Rota-Baxter algebras and new combinatorial identities

The word problem for an arbitrary associative Rota-Baxter algebra is solved. This leads to a noncommutative generalization of the classical Spitzer identities. Links to other combinatorial aspects, particularly of interest in physics, are indicated.Comment: 8 pages, improved versio

Biotechnology approaches to overcome biotic and abiotic stress constraints in legumes

Biotic and abiotic stresses cause significant yield losses in legumes and can significantly affect their productivity. Biotechnology tools such as marker-assisted breeding, tissue culture, in vitro mutagenesis and genetic transformation can contribute to solve or reduce some of these constraints. However, only limited success has been achieved so far. The emergence of “omic” technologies and the establishment of model legume plants such as Medicago truncatula and Lotus japonicus are promising strategies for understanding the molecular genetic basis of stress resistance, which is an important bottleneck for molecular breeding. Understanding the mechanisms that regulate the expression of stress-related genes is a fundamental issue in plant biology and will be necessary for the genetic improvement of legumes. In this review, we describe the current status of biotechnology approaches in relation to biotic and abiotic stresses in legumes and how these useful tools could be used to improve resistance to important constraints affecting legume crops.E. Prats is funded by an European Marie Curie Reintegration Grant, N. Rispail by (FP5) Eufaba project. Our work in this area is supported by Spanish CICYT project AGL-2002-03248 and European Union project FP6-2002-FOOD-1-506223. K. Singh’s work in this area is supported in part by the Grains Research and Development Corporation (GRDC) and the Department of Education, Science and Training (DEST) in Australia.Peer reviewe

Astrobiology and the possibility of life on Earth and elsewhere…

Astrobiology is an interdisciplinary scientific field not only focused on the search of extraterrestrial life, but also on deciphering the key environmental parameters that have enabled the emergence of life on Earth. Understanding these physical and chemical parameters is fundamental knowledge necessary not only for discovering life or signs of life on other planets, but also for understanding our own terrestrial environment. Therefore, astrobiology pushes us to combine different perspectives such as the conditions on the primitive Earth, the physicochemical limits of life, exploration of habitable environments in the Solar System, and the search for signatures of life in exoplanets. Chemists, biologists, geologists, planetologists and astrophysicists are contributing extensively to this interdisciplinary research field. From 2011 to 2014, the European Space Agency (ESA) had the initiative to gather a Topical Team of interdisciplinary scientists focused on astrobiology to review the profound transformations in the field that have occurred since the beginning of the new century. The present paper is an interdisciplinary review of current research in astrobiology, covering the major advances and main outlooks in the field. The following subjects will be reviewed and most recent discoveries will be highlighted: the new understanding of planetary system formation including the specificity of the Earth among the diversity of planets, the origin of water on Earth and its unique combined properties among solvents for the emergence of life, the idea that the Earth could have been habitable during the Hadean Era, the inventory of endogenous and exogenous sources of organic matter and new concepts about how chemistry could evolve towards biological molecules and biological systems. In addition, many new findings show the remarkable potential life has for adaptation and survival in extreme environments. All those results from different fields of science are guiding our perspectives and strategies to look for life in other Solar System objects as well as beyond, in extrasolar worlds