Graph-theoretical approach to qualitative solvability of linear systems

Linear Solvability in the Viewing Graph

The Viewing Graph [1] represents several views linked by the corresponding fundamental matrices, estimated pairwise. Given a Viewing Graph, the tuples of consistent camera matrices form a family that we call the Solution Set. This paper provides a theoretical framework that formalizes different properties of the topology, linear solvability and number of solutions of multi-camera systems. We sy...

Solvability of Systems of Linear Operator Equations

Let G be a semigroup of commuting linear operators on a linear space S with the group operation of composition. The solvability of the system of equations /,/ = ,■, i = I, ... , r, where /, e G and j e S , was considered by Dahmen and Micchelli in their studies of the dimension of the kernel space of certain linear operators. The compatibility conditions Ijfr = Irfj , i ^ j , are necessar...

Solvability of Systems of Linear Interval Equations

A Graph Approach to Observability in Physical Sparse Linear Systems

A sparse linear system constitutes a valid model for a broad range of physical systems, such as electric power networks, industrial processes, control systems or traffic models. The physical magnitudes in those systems may be directly measured by means of sensor networks that, in conjunction with data obtained from contextual and boundary constraints, allow the estimation of the state of the sy...

A graph theoretical approach to data fusion.

The rapid development of high throughput experimental techniques has resulted in a growing diversity of genomic datasets being produced and requiring analysis. Therefore, it is increasingly being recognized that we can gain deeper understanding about underlying biology by combining the insights obtained from multiple, diverse datasets. Thus we propose a novel scalable computational approach to ...