Approximation schemes for McKean-Vlasov and Boltzmann type equations (error analyses in total variation distance)

We deal with Mckean-Vlasov and Boltzmann type jump equations. This means that the coefficients of the stochastic equation depend on the law of the solution, and the equation is driven by a Poisson point measure with intensity measure which depends on the law of the solution as well. In [3], Alfonsi and Bally have proved that under some suitable conditions, the solution $X_t$ of such equation exists and is unique. One also proves that $X_t$ is the probabilistic interpretation of an analytical weak equation. Moreover, the Euler scheme $X_t^{\mathcal{P}}$ of this equation converges to $X_t$ in Wasserstein distance. In this paper, under more restricted assumptions, we show that the Euler scheme $X_t^{\mathcal{P}}$ converges to $X_t$ in total variation distance and $X_t$ has a smooth density (which is a function solution of the analytical weak equation). On the other hand, in view of simulation, we use a truncated Euler scheme $X^{\mathcal{P},M}_t$ which has a finite numbers of jumps in any compact interval. We prove that $X^{\mathcal{P},M}_{t}$ also converges to $X_t$ in total variation distance. Finally, we give an algorithm based on a particle system associated to $X^{\mathcal{P},M}_t$ in order to approximate the density of the law of $X_t$. Complete estimates of the error are obtained

Approximation for the invariant measure with applications for jump processes (convergence in total variation distance)

In this paper, we establish an abstract framework for the approximation of the invariant probability measure for a Markov semigroup. Following Pag{\`e}s and Panloup [40] we use an Euler scheme with decreasing step (unadjusted Langevin algorithm). Under some contraction property with exponential rate and some regularization properties, we give an estimate of the error in total variation distance. This abstract framework covers the main results in [40] and [14]. As a specific application we study the convergence in total variation distance to the invariant measure for jump type equations. The main technical difficulty consists in proving the regularzation properties-this is done under an ellipticity condition, using Malliavin calculus for jump processes.Comment: arXiv admin note: text overlap with arXiv:2212.0741

On Information Coverage for Location Category Based Point-of-Interest Recommendation

Point-of-interest(POI) recommendation becomes a valuable service in location-based social networks. Based on the norm that similar users are likely to have similar preference of POIs, the current recommendation techniques mainly focus on users' preference to provide accurate recommendation results. This tends to generate a list of homogeneous POIs that are clustered into a narrow band of location categories(like food, museum, etc.) in a city. However, users are more interested to taste a wide range of flavors that are exposed in a global set of location categories in the city.In this paper, we formulate a new POI recommendation problem, namely top-K location category based POI recommendation, by introducing information coverage to encode the location categories of POIs in a city.The problem is NP-hard. We develop a greedy algorithm and further optimization to solve this challenging problem. The experimental results on two real-world datasets demonstrate the utility of new POI recommendations and the superior performance of the proposed algorithms

Diffusion Probabilistic Model Based Accurate and High-Degree-of-Freedom Metasurface Inverse Design

Conventional meta-atom designs rely heavily on researchers' prior knowledge and trial-and-error searches using full-wave simulations, resulting in time-consuming and inefficient processes. Inverse design methods based on optimization algorithms, such as evolutionary algorithms, and topological optimizations, have been introduced to design metamaterials. However, none of these algorithms are general enough to fulfill multi-objective tasks. Recently, deep learning methods represented by Generative Adversarial Networks (GANs) have been applied to inverse design of metamaterials, which can directly generate high-degree-of-freedom meta-atoms based on S-parameter requirements. However, the adversarial training process of GANs makes the network unstable and results in high modeling costs. This paper proposes a novel metamaterial inverse design method based on the diffusion probability theory. By learning the Markov process that transforms the original structure into a Gaussian distribution, the proposed method can gradually remove the noise starting from the Gaussian distribution and generate new high-degree-of-freedom meta-atoms that meet S-parameter conditions, which avoids the model instability introduced by the adversarial training process of GANs and ensures more accurate and high-quality generation results. Experiments have proven that our method is superior to representative methods of GANs in terms of model convergence speed, generation accuracy, and quality

Runoff regulation and nitrogen and phosphorus removal performance of a bioretention substrate with HDTMA-modified zeolite

