ASU Scholarship Showcase

This chapter is not a guide to embodied thinking, but rather a critical call to action. It highlights the deep history of embodied practice within the fields of dance and somatics, and outlines the value of embodied thinking within human-computer interaction (HCI) design and, more specifically, wearable technology (WT) design. What this chapter does not do is provide a guide or framework for embodied practice. As a practitioner and scholar grounded in the fields of dance and somatics, I argue that a guide to embodiment cannot be written in a book. To fully understand embodied thinking, one must act, move, and do. Terms such as embodiment and embodied thinking are often discussed and analyzed in writing; but if the purpose is to learn how to engage in embodied thinking, then the answers will not come from a text. The answers come from movement-based exploration, active trial-and-error, and improvisation practices crafted to cultivate physical attunement to one's own body. To this end, my "call to action" is for the reader to move beyond a text-based understanding of embodiment to active engagement in embodied methodologies. Only then, I argue, can one understand how to apply embodied thinking to a design process.

Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. The Golub{Kahan iterative bidiagonalization is used to project the problem onto a subspace and regularization then applied to nd a subspace approximation to the full problem. Determination of the regularization, parameter for the projected problem by unbiased predictive risk estimation, generalized cross validation, and discrepancy principle techniques is investigated. It is shown that the regularized parameter obtained by the unbiased predictive risk estimator can provide a good estimate which can be used for a full problem that is moderately to severely ill-posed. A similar analysis provides the weight parameter for the weighted generalized cross validation such that the approach is also useful in these cases, and also explains why the generalized cross validation without weighting is not always useful. All results are independent of whether systems are over- or underdetermined. Numerical simulations for standard one-dimensional test problems and two- dimensional data, for both image restoration and tomographic image reconstruction, support the analysis and validate the techniques. The size of the projected problem is found using an extension of a noise revealing function for the projected problem [I. Hn etynkov a, M. Ple singer, and Z. Strako s, BIT Numer. Math., 49 (2009), pp. 669{696]. Furthermore, an iteratively reweighted regularization approach for edge preserving regularization is extended for projected systems, providing stabilization of the solutions of the projected systems and reducing dependence on the determination of the size of the projected subspace.