Analytic solution for kinetic equilibrium of beta-processes in nucleonic plasma with relativistic pairs

The analytic solution is obtained describing kinetic equilibrium of the $\beta$-processes in the nucleonic plasma with relativistic pairs. The nucleons $(n,p)$ are supposed to be non-relativistic and non-degenerate, while the electrons and positrons are ultra-relativistic due to high temperature $(T>6\cdot 10^9$K), or high density $(\rho>\mu 10^6$g/cm$^3$), or both, where $\mu$ is a number of nucleons per one electron. The consideration is simplified because of the analytic connection of the density with the electron chemical potential in the ultra-relativistic plasma, and Gauss representation of Fermi functions. Electron chemical potential and number of nucleons per one initial electron are calculated as functions of $\rho$ and $T$.Comment: 16 pages, 6 figure

An analysis of single amino acid repeats as use case for application specific background models

Background Sequence analysis aims to identify biologically relevant signals against a backdrop of functionally meaningless variation. Increasingly, it is recognized that the quality of the background model directly affects the performance of analyses. State-of-the-art approaches rely on classical sequence models that are adapted to the studied dataset. Although performing well in the analysis of globular protein domains, these models break down in regions of stronger compositional bias or low complexity. While these regions are typically filtered, there is increasing anecdotal evidence of functional roles. This motivates an exploration of more complex sequence models and application-specific approaches for the investigation of biased regions. Results Traditional Markov-chains and application-specific regression models are compared using the example of predicting runs of single amino acids, a particularly simple class of biased regions. Cross-fold validation experiments reveal that the alternative regression models capture the multi-variate trends well, despite their low dimensionality and in contrast even to higher-order Markov-predictors. We show how the significance of unusual observations can be computed for such empirical models. The power of a dedicated model in the detection of biologically interesting signals is then demonstrated in an analysis identifying the unexpected enrichment of contiguous leucine-repeats in signal-peptides. Considering different reference sets, we show how the question examined actually defines what constitutes the 'background'. Results can thus be highly sensitive to the choice of appropriate model training sets. Conversely, the choice of reference data determines the questions that can be investigated in an analysis. Conclusions Using a specific case of studying biased regions as an example, we have demonstrated that the construction of application-specific background models is both necessary and feasible in a challenging sequence analysis situation