A class of Hamilton-Jacobi equations on Banach-Finsler manifolds

The concept of subdifferentiability is studied in the context of $C^1$ Finsler manifolds (modeled on a Banach space with a Lipschitz $C^1$ bump function). A class of Hamilton-Jacobi equations defined on $C^1$ Finsler manifolds is studied and several results related to the existence and uniqueness of viscosity solutions are obtained.Comment: 24 page

A network-based approach for predicting key enzymes explaining metabolite abundance alterations in a disease phenotype

<p>Background The study of metabolism has attracted much attention during the last years due to its relevance in various diseases. The advance in metabolomics platforms allows us to detect an increasing number of metabolites in abnormal high/low concentration in a disease phenotype. Finding a mechanistic interpretation for these alterations is important to understand pathophysiological processes, however it is not an easy task. The availability of genome scale metabolic networks and Systems Biology techniques open new avenues to address this question.</p> <p>Results In this article we present a novel mathematical framework to find enzymes whose malfunction explains the accumulation/depletion of a given metabolite in a disease phenotype. Our approach is based on a recently introduced pathway concept termed Carbon Flux Paths (CFPs), which extends classical topological definition by including network stoichiometry. Using CFPs, we determine the Connectivity Curve of an altered metabolite, which allows us to quantify changes in its pathway structure when a certain enzyme is removed. The influence of enzyme removal is then ranked and used to explain the accumulation/depletion of such metabolite. For illustration, we center our study in the accumulation of two metabolites (L-Cystine and Homocysteine) found in high concentration in the brain of patients with mental disorders. Our results were discussed based on literature and found a good agreement with previously reported mechanisms. In addition, we hypothesize a novel role of several enzymes for the accumulation of these metabolites, which opens new strategies to understand the metabolic processes underlying these diseases.</p> <p>Conclusions With personalized medicine on the horizon, metabolomic platforms are providing us with a vast amount of experimental data for a number of complex diseases. Our approach provides a novel apparatus to rationally investigate and understand metabolite alterations under disease phenotypes. This work contributes to the development of Systems Medicine, whose objective is to answer clinical questions based on theoretical methods and high-throughput “omics” data.</p&gt

Changes in organic aerosol composition with aging inferred from aerosol mass spectra

Organic aerosols (OA) can be separated with factor analysis of aerosol mass spectrometer (AMS) data into hydrocarbon-like OA (HOA) and oxygenated OA (OOA). We develop a new method to parameterize H:C of OOA in terms of f_(43)(ratio of m/z 43, mostly C_2H_3O^+, to total signal in the component mass spectrum). Such parameterization allows for the transformation of large database of ambient OOA components from the f_(44) (mostly CO^+_2, likely from acid groups) vs. f_(43) space ("triangle plot") (Ng et al., 2010) into the Van Krevelen diagram (H:C vs. O:C) (Van Krevelen, 1950). Heald et al. (2010) examined the evolution of total OA in the Van Krevelen diagram. In this work total OA is deconvolved into components that correspond to primary (HOA and others) and secondary (OOA) organic aerosols. By deconvolving total OA into different components, we remove physical mixing effects between secondary and primary aerosols which allows for examination of the evolution of OOA components alone in the Van Krevelen space. This provides a unique means of following ambient secondary OA evolution that is analogous to and can be compared with trends observed in chamber studies of secondary organic aerosol formation. The triangle plot in Ng et al. (2010) indicates that f_(44) of OOA components increases with photochemical age, suggesting the importance of acid formation in OOA evolution. Once they are transformed with the new parameterization, the triangle plot of the OOA components from all sites occupy an area in Van Krevelen space which follows a ΔH:C/ΔO:C slope of ~ −0.5. This slope suggests that ambient OOA aging results in net changes in chemical composition that are equivalent to the addition of both acid and alcohol/peroxide functional groups without fragmentation (i.e. C-C bond breakage), and/or the addition of acid groups with fragmentation. These results provide a framework for linking the bulk aerosol chemical composition evolution to molecular-level studies

F stars, metallicity, and the ages of red galaxies at z > 1

We explore whether the rest-frame near-UV spectral region, observable in high-redshift galaxies via optical spectroscopy, contains sufficient information to allow the degeneracy between age and metallicity to be lifted. We do this by testing the ability of evolutionary synthesis models to reclaim the correct metallicity when fitted to the near-UV spectra of F stars of known (sub-solar and super-solar) metallicity. F stars are of particular interest because the rest-frame near-UV spectra of the oldest known elliptical galaxies at z > 1 appear to be dominated by F stars near to the main-sequence turnoff. We find that, in the case of the F stars, where the HST ultraviolet spectra have high signal:noise, model-fitting with metallicity allowed to vary as a free parameter is rather successful at deriving the correct metallicity. As a result, the estimated turnoff ages of these stars yielded by the model fitting are well constrained. Encouraged by this we have fitted these same variable- metallicity models to the deep, optical spectra of the z \simeq 1.5 mJy radio galaxies 53W091 and 53W069 obtained with the Keck telescope. While the age-metallicity degeneracy is not so easily lifted for these galaxies, we find that even when metallicity is allowed as a free parameter, the best estimates of their ages are still \geq 3 Gyr, with ages younger than 2 Gyr now strongly excluded. Furthermore, we find that a search of the entire parameter space of metallicity and star formation history using MOPED (Heavens et al., 2000) leads to the same conclusion. Our results therefore continue to argue strongly against an Einstein-de Sitter universe, and favour a lambda-dominated universe in which star formation in at least these particular elliptical galaxies was completed somewhere in the redshift range z = 3 - 5.Comment: 10 pages, LaTeX, uses MNRAS style file, incorporates 14 postscript figures, submitted to MNRAS. Changes include: inclusion of single stellar atmosphere model fits; more rigorous calculation of confidence regions; some re-structurin

Ejection mechanisms in the sublayer of a turbulent channel

A possible model for the inception of vorticity ejections in the viscous sublayer of a turbulent rectangular channel is presented. It was shown that this part of the flow is dominated by protruding strong shear layers of z-vorticity, and it was proposed as a mechanism for their maintenance and reproduction which is essentially equivalent to that responsible for the instability of 2-D Tollmien-Schlichting waves. The efforts to isolate computationally a single structure for its study have failed up to now, since it appears that single structures decay in the absence of external forcing, but a convenient computation model was identified in the form of a long and narrow periodic computational box containing at each moment only a few structures. Further work in the identification of better reduced systems is in progress