N-Body Potential Interaction as a Cost Function in the Elastic Model for SANET Cloud Computing

摘要

Given a connection graph of entities that send and receive a flow of data controlled by effort and given the parameters, the metric tensor is computed that is in the elastic relational flow to effort. The metric tensor can be represented by the Hessian of the interaction potential. Now the interaction potential or cost function can be among two entities: 3 entities or 'N' entities and can be separated into two main parts. The first part is the repulsion potential the entities move further from the others to obtain minimum cost, the second part is the attraction potential for which the entities move near to others to obtain the minimum cost. For Pauli's model [1], the attraction potential is a functional set of parameters given from the environment (all the elements that have an influence in the module can be the attraction of one entity to another). Now the cost function can be created in a space of macro-variables or macro-states that is less of all possible variables. Any macro-variable collect a set of micro-variables or microstates. Now from the hessian of the macro-variables, the Hessian is computed of the micro-variables in the singular points as stable or unstable only by matrix calculus without any analytical computation - possible when the macro-states are distant among entities. Trivially, the same method can be obtained by a general definition of the macro-variable or macro-states and micro-states or variables. As cloud computing for Sensor-Actor Networks (SANETS) is based on the bonding concept for complex interrelated systems; the bond valence or couple corresponds to the minimum of the interaction potential V and in the SANET cloud as the minimum cost.