Local convergence of the Levenberg-Marquardt method under H\"{o}lder metric subregularity

We describe and analyse Levenberg-Marquardt methods for solving systems of nonlinear equations. More specifically, we propose an adaptive formula for the Levenberg-Marquardt parameter and analyse the local convergence of the method under H\"{o}lder metric subregularity of the function defining the equation and H\"older continuity of its gradient mapping. Further, we analyse the local convergence of the method under the additional assumption that the \L{}ojasiewicz gradient inequality holds. We finally report encouraging numerical results confirming the theoretical findings for the problem of computing moiety conserved steady states in biochemical reaction networks. This problem can be cast as finding a solution of a system of nonlinear equations, where the associated mapping satisfies the \L{}ojasiewicz gradient inequality assumption.Comment: 30 pages, 10 figure

Whole-body metabolic modelling predicts isoleucine dependency of SARS-CoV-2 replication

We aimed at investigating host-virus co-metabolism during SARS-CoV-2 infection. Therefore, we extended comprehensive sex-specific, whole-body organ resolved models of human metabolism with the necessary reactions to replicate SARS-CoV-2 in the lung as well as selected peripheral organs. Using this comprehensive host-virus model, we obtained the following key results: 1. The predicted maximal possible virus shedding rate was limited by isoleucine availability. 2. The supported initial viral load depended on the increase in CD4+ T-cells, consistent with the literature. 3. During viral infection, the whole-body metabolism changed including the blood metabolome, which agreed well with metabolomic studies from COVID-19 patients and healthy controls. 4. The virus shedding rate could be reduced by either inhibition of the guanylate kinase 1 or availability of amino acids, e.g., in the diet. 5. The virus variants differed in their maximal possible virus shedding rates, which could be inversely linked to isoleucine occurrences in the sequences. Taken together, this study presents the metabolic crosstalk between host and virus and emphasises the role of amino acid metabolism during SARS-CoV-2 infection, in particular of isoleucine. As such, it provides an example of how computational modelling can complement more canonical approaches to gain insight into host-virus crosstalk and to identify potential therapeutic strategies.Analytical BioScience

Relativistic BB84, relativistic errors, and how to correct them

The Bennett-Brassard cryptographic scheme (BB84) needs two bases, at least one of them linearly polarized. The problem is that linear polarization formulated in terms of helicities is not a relativistically covariant notion: State which is linearly polarized in one reference frame becomes depolarized in another one. We show that a relativistically moving receiver of information should define linear polarization with respect to projection of Pauli-Lubanski's vector in a principal null direction of the Lorentz transformation which defines the motion, and not with respect to the helicity basis. Such qubits do not depolarize.Comment: revtex

MetaboAnnotator: an efficient toolbox to annotate metabolites in genome-scale metabolic reconstructions

MOTIVATION\nRESULTS\nAVAILABILITY AND IMPLEMENTATION\nSUPPLEMENTARY INFORMATION\nGenome-scale metabolic reconstructions have been assembled for thousands of organisms using a wide range of tools. However, metabolite annotations, required to compare and link metabolites between reconstructions, remain incomplete. Here, we aim to further extend metabolite annotation coverage using various databases and chemoinformatic approaches.\nWe developed a COBRA toolbox extension, deemed MetaboAnnotator, which facilitates the comprehensive annotation of metabolites with database independent and dependent identifiers, obtains molecular structure files, and calculates metabolite formula and charge at pH 7.2. The resulting metabolite annotations allow for subsequent cross-mapping between reconstructions and mapping of, e.g., metabolomic data.\nMetaboAnnotator and tutorials are freely available at https://github.com/opencobra.\nSupplementary data are available at Bioinformatics online.Analytical BioScience

Structure and properties of a novel fulleride Sm6C60

A novel fulleride Sm6C60 has been synthesized using high temperature solid state reaction. The Rietveld refinement on high resolution synchrotron X-ray powder diffraction data shows that Sm6C60 is isostructural with body-centered cubic A6C60 (A=K, Ba). Raman spectrum of Sm6C60 is similar to that of Ba6C60, and the frequencies of two Ag modes in Sm6C60 are nearly the same as that of Ba6C60, suggesting that Sm is divalent and hybridization between C60 molecules and the Sm atom could exist in Sm6C60. Resistivity measurement shows a weak T-linear behavior above 180 K, the transport at low temperature is mainly dominated by granular-metal theory.Comment: 9 pages, 3 figures, submitted to Phys. Rev. B (March 12, 1999

Study of the dependence of 198Au half-life on source geometry

We report the results of an experiment to determine whether the half-life of \Au{198} depends on the shape of the source. This study was motivated by recent suggestions that nuclear decay rates may be affected by solar activity, perhaps arising from solar neutrinos. If this were the case then the $\beta$-decay rates, or half-lives, of a thin foil sample and a spherical sample of gold of the same mass and activity could be different. We find for \Au{198}, $(T_{1/2})_{\rm foil}/(T_{1/2})_{\rm sphere} = 0.999 \pm 0.002$, where $T_{1/2}$ is the mean half-life. The maximum neutrino flux at the sample in our experiments was several times greater than the flux of solar neutrinos at the surface of the Earth. We show that this increase in flux leads to a significant improvement in the limits that can be inferred on a possible solar contribution to nuclear decays.Comment: 5 pages, 1 figur

Rotational and Vibrational Dynamics of Interstitial Molecular Hydrogen

The calculation of the hindered roton-phonon energy levels of a hydrogen molecule in a confining potential with different symmetries is systematized for the case when the rotational angular momentum $J$ is a good quantum number. One goal of this program is to interpret the energy-resolved neutron time of flight spectrum previously obtained for H$_{2}$C$_{60}$. This spectrum gives direct information on the energy level spectrum of H$_2$ molecules confined to the octahedral interstitial sites of solid C$_{60}$. We treat this problem of coupled translational and orientational degrees of freedom a) by construction of an effective Hamiltonian to describe the splitting of the manifold of states characterized by a given value of $J$ and having a fixed total number of phonon excitations, b) by numerical solutions of the coupled translation-rotation problem on a discrete mesh of points in position space, and c) by a group theoretical symmetry analysis. Results obtained from these three different approaches are mutually consistent. The results of our calculations explain several hitherto uninterpreted aspects of the experimental observations, but show that a truly satisfactory orientational potential for the interaction of an H$_2$ molecule with a surrounding array of C atoms has not yet been developed.Comment: 53 pages, 9 figures, to appear in Phys. Rev B (in press). Phys. Rev. B (in press