A second-order, unconditionally positive, mass-conserving integration scheme for biochemical systems.

Biochemical systems are bound by two mathematically-relevant restrictions. First, state variables in such systems represent non-negative quantities, such as concentrations of chemical compounds. Second, biochemical systems conserve mass and energy. Both properties must be reflected in results of an integration scheme applied to biochemical models. This paper first presents a mathematical framework for biochemical problems, which includes an exact definition of biochemical conservation: elements and energy, rather than state variable units, are conserved. We then analyze various fixed-step integration schemes, including traditional Euler-based schemes and the recently published modified Patankar schemes, and conclude that none of these deliver unconditional positivity and biochemical conservation in combination with higher-order accuracy. Finally, we present two new fixed-step integration schemes, one first-order and one second-order accurate, which do guarantee positivity and (biochemical) conservatio

Thermochemistry of monazite-(La) and dissakisite-(La): implications for monazite and allanite stability in metapelites

Thermochemical properties have been either measured or estimated for synthetic monazite, LaPO4, and dissakisite, CaLaMgAl2(SiO4)3OH, the Mg-equivalent of allanite. A dissakisite formation enthalpy of −6,976.5±10.0kJmol−1 was derived from high-temperature drop-solution measurements in lead borate at 975K. A third-law entropy value of 104.9±1.6Jmol−1K−1 was retrieved from low-temperature heat capacity (C p) measured on synthetic LaPO4 with an adiabatic calorimeter in the 30-300K range. The C p values of lanthanum phases were measured in the 143-723K range by differential scanning calorimetry. In this study, La(OH)3 appeared as suitable for drop solution in lead borate and represents an attractive alternative to La2O3. Pseudo-sections were calculated with the THERIAK-DOMINO software using the thermochemical data retrieved here for a simplified metapelitic composition (La=∑REE+Y) and considering monazite and Fe-free epidotes along the dissakisite-clinozoïsite join, as the only REE-bearing minerals. Calculation shows a stability window for dissakisite-clinozoïsite epidotes (T between 250 and 550°C and P between 1 and 16kbar), included in a wide monazite field. The P-T extension of this stability window depends on the bulk-rock Ca-content. Assuming that synthetic LaPO4 and dissakisite-(La) are good analogues of natural monazite and allanite, these results are consistent with the REE-mineralogy sequence observed in metapelites, where (1) monazite is found to be stable below 250°C, (2) around 250-450°C, depending on the pressure, allanite forms at the expense of monazite and (3) towards amphibolite conditions, monazite reappears at the expense of allanit

Generation of single colour centers by focussed nitrogen implantation

Single defect centers in diamond have been generated via nitrogen implantation. The defects have been investigated by single defect center fluorescence microscopy. Optical and EPR spectra unambiguously show that the produced defect is the nitrogen-vacancy colour center. An analysis of the nitrogen flux together with a determination of the number of nitrogen-vacancy centers yields that on average two 2 MeV nitrogen atoms need to be implanted per defect center.Comment: 6 pages, 3 figure

A non-variational approach to nonlinear stability in stellar dynamics applied to the King model

In previous work by Y. Guo and G. Rein, nonlinear stability of equilibria in stellar dynamics, i.e., of steady states of the Vlasov-Poisson system, was accessed by variational techniques. Here we propose a different, non-variational technique and use it to prove nonlinear stability of the King model against a class of spherically symmetric, dynamically accessible perturbations. This model is very important in astrophysics and was out of reach of the previous techniques

Population sequencing data reveal a compendium of mutational processes in human germline

Mechanistic processes underlying human germline mutations remain largely unknown.Variation in mutation rate and spectra along the genome is informative about the biological mechanisms. We statistically decompose this variation into separate processes using a blind source separation technique. The analysis of a large-scale whole genome sequencing dataset (TOPMed) reveals nine processes that explain the variation in mutation properties between loci. Seven of these processes lend themselves to a biological interpretation. One process is driven by bulky DNA lesions that resolve asymmetrically with respect to transcription and replication. Two processes independently track direction of replication fork and replication timing. We identify a mutagenic effect of active demethylation primarily acting in regulatory regions. We also demonstrate that a recently discovered mutagenic process specific to oocytes can be localized solely from population sequencing data. This process is spread across all chromosomes and is highly asymmetric with respect to the direction of transcription, suggesting a major role of DNA damage

PCA-Correlated SNPs for Structure Identification in Worldwide Human Populations

Existing methods to ascertain small sets of markers for the identification of human population structure require prior knowledge of individual ancestry. Based on Principal Components Analysis (PCA), and recent results in theoretical computer science, we present a novel algorithm that, applied on genomewide data, selects small subsets of SNPs (PCA-correlated SNPs) to reproduce the structure found by PCA on the complete dataset, without use of ancestry information. Evaluating our method on a previously described dataset (10,805 SNPs, 11 populations), we demonstrate that a very small set of PCA-correlated SNPs can be effectively employed to assign individuals to particular continents or populations, using a simple clustering algorithm. We validate our methods on the HapMap populations and achieve perfect intercontinental differentiation with 14 PCA-correlated SNPs. The Chinese and Japanese populations can be easily differentiated using less than 100 PCA-correlated SNPs ascertained after evaluating 1.7 million SNPs from HapMap. We show that, in general, structure informative SNPs are not portable across geographic regions. However, we manage to identify a general set of 50 PCA-correlated SNPs that effectively assigns individuals to one of nine different populations. Compared to analysis with the measure of informativeness, our methods, although unsupervised, achieved similar results. We proceed to demonstrate that our algorithm can be effectively used for the analysis of admixed populations without having to trace the origin of individuals. Analyzing a Puerto Rican dataset (192 individuals, 7,257 SNPs), we show that PCA-correlated SNPs can be used to successfully predict structure and ancestry proportions. We subsequently validate these SNPs for structure identification in an independent Puerto Rican dataset. The algorithm that we introduce runs in seconds and can be easily applied on large genome-wide datasets, facilitating the identification of population substructure, stratification assessment in multi-stage whole-genome association studies, and the study of demographic history in human populations