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This paper addresses the problem of selecting the minimum number of dedicated sensors to achieve observability in the presence of unknown inputs, namely, the state and input observability, for linear time-invariant systems. We assume that the only available information is the zero-nonzero structure of system matrices, and approach this problem within a structured system model. We revisit the concept of state and input observability for structured systems, providing refined necessary and sufficient conditions for placing dedicated sensors via the Dulmage-Mendelsohn decomposition. Based on these conditions, we prove that determining the minimum number of dedicated sensors to achieve generic state and input observability is NP-hard, which contrasts sharply with the polynomial-time complexity of the corresponding problem with known inputs. We also demonstrate that this problem is hard to approximate within a factor of $(1-o(1)){\rm{log}}(n)$, where $n$ is the state dimension. Notwithstanding, we propose nontrivial upper and lower bounds that can be computed in polynomial time, which confine the optimal value of this problem to an interval with length being the number of inputs. We further present a special case for which the exact optimal value can be determined in polynomial time. Additionally, we propose a two-stage algorithm to solve this problem approximately. Each stage of the algorithm is either optimal or suboptimal and can be completed in polynomial time., Comment: 12 pages, 6 figures

Rapid urbanization and improved living standards have led to a substantial increase in the number of vehicles on the road, consequently resulting in a rise in the frequency of accidents. Among these accidents, motorbike accidents pose a particularly high risk, often resulting in serious injuries or deaths. A significant number of these fatalities occur due to delayed or inadequate medical attention. To this end, we propose a novel automatic detection and notification system specifically designed for motorbike accidents. The proposed system comprises two key components: a detection system and a physiological signal monitoring system. The detection system is integrated into the helmet and consists of a microcontroller, accelerometer, GPS, GSM, and Wi-Fi modules. The physio-monitoring system incorporates a sensor for monitoring pulse rate and SpO$_{2}$ saturation. All collected data are presented on an LCD display and wirelessly transmitted to the detection system through the microcontroller of the physiological signal monitoring system. If the accelerometer readings consistently deviate from the specified threshold decided through extensive experimentation, the system identifies the event as an accident and transmits the victim's information -- including the GPS location, pulse rate, and SpO$_{2}$ saturation rate -- to the designated emergency contacts. Preliminary results demonstrate the efficacy of the proposed system in accurately detecting motorbike accidents and promptly alerting emergency contacts. We firmly believe that the proposed system has the potential to significantly mitigate the risks associated with motorbike accidents and save lives.

This research provides an in-depth comprehensive review of the progress of chatbot technology over time, from the initial basic systems relying on rules to today's advanced conversational bots powered by artificial intelligence. Spanning many decades, the paper explores the major milestones, innovations, and paradigm shifts that have driven the evolution of chatbots. Looking back at the very basic statistical model in 1906 via the early chatbots, such as ELIZA and ALICE in the 1960s and 1970s, the study traces key innovations leading to today's advanced conversational agents, such as ChatGPT and Google Bard. The study synthesizes insights from academic literature and industry sources to highlight crucial milestones, including the introduction of Turing tests, influential projects such as CALO, and recent transformer-based models. Tracing the path forward, the paper highlights how natural language processing and machine learning have been integrated into modern chatbots for more sophisticated capabilities. This chronological survey of the chatbot landscape provides a holistic reference to understand the technological and historical factors propelling conversational AI. By synthesizing learnings from this historical analysis, the research offers important context about the developmental trajectory of chatbots and their immense future potential across various field of application which could be the potential take ways for the respective research community and stakeholders.

Malaria is the leading cause of death globally, especially in sub-Saharan African countries claiming over 400,000 deaths globally each year, underscoring the critical need for continued efforts to combat this preventable and treatable disease. The objective of this study is to provide statistical guidance on the optimal preventive and control measures against malaria. Data have been collected from reliable sources, such as World Health Organization, UNICEF, Our World in Data, and STATcompiler. Data were categorized according to the factors and sub-factors related to deaths caused by malaria. These factors and sub-factors were determined based on root cause analysis and data sources. Using JMP 16 Pro software, both linear and multiple linear regression were conducted to analyze the data. The analyses aimed to establish a linear relationship between the dependent variable (malaria deaths in the overall population) and independent variables, such as life expectancy, malaria prevalence in children, net usage, indoor residual spraying usage, literate population, and population with inadequate sanitation in each selected sample country. The statistical analysis revealed that using insecticide treated nets (ITNs) by children and individuals significantly decreased the death count, as 1,000 individuals sleeping under ITNs could reduce the death count by eight. Based on the statistical analysis, this study suggests more rigorous research on the usage of ITNs.

Healthcare data is sensitive and requires great protection. Encrypted electronic health records (EHRs) contain personal and sensitive data such as names and addresses. Having access to patient data benefits all of them. This paper proposes a blockchain-based distributed healthcare application platform for Bangladeshi public and private healthcare providers. Using data immutability and smart contracts, the suggested application framework allows users to create safe digital agreements for commerce or collaboration. Thus, all enterprises may securely collaborate using the same blockchain network, gaining data openness and read/write capacity. The proposed application consists of various application interfaces for various system users. For data integrity, privacy, permission and service availability, the proposed solution leverages Hyperledger fabric and Blockchain as a Service. Everyone will also have their own profile in the portal. A unique identity for each person and the installation of digital information centres across the country have greatly eased the process. It will collect systematic health data from each person which will be beneficial for research institutes and health-related organisations. A national data warehouse in Bangladesh is feasible for this application and It is also possible to keep a clean health sector by analysing data stored in this warehouse and conducting various purification algorithms using technologies like Data Science. Given that Bangladesh has both public and private health care, a straightforward digital strategy for all organisations is essential., Comment: 21 pages, 16 figures, 4 tables