Application of the inhomogeneous Lippmann-Schwinger equation to inverse scattering problems

In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it merges a qualitative and a quantitative method to optimize the way of exploiting the a priori information on the background within the inversion procedure, thus improving the quality of the reconstruction and reducing the data amount necessary for a satisfactory result. In the qualitative step, this a priori knowledge is utilized to implement the linear sampling method in its near-field formulation for an inhomogeneous background, in order to identify the region where the scatterer is located. On the other hand, the same a priori information is also encoded in the quantitative step by extending and applying the contrast source inversion method to what we call the `inhomogeneous Lippmann-Schwinger equation': the latter is a generalization of the classical Lippmann-Schwinger equation to the case of an inhomogeneous background, and in our paper is deduced from the differential formulation of the direct scattering problem to provide the reconstruction algorithm with an appropriate theoretical basis. Then, the point values of the refractive index are computed only in the region identified by the linear sampling method at the previous step. The effectiveness of this hybrid approach is supported by numerical simulations presented at the end of the paper.Comment: accepted in SIAM Journal on Applied Mathematic

Green Roofs Over Time: A Spatially Explicit Method for Studying Green Roof Vegetative Dynamics and Performance

In the past decade, conventional green roof research methodology has emphasized performance measures that assume a static state condition of vegetative composition based on design intent and establishment conditions. Such research has predominantly been limited to short-term observations for low diversity, rigorously maintained systems. These conditions, however, are not the reality of many installed green roofs, and as a result knowledge of how these living systems change over time is limited. Given this perspective, this paper presents an ecologically grounded and spatially explicit methodology aimed at assessing the long-term performance and dynamics of green roof vegetation. The method allows for observations of plant composition and performance based on both statistical and graphical analysis of plant cover and diversity measures. Application of this methodology is presented through a multi-year case study of a single, six year-old, intensive green roof in Ithaca, New York. Applicable to any green roof, this method promotes an understanding of green roofs as adaptive, ecological systems, a perspective that will aid in better predicting green roof performance over time, and inform the design, construction, and maintenance of resilient, high-performance roofscapes

Analysis of movement quality in full-body physical activities

Full-body human movement is characterized by fine-grain expressive qualities that humans are easily capable of exhibiting and recognizing in others' movement. In sports (e.g., martial arts) and performing arts (e.g., dance), the same sequence of movements can be performed in a wide range of ways characterized by different qualities, often in terms of subtle (spatial and temporal) perturbations of the movement. Even a non-expert observer can distinguish between a top-level and average performance by a dancer or martial artist. The difference is not in the performed movements-the same in both cases-but in the \u201cquality\u201d of their performance. In this article, we present a computational framework aimed at an automated approximate measure of movement quality in full-body physical activities. Starting from motion capture data, the framework computes low-level (e.g., a limb velocity) and high-level (e.g., synchronization between different limbs) movement features. Then, this vector of features is integrated to compute a value aimed at providing a quantitative assessment of movement quality approximating the evaluation that an external expert observer would give of the same sequence of movements. Next, a system representing a concrete implementation of the framework is proposed. Karate is adopted as a testbed. We selected two different katas (i.e., detailed choreographies of movements in karate) characterized by different overall attitudes and expressions (aggressiveness, meditation), and we asked seven athletes, having various levels of experience and age, to perform them. Motion capture data were collected from the performances and were analyzed with the system. The results of the automated analysis were compared with the scores given by 14 karate experts who rated the same performances. Results show that the movement-quality scores computed by the system and the ratings given by the human observers are highly correlated (Pearson's correlations r = 0.84, p = 0.001 and r = 0.75, p = 0.005)

Fast electron slowing-down and diffusion in a high temperature coronal X-ray source

Finite thermal velocity modifications to electron slowing-down rates may be important for the deduction of solar flare total electron energy. Here we treat both slowing-down and velocity diffusion of electrons in the corona at flare temperatures, for the case of a simple, spatially homogeneous source. Including velocity diffusion yields a consistent treatment of both "accelerated" and "thermal" electrons. It also emphasises that one may not invoke finite thermal velocity target effects on electron lifetimes without simultaneously treating the contribution to the observed X-ray spectrum from thermal electrons. We present model calculations of the X-ray spectra resulting from injection of a power-law energy distribution of electrons into a source with finite temperature. Reducing the power-law distribution low-energy cutoff to lower and lower energies only increases the relative magnitude of the thermal component of the spectrum, because the lowest energy electrons simply join the background thermal distribution. Acceptable fits to RHESSI flare data are obtained using this model. These also demonstrate, however, that observed spectra may in consequence be acceptably consistent with rather a wide range of injected electron parameters