Analysis of Linsker's simulations of Hebbian rules

Linsker has reported the development of center-surround receptive fields and oriented receptive fields in simulations of a Hebb-type equation in a linear network. The dynamics of the learning rule are analyzed in terms of the eigenvectors of the covariance matrix of cell activities. Analytic and computational results for Linsker's covariance matrices, and some general theorems, lead to an explanation of the emergence of center-surround and certain oriented structures. We estimate criteria for the parameter regime in which center-surround structures emerge

Torsional path integral Monte Carlo method for calculating the absolute quantum free energy of large molecules

A new technique for evaluating the absolute free energy of large molecules is presented. Quantum-mechanical contributions to the intramolecular torsions are included via the torsional path integral Monte Carlo (TPIMC) technique. Importance sampling schemes based on uncoupled free rotors and harmonic oscillators facilitate the use of the TPIMC technique for the direct evaluation of quantum partition functions. Absolute free energies are calculated for the molecules ethane, n-butane, n-octane, and enkephalin, and quantum contributions are found to be significant. Comparison of the TPIMC technique with the harmonic oscillator approximation and a variational technique is performed for the ethane molecule. For all molecules, the quantum contributions to free energy are found to be significant but slightly smaller than the quantum contributions to internal energy

Quantum free energies of the conformers of glycine on an ab initio potential energy surface

The torsional path integral Monte Carlo (TPIMC) technique is used to study the five lowest-energy conformers of glycine. The theoretical method provides an anharmonic and quantum-mechanical description of conformational free energy and is used for the first time with an ab initio potential energy surface. The 3-dimensional torsional potential energy surface of glycine was obtained at the MP2/6-311++G** level of theory and is optimized with respect to the non-torsional degrees of freedom. Calculated conformer populations compare well with those reported in recent matrix-isolation infrared spectroscopy experiments. An additional conformer, not yet observed, is predicted to be heavily populated in the thermal equilibria probed by experiment, and a new explanation for its elusiveness is provided. Quantum effects, such as zero point energy, are found to substantially alter conformer populations, and an algorithm for estimating the role of non-torsional vibrations in the conformational thermodynamics of a molecule is introduced

Torsional path integral Monte Carlo method for the quantum simulation of large molecules

A molecular application is introduced for calculating quantum statistical mechanical expectation values of large molecules at nonzero temperatures. The Torsional Path Integral Monte Carlo (TPIMC) technique applies an uncoupled winding number formalism to the torsional degrees of freedom in molecular systems. The internal energy of the molecules ethane, n-butane, n-octane, and enkephalin are calculated at standard temperature using the TPIMC technique and compared to the expectation values obtained using the harmonic oscillator approximation and a variational technique. All studied molecules exhibited significant quantum mechanical contributions to their internal energy expectation values according to the TPIMC technique. The harmonic oscillator approximation approach to calculating the internal energy performs well for the molecules presented in this study but is limited by its neglect of both anharmonicity effects and the potential coupling of intramolecular torsion

Torsional anharmonicity in the conformational thermodynamics of flexible molecules

We present an algorithm for calculating the conformational thermodynamics of large, flexible molecules that combines ab initio electronic structure theory calculations with a torsional path integral Monte Carlo (TPIMC) simulation. The new algorithm overcomes the previous limitations of the TPIMC method by including the thermodynamic contributions of non-torsional vibrational modes and by affordably incorporating the ab initio calculation of conformer electronic energies, and it improves the conventional ab initio treatment of conformational thermodynamics by accounting for the anharmonicity of the torsional modes. Using previously published ab initio results and new TPIMC calculations, we apply the algorithm to the conformers of the adrenaline molecule

The Role of Constraints in Hebbian Learning

Models of unsupervised, correlation-based (Hebbian) synaptic plasticity are typically unstable: either all synapses grow until each reaches the maximum allowed strength, or all synapses decay to zero strength. A common method of avoiding these outcomes is to use a constraint that conserves or limits the total synaptic strength over a cell. We study the dynamic effects of such constraints. Two methods of enforcing a constraint are distinguished, multiplicative and subtractive. For otherwise linear learning rules, multiplicative enforcement of a constraint results in dynamics that converge to the principal eigenvector of the operator determining unconstrained synaptic development. Subtractive enforcement, in contrast, typically leads to a final state in which almost all synaptic strengths reach either the maximum or minimum allowed value. This final state is often dominated by weight configurations other than the principal eigenvector of the unconstrained operator. Multiplicative enforcement yields a “graded” receptive field in which most mutually correlated inputs are represented, whereas subtractive enforcement yields a receptive field that is “sharpened” to a subset of maximally correlated inputs. If two equivalent input populations (e.g., two eyes) innervate a common target, multiplicative enforcement prevents their segregation (ocular dominance segregation) when the two populations are weakly correlated; whereas subtractive enforcement allows segregation under these circumstances. These results may be used to understand constraints both over output cells and over input cells. A variety of rules that can implement constrained dynamics are discussed

Acoustic Oscillations in the Early Universe and Today

During its first ~100,000 years, the universe was a fully ionized plasma with a tight coupling by Thompson scattering between the photons and matter. The trade--off between gravitational collapse and photon pressure causes acoustic oscillations in this primordial fluid. These oscillations will leave predictable imprints in the spectra of the cosmic microwave background and the present day matter-density distribution. Recently, the BOOMERANG and MAXIMA teams announced the detection of these acoustic oscillations in the cosmic microwave background (observed at redshift ~1000). Here, we compare these CMB detections with the corresponding acoustic oscillations in the matter-density power spectrum (observed at redshift ~0.1). These consistent results, from two different cosmological epochs, provide further support for our standard Hot Big Bang model of the universe.Comment: To appear in the journal Science. 6 pages, 1 color figur

Species, spacing and their interactions in four southern pines

The effect of initial spacing on plantations of loblolly pine (Pinus taeda), shortleaf pine (P. echinata), Virginia pine (P. Virginiana). and eastern white pine (P. strobus) in Tennessee is not well understood. A study of these four pines was established at the Highland Rim Forestry Field Station near Tullahoma, Tennessee. The plantation was laid out in a split plot design with the four species as main plots and four spacings as split plots. The study was measured at age 16 and total height, diameter at breast height, crown radius, height to first remaining branch, height to first live branch, percent live crown, volume per tree, basal area per tree, volume per hectare, and basal area per hectare were analyzed for all species. Number of branches per whorl nearest breast height and diameter of the largest branch in that whorl were analyzed for white pine only. Generally, the trees showed increased growth as spacing widened. Total height showed a significant effect of spacing. It was concluded that loblolly and white pine are the preferred species for planting

No well-defined remnant Fermi surface in Sr2CuO2Cl2

In angle-resolved photoelectron spectra of the antiferromagnetic insulators Ca2CuO2Cl2 and Sr2CuO2Cl2 a sharp drop of the spectral intensity of the lowest-lying band is observed along a line in k space equivalent to the Fermi surface of the optimally doped high-temperature superconductors. This was interpreted as a signature of the existence of a remnant Fermi surface in the insulating phase of the high-temperature superconductors. In this paper it is shown that the drop of the spectral intensity is not related to the spectral function but is a consequence of the electron-photon matrix elementComment: 4 pages, 3 figure