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Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinates that describe the data manifold. The coordinates returned by the embedding algorithm are abstract, and finding their physical or domain-related meaning is not formalized and often left to domain experts. This paper studies the problem of recovering the meaning of the new low-dimensional representation in an automatic, principled fashion. We propose a method to explain embedding coordinates of a manifold as non-linear compositions of functions from a user-defined dictionary. We show that this problem can be set up as a sparse linear Group Lasso recovery problem, find sufficient recovery conditions, and demonstrate its effectiveness on data 

Abstract Conformable electronics are regarded as the next generation of personal healthcare monitoring and remote diagnosis devices. In recent years, piezoelectric‐based conformable ultrasound electronics (cUSE) have been intensively studied due to their unique capabilities, including nonradiative monitoring, soft tissue imaging, deep signal decoding, wireless power transfer, portability, and compatibility. This review provides a comprehensive understanding of cUSE for use in biomedical and healthcare monitoring systems and a summary of their recent advancements. Following an introduction to the fundamentals of piezoelectrics and ultrasound transducers, the critical parameters for transducer design are discussed. Next, five types of cUSE with their advantages and limitations are highlighted, and the fabrication of cUSE using advanced technologies is discussed. In addition, the working function, acoustic performance, and accomplishments in various applications are thoroughly summarized. It is noted that application considerations must be given to the tradeoffs between material selection, manufacturing processes, acoustic performance, mechanical integrity, and the entire integrated system. Finally, current challenges and directions for the development of cUSE are highlighted, and research flow is provided as the roadmap for future research. In conclusion, these advances in the fields of piezoelectric materials, ultrasound transducers, and conformable electronics spark an emerging era of biomedicine and personal healthcare. 

Abstract Painless, needleless delivery of drugs through the skin can be realized through aphenomenon called sonophoresis by applying an ultrasound field to the biological tissue. Development of wearable embodiments of such systems demands comprehensive characterization of both the physical mechanism of sonophoresisas well as wearability parameters. Here, we present a framework for analyzing disk‐type piezoelectric transducers in a polymeric substrate to create acoustic cavitation in a fluid coupling medium for sonophoresis applications. The device design and operating parameters such as the working frequency, applied voltage range, acoustic pressure distribution, and transducer spacing were determine dusing a finite element methods (FEM),and verified with experimental measurements. The influence of the surrounding water and tank reflections on the acoustic pressure field, and the interaction between the elements in the array structure were also studied.Finally, the impact of skin and the substrate geometry on the acoustic pressure fields was characterized to simulate the invivo use‐case of the system. These analytical models can be used to guide critical parameters for device design such as the separation distance of the piezoelectric transducer from the skin boundary. We envision that this tool boxwill support rapid design iteration for realization of wearable ultrasound systems.