The purpose of this paper is to find out a set of general recurrence formulas for the calculus of the SU(3) Clebsch-Gordan coefficients. The first six sections are introductory, presenting the notations and general group theoretical methods applied to SU(3). The following eight sections are devoted to a detailed treatment of the carrier spaces of the irreducible representations and their direct...

BACKGROUND AND PURPOSE DTI is a tool for microstructural spinal cord injury evaluation. This study evaluated the reproducibility of a semiautomated segmentation algorithm of spinal cord DTI. MATERIALS AND METHODS Forty-two consecutive patients undergoing acute trauma cervical spine MR imaging underwent 2 axial DTI scans in addition to their clinical scan. The datasets were put through a semia...

Modeling the movement and consequence of radioactive pollutants is critical for environmental protection and control of nuclear facilities. Sensitivity analysis is an integral part of model development and involves analytical examination of input parameters to aid in model validation and provide guidance for future research. Sensitivities of 21 input parameters have been analyzed for a specific...

The quality of rankings can be evaluated by computing their correlation to an optimal ranking. State of the art ranking correlation coefficients like Kendall’s τ and Spearman’s ρ do not allow for the user to specify similarities between differing object classes and thus treat the transposition of objects from similar classes the same way as that of objects from dissimilar classes. We propose Cl...

Selection and identification of a subset of compounds from libraries or databases, which are likely to possess a desired biological activity is the main target of ligand-based virtual screening approaches. The main challenge of such approaches is achieving of high recall of active molecules. In this paper we presented fuzzy correlation coefficients (FCC), which is used as a similarity coefficie...

We identify “spurious” states in meson-baryon scattering, those that appear in QCD for Nc > 3 but decouple for Nc = 3. The key observation is that the relevant flavor SU(3) Clebsch-Gordan coefficients contain factors of 1−3/Nc. We show that this method works even if SU(3) is badly broken. We also observe that resonant scattering poles lying outside naive quark model multiplets are not necessari...

This paper introduces a causation coefficient which is defined in terms of probabilistic causal models. This coefficient is suggested as the natural causal analogue of the Pearson correlation coefficient and permits comparing causation and correlation to each other in a simple, yet rigorous manner. Together, these coefficients provide a natural way to classify the possible correlation/causation...