By mapping the vertices of a graph G to points in ℝ3, and its edges corresponding line segments, we obtain three-dimensional realization G. A is said be globally rigid if edge lengths uniquely determine realization, up congruence. The called every generic rigid. We consider global rigidity properties braced triangulations, which are graphs obtained from maximal planar by adding extra edges, bra...

We present a technique for partitioning an audio file into maximally-sized segments having nearly uniform spectral content, ideally corresponding to notes or chords. Our method uses dynamic programming to globally optimize a measure of simplicity or homogeneity of the intervals in the partition. Here we have focused on an entropy-like measure, though there is considerable flexibility in choosin...

In a large cyber-physical system, even if individual system elements interact with one another only locally, effects of local decisions quickly spread across the system and combine to yield global consequences. In order to reason about such a system without impractical amounts of communication and computation, we must summarize the system’s global state, and base individual decisions at least p...

this paper is concerned with global analysis of a delay sveir epidemiological model in a population of varying size. by using lyapunov stability method and lasalle’s invariance principle for delay systems, we prove that when there is no endemic equilibrium, the disease free equilibrium is globally asymptotically stable, otherwise the endemic equilibrium is globally stable.

The robust approach to data analysis uses models that do not completely specify the distribution of the data, but rather assume that this distribution belongs to a certain neighborhood of a parametric model. Consequently, robust inference should be valid under all the distributions in these neighborhoods. Regarding robust inference, there are two important sources of uncertainty: (i) sampling v...

Here it is shown how to combine two generically globally rigid bar frameworks in d-space to get another generically globally rigid framework. The construction is to identify d+1 vertices from each of the frameworks and erase one of the edges that they have in common.

We establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. A corresponding novel neural network model, which is globally convergent and stable in the sense of Lyapunov, is proposed. Both theoretical and numerical approaches are considered. Numerical simulations for three constrained nonlinear optimization problems a...