The 2+2-Signature and the 1+1-Matrix-Brane

We discuss different aspects of the 2+2-signature from the point of view of the quatl theory. In particular, we compare two alternative approaches to such a spacetime signature, namely the 1+1-matrix-brane and the 2+2-target spacetime of a string. This analysis also reveals hidden discrete symmetries of the 2+2-brane action associated with the 2+2-dimensional sector of a 2+10-dimensional target background.Comment: 12 pages, Latex, to appear in Mod. Phys. Lett.

Remarks on Weyl invariant p-branes and Dp-branes

A mechanism to find different Weyl invariant p-branes and Dp-branes actions is explained. Our procedure clarifies the Weyl invariance for such systems. Besides, by considering gravity-dilaton effective action in higher dimensions we also derive a Weyl invariant action for p-branes. We argue that this derivation provides a geometrical scenario for the Weyl invariance of p-branes. Our considerations can be extended to the case of super-p-branes.Comment: 18 pages, Late

Some Exceptional Cases in Mathematics: Euler Characteristic, Division Algebras, Cross Vector Product and Fano Matroid

We review remarkable results in several mathematical scenarios, including graph theory, division algebras, cross product formalism and matroid theory. Specifically, we mention the following subjects: (1) the Euler relation in graph theory, and its higher-dimensional generalization, (2) the dimensional theorem for division algebras and in particular the Hurwitz theorem for normed division algebras, (3) the vector cross product dimensional possibilities, (4) some theorems for graphs and matroids. Our main goal is to motivate a possible research work in these four topics, putting special interest in their possible links.Comment: 14 pages, Late

Scale-Free Growing Networks and Gravity

We propose a possible relation between complex networks and gravity. Our guide in our proposal is the power-law distribution of the node degree in network theory and the information approach to gravity. The established bridge may allow us to carry geometric mathematical structures, which are considered in gravitational theories, to probabilistic aspects studied in the framework of complex networks and vice versa.Comment: Latex, 10 pages, improved versio

Duality, matroids, qubits, twistors and surreal numbers

We show that via the Grassmann-Pl\"ucker relations, the various apparent unrelated concepts, such as duality, matroids, qubits, twistors and surreal numbers are, in fact, deeply connected. Moreover, we conjecture the possibility that these concepts may be considered as underlying mathematical structures in quantum gravity.Comment: 17 pages, published in Frontier in Physic

Phirotopes, Super p-branes and Qubit Theory

The phirotope is a complex generalization of the concept of chirotope in oriented matroid theory. Our main goal in this work is to establish a link between phirotopes, super p-branes and qubit theory. For this purpose we first discuss maximally supersymmetric solutions of 11-dimensional supergravity from the point of view of the oriented matroid theory. We also clarify a possible connection between oriented matroid theory and supersymmetry via the Grassmann-Pl\"ucker relations. These links are in turn useful for explaining how our approach can be connected with qubit theory.Comment: Latex, 32 pages, improved versio