Alan V. Sahakian

Abstract Objective. When electrical impedance tomography is applied to a known system, such as the human body, a parameterized model is shown to produce a more accurate reconstruction than a conductivity map. Furthermore, if the number of free parameters is less than the total number of independent measurements, the sensitivity volume method can be employed to identify a significantly reduced number of data measurements with the highest value for distinguishing these parameters. Approach. To achieve direct parametric inversion from this reduced set of measurements, a simple algorithm establishes the correspondence between training data and parameterized model cases. Here two training algorithms will be demonstrated. For sparse sampling, the parameters associated with each trained case are interpolated to generate a high density of invertible data cases. For dense sampling, enough cases are directly measured that a simple nearest-neighbor search in data space can invert the data. Main result. Once the training is established, a simple nearest-neighbor query in data space has a one-to-one correspondence with the model parameters for reconstruction. Sparse sampling is demonstrated with an insulating cylinder in a saltwater tub whose diameter and angular position constitute a two-dimensional (2D) model space, and whose reduced high-value data space consists of 9 independent tetrapolar data measurements made with 15 available electrodes. Dense sampling is demonstrated with a mechanical goldfish in a saltwater tub whose coordinates and orientation define a 3D model space, and whose reduced high-value data space consists of 16 tetrapolar data measurements made from 128 available electrodes. Significance. The parametric method demonstrated here reduces the necessary number of data measurements by orders of magnitude compared to standard electrical impedance tomography to achieve higher accuracy within the parametric representation, and can, in principle, be expanded to complex 3D systems such as organs within the human body to achieve fast, high fidelity parametric reconstructions.

Abstract In constrained inverse problems, such as biomedicine where human anatomy constitutes a known prior, a parameterized model can at times be just as effective at producing an accurate image directly from EIT data without resorting to an intermediate conductivity map. A reduced measurement set of high-value data can be mapped directly to the limited number of model space parameters of interest. To achieve this direct inversion, the high-value data can be identified with the sensitivity volume method, and a sparse data sampling of the model space can be continuously interpolated to span the complete model space. A simple nearest-neighbor query in data space then maps directly to a parametric representation for reconstruction. This method is experimentally demonstrated in a salt water tub with an insulating cylindrical inclusion whose diameter and angular position constitute a two-dimensional model space. The parametric method demonstrated here requires an order of magnitude fewer data measurements than standard EIT to achieve equivalent accuracy within the parametric representation of the model, and can be expanded to 3D and systems of higher complexity such as organs within the human body to achieve high fidelity parametric reconstructions with minimal data collection and fast, real-time image generation and diagnostics.

Remarkable breakthroughs have established the functionality of graphene and carbon nanotube transistors as replacements to silicon in conventional computing structures, and numerous spintronic logic gates have been presented. This chapter introduces a cascaded spintronic computing system composed solely of low-dimensional carbon materials. Covalently connected carbon nanotubes create magnetic fields through graphene nanoribbons, cascading logic gates through incoherent spintronic switching. All-carbon spin logic permits the development of cascaded spintronic logic circuits composed solely of low-dimensional carbon materials without intermediate circuits between gates, resulting in compact circuits with reduced area that are far more efficient than CMOS. By exploiting the exotic behaviour of graphene nanoribbons and carbon nanotubes, all-carbon spin logic enables a spintronic paradigm for the next generation of high-performance computing. In the mean-field approximation, the expectation of the on-site occupation is used to reduce the complexity of the Hamiltonian, which can be solved with iterative methods.