Hydrogen as fuel has been a promising technology toward climate change mitigation efforts. To this end, in this paper we analyze the contribution of hydrogen technology to our future environmental goals. It is assumed that hydrogen is being produced in higher efficiency across time and this is simulated on Global Change Assessment Model (GCAM). The environmental restrictions applied are the expected emissions representative concentration pathways (RCP) 2.6, 4.5, and 6.0. Our results have shown increasing hydrogen production as the environmental constraints become stricter and hydrogen more efficient in being produced. This increase has been quantified and provided on open access as Supporting Information to this manuscript.

A crucial aspect in clinical practice is the knowledge of whether Electroencephalographic (EEG) measurements can be assigned to the functioning of the brain or to geometrical deviations of the human cranium. The present work is focused on continuing to advance understanding on how sensitive the solution of the forward EEG problem is in regard to the geometry of the head. This has been achieved by developing a novel analytic algorithm by performing a perturbation analysis in the linear regime using a homogenous spherical model. Notably, the suggested procedure provides a criterion which recognizes whether surface deformations will have an impact on EEG recordings. The presented deformations represent two major cases: (1) acquired alterations of the surface inflicted by external forces and (2) deformations of the upper part of the human head where EEG signals are recorded. Our results illustrate that neglecting geometric variations present on the heads surface leads to errors in the recorded EEG measurements less than 2%. However, for severe instances of deformations combined with cortical brain activity in the vicinity of the distortion site, the errors rise to almost 25%. Therefore, the accurate description of the head shape plays an important role in understanding the forward EEG problem only in these cases.

Albanese and Monk (2006) have shown that, it is impossible to recover the support of a three-dimensional current distribution within a conducting medium from the knowledge of the electric potential outside the conductor. On the other hand, it is possible to obtain the support of a current which lives in a subspace of dimension lower than three. In the present work, we actually demonstrate this possibility by assuming a one-dimensional current distribution supported on a small line segment having arbitrary location and orientation within a uniform spherical conductor. The immediate representation of this problem refers to the inverse problem of electroencephalography (EEG) with a linear current distribution and the spherical model of the brain-head system. It is shown that the support is identified through the solution of a nonlinear algebraic system which is investigated thoroughly. Numerical tests show that this system has exactly one real solution. Exact solutions are analytically obtained for a couple of special cases.

A fundamental principle of Cognitive Psychology states that the rate at which the human brain learns a certain amount of knowledge is proportional to the amount of knowledge yet to be learned. This is the so called pure memory or tabula raza law of learning. The mathematical formulation of this principle leads to a simple ordinary differential equation of the first order. Here we expand the existing mathematical model to a fractional differential equation which allows for a more realistic model having a much higher freedom to fit possible experimental data, as well as allowing for memory effects during the learning process. Two different definitions of the fractional derivative are used, one is the standard Riemann-Liouville global definition and the other is a local definition based on the choice of the unit that measures functional variation. A detailed comparison with the conventional model both at the analytical and the numerical level is included.