The Triangle Operator

We examine the averaging operator corresponding to the manifold in $\mathbb{R}^{2d}$ of pairs of points $(u,v)$ satisfying $|u| = |v| = |u - v| = 1$, so that $\{0,u,v\}$ is the set of vertices of an equilateral triangle. We establish $L^p \times L^q \rightarrow L^r$ boundedness for $T$ for $(1/p, 1/q, 1/r)$ in the convex hull of the set of points $\lbrace (0, 0, 0) ,\, (1, 0 , 1) ,\, (0, 1, 1) , \, ({1}/{p_d}, {1}/{p_d}, {2}/{p_d}) \rbrace$, where $p_d = \frac{5d}{3d - 2}$.Comment: 15 pages, discussion on the maximal variant expande

Variation-norm and fluctuation estimates for ergodic bilinear averages

For any dynamical system, we show that higher variation-norms for the sequence of ergodic bilinear averages of two functions satisfy a large range of bilinear Lp estimates. It follows that, with probability one, the number of fluctuations along this sequence may grow at most polynomially with respect to (the growth of) the underlying scale. These results strengthen previous works of Lacey and Bourgain where almost surely convergence of the sequence was proved (which is equivalent to the qualitative statement that the number of fluctuations is finite at each scale). Via transference, the proof reduces to establishing new bilinear Lp bounds for variation-norms of truncated bilinear operators on R, and the main ingredient of the proof of these bounds is a variation-norm extension of maximal Bessel inequalities of Lacey and Demeter--Tao--Thiele.Comment: 37 pages, new version fixed some references not displaying correctl

solveME: fast and reliable solution of nonlinear ME models.

BackgroundGenome-scale models of metabolism and macromolecular expression (ME) significantly expand the scope and predictive capabilities of constraint-based modeling. ME models present considerable computational challenges: they are much (>30 times) larger than corresponding metabolic reconstructions (M models), are multiscale, and growth maximization is a nonlinear programming (NLP) problem, mainly due to macromolecule dilution constraints.ResultsHere, we address these computational challenges. We develop a fast and numerically reliable solution method for growth maximization in ME models using a quad-precision NLP solver (Quad MINOS). Our method was up to 45 % faster than binary search for six significant digits in growth rate. We also develop a fast, quad-precision flux variability analysis that is accelerated (up to 60× speedup) via solver warm-starts. Finally, we employ the tools developed to investigate growth-coupled succinate overproduction, accounting for proteome constraints.ConclusionsJust as genome-scale metabolic reconstructions have become an invaluable tool for computational and systems biologists, we anticipate that these fast and numerically reliable ME solution methods will accelerate the wide-spread adoption of ME models for researchers in these fields

Genome-scale reconstruction of the metabolic network in Staphylococcus aureus N315: an initial draft to the two-dimensional annotation

BACKGROUND: Several strains of bacteria have sequenced and annotated genomes, which have been used in conjunction with biochemical and physiological data to reconstruct genome-scale metabolic networks. Such reconstruction amounts to a two-dimensional annotation of the genome. These networks have been analyzed with a constraint-based formalism and a variety of biologically meaningful results have emerged. Staphylococcus aureus is a pathogenic bacterium that has evolved resistance to many antibiotics, representing a significant health care concern. We present the first manually curated elementally and charge balanced genome-scale reconstruction and model of S. aureus' metabolic networks and compute some of its properties. RESULTS: We reconstructed a genome-scale metabolic network of S. aureus strain N315. This reconstruction, termed iSB619, consists of 619 genes that catalyze 640 metabolic reactions. For 91% of the reactions, open reading frames are explicitly linked to proteins and to the reaction. All but three of the metabolic reactions are both charge and elementally balanced. The reaction list is the most complete to date for this pathogen. When the capabilities of the reconstructed network were analyzed in the context of maximal growth, we formed hypotheses regarding growth requirements, the efficiency of growth on different carbon sources, and potential drug targets. These hypotheses can be tested experimentally and the data gathered can be used to improve subsequent versions of the reconstruction. CONCLUSION: iSB619 represents comprehensive biochemically and genetically structured information about the metabolism of S. aureus to date. The reconstructed metabolic network can be used to predict cellular phenotypes and thus advance our understanding of a troublesome pathogen