Models of social influence may present discontinuous dynamical rules, which are unavoidable with topological interactions, i.e. when the dynamics is outcome interactions a limited number nearest neighbors. Here, we show that classical solutions not sufficient to describe resulting dynamics. We first time evolution interaction graph associated Caratheodory solutions, whose properties depend on d...

Let M be a C∞ Riemannian manifold, dimM = n. A distribution on M is a smooth linear subbundle of the tangent bundle TM . We denote by q the fiber of at q ∈M ; q ⊂ TqM . The number k = dim q is the rank of the distribution. We assume that 1 < k < n. The restriction of the Riemannian structure to is a sub-Riemannian structure. Lipschitz integral curves of the distribution are called admissible pa...

Let Ω denote an algebra of sets and μ a σ-finite measure. We then prove that the completion of Ω under the pseudometric d(A,B) = μ∗(A△B) is σ-algebra isomorphic and isometric to the Caratheodory Extension of Ω under the equivalence relation ∼.

We present a numerical code for the computation of nodes and weights low-cardinality positive quadrature formula on spherical triangles, nearly exact polynomials given degree. The algorithm is based subperiodic trigonometric Gaussian planar elliptical sectors Caratheodory–Tchakaloff compression via NNLS.