BACKGROUND Fuzzy connectedness method has shown its effectiveness for fuzzy object extraction in recent years. However, two problems may occur when applying it to hepatic vessel segmentation task. One is the excessive computational cost, and the other is the difficulty of choosing a proper threshold value for final segmentation. METHODS In this paper, an accelerated strategy based on a lookup...

Knowledge about protein function is often encoded in the form of large and sparse undirected graphs where vertices are proteins and edges represent their functional relationships. One elementary task in the computational utilization of these networks is that of quantifying the density of edges, referred to as connectedness, inside a prescribed protein set. For instance, many functional modules ...

A new technique for the study of geodesic connectedness in a class of Lorentzian manifolds is introduced. It is based on arguments of Brouwer’s topological degree for the solution of functional equations. It is shown to be very useful for multiwarped spacetimes, which include different types of relativistic spacetimes. Connectedness by causal geodesics is also proved. r 2002 Elsevier Science (U...

We prove a homogenization theorem for non-convex functionals depending on vector-valued functions, defined on Sobolev spaces with respect to oscillating measures. The proof combines the use of the localization methods of Γ-convergence with a ‘discretization’ argument, which allows to link the oscillating energies to functionals defined on a single Lebesgue space, and to state the hypothesis of ...

We prove the Feigenbaum-Coullet-Tresser conjecture on the hyperbolicity of the renormalization transformation of bounded type. This gives the first computer-free proof of the original Feigenbaum observation of the universal parameter scaling laws. We use the Hyperbolicity Theorem to prove Milnor’s conjectures on self-similarity and “hairiness” of the Mandelbrot set near the corresponding parame...

where I denotes the class of dendrites, II is the regular curves, III is the hereditarily locally connected continua, IV is the rational curves, and V» is the class of continua of dimension not exceeding n. Now it should be remarked that, for each of these classes save the first, if a continuum possesses the defining property in the small then it is a member of the class. That is, a local regul...