Full operators and algebras generated by invertible operators

In the present work we characterized full operators and we showed some properties that have nonfull injectives operators. With the results developed for full operators, we affirmatively respond two questions formulated by Bravo and Feintuch on when the inverse of an operator can be weakly approximated by polynomials in the operatorComment: 5 page

A multidimensional perspective on microbial interactions

Beyond being simply positive or negative, beneficial or inhibitory, microbial interactions can involve a diverse set of mechanisms, dependencies and dynamical properties. These more nuanced features have been described in great detail for some specific types of interactions, (e.g. pairwise metabolic cross-feeding, quorum sensing or antibiotic killing), often with the use of quantitative measurements and insight derived from modeling. With a growing understanding of the composition and dynamics of complex microbial communities for human health and other applications, we face the challenge of integrating information about these different interactions into comprehensive quantitative frameworks. Here, we review the literature on a wide set of microbial interactions, and explore the potential value of a formal categorization based on multidimensional vectors of attributes. We propose that such an encoding can facilitate systematic, direct comparisons of interaction mechanisms and dependencies, and we discuss the relevance of an atlas of interactions for future modeling and rational design efforts.R01 GM121950 - NIGMS NIH HHSPublished versio

Costless metabolic secretions as drivers of interspecies interactions in microbial ecosystems

Metabolic exchange mediates interactions among microbes, helping explain diversity in microbial communities. As these interactions often involve a fitness cost, it is unclear how stable cooperation can emerge. Here we use genome-scale metabolic models to investigate whether the release of “costless” metabolites (i.e. those that cause no fitness cost to the producer), can be a prominent driver of intermicrobial interactions. By performing over 2 million pairwise growth simulations of 24 species in a combinatorial assortment of environments, we identify a large space of metabolites that can be secreted without cost, thus generating ample cross-feeding opportunities. In addition to providing an atlas of putative interactions, we show that anoxic conditions can promote mutualisms by providing more opportunities for exchange of costless metabolites, resulting in an overrepresentation of stable ecological network motifs. These results may help identify interaction patterns in natural communities and inform the design of synthetic microbial consortia.We thank Dr. Niels Klitgord for pioneering ideas that inspired launch of this work. We are also grateful to David Bernstein, Joshua E. Goldford, Meghan Thommes, Demetrius DiMucci, and all members of the Segre Lab for helpful discussions. A.R.P. is supported by a National Academies of Sciences, Engineering, and Medicine Ford Foundation Predoctoral Fellowship and a Howard Hughes Medical Institute Gilliam Fellowship. This work was supported by funding from the Defense Advanced Research Projects Agency (purchase request no. HR0011515303, contract no. HR0011-15-C-0091), the U.S. Department of Energy (grants DE-SC0004962 and DE-SC0012627), the NIH (grants 5R01DE024468, R01GM121950, and Sub_P30DK036836_P&F), the National Science Foundation (grants 1457695 and NSFOCE-BSF 1635070), MURI Grant W911NF-12-1-0390, the Human Frontiers Science Program (grant RGP0020/2016), and the Boston University Inter-disciplinary Biomedical Research Office. (National Academies of Sciences, Engineering, and Medicine Ford Foundation Predoctoral Fellowship; Howard Hughes Medical Institute Gilliam Fellowship; HR0011515303 - Defense Advanced Research Projects Agency; HR0011-15-C-0091 - Defense Advanced Research Projects Agency; DE-SC0004962 - U.S. Department of Energy; DE-SC0012627 - U.S. Department of Energy; 5R01DE024468 - NIH; R01GM121950 - NIH; Sub_P30DK036836_PF - NIH; 1457695 - National Science Foundation; NSFOCE-BSF 1635070 - National Science Foundation; W911NF-12-1-0390 - MURI Grant; RGP0020/2016 - Human Frontiers Science Program; Boston University Inter-disciplinary Biomedical Research Office)Published versio

Three-dimensional Dirac oscillator in a thermal bath

The thermal properties of the three-dimensional Dirac oscillator are considered. The canonical partition function is determined, and the high-temperature limit is assessed. The degeneracy of energy levels and their physical implications on the main thermodynamic functions are analyzed, revealing that these functions assume values greater than the one-dimensional case. So that at high temperatures, the limit value of the specific heat is three times bigger.Comment: 9 pages, 4 figures. Text improved, references added. Revised to match accepted version in Europhysics Letters