Prime numbers could be formalized with using notation of sequence.

In this paper, sequence of prime numbers would be investigated in even numbers. Goldbach’s conjecture is true.

This paper is about understanding Collatz conjecture in hailstone numbers.

A document by Jihyeon Yoon . Click on the document to view its contents.

This paper is about understanding Poincaré theorem in the view of observation. And suggests counterexample of the proved theorem.

Investigating the base ground of economic growth as a mathematical model is an essential economic issue. Every economic entity does economic behaviors to maximize its goal, total utility, in a given time. By bringing out the premises of the game theory, market participants, transactions, and market entities-related agents are defined. Next, concerning the general regional economy, the transaction model in the market participants could be set. And finally, a law and economics notion to set a model of economic growth would be drawn.

In this paper, we propose BiTDB, a built-in Trusted Execution Environment (TEE) database for embedded systems, to realize higher system availability while ensuring data confidentiality. With BiTDB, dilemmas the state-of-the-art research work on secure embedded databases has to face can be significantly reduced and eliminated, including (i) complicated research and realization on searchable encryption algorithms (SEA), (ii) limited support to all database operations, and (iii) almost none of specific design and optimizations toward build-in TEE embedded databases. Through BiTDB, all database operations can process plaintext in TEE instead of retrieving on ciphertext by developing complicated SEAs. To enable BiTDB to handle database files in Rich Execution Environmen (REE) as local ones, we extend the TEE OS with generic file I/O libraries. Then, we contribute three critical optimizations to significantly reduce redundant memory and file operations between TEE and REE, and BiTDB achieve better system performance and availability in embedded systems. Finally, we have implemented the prototype system based on OP-TEE and SQLite for several typical platforms, including virtualization and hardware environments. The TPC-H test shows BiTDB can achieve 85% (on average) of the original database performance while guaranteeing data confidentiality and integrity. Our project repository is at https://github.com/CharlieMCY/BiTDB.

This paper explores the potential of biomimetics to revolutionize medical and food waste management systems in the United States. By forging circular economies in these fields, biomimetics can provide robust financial benefits. Furthermore, biomimetics can mitigate waste accumulation and related health hazards from such systems. In light of this paper's findings, ongoing and long-term financial investments in biomimetic technology are recommended to create sustainable medical and food waste systems on a nationwide scale.

Despite the progresses in upper limb prosthetic technologies of the past decades, there is still a large gap between the user needs and the available devices. Here, we describe the design and validation of a fully integrated, multi-degree of freedom upper limb prosthetic system designed on the basis of user survey studies. The system has five degrees of freedom, sufficient grasping/pinching force achieved by a combination of direct and underactuated activation to perform activities of daily living, an active wrist, a closed-loop tactile biofeedback system, and simultaneous/proportional myoelectric control. The aforementioned components have been successfully integrated into a standalone prosthetic system. The system has been tested for its capacity to reproduce the human grasp when applied to objects common in daily living. Moreover, we tested the system in standardized clinical tests that showed a reduction of shoulder and trunk compensatory movements with respect to a state-of- the-art commercial prosthesis.

Regarding the passive WiFi sensing based crowd analysis, this paper first theoretically investigates its limitations, and then proposes a deep learning based scheme targeted for returning fine-grained crowd states in large surveillance areas. To this end, three key challenges are coped with: to relieve the influences of the randomness and sparsity induced by passive WiFi sensing, an attention-based deep convolutional autoencoder model is designed to recover accurate crowd density maps in a way similar to image reconstruction; to combat the anonymity caused by MAC randomization, following the identification of local high-density crowds (LHDCs) with the density clustering algorithm, i.e. DM-DBSCAN, a bidirectional convolutional LSTM based model is employed to infer LHDC speeds; to overcome the absence of passive WiFi sensing datasets for model training, three semi-synthetic datasets are produced by emulating passive WiFi sensing with practical pedestrian tracking datasets. Extensive experiments confirm that, the proposed scheme significantly outperforms existing WiFi-based methods in terms of crowd density estimation and provides superior crowd speed estimation. More importantly, the scheme can also produce consistent crowd states on a real-world dataset, revealing that it has the ability to support accurate, visualized and real-time crowd monitoring in large surveillance areas.

