2} 0$is a constant depending on the noise intensity,$\circ$represent the Stratonovich-type stochastic differential. We prove that under some extra hypothese about$\zeta$, the multiplicative noise can delay the blow-up of the deterministic solution, and the above equation admits a pathwise unique solution with infinite life time with large probability. The existence and uniqueness of the solutions of the above stochastic equation are proved by using Galerkin approximations and priori estimates. We also verify the validation of hypotheses in the time fractional Keller-Segel and time fractional Fisher-KPP equations in 3D case.Comment: there was some errors, fatal and severe errors to make the main results wrong in this pape

Association between atherosclerosis-related cardiovascular disease and uveitis: A systematic review and meta-analysis

Background: Uveitis is not only an intraocular inflammatory disease, but also an indicator of systemic inflammation. It is unclear whether uveitis can increase the risk of cardiovascular disease (CVD) through the atherosclerotic pathway. Methods: PubMed and Embase databases were searched until 5 September, 2022. Original studies investigating uveitis and cardiovascular events were selected. The random-effects model was used to calculate the difference of groups in pooled estimates. Results: A total of six observational studies that included mainly ankylosing spondylitis (AS) patients were included. Of these, three studies reported data on carotid plaques and carotid intima-media thickness (cIMT) and the other three studies provided data on atherosclerosis-related CVD. No significant difference was found in cIMT between uveitis and controls (MD = 0.01, 95% CI = -0.03-0.04, p = 0.66), consistent with the findings of carotid plaque incidence (OR = 1.30, 95% CI = 0.71-2.41, p = 0.39). However, uveitis was associated with a 1.49-fold increase in atherosclerosis-related CVD (HR = 1.49, 95% CI = 1.20-1.84, p = 0.0002). Conclusions: Uveitis is a predictor of atherosclerosis-related CVD in AS patients. For autoimmune disease patients with uveitis, earlier screening of cardiovascular risk factors and the implementation of corresponding prevention strategies may be associated with a better prognosis. Keywords: ankylosing spondylitis; atherosclerosis; cardiovascular risk; carotid plaques; intima-media thickness; uveiti

Automatic prediction of non-iodine-avid status in lung metastases for radioactive I131 treatment in differentiated thyroid cancer patients

ObjectivesThe growing incidence of differentiated thyroid cancer (DTC) have been linked to insulin resistance and metabolic syndrome. The imperative need for developing effective diagnostic imaging tools to predict the non-iodine-avid status of lung metastasis (LMs) in differentiated thyroid cancer (DTC) patients is underscored to prevent unnecessary radioactive iodine treatment (RAI).MethodsPrimary cohort consisted 1962 pretreated LMs of 496 consecutive DTC patients with pretreated initially diagnosed LMs who underwent chest CT and subsequent post-treatment radioiodine SPECT. After automatic lesion segmentation by SE V-Net, SE Net deep learning was trained to predict non-iodine-avid status of LMs. External validation cohort contained 123 pretreated LMs of 24 consecutive patients from other two hospitals. Stepwise validation was further performed according to the nodule’s largest diameter.ResultsThe SE-Net deep learning network yielded area under the receiver operating characteristic curve (AUC) values of 0.879 (95% confidence interval: 0.852–0.906) and 0.713 (95% confidence interval: 0.613–0.813) for internal and external validation. With the LM diameter decreasing from ≥10mm to ≤4mm, the AUCs remained relatively stable, for smallest nodules (≤4mm), the model yielded an AUC of 0.783. Decision curve analysis showed that most patients benefited using deep learning to decide radioactive I131 treatment.ConclusionThis study presents a noninvasive, less radioactive and fully automatic approach that can facilitate suitable DTC patient selection for RAI therapy of LMs. Further prospective multicenter studies with larger study cohorts and related metabolic factors should address the possibility of comprehensive clinical transformation

Intermittent Prediction Method Based On Marcov Method And Grey Prediction Method

This paper concentrates on the intermittent demand for electric power supply and studies the method of demand prediction. This chapter first divides the demand for electric power supply into two statistical sequences: (1) sequence of demand occurrence, among which “1”stands for the occurrence of demand,“0”means that the demand fails to occur; (2) sequence of demand quantity. Next the author predicts the moment of time and the number of times n that demand occurs within a specific time interval in the future based on 0-1 sequence using Markov arrival process (MAP). Then the paper forecasts the demand quantity in subsequent n intervals using Grey prediction model GM (1, 1) based on the sequence of demand quantity. Finally, the author places the demand quantity in the n intervals in order at the moments where demand occurs to get the predicted result of demand for electric material with intermittent demand. According to instance analysis, the integrated approach mentioned in this paper surpasses existing methods in providing accurate prediction on data of product with intermittent demand

Challenging Low Homophily in Social Recommendation

Social relations are leveraged to tackle the sparsity issue of user-item interaction data in recommendation under the assumption of social homophily. However, social recommendation paradigms predominantly focus on homophily based on user preferences. While social information can enhance recommendations, its alignment with user preferences is not guaranteed, thereby posing the risk of introducing informational redundancy. We empirically discover that social graphs in real recommendation data exhibit low preference-aware homophily, which limits the effect of social recommendation models. To comprehensively extract preference-aware homophily information latent in the social graph, we propose Social Heterophily-alleviating Rewiring (SHaRe), a data-centric framework for enhancing existing graph-based social recommendation models. We adopt Graph Rewiring technique to capture and add highly homophilic social relations, and cut low homophilic (or heterophilic) relations. To better refine the user representations from reliable social relations, we integrate a contrastive learning method into the training of SHaRe, aiming to calibrate the user representations for enhancing the result of Graph Rewiring. Experiments on real-world datasets show that the proposed framework not only exhibits enhanced performances across varying homophily ratios but also improves the performance of existing state-of-the-art (SOTA) social recommendation models.Comment: This paper has been accepted by The Web Conference (WWW) 202