The Boundedness of Hausdorff Operators on Function Spaces

For a fixed kernel function $\Phi$, the one dimensional Hausdorff operator is defined in the integral form by \hphi (f)(x)=\int_{0}^{\infty}\frac{\Phi(t)}{t}f(\frac{x}{t})\dt. By the Minkowski inequality, it is easy to check that the Hausdorff operator is bounded on the Lebesgue spaces $L^{p}$ when $p\geq 1$, with some size condition assumed on the kernel functions $\Phi$. However, people discovered that the above boundedness property is quite different on the Hardy space $H^{p}$ when $0 In this thesis, we first study the boundedness of$\hphi$on the Hardy space$H^{1}$, and on the local Hardy space$h^{1}(\bbR)$. Our work shows that for$\Phi(t)\geq 0$, the Hausdorff operator$\hphi$is bounded on the Hardy space$H^{1}$if and only if$\Phi$is a Lebesgue integrable function; and$\hphi$is bounded on the local Hardy space$h^{1}(\bbR)$if and only if the functions$\Phi(t)\chi_{(1,\infty)}(t)$and$\Phi(t)\chi_{(0,1)(t)}\log(\recip{t})$are Lebesgue integrable. These results solve an open question posed by the Israeli mathematician Liflyand. We also establish an$H^{1}(\bbR)\rightarrow H^{1,\infty}(\bbR)$boundedness theorem for$\hphi$. As applications, we obtain many decent properties for the Hardy operator and the$k$th order Hardy operators. For instance, we know that the Hardy operator$\scrH$is bounded from$H^{1}(\bbR)\rightarrow H^{1,\infty}(\bbR)$, bounded on the atomic space$H_{A}^{1}(\bbR_{+})$, but it is not bounded on both$H^{1}(\bbR)$and the local Hardy space$h^{1}(\bbR).$We also extend part of these results to the high dimensional Hausdorff operators. Here, we study two high dimensional extentions on the Hausdorff operator$\hphi: \[ \tilde{H}_{\Phi,\beta}(f)(x)=\int_{\bbR^{n}}\frac{\Phi(y)}{\Abs{y}^{n-\beta}}f(\frac{x}{\Abs{y}})\dy,\quad n\geq \beta\geq 0, \] and \[ H_{\Phi,\beta}(f)(x)=\int_{\bbR^{n}}\frac{\Phi(\frac{x}{\Abs{y}})}{\Abs{y}^{n-\beta}}f(y)\dy, \quad n\geq \beta\geq 0, \] where \Phi$is a local integrable function. For$0 Additionally, we study boundedness of Hausdorff operators on some Herz type spaces, and some bilinear Hausdorff operators and fractional Hausdorff operators

Evaluation of sonic, ultrasonic, and laser irrigation activation systems to eliminate bacteria from the dentinal tubules of the root canal system

Aiming to kill bacteria in dentin tubules of infected dental pulp cavities, we evaluated the effects of sodium hypochlorite (NaOCl) solution agitated by different irrigation protocols, i.e., conventional needle irrigation (CNI), passive ultrasonic irrigation (PUI), the EDDY tip, and the neodymium-doped yttrium aluminum perovskite (Nd:YAP) laser. The EDDY achieved good antibacterial effects as passive ultrasonic irrigation in the coronal and middle thirds. Nd:YAP laser irradiation and PUI were effective in the apical third of the root canal. Objectives: To evaluate the ability of NaOCl agitated by high-frequency sonic irrigation–EDDY, PUI, and Nd:YAP laser–to kill bacteria in infected root canal walls and if the associated temperature increases at the root surface during application. Methodology: Infected root canal models were established, and roots were randomly divided into six groups: negative control, positive control, CNI, PUI, sonic agitation with EDDY, and Nd:YAP laser groups. After irrigation, the teeth were split and stained using the LIVE/DEAD BacLight Bacterial Viability Kit. Dead bacteria depth was evaluated by a confocal laser scanning microscopy and the temperature at the root surface was assessed using a thermal imaging camera during the irrigation process. Results: In the coronal and middle thirds of the root canal, PUI and EDDY had stronger antibacterial effects than CNI (p<0.05); in the apical third, the antibacterial effects of PUI and Nd:YAP laser-activated irrigation were better than CNI (p<0.05). The maximum change in temperature was significantly greater during continuous Nd:YAP laser application compared with the other methods, but intermittent irrigation helped lessening this trend. Conclusions: NaOCl agitated by EDDY tip and PUI exhibited a similar bacteria elimination effect in the coronal and middle root canal. Nd:YAP laser was effective in the apical third and intermittent irrigation reduced its thermal impact

