Recently, an accurate solution to the interior problem was proposed based on the total variation (TV) minimization, assuming that a region of interest (ROI) is piecewise constant. In this paper, we generalize that assumption to allow a piecewise polynomial ROI, introduce the high order TV (HOT), and prove that an ROI can be accurately reconstructed from projection data associated with x-rays through the ROI through the HOT minimization if the ROI is piecewise polynomial. Then, we verify our theoretical results in numerical simulation.

Researchers collaborate on scientific projects that are often measured by both the quantity and the quality of the resultant peerreviewed publications. However, not all collaborators contribute to these publications equally, making metrics such as the total number of publications and the H-index insufficient measurements of individual scientific impact. To remedy this, we use an axiomatic approach to assign relative credits to the coauthors of a given paper, referred to as the A-index for its axiomatic foundation. In this paper, we use the A-index to compute the weighted sums of peer-reviewed publications and journal impact factors, denoted as the C-and P-indexes for collaboration and productivity, respectively. We perform an in-depth analysis of bibliometric data for 186 biomedical engineering faculty members and from extensive simulation. It is found that these axiomatically weighted indexes better capture a researcher's scientific caliber than do the total number of publications and the H-index, allowing for fairer and sharper evaluation of researchers with diverse collaborative behaviors.

Nuclear B-catenin forms a transcription complex with TCF-4, which is implicated in colon cancer development and progression. Recently, we and others have shown that B-catenin could be a regulator of RNA splicing and it also stabilizes the cyclooxygenase-2 (COX-2) mRNA. Here, we further explored the role of B-catenin in the RNA metabolism in colon cancer cells. To specifically modulate the subcellular functions of B-catenin, we expressed the RNA aptamer in the form of RNA intramers with unique cellular localizations. The nucleus-expressed RNA intramer proved to be effective in reducing the protein-protein interaction between B-catenin and TCF-4, thus shown to be a specific regulator of B-cateninactivated transcription. It could also regulate the alternative splicing of E1A minigene in diverse colon cancer cell lines. In addition, we tested whether B-catenin could stabilize any other mRNAs and found that cyclin D1 mRNA was also bound and stabilized by B-catenin. Significantly, the cytoplasmexpressed RNA intramer reverted the B-catenin-induced COX-2 and cyclin D1 mRNA stabilization. We show here that B-catenin regulated multiple steps of RNA metabolism in colon cancer cells and might be the protein factor coordinating RNA metabolism. We suggest that the RNA intramers could provide useful ways for inhibiting B-catenin-mediated transcription and RNA metabolism, which might further enhance the antitumorigenic effects of these molecules in colon cancer cells. [Cancer Res 2007;67(19):9315-21]

Recently, in the compressed sensing framework we proved that an interior ROI can be exactly reconstructed via the total variation minimization if the ROI is piecewise constant. In the proofs, we implicitly utilized the property that if an artifact image assumes a constant value within the ROI then this constant must be zero. Here we prove this property in the space of square integrable functions.

Recently, we developed an approach for solving the computed tomography (CT) interior problem based on the high-order TV (HOT) minimization, assuming that a region-of-interest (ROI) is piecewise polynomial. In this paper, we generalize this finding from the CT field to the single-photon emission computed tomography (SPECT) field, and prove that if an ROI is piecewise polynomial, then the ROI can be uniquely reconstructed from the SPECT projection data associated with the ROI through the HOT minimization. Also, we propose a new formulation of HOT, which has an explicit formula for any n-order piecewise polynomial function, while the original formulation has no explicit formula for n ≥ 2. Finally, we verify our theoretical results in numerical simulation, and discuss relevant issues.