The Gravitational Constant as a quantum mechanical expression

A quantitatively verifiable expression for the Gravitational Constant is derived in terms of quantum mechanical quantities. This derivation appears to be possible by selecting a suitable physical process in which the transformation of the equation of motion into a quantum mechanical wave equation can be obtained by Einstein's geodesic approach. The selected process is the pi-meson, modeled as the one-body equivalent of a two-body quantum mechanical oscillator in which the vibrating mass is modeled as the result of the two energy fluxes from the quark and the antiquark. The quantum mechanical formula for the Gravitational Constant appears to show a quantitatively verifiable relationship with the Higgs boson as conceived in the Standard Model.Comment: 17 page

Mutual Information in Frequency and its Application to Measure Cross-Frequency Coupling in Epilepsy

We define a metric, mutual information in frequency (MI-in-frequency), to detect and quantify the statistical dependence between different frequency components in the data, referred to as cross-frequency coupling and apply it to electrophysiological recordings from the brain to infer cross-frequency coupling. The current metrics used to quantify the cross-frequency coupling in neuroscience cannot detect if two frequency components in non-Gaussian brain recordings are statistically independent or not. Our MI-in-frequency metric, based on Shannon's mutual information between the Cramer's representation of stochastic processes, overcomes this shortcoming and can detect statistical dependence in frequency between non-Gaussian signals. We then describe two data-driven estimators of MI-in-frequency: one based on kernel density estimation and the other based on the nearest neighbor algorithm and validate their performance on simulated data. We then use MI-in-frequency to estimate mutual information between two data streams that are dependent across time, without making any parametric model assumptions. Finally, we use the MI-in- frequency metric to investigate the cross-frequency coupling in seizure onset zone from electrocorticographic recordings during seizures. The inferred cross-frequency coupling characteristics are essential to optimize the spatial and spectral parameters of electrical stimulation based treatments of epilepsy.Comment: This paper is accepted for publication in IEEE Transactions on Signal Processing and contains 15 pages, 9 figures and 1 tabl

Quality factors and coding standards - a comparison between open source forges

Enforcing adherence to standards in software development in order to produce high quality software artefacts has long been recognised as best practice in traditional software engineering. In a distributed heterogeneous development environment such those found within the Open Source paradigm, coding standards are informally shared and adhered to by communities of loosely coupled developers. Following these standards could potentially lead to higher quality software. This paper reports on the empirical analysis of two major forges where OSS projects are hosted. The first one, the KDE forge, provides a set of guidelines and coding standards in the form of a coding style that developers may conform to when producing the code source artefacts. The second studied forge, SourceForge, imposes no formal coding standards on developers. A sample of projects from these two forges has been analysed to detect whether the SourceForge sample, where no coding standards are reinforced, has a lower quality than the sample from KDE. Results from this analysis form a complex picture; visually, all the selected metrics show a clear divide between the two forges, but from the statistical standpoint, clear distinctions cannot be drawn amongst these quality related measures in the two forge samples

Compactifications of Heterotic Strings on Non-Kahler Complex Manifolds: II

We continue our study of heterotic compactifications on non-Kahler complex manifolds with torsion. We give further evidence of the consistency of the six-dimensional manifold presented earlier and discuss the anomaly cancellation and possible supergravity description for a generic non-Kahler complex manifold using the newly proposed superpotential. The manifolds studied in our earlier papers had zero Euler characteristics. We construct new examples of non-Kahler complex manifolds with torsion in lower dimensions, that have non-zero Euler characteristics. Some of these examples are constructed from consistent backgrounds in F-theory and therefore are solutions to the string equations of motion. We discuss consistency conditions for compactifications of the heterotic string on smooth non-Kahler manifolds and illustrate how some results well known for Calabi-Yau compactifications, including counting the number of generations, apply to the non-Kahler case. We briefly address various issues regarding possible phenomenological applications.Comment: 106 pages, 8 .eps figures, Harvmac; v2: Some sections expanded, typos corrected and references updated; v3: More typos corrected, one section expanded and references added. Final version to appear in Nucl. Phys.

Classification of String-like Solutions in Dilaton Gravity

The static string-like solutions of the Abelian Higgs model coupled to dilaton gravity are analyzed and compared to the non-dilatonic case. Except for a special coupling between the Higgs Lagrangian and the dilaton, the solutions are flux tubes that generate a non-asymptotically flat geometry. Any point in parameter space corresponds to two branches of solutions with two different asymptotic behaviors. Unlike the non-dilatonic case, where one branch is always asymptotically conic, in the present case the asymptotic behavior changes continuously along each branch.Comment: 15 pages, 6 figures. To be published in Phys. Rev.