On a pseudodifferential calculus with modest boundary decay condition

A boundary decay condition, called vanishing to infinite logarithmic order is introduced. A pseudodifferential calculus, extending the b-calculus of Melrose, is proposed based on this modest decay condition. The mapping properties, composition rule, and normal operators are studied. Instead of functional analytic methods, a geometric approach is invoked in pursuing the Fredholm criterion. As an application, a detailed proof of the Atiyah-Patodi-Singer index theorem, including a review of Dirac operators of product type and construction of the heat kernel, is presented

3D-aware Image Generation using 2D Diffusion Models

In this paper, we introduce a novel 3D-aware image generation method that leverages 2D diffusion models. We formulate the 3D-aware image generation task as multiview 2D image set generation, and further to a sequential unconditional-conditional multiview image generation process. This allows us to utilize 2D diffusion models to boost the generative modeling power of the method. Additionally, we incorporate depth information from monocular depth estimators to construct the training data for the conditional diffusion model using only still images. We train our method on a large-scale dataset, i.e., ImageNet, which is not addressed by previous methods. It produces high-quality images that significantly outperform prior methods. Furthermore, our approach showcases its capability to generate instances with large view angles, even though the training images are diverse and unaligned, gathered from "in-the-wild" real-world environments.Comment: Website: https://jeffreyxiang.github.io/ivid

Empirical ResearchonTeaching KnowledgeSharingin University Townand Its Influential Factors

The implement of knowledge sharing in University Town facilitates to aggregate education resource and improve overall strength of University Town. According to factors and performance of teaching knowledge sharing in University Town, the model and theoretical hypothesis of teaching knowledge sharing in University Town are proposed. Questionnaire and structural equation model are used to empirically study teaching knowledge sharing model in University Town. The results indicate that three factors including the characteristics of knowledge, the cluster of University Town and the system and mechanism for University Town have a significant correlation with teaching knowledge sharing in University Town, while teaching knowledge sharing in University Town has a significant correlation with Knowledge Innovation, comprehensive strength and education quality of University Town. By analysis results, effective strategies are designed for knowledge sharing mechanism in University Town

Application of BEMD in Extraction of Regional and Local Gravity Anomalies Reflecting Geological Structures Associated with Mineral Resources

The bi-dimensional empirical mode decomposition (BEMD) method is an adaptive analysis method for nonlinear and nonstationary data. With the sifting process of BEMD, the data can be decomposed into a series of bi-dimensional intrinsic mode functions (BIMFs), which may present the relative local feature of the data. In this study, the BEMD method was successfully used for analyzing the Bouguer gravity data of Gejiu tin-copper polymetallic ore field in Yunnan Province and Tongshi gold field in Western Shandong Uplift Block to extract different-scale anomalies. In these two cases, regional and local components were separated, which can reflect the geological structures at different depths and some intrusive bodies which may be associated with mineral deposits. The results reveals the spatial distribution relationship between the different intrusive bodies and the various types of mineral deposits in the aforementioned two study area, which provide some reliable evidence for exploration of new concealed mineral deposits

PREF: Phasorial Embedding Fields for Compact Neural Representations

We present an efficient frequency-based neural representation termed PREF: a shallow MLP augmented with a phasor volume that covers significant border spectra than previous Fourier feature mapping or Positional Encoding. At the core is our compact 3D phasor volume where frequencies distribute uniformly along a 2D plane and dilate along a 1D axis. To this end, we develop a tailored and efficient Fourier transform that combines both Fast Fourier transform and local interpolation to accelerate na\"ive Fourier mapping. We also introduce a Parsvel regularizer that stables frequency-based learning. In these ways, Our PREF reduces the costly MLP in the frequency-based representation, thereby significantly closing the efficiency gap between it and other hybrid representations, and improving its interpretability. Comprehensive experiments demonstrate that our PREF is able to capture high-frequency details while remaining compact and robust, including 2D image generalization, 3D signed distance function regression and 5D neural radiance field reconstruction

Hybrid ceramics-based cancer theranostics

Cancer is a major threat to human lives. Early detection and precisely targeted therapy/therapies for cancer is the most effective way to reduce the difficulties (e.g., side effects, low survival rate, etc.) in treating cancer. To enable effective cancer detection and treatment, ceramic biomaterials have been intensively and extensively investigated owing to their good biocompatibility, high bioactivity, suitable biodegradability and other distinctive properties that are required for medical devices in oncology. Through hybridization with other materials and loading of imaging agents and therapeutic agents, nanobioceramics can form multifunctional nanodevices to simultaneously provide diagnostic and therapeutic functions for cancer patients, and these nanodevices are known as hybrid ceramics-based cancer theranostics. In this review, the recent developments of hybrid ceramics-based cancer theranostics, which include the key aspects such as their preparation, biological evaluation and applications, are summarized and discussed. The challenges and future perspectives for the clinical translation of hybrid ceramics-based cancer theranostics are also discussed. It is believed that the potential of hybrid ceramic nanoparticles as cancer theranostics is high and that the future of these theranostics is bright despite the difficulties along the way for their clinical translation

Security and Energy-aware Collaborative Task Offloading in D2D communication

Device-to-device (D2D) communication technique is used to establish direct links among mobile devices (MDs) to reduce communication delay and increase network capacity over the underlying wireless networks. Existing D2D schemes for task offloading focus on system throughput, energy consumption, and delay without considering data security. This paper proposes a Security and Energy-aware Collaborative Task Offloading for D2D communication (Sec2D). Specifically, we first build a novel security model, in terms of the number of CPU cores, CPU frequency, and data size, for measuring the security workload on heterogeneous MDs. Then, we formulate the collaborative task offloading problem that minimizes the time-average delay and energy consumption of MDs while ensuring data security. In order to meet this goal, the Lyapunov optimization framework is applied to implement online decision-making. Two solutions, greedy approach and optimal approach, with different time complexities, are proposed to deal with the generated mixed-integer linear programming (MILP) problem. The theoretical proofs demonstrate that Sec2D follows a [O(1∕V),O(V)] energy-delay tradeoff. Simulation results show that Sec2D can guarantee both data security and system stability in the collaborative D2D communication environment