As a commonly used material in bioretention substrates, natural zeolite (NZ) provides decent adsorption capacity for cation pollutants and heavy metals, but limited ability to remove anion pollutants. Hexadecyltrimethylammonium bromide (HDTMA)-modified zeolite (MZ) was used as the bioretention substrate material. The performance of the media including runoff reduction, nitrate nitrogen (NO3−-N) removal, ammonium nitrogen (NH4+-N) removal, and total phosphorus (TP) removal was assessed by the column experiment. The effects of different levels of modification, ratio of zeolite in the substrate, and rainfall intensity on media performance were investigated. The results indicate that HDTMA-modified zeolite significantly improves the NO3−-N (up to 38.2 times of NZ) and TP (up to17.5 times of NZ) removal rate of media and slightly increases the NH4+-N (up to 1.5 times of NZ) purification performance of the substrate. Compared with the media with NZ, decline on both runoff volume reduction (maximum decline up to 32.9%) and flow rate reduction (maximum decline up to 29.9%) of the media with MZ were observed. Based on multiple regression analysis, quantitative relationship models between influencing factors and response variables were established (R2 > 0.793), the level of the effect of influencing factors on response variables was investigated, and the interactions between influencing factors were explored. The main effect analysis found that the degree of modification affects NO3−-N and TP removal rate of the substrate the most, and when the amount of HDTMA molecules loaded on the zeolite surface exceeds 0.09meq/g, the modification can no longer improve NO3−-N removal efficiency

Navigating Discrete Difference Equation Governed WMR by Virtual Linear Leader Guided HMPC

In this paper, we revisit model predictive control (MPC) for the classical wheeled mobile robot (WMR) navigation problem. We prove that the reachable set based hierarchical MPC (HMPC), a state-of-the-art MPC, cannot handle WMR navigation in theory due to the non-existence of non-trivial linear system with an under-approximate reachable set of WMR. Nevertheless, we propose a virtual linear leader guided MPC (VLL-MPC) to enable HMPC structure. Different from current HMPCs, we use a virtual linear system with an under-approximate path set rather than the traditional trace set to guide the WMR. We provide a valid construction of the virtual linear leader. We prove the stability of VLL-MPC, and discuss its complexity. In the experiment, we demonstrate the advantage of VLL-MPC empirically by comparing it with NMPC, LMPC and anytime RRT* in several scenarios

Effects and mechanism of stem cells from human exfoliated deciduous teeth combined with hyperbaric oxygen therapy in type 2 diabetic rats

OBJECTIVES: Mesenchymal stem cells (MSCs) are potentially ideal for type 2 diabetes treatment, owing to their multidirectional differentiation ability and immunomodulatory properties. Here we investigated whether the stem cells from human exfoliated deciduous teeth (SHED) in combination with hyperbaric oxygen (HBO) could treat type 2 diabetic rats, and explored the underlying mechanism. METHODS: SD rats were used to generate a type 2 diabetes model, which received stem cell therapy, HBO therapy, or both together. Before and after treatment, body weight, blood glucose, and serum insulin, blood lipid, pro-inflammatory cytokines (tumor necrosis factor-alpha and interleukin-6), and urinary proteins were measured and compared. After 6 weeks, rats were sacrificed and their organs were subjected to hematoxylin and eosin staining and immunofluorescence staining for insulin and glucagon; apoptosis and proliferation were analyzed in islet cells. Structural changes in islets were observed under an electron microscope. Expression levels of Pdx1, Ngn3, and Pax4 mRNAs in the pancreas were assessed by real-time quantitative polymerase chain reaction (RT-qPCR). RESULTS: In comparison with diabetic mice, those treated with the combination or SHE therapy showed decreased blood glucose, insulin resistance, serum lipids, and pro-inflammatory cytokines and increased body weight and serum insulin. The morphology and structure of pancreatic islets improved, as evident from an increase in insulin-positive cells and a decrease in glucagon-positive cells. Terminal deoxynucleotidyl transferasemediated dUTP nick end labeling (TUNEL) staining of islet cells revealed the decreased apoptosis index, while Ki67 and proliferating cell nuclear antigen staining showed increased proliferation index. Pancreatic expression of Pdx1, Ngn3, and Pax4 was upregulated. CONCLUSION: SHED combined with HBO therapy was effective for treating type 2 diabetic rats. The underlying mechanism may involve SHED-mediated increase in the proliferation and trans-differentiation of islet b-cells and decrease in pro-inflammatory cytokines and apoptosis of islets

