Chirp-wave Expansion of the Electron Wavefunctions in Atoms

The description of the electron wavefunctions in atoms is generalized to the fractional Fourier series. This method introduces a continuous and infinite number of chirp basis sets with linear variation of the frequency to expand the wavefunctions, in which plane-waves are a special case. The chirp characteristics of each basis set can be adjusted through a single parameter. Thus, the basis set cutoff can be optimized variationally. The approach is tested with the expansion of the electron wavefunctions in atoms, and it is shown that chirp basis sets substantially improve the convergence in the description of the electron density. We have found that the natural oscillations of the electron core states are efficiently described in chirp-waves

Statistical mechanics and the description of the early universe II. Principle of detailed balance and primordial 4He formation

If the universe is slightly non-extensive, and the distribution functions are not exactly given by those of Boltzmann-Gibbs, the primordial production of light elements will be non-trivially modified. In particular, the principle of detailed balance (PDB), of fundamental importance in the standard analytical analysis, is no longer valid, and a non-extensive correction appears. This correction is computed and its influence is studied and compared with previous works, where, even when the universe was considered as an slightly non-extensive system, the PDB was assumed valid. We analytically track the formation of Helium and Deuterium, and study the kind of deviation one could expect from the standard regime. The correction to the capture time, the moment in which Deuterium can no longer be substantially photo-disintegrated, is also presented. This allows us to take into account the process of the free decay of neutrons, which was absent in all previous treatments of the topic. We show that even when considering a first (linear) order correction in the quantum distribution functions, the final output on the primordial nucleosynthesis yields cannot be reduced to a linear correction in the abundances. We finally obtain new bounds upon the non-extensive parameter, both comparing the range of physical viability of the theory, and using the latest observational data.Comment: 24 pages, to appear in Physica A (2001

PLATYPUS: a code for fusion and breakup in reactions induced by weakly-bound nuclei within a classical trajectory model with stochastic breakup

A self-contained Fortran-90 program based on a classical trajectory model with stochastic breakup is presented, which should be a powerful tool for quantifying complete and incomplete fusion, and breakup in reactions induced by weakly-bound two-body projectiles near the Coulomb barrier. The code calculates complete and incomplete fusion cross sections and their angular momentum distribution, as well as breakup observables (angle, kinetic energy and relative energy distributions).Comment: Accepted in Computer Physics Communications (2011

Stochastic signatures of involuntary head micro-movements can be used to classify females of ABIDE into different subtypes of neurodevelopmental disorders.

© 2017 Torres, Mistry, Caballero and Whyatt. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY).Background: The approximate 5:1 male to female ratio in clinical detection of Autism Spectrum Disorder (ASD) prevents research from characterizing the female phenotype. Current open access repositories [such as those in the Autism Brain Imaging Data Exchange (ABIDE I-II)] contain large numbers of females to help begin providing a new characterization of females on the autistic spectrum. Here we introduce new methods to integrate data in a scale-free manner from continuous biophysical rhythms of the nervous systems and discrete (ordinal) observational scores. Methods: New data-types derived from image-based involuntary head motions and personalized statistical platform were combined with a data-driven approach to unveil sub-groups within the female cohort. Further, to help refine the clinical DSM-based ASD vs. Asperger's Syndrome (AS) criteria, distributional analyses of ordinal score data from Autism Diagnostic Observation Schedule (ADOS)-based criteria were used on both the female and male phenotypes. Results: Separate clusters were automatically uncovered in the female cohort corresponding to differential levels of severity. Specifically, the AS-subgroup emerged as the most severely affected with an excess level of noise and randomness in the involuntary head micro-movements. Extending the methods to characterize males of ABIDE revealed ASD-males to be more affected than AS-males. A thorough study of ADOS-2 and ADOS-G scores provided confounding results regarding the ASD vs. AS male comparison, whereby the ADOS-2 rendered the AS-phenotype worse off than the ASD-phenotype, while ADOS-G flipped the results. Females with AS scored higher on severity than ASD-females in all ADOS test versions and their scores provided evidence for significantly higher severity than males. However, the statistical landscapes underlying female and male scores appeared disparate. As such, further interpretation of the ADOS data seems problematic, rather suggesting the critical need to develop an entirely new metric to measure social behavior in females. Conclusions: According to the outcome of objective, data-driven analyses and subjective clinical observation, these results support the proposition that the female phenotype is different. Consequently the “social behavioral male ruler” will continue to mask the female autistic phenotype. It is our proposition that new observational behavioral tests ought to contain normative scales, be statistically sound and combined with objective data-driven approaches to better characterize the females across the human lifespan.Peer reviewe

Gauge symmetries and Noether currents in optimal control

We extend the second Noether theorem to optimal control problems which are invariant under symmetries depending upon k arbitrary functions of the independent variable and their derivatives up to some order m. As far as we consider a semi-invariance notion, and the transformation group may also depend on the control variables, the result is new even in the classical context of the calculus of variations