Supramenable groups and partial actions

We characterize supramenable groups in terms of existence of invariant probability measures for partial actions on compact Hausdorff spaces and existence of tracial states on partial crossed products. These characterizations show that, in general, one cannot decompose a partial crossed product of a C*-algebra by a semi-direct product of groups as two iterated partial crossed products. We give conditions which ensure that such decomposition is possible.Comment: 17 pages. Corrected typos. To appear in Ergodic Theory and Dynamical System

Discussion on complexity and TCAS indicators for coherent safety net transitions

Transition between Separation Management in ATM and Collision Avoidance constitutes a source of potential risks due to non-coherent detection and resolution clearances between them. To explore an operational integration between these two safety nets, a complexity metric tailored for both Separation Management and Collision Avoidance, based on the intrinsic complexity, is proposed. To establish the framework to compare the complexity metric with current Collision Avoidance detection metrics, a basic pair-wise encounter model has been considered. Then, main indicators for horizontal detection of TCAS, i.e. tau and taumod, have been contrasted with the complexity metric. A simple method for determining the range locus for specific TCAS tau values, depending on relative speeds and encounter angles, was defined. In addition, range values when detection thresholds were infringed have been found to be similar, as well as its sensitivity to relative angles. Further work should be conducted for establishing a framework for the evaluation and validation of this complexity metric. This paper defines basic principles for an extended evaluation, including multi-encounter scenarios and longer look ahead times

Statistical dynamics of spatial-order formation by communicating cells

Communicating cells can coordinate their gene expressions to form spatial patterns. 'Secrete-and-sense cells' secrete and sense the same molecule to do so and are ubiquitous. Here we address why and how these cells, from disordered beginnings, can form spatial order through a statistical mechanics-type framework for cellular communication. Classifying cellular lattices by 'macrostate' variables - 'spatial order paramete' and average gene-expression level - reveals a conceptual picture: cellular lattices act as particles rolling down on 'pseudo-energy landscapes' shaped by a 'Hamiltonian' for cellular communication. Particles rolling down represent cells' spatial order increasing. Particles trapped on the landscapes represent metastable spatial configurations. The gradient of the Hamiltonian and a 'trapping probability' determine the particle's equation of motion. This framework is extendable to more complex forms of cellular communication