Intelligent detection method of lightweight blasthole based on deep learning

In the construction process of tunnel (roadway) drilling and blasting, intelligent charging can replace manual operation and reduce the occurrence of dangerous accidents in charging operation. However, some factors such as poor light conditions in the tunnel, small blasthole targets, and cracks in the tunnel face will cause the misdetection and missed detection of blastholes during intelligent charging. At the same time, the limited computing power of the vehicle-mounted computer is also a difficulty that restricts the use of large models for blasthole identification. The MCIW-2 deep learning model can solve the problem of high-precision blasthole detection and real-time deployment in the tunnel excavation environment. According to the size characteristics of the collected blasthole images, the model adopts the adaptive anchor frame clustering algorithm module to optimize the aspect ratio size parameters of the detection frame. The loss function WIoU (Wise Intersection over Union) with a dynamic non-monotonic focusing mechanism is used to deal with the challenge of low-quality blasthole images for achieving a high-precision detection. The MobileNetv3-Small network and CBAM (Convolutional Block Attention Module) are used to build a backbone network structure, reducing model parameters to ensure detection accuracy and meet the lightweight deployment requirements of vehicle equipment. Experiments have proved that the MCIW-2 model has reached 96.18% accuracy in blasthole recognition, and the detection speed has reached 59 fps. Compared with the benchmark YOLO (You Only Look Once) series target detection model with the smallest file, the lightweight blasthole intelligent detection model constructed is reduced by 75.86%, and the model file is only 2.80 Mb, which is better than the benchmark target detection model of the YOLO series. The MCIW-2 deep learning model is used to test the live video of the working face, and the rapid and accurate detection of blasthole is realized. The test results show that the model is suitable for the lightweight deployment requirements of intelligent charge engineering, has a good adaptability, and some significant advantages in comprehensive performance

Knowledge, attitude, and practice toward ultrasound screening for breast cancer among women

BackgroundSeveral obstacles can hinder breast cancer screening. This study aimed to investigate the knowledge, attitude, and practice (KAP) toward ultrasound screening for breast cancer in women.MethodsThis cross-sectional study recruited women who visited the breast specialist clinic of Zhongshan City People’s Hospital (a tertiary hospital) between August 2022 and April 2023 through convenience sampling. KAP scores ≥70% were considered adequate.ResultsThis study enrolled 501 participants. The mean knowledge, attitude, and practice levels were 8.56 ± 1.81/12 (possible range 0–12, 71.33%), 29.80 ± 2.71 (possible range 8–40, 74.50%), and 32.04 ± 3.09 (possible range 8–40, 80.10%). Senior high school education (vs. junior high school and below, coefficient = 1.531, 95%CI: 1.013–2.312, p = 0.044), bachelor’s education and above (vs. junior high school and below, coefficient = 5.315, 95%CI: 3.546–7.966, p < 0.001), housewife or unemployed (vs. employed, coefficient = 0.671, 95%CI: 0.466–0.966, p = 0.032), and a history of breast ultrasound (vs. no, coefficient = 1.466, 95%CI: 1.121–1.917, p = 0.005) were independently and positively associated with knowledge. Knowledge (coefficient = 1.303, 95%CI: 1.100–1.544, p = 0.002) and monthly income >10,000 (vs. <5,000, coefficient = 4.364, 95%CI: 1.738–10.956, p = 0.002) were independently and positively associated with attitude. Only attitude (coefficient = 1.212, 95%CI: 1.096–1.340, p < 0.001) was independently and positively associated with the practice. A structural equation modeling (SEM) analysis was used to estimate causality among KAP dimensions, showing that knowledge directly influenced attitude (β = −1.090, p = 0.015), knowledge did not directly influence practice (β = −0.117, p = 0.681) but had an indirect influence (β = 0.826, p = 0.028), and attitude directly influenced practice (β = −0.757, p = 0.016).ConclusionWomen in Zhongshan City had good knowledge, favorable attitudes, and active practice toward breast ultrasound screening for breast cancer. Women’s characteristics associated with a poorer KAP were identified, allowing for more targeted interventions