On Structure and Organization: An Organizing Principle

We discuss the nature of structure and organization, and the process of making new Things. Hyperstructures are introduced as binding and organizing principles, and we show how they can transfer from one situation to another. A guiding example is the hyperstructure of higher order Brunnian rings and similarly structured many-body systems.Comment: Minor revision of section

Computational Design of Axion Insulators Based on 5d Spinels Compounds

Based on density functional calculation with LDA+U method, we propose that hypothetical Osmium compounds such as CaOs2O4 and SrOs2O4 can be stabilized in the geometrically frustrated spinel crystal structure. They also show some exotic electronic and magnetic properties in a reasonable range of on-site Coulomb correlation U such as ferromagnetism and orbital magnetoelectric effect characteristic to Axion electrodynamics. Other electronic phases including 3D Dirac metal and Mott insulator exist and would make perspective 5d spinels ideal for applications.Comment: 5 pages, 3 figure

(1,q=−1)(1,q=-1) Model as a Topological Description of 2d2d String Theory

We study the $(1,q=-1)$ model coupled to topological gravity as a candidate to describing $2d$ string theory at the self-dual radius. We define the model by analytical continuation of $q>1$ topological recursion relations to $q=-1$. We show that at genus zero the $q=-1$ recursion relations yield the $W_{1+\infty}$ Ward identities for tachyon correlators on the sphere. A scheme for computing correlation functions of $q=-1$ gravitational descendants is proposed and applied for the computation of several correlators. It is suggested that the latter correspond to correlators of discrete states of the $c=1$ string. In a similar manner to the $q>1$ models, we show that there exist topological recursion relations for the correlators in the $q=-1$ theory that consist of only one and two splittings of the Riemann surface. Using a postulated regularized contact, we prove that the genus one $q=-1$ recursion relations for tachyon correlators coincide with the $W_{1+\infty}$ Ward identities on the torus. We argue that the structure of these recursion relations coincides with that of the $W_{1+\infty}$ Ward identities for any genus.Comment: 39 pages,latex,taup-2170 -9