Excitations of amorphous solid helium

We present neutron scattering measurements of the dynamic structure factor, $S(Q,\omega)$, of amorphous solid helium confined in 47 $\AA$ pore diameter MCM-41 at pressure 48.6 bar. At low temperature, $T$ = 0.05 K, we observe $S(Q,\omega)$ of the confined quantum amorphous solid plus the bulk polycrystalline solid between the MCM-41 powder grains. No liquid-like phonon-roton modes, other sharply defined modes at low energy ($\omega<$ 1.0 meV) or modes unique to a quantum amorphous solid that might suggest superflow are observed. Rather the $S(Q,\omega)$ of confined amorphous and bulk polycrystalline solid appear to be very similar. At higher temperature ($T>$ 1 K), the amorphous solid in the MCM-41 pores melts to a liquid which has a broad $S(Q,\omega)$ peaked near $\omega \simeq$ 0 characteristic of normal liquid $^4$He under pressure. Expressions for the $S(Q,\omega)$ of amorphous and polycrystalline solid helium are presented and compared. In previous measurements of liquid $^4$He confined in MCM-41 at lower pressure the intensity in the liquid roton mode decreases with increasing pressure until the roton vanishes at the solidification pressure (38 bars), consistent with no roton in the solid observed here

Theoretical connections between mathematical neuronal models corresponding to different expressions of noise

Identifying the right tools to express the stochastic aspects of neural activity has proven to be one of the biggest challenges in computational neuroscience. Even if there is no definitive answer to this issue, the most common procedure to express this randomness is the use of stochastic models. In accordance with the origin of variability, the sources of randomness are classified as intrinsic or extrinsic and give rise to distinct mathematical frameworks to track down the dynamics of the cell. While the external variability is generally treated by the use of a Wiener process in models such as the Integrate-and-Fire model, the internal variability is mostly expressed via a random firing process. In this paper, we investigate how those distinct expressions of variability can be related. To do so, we examine the probability density functions to the corresponding stochastic models and investigate in what way they can be mapped one to another via integral transforms. Our theoretical findings offer a new insight view into the particular categories of variability and it confirms that, despite their contrasting nature, the mathematical formalization of internal and external variability are strikingly similar

L’efficacité, l’égalité, l’équité et la répartition personnelle des revenus

The analysis of the impact of economic policy and of the process of growth on personal income distribution is getting greater priority in the literature. Such an analysis cannot usefully be pursued in the light of efficiency considerations alone; it must also take equality and equity into account. Equity is defined here as a characterization of a state of affairs in terms of three parameters: (1) the choice of a distributive norm, (2) the specification of what is to be distributed, and (3) a measure of the degree of inequality that exists. A general "equity function" (E) is defined, whose particular form reflects the chosen distributive norm, and whose two arguments are the sum total to be distributed and a measure of the inequality that characterizes the distribution of that sum. Then, a number of critera of distributive justice are compared, and the criteria based on the relative and absolute income gaps are found to be the most useful. This suggests the formulation of an "equity index" (e) which is sensitive to both growth, relative inequality and absolute inequality. Unsurprisingly, empirical estimates show that the "equity index" has risen in socialist countries and fallen in non-socialist countries as a group. The "equity index" is also estimated for a number of individual countries, but the results are difficult to interpret without an in depth analysis of the circumstances of each country