A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

Estimating genomic instability mediated by Alu retroelements in breast cancer

Alu-PCR is a relatively simple technique that can be used to investigate genomic instability in cancer. This technique allows identification of the loss, gain or amplification of gene sequences based on the analysis of segments between two Alu elements coupled with quantitative and qualitative analyses of the profiles obtained from tumor samples, surgical margins and blood. In this work, we used Alu-PCR to identify gene alterations in ten patients with invasive ductal breast cancer. Several deletions and insertions were identified, indicating genomic instability in the tumor and adjacent normal tissue. Although not associated with specific genes, the alterations, which involved chromosomal bands 1p36.23, 1q41, 11q14.3, 13q14.2, occurred in areas of well-known genomic instability in breast and other types of cancer. These results indicate the potential usefulness of Alu-PCR in identifying altered gene sequences in breast cancer. However, caution is required in its application since the Alu primer can produce non-specific amplification

RAD59 and RAD1 cooperate in translocation formation by single-strand annealing in Saccharomyces cerevisiae

Studies in the budding yeast, Saccharomyces cerevisiae, have demonstrated that a substantial fraction of double-strand break repair following acute radiation exposure involves homologous recombination between repetitive genomic elements. We have previously described an assay in S. cerevisiae that allows us to model how repair of multiple breaks leads to the formation of chromosomal translocations by single-strand annealing (SSA) and found that Rad59, a paralog of the single-stranded DNA annealing protein Rad52, is critically important in this process. We have constructed several rad59 missense alleles to study its function more closely. Characterization of these mutants revealed proportional defects in both translocation formation and spontaneous direct-repeat recombination, which is also thought to occur by SSA. Combining the rad59 missense alleles with a null allele of RAD1, which encodes a subunit of a nuclease required for the removal of non-homologous tails from annealed intermediates, substantially suppressed the low frequency of translocations observed in rad1-null single mutants. These data suggest that at least one role of Rad59 in translocation formation by SSA is supporting the machinery required for cleavage of non-homologous tails

Large landslides on passive continental margins: processes, hypotheses and outstanding questions

The volume, area affected, and runout of submarine landslides can exceed those of terrestrial events by two orders of magnitude. The Storegga Slide off Norway affected an area the size of Scotland and moved enough sediment to bury the entire country to a depth of 80 m. Modern geophysics provides a clear picture of large landslides and what their source and depositional areas look like. From this, we can deduce the processes that operated during downslope transport. However, our understanding of many aspects of landslide processes is based on hypotheses that are difficult to test. Elevated pore pressures are essential for landslide initiation on low continental margin slopes, yet understanding of how high pressures are generated or how fluid migration affects slope stability is limited. Sediments may be pre-conditioned for failure by the processes that originally deposited them, e.g., through creation of weak layers, but the processes and parameters that might control this are largely unknown. <br/