4,618 research outputs found
L^p estimates for a singular integral operator motivated by Calder\'on's second commutator
We prove a wide range of L^p estimates for a trilinear singular integral
operator motivated by dropping one average in Calder\'{o}n's second commutator.
For comparison by dropping two averages in Calder\'{o}n's second commutator one
faces the trilinear Hilbert transform. The novelty in this paper is that in
order to avoid difficulty of the level of the trilinear Hilbert transform, we
choose to view the symbol of the operator as a non-standard symbol. The methods
used come from time-frequency analysis but must be adapted to the fact that our
symbol is non-standard.Comment: 29 pages; corrected typo
Genomic stuff: Governing the (im)matter of life
Emphasizing the context of what has often been referred to as “scarce natural resources”, in particular forests, meadows, and fishing stocks, Elinor Ostrom’s important work Governing the commons (1990) presents an institutional framework for discussing the development and use of collective action with respect to environmental problems. In this article we discuss extensions of Ostrom’s approach to genes and genomes and explore its limits and usefulness. With the new genetics, we suggest, the biological gaze has not only been turned inward to the management and mining of the human body, also the very notion of the “biological” has been destabilized. This shift and destabilization, we argue, which is the result of human refashioning and appropriation of “life itself”, raises important questions about the relevance and applicability of Ostrom’s institutional framework in the context of what we call “genomic stuff”, genomic material, data, and information
Using in silico models to simulate dual perturbation experiments: procedure development and interpretation of outcomes.
BackgroundA growing number of realistic in silico models of metabolic functions are being formulated and can serve as 'dry lab' platforms to prototype and simulate experiments before they are performed. For example, dual perturbation experiments that vary both genetic and environmental parameters can readily be simulated in silico. Genetic and environmental perturbations were applied to a cell-scale model of the human erythrocyte and subsequently investigated.ResultsThe resulting steady state fluxes and concentrations, as well as dynamic responses to the perturbations were analyzed, yielding two important conclusions: 1) that transporters are informative about the internal states (fluxes and concentrations) of a cell and, 2) that genetic variations can disrupt the natural sequence of dynamic interactions between network components. The former arises from adjustments in energy and redox states, while the latter is a result of shifting time scales in aggregate pool formation of metabolites. These two concepts are illustrated for glucose-6 phosphate dehydrogenase (G6PD) and pyruvate kinase (PK) in the human red blood cell.ConclusionDual perturbation experiments in silico are much more informative for the characterization of functional states than single perturbations. Predictions from an experimentally validated cellular model of metabolism indicate that the measurement of cofactor precursor transport rates can inform the internal state of the cell when the external demands are altered or a causal genetic variation is introduced. Finally, genetic mutations that alter the clinical phenotype may also disrupt the 'natural' time scale hierarchy of interactions in the network
Formulating genome-scale kinetic models in the post-genome era.
The biological community is now awash in high-throughput data sets and is grappling with the challenge of integrating disparate data sets. Such integration has taken the form of statistical analysis of large data sets, or through the bottom-up reconstruction of reaction networks. While progress has been made with statistical and structural methods, large-scale systems have remained refractory to dynamic model building by traditional approaches. The availability of annotated genomes enabled the reconstruction of genome-scale networks, and now the availability of high-throughput metabolomic and fluxomic data along with thermodynamic information opens the possibility to build genome-scale kinetic models. We describe here a framework for building and analyzing such models. The mathematical analysis challenges are reflected in four foundational properties, (i) the decomposition of the Jacobian matrix into chemical, kinetic and thermodynamic information, (ii) the structural similarity between the stoichiometric matrix and the transpose of the gradient matrix, (iii) the duality transformations enabling either fluxes or concentrations to serve as the independent variables and (iv) the timescale hierarchy in biological networks. Recognition and appreciation of these properties highlight notable and challenging new in silico analysis issues
The Triangle Operator
We examine the averaging operator corresponding to the manifold in
of pairs of points satisfying , so that is the set of vertices of an equilateral triangle. We
establish boundedness for for in the convex hull of the set of points , where .Comment: 15 pages, discussion on the maximal variant expande
What do cells actually want?
Genome-scale models require an objective function representing what an organism strives for. A method has been developed to infer this fundamental biological function from data.Please see related Research article: www.dx.doi.org/10.1186/s13059-016-0968-2
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