On the definition and examples of cones and finsler spacetimes

The authors warmly acknowledge Professor Daniel Azagra (Universidad Complutense, Madrid) his advise on approximation of convex functions as well as Profs. Kostelecky (Indiana University), Fuster (University of Technology, Eindhoven), Stavrinos (University of Athens), Pfeifer (University of Tartu), Perlick (University of Bremen) and Makhmali (Institute of Mathematics, Warsaw) their comments on a preliminary version of the article. The careful revision by the referee is also acknowledged. This work is a result of the activity developed within the framework of the Programme in Support of Excellence Groups of the Region de Murcia, Spain, by Fundacion Seneca, Science and Technology Agency of the Region de Murcia. MAJ was partially supported by MINECO/FEDER project reference MTM2015-65430-P and Fundacion Seneca project reference 19901/GERM/15, Spain and MS by Spanish MINECO/ERDF project reference MTM2016-78807-C2-1-P.A systematic study of (smooth, strong) cone structures C and Lorentz–Finsler metrics L is carried out. As a link between both notions, cone triples (Ω,T,F), where Ω (resp. T) is a 1-form (resp. vector field) with Ω(T)≡1 and F, a Finsler metric on ker(Ω), are introduced. Explicit descriptions of all the Finsler spacetimes are given, paying special attention to stationary and static ones, as well as to issues related to differentiability. In particular, cone structures C are bijectively associated with classes of anisotropically conformal metrics L, and the notion of cone geodesic is introduced consistently with both structures. As a non-relativistic application, the time-dependent Zermelo navigation problem is posed rigorously, and its general solution is provided.MINECO/FEDER project, Spain MTM2015-65430-PFundacion Seneca 19901/GERM/15Spanish MINECO/ERDF project MTM2016-78807-C2-1-

An Introduction to Sphingolipid Metabolism and Analysis by New Technologies

Sphingolipids (SP) are a complex class of molecules found in essentially all eukaryotes and some prokaryotes and viruses where they influence membrane structure, intracellular signaling, and interactions with the extracellular environment. Because of the combinatorial nature of their biosynthesis, there are thousands of SP subspecies varying in the lipid backbones and complex phospho- and glycoheadgroups. Therefore, comprehensive or “sphingolipidomic” analyses (structure-specific, quantitative analyses of all SP, or at least all members of a critical subset) are needed to know which and how much of these subspecies are present in a system as a step toward understanding their functions. Mass spectrometry and related novel techniques are able to quantify a small fraction, but nonetheless a substantial number, of SP and are beginning to provide information about their localization. This review summarizes the basic metabolism of SP and state-of-art mass spectrometric techniques that are producing insights into SP structure, metabolism, functions, and some of the dysfunctions of relevance to neuromedicine