CNDOL: A fast and reliable method for the calculation of electronic properties of very large systems. Applications to retinal binding pocket in rhodopsin and gas phase porphine.

Very large molecular systems can be calculated with the so called CNDOL approximate Hamiltonians that have been developed by avoiding oversimplifications and only using a priori parameters and formulas from the simpler NDO methods. A new diagonal monoelectronic term named CNDOL/21 shows great consistency and easier SCF convergence when used together with an appropriate function for charge repulsion energies that is derived from traditional formulas. It is possible to obtain a priori molecular orbitals and electron excitation properties after the configuration interaction of single excited determinants with reliability, maintaining interpretative possibilities even being a simplified Hamiltonian. Tests with some unequivocal gas phase maxima of simple molecules (benzene, furfural, acetaldehyde, hexyl alcohol, methyl amine, 2,5 dimethyl 2,4 hexadiene, and ethyl sulfide) ratify the general quality of this approach in comparison with other methods. The calculation of large systems as porphine in gas phase and a model of the complete retinal binding pocket in rhodopsin with 622 basis functions on 280 atoms at the quantum mechanical level show reliability leading to a resulting first allowed transition in 483 nm, very similar to the known experimental value of 500 nm of "dark state." In this very important case, our model gives a central role in this excitation to a charge transfer from the neighboring Glu(-) counterion to the retinaldehyde polyene chain. Tests with gas phase maxima of some important molecules corroborate the reliability of CNDOL/2 Hamiltonians.

Efficient total variation algorithm for fetal MRI reconstruction

Fetal MRI reconstruction aims at finding a high-resolution image given a small set of low-resolution images. It is usually modeled as an inverse problem where the regularization term plays a central role in the reconstruction quality. Literature has considered several regularization terms s.a. Dirichlet/Laplacian energy [1], Total Variation (TV)based energies [2,3] and more recently non-local means [4]. Although TV energies are quite attractive because of their ability in edge preservation, standard explicit steepest gradient techniques have been applied to optimize fetal-based TV energies. The main contribution of this work lies in the introduction of a well-posed TV algorithm from the point of view of convex optimization. Specifically, our proposed TV optimization algorithm for fetal reconstruction is optimal w.r.t. the asymptotic and iterative convergence speeds O(1/n(2)) and O(1/root epsilon), while existing techniques are in O(1/n) and O(1/epsilon). We apply our algorithm to (1) clinical newborn data, considered as ground truth, and (2) clinical fetal acquisitions. Our algorithm compares favorably with the literature in terms of speed and accuracy.

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The present article examines the final part of the regnal formulas in the Book of Kings, i.e. the epilogue formulary. Most reports of the kings of Israel and Judah end with an epilogue containing formulaic statements about the death of the king and his succession. Typically, the epilogue formula is introduced by the phrase (source reference): 'Now the rest of the acts of PN1, are they not written in the Book of the Chronicles of the Kings of Judah (of the Chronicles of the Kings of Israel)?' and consists of three elements: 1. Dynastic notice ('PN1 slept with his fathers'); 2. Statement of burial; 3. Statement of succession. Sometimes one, two or all three of these elements are altered or lacking. The epilogue formulae of the Judean kings are more consistent than those of the Israelite kings; the latter often lacks a burial notice. Interestingly, the accounts of the deported (arrested) kings (Hoshea: 2 Kgs 17:6, Jehoahaz: 23:34, Zedekiah:25:7 and Jehoiachin: 25:27-30) do not contain an epilogue at all, nor the accounts of the reigns of Ahaziah and Athaliah which mark an episode of disruption in the history of the Davidic kingdom. For all these kings even the phrase 'Now the rest of the acts of PN1, are they not written in the Book of the Chronicles of... ?' is lacking. The absence of an epilogue in these cases is probably due to the fact that the king's succession (cf. element 3) is considered a constitutive and indispensable component of the epilogue. In the first instance, the approach of this study is descriptive and philological; it aims to contribute to the understanding of the notices. Secondly, the study addresses the question how the irregularities and variations within the formulae are to be explained. In particular, the study will pay attention to differences between the epilogue formulae concerning the kings of Israel and those concerning the Judean kings. At the end, questions concerning the epilogues formula's provenance and its formation date and concerning further redactional developments will be considered.