Eric Howard

In this manuscript we discuss improved estimation of the population mean when non-response occurs only on the study variable. The suggested estimator uses known parameters of the auxiliary variable within the framework of ratio estimation under basic probability sampling. Expressions for the bias and mean squared error (MSE) of the proposed estimator are derived using a first-order Taylor series approximation. Several mathematical conditions are obtained under which the proposed estimator performs better, in the sense of having a smaller MSE, than well-known existing estimators. A numerical study is conducted using a real dataset (diamonds dataset from the ggplot2 package) to validate the theoretical findings.

Quantum computing can transform the field of highly-precise measurement systems in the physical sciences with new levels of sensitivity, resolution, and capability to compute data. Quantum-enhanced measurement systems may also reach levels of precision that are constrained by the inherent quantum noise due to quantum superposition, entanglement and coherence. This opens up to innovations in such research as magnetic field sensing, atomic clock synchronization, and seeing gravitational waves. Quantum computing can be used to retrieve high-fidelity information in noisy data, improvements in signal-to-noise ratios by quantum techniques, like phase estimation and the Quantum Fourier Transform, are possible, and quantum techniques have been demonstrated to surpass classical limits. Moreover, quantum sensors that are integrated into quantum computing structures make real-time feedback and adaptive measurement methods feasible, dynamically optimising system efficiency. Moreover, quantity metrology combined with quantum computing enables sensitive studies in fundamental physics, including experimental tests of quantum gravity or a study of the dark matter. Current developments in error correction and hardware design are rapidly enhancing the usefulness of quantum systems in practice, even in the face of the current technological challenges of qubit decoherence and scalability. This paper discusses the current state of quantum computing in the field of precision measurement and potential future directions, the way that quantum computing might transform the physical sciences and push the boundaries of experimental accuracy.

We propose a low energy model for simulating an analog black hole on an optical lattice using ultracold atoms. Assuming the validity of the holographic principle, we employ the Sachdev-Ye-Kitaev (SYK) model, which describes a system of randomly infinite range interacting fermions, also conjectured to be an exactly solvable UV-complete model for an extremal black hole in a higher dimensional Anti-de Sitter (AdS) dilaton gravity. At low energies, the SYK model exhibits an emergent conformal symmetry and is dual to the extremal black hole solution in near AdS2 spacetime. Furthermore, we show how the SYK maximally chaotic behaviour at large N limit, found to be dual to a gauge theory in higher dimensions, can also be employed as a non-trivial investigation tool for the holographic principle. The proposed setup is a theoretical platform to realize the SYK model with relevant exotic effects and behaviour at low energies as a highly non-trivial example of the AdS/CFT duality and a framework for studying black holes.

The healthcare sector has benefited greatly from the integration of AI/ML with distributed technologies like edge computing, blockchain, and Internet of Things (IoT) to address challenges like data interoperability, security, and scalability. This synergy has a major impact on patient care, medical research, and the efficiency of the healthcare system. AI/ML techniques are used in a variety of fields, including drug development, medical imaging interpretation, picture identification, predictive analytics, and sickness prediction. The relationship between AI/ML and distributed technologies—such as decentralized architectures for safe access to real-time data sources, blockchain for data integrity and privacy, and edge computing for low-latency processing—is discussed. When combining AI/ML with dispersed technology, the healthcare business faces trends and concerns related to interoperability, legal compliance, and ethical issues.

Coupled Schrödinger equations with fractional damping represent a complex yet fascinating area of study in quantum mechanics. This research paper delves into the analytical investigation of such systems, focusing on deriving decay solutions and conducting stability analysis. By combining theoretical frameworks with numerical methods, we explore the behavior of these coupled equations under varying parameters and conditions. Through a thorough analysis, we aim to deepen our understanding of the dynamics and stability properties of quantum systems subject to fractional damping, with potential implications for diverse fields ranging from quantum mechanics to condensed matter physics.

This study investigates the stability and decay properties of solutions to nonlinear Schrödinger equations (NLSEs) with time-dependent coefficients. Employing a blend of analytical and numerical methods, we delve into how temporal variations in coefficients influence the dynamics of wave functions. Our analysis reveals that time-dependent coefficients significantly affect the stability and decay rates of solutions, uncovering conditions that lead to either enhanced stability or accelerated decay. The findings highlight the critical role of coefficient temporality in dictating the behavior of NLSE solutions. These insights not only advance our theoretical understanding of NLSEs but also bear implications for practical applications in fields modeled by these equations. Our research opens avenues for exploiting time-dependent behaviors in designing systems with desired dynamical properties.

To monitor and comprehend the thermal environment, it is vital to deploy Internet of Things (IoT) temperature sensors in metropolitan areas. Overheating and err To monitor and comprehend the thermal environment, it is vital to deploy Internet of Things (IoT) temperature sensors in metropolitan areas. Overheating and err

This fine compendium of essays is a fascinating compilation of articles written by Professor James B. Hartle over a period of thirty years. The volume is well presented, organised in 29 essays addr...