FedRec+: Enhancing Privacy and Addressing Heterogeneity in Federated Recommendation Systems

Preserving privacy and reducing communication costs for edge users pose significant challenges in recommendation systems. Although federated learning has proven effective in protecting privacy by avoiding data exchange between clients and servers, it has been shown that the server can infer user ratings based on updated non-zero gradients obtained from two consecutive rounds of user-uploaded gradients. Moreover, federated recommendation systems (FRS) face the challenge of heterogeneity, leading to decreased recommendation performance. In this paper, we propose FedRec+, an ensemble framework for FRS that enhances privacy while addressing the heterogeneity challenge. FedRec+ employs optimal subset selection based on feature similarity to generate near-optimal virtual ratings for pseudo items, utilizing only the user's local information. This approach reduces noise without incurring additional communication costs. Furthermore, we utilize the Wasserstein distance to estimate the heterogeneity and contribution of each client, and derive optimal aggregation weights by solving a defined optimization problem. Experimental results demonstrate the state-of-the-art performance of FedRec+ across various reference datasets.Comment: Accepted by 59th Annual Allerton Conference on Communication, Control, and Computin

FedEBA+: Towards Fair and Effective Federated Learning via Entropy-Based Model

Ensuring fairness is a crucial aspect of Federated Learning (FL), which enables the model to perform consistently across all clients. However, designing an FL algorithm that simultaneously improves global model performance and promotes fairness remains a formidable challenge, as achieving the latter often necessitates a trade-off with the former. To address this challenge, we propose a new FL algorithm, FedEBA+, which enhances fairness while simultaneously improving global model performance. FedEBA+ incorporates a fair aggregation scheme that assigns higher weights to underperforming clients and an alignment update method. In addition, we provide theoretical convergence analysis and show the fairness of FedEBA+. Extensive experiments demonstrate that FedEBA+ outperforms other SOTA fairness FL methods in terms of both fairness and global model performance

Radiomics-Based Outcome Prediction for Pancreatic Cancer Following Stereotactic Body Radiotherapy

(1) Background: Radiomics use high-throughput mining of medical imaging data to extract unique information and predict tumor behavior. Currently available clinical prediction models poorly predict treatment outcomes in pancreatic adenocarcinoma. Therefore, we used radiomic features of primary pancreatic tumors to develop outcome prediction models and compared them to traditional clinical models. (2) Methods: We extracted and analyzed radiomic data from pre-radiation contrast-enhanced CTs of 74 pancreatic cancer patients undergoing stereotactic body radiotherapy. A panel of over 800 radiomic features was screened to create overall survival and local-regional recurrence prediction models, which were compared to clinical prediction models and models combining radiomic and clinical information. (3) Results: A 6-feature radiomic signature was identified that achieved better overall survival prediction performance than the clinical model (mean concordance index: 0.66 vs. 0.54 on resampled cross-validation test sets), and the combined model improved the performance slightly further to 0.68. Similarly, a 7-feature radiomic signature better predicted recurrence than the clinical model (mean AUC of 0.78 vs. 0.66). (4) Conclusion: Overall survival and recurrence can be better predicted with models based on radiomic features than with those based on clinical features for pancreatic cancer

PRIOR: Prototype Representation Joint Learning from Medical Images and Reports

Contrastive learning based vision-language joint pre-training has emerged as a successful representation learning strategy. In this paper, we present a prototype representation learning framework incorporating both global and local alignment between medical images and reports. In contrast to standard global multi-modality alignment methods, we employ a local alignment module for fine-grained representation. Furthermore, a cross-modality conditional reconstruction module is designed to interchange information across modalities in the training phase by reconstructing masked images and reports. For reconstructing long reports, a sentence-wise prototype memory bank is constructed, enabling the network to focus on low-level localized visual and high-level clinical linguistic features. Additionally, a non-auto-regressive generation paradigm is proposed for reconstructing non-sequential reports. Experimental results on five downstream tasks, including supervised classification, zero-shot classification, image-to-text retrieval, semantic segmentation, and object detection, show the proposed method outperforms other state-of-the-art methods across multiple datasets and under different dataset size settings. The code is available at https://github.com/QtacierP/PRIOR.Comment: Accepted by ICCV 202