Quartic quantum theory: an extension of the standard quantum mechanics

We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability distributions can be embedded inside a higher dimensional convex body of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system described in N dimensional Hilbert space is coupled with an auxiliary subsystem of the same dimensionality. The extended theory works for simple quantum systems and is shown to be a non-trivial generalisation of the standard quantum theory for which K=N^2. Imposing certain restrictions on initial conditions and dynamics allowed in the quartic theory one obtains quadratic theory as a special case. By imposing even stronger constraints one arrives at the classical theory, for which K=N.Comment: 30 pages in latex with 6 figures included; ver.2: several improvements, new references adde

Inter-Individual Differences in RNA Levels in Human Peripheral Blood

<div><p>Relatively little is known about the range of RNA levels in human blood. This report provides assessment of peripheral blood RNA level and its inter-individual differences in a group of 35 healthy humans consisting of 25 females and 10 males ranging in age from 50 to 89 years. In this group, the average total RNA level was 14.59 μg/ml of blood, with no statistically significant difference between females and males. The individual RNA level ranged from 6.7 to 22.7 μg/ml of blood. In healthy subjects, the repeated sampling of an individual’s blood showed that RNA level, whether high or low, was stable. The inter-individual differences in RNA level in blood can be attributed to both, differences in cell number and the amount of RNA per cell. The 3.4-fold range of inter-individual differences in total RNA levels, documented herein, should be taken into account when evaluating the results of quantitative RT-PCR and/or RNA sequencing studies of human blood. Based on the presented results, a comprehensive assessment of gene expression in blood should involve determination of both the amount of mRNA per unit of total RNA (U / ng RNA) and the amount of mRNA per unit of blood (U / ml blood) to assure a thorough interpretation of physiological or pathological relevance of study results.</p></div

Characteristics of RNA isolated from healthy donors.

<p>a) Proportion of the large and small RNA fractions in relation to increasing quantities of total RNA in human peripheral blood. Samples of RNA from the 35 individuals are sequentially ranked in accord with the increasing amount of total RNA in the sample. For each sample, the amounts of the large RNA fraction (inverted triangle) and small RNA fraction (square) are depicted. b) The large RNA and small RNA fractions are expressed as a percentage of the total RNA in the sample. c) Bioanalyzer RIN values of the large RNA fractions from 35 samples.</p

Bioanalyzer profiles of the large RNA fractions isolated from donors with the lowest and highest blood RNA level.

<p>The large RNA fractions (200 ng) from the low RNA level sample 180 (6.7 μg RNA/ml blood) and the high RNA level sample 162 (22.7 μg RNA/ml blood) were separated using the Bioanalyzer RNA Nano 6000 Kit. Shown are positions of: the (18S) and (28S) ribosomal RNA; the 600 nt globin region (G); and Bioanalyzer marker (M).</p

Robust regression analysis of total RNA vs the product of blood DNA level (μg DNA / ml blood) and cellular RNA content (pg RNA/ cell).

<p>The blue dashed line represents the 95% prediction interval for the group of 35 samples. An adjusted R-square value for this regression analysis is 0.947.</p

The total RNA level in blood collected over a period of 30 to 270 days from female (F) and male (M) donors.

<p>Total RNA was extracted from six blood donors using RNAzol BD as described in the Methods section. The calculated within-individual coefficient of variation of blood RNA level for the six donors was 9.2, 4.8, 6.2, 1.1, 7.6 and 6.9, respectively.</p