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

Modelling fast forms of visual neural plasticity using a modified second-order motion energy model

The Adelson-Bergen motion energy sensor is well established as the leading model of low-level visual motion sensing in human vision. However, the standard model cannot predict adaptation effects in motion perception. A previous paper Pavan et al.(Journal of Vision 10:1-17, 2013) presented an extension to the model which uses a first-order RC gain-control circuit (leaky integrator) to implement adaptation effects which can span many seconds, and showed that the extended model's output is consistent with psychophysical data on the classic motion after-effect. Recent psychophysical research has reported adaptation over much shorter time periods, spanning just a few hundred milliseconds. The present paper further extends the sensor model to implement rapid adaptation, by adding a second-order RC circuit which causes the sensor to require a finite amount of time to react to a sudden change in stimulation. The output of the new sensor accounts accurately for psychophysical data on rapid forms of facilitation (rapid visual motion priming, rVMP) and suppression (rapid motion after-effect, rMAE). Changes in natural scene content occur over multiple time scales, and multi-stage leaky integrators of the kind proposed here offer a computational scheme for modelling adaptation over multiple time scales. © 2014 Springer Science+Business Media New York

Modelling adaptation to directional motion using the Adelson-Bergen energy sensor

The motion energy sensor has been shown to account for a wide range of physiological and psychophysical results in motion detection and discrimination studies. It has become established as the standard computational model for retinal movement sensing in the human visual system. Adaptation effects have been extensively studied in the psychophysical literature on motion perception, and play a crucial role in theoretical debates, but the current implementation of the energy sensor does not provide directly for modelling adaptation-induced changes in output. We describe an extension of the model to incorporate changes in output due to adaptation. The extended model first computes a space-time representation of the output to a given stimulus, and then a RC gain-control circuit ("leaky integrator") is applied to the time-dependent output. The output of the extended model shows effects which mirror those observed in psychophysical studies of motion adaptation: a decline in sensor output during stimulation, and changes in the relative of outputs of different sensors following this adaptation

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/