Even though achieving global connectivity represents one of the main goals of 5G and beyond wireless networks, exurban areas are still suffering frequent outages due to the lack of proper telecom infrastructures, which are often available only in urban areas. Indeed, cellular network design is usually capacity-driven, and thus base stations’ densities mostly follow population and especially revenue densities. Contextually, we focus on one of the most promising solutions to provide sufficient and reliable coverage in far-flung areas: aerial base stations, which consist of unmanned aerial vehicles carrying cellular base station equipment. In this paper, we extensively discuss the problem of bridging the so-called urban-rural digital divide (i.e., the connectivity gap between urban and rural areas) from various perspectives. First, we showcase various alternative solutions, and compare conventional terrestrial networks with aerial networks from a techno-economic point of view. Then, we highlight the topological aspects of rural environments and explain how they can affect the actual design of cellular networks. In addition, we investigate both the coverage probability and the reliability of the communication links via simulations, proving that the integration of aerial base stations can be quite promising in a 6G perspective. Finally, we propose two original extensions of our case study as open problems.

In the context of India's document printing practices, this research paper sheds light on the existing shortfalls in privacy and security. Despite the prevalence of digital sharing, conventional methods such as email and messaging platforms continue to be widely used, putting sensitive documents at risk of unauthorized access, data breaches, and potential misuse. This paper aims to address these concerns by proposing a practical approach tailored to the unique needs of photocopy making shops and cyber centers. By focusing on enhancing privacy and security measures, the proposed approach aims to empower individuals and organizations with greater control over their sensitive documents. The research delves into the pressing concerns surrounding document handling in these environments and explores ways to ensure data protection while utilizing modern document printing and sharing technologies. Through this timely endeavor, the aim is to create a safer and more secure ecosystem for document management in India's photocopy making shops and cyber centers.

How to experimentally show that a quantum gate protected by a fully error-corrected code (e.g. [[7,1,3]] has higher fidelity than that of its physical counterpart, without encoded state-preparation. The experimental results are based on IBMQ device ibmq_melbourne.

A document by Zixuan Wang . Click on the document to view its contents.

To provide various intelligent services in Internet of Vehicles (IoVs), such as autonomous driving, data sharing technologies enable vehicles to overcome information barriers and provide a big data foundation. Federated Learning (FL), which shares models instead of raw data, has emerged as a popular solution to address privacy concerns. However, current approaches are limited scalability and security, which are not suitable for the dynamic network topology of IoV scenarios. In this letter, we propose a Multi-Region Asynchronous Swarm Learning (MASL) framework in IoVs, which is empowered by the hierarchical blockchain and executed parallel between multiple regions. The MASL integrates identity verification and asynchronous model training while ensuring secure aggregation as well as data privacy. Through intra-regional and cross-regional sharing, the security and efficiency during large-scale data sharing in IoVs are effectively improved while alleviating the Non-IID data problem. Finally, both the simulation and hardware testbed results demonstrate that the proposed MASL framework could achieve better performances in terms of efficiency and security compared with the existing algorithms.

Integrated Thermal and Energy Management of Connected Hybrid Electric Vehicles Using Deep Reinforcement Learning

How to correct quantum errors without encoding and parity checks? what forms of real-life quantum noise can actually be reversed on the run-time? and how can we engineer more noise-robust quantum circuits? learn more on these new findings in this PRA research article.

This work deals with the spatial characteristics of the wind fields evaluated from synthetic aperture radar (SAR) images and simulated by the weather research and  forecasting (WRF) atmospheric model in the Gulf of  Oristano, a small coastal area about 10 km × 18 km wide in western coast of Sardinia (Western Mediterranean Sea). The SAR-derived wind fields have been obtained analyzing images of the COSMO-SkyMed, Radarsat-2, and Sentinel-1A satellites through a fully two-dimensional continuous wavelet transform (2-D-CWT) method. The analysis of the wind directions has shown that the model variability is limited if compared to that inferred by 2-D-CWT method, which mostly respects the variability evidenced by in situ data. As the use of model directions to compute the SAR wind fields is a standard in many studies, the impact on the SAR wind speed retrieval of using the model instead of the SAR-derived directions has been assessed: differences of wind speed greater than ±10% occur for about the 20% of data. The spatial variability of the SAR and model wind speed fields results quite different at both local and domain scales. The knowledge of the spatial variations of the surface wind fields can be very important for the oceanographic applications and constitutes the added value brought by SAR in the description of the coastal wind. For this reason, the SAR-derived wind fields should be taken as reference in many kind of applications.