This paper discusses a technique that combines bond graph energy-flow modeling and signal-flow modeling schemes for modeling discontinuities in physical systems. This enables the generation of complex, multi-mode behaviors without violating the energy flow principles imposed by bond graphs . Mode switching is achieved by controlled junctions which assume one of two states : on and off. The cont...

Auter space An is contractible. A. Hatcher and K. Vogtmann constructd a stratification of An into subspaces An,k such that An,k is kconnected. Their argument that An,k is (k−1)-connected, the Degree Theorem and its proof, is somewhat global in nature. Here we present a combinatorial substitue for the Degree Theorem that uses only local considerations to show that An,k is (k − 1)-connected. LetR...

Recent studies in linear inverse problems have recognized the sparse representation of unknown signal in a certain basis as an useful and effective prior information to solve those problems. In many multiscale bases (e.g. wavelets), signals of interest (e.g. piecewise-smooth signals) not only have few significant coefficients, but also those significant coefficients are well-organized in trees....

We undertake a combinatorial study of the piecewise linear map g : R → R which assigns to the four vectors a,A in R and b, B in R the m×n matrix given by gij = min(ai + bj, Ai +Bj). This map arises naturally in Pachter and Sturmfels’s work on the tropical geometry of statistical models. The image of g has been a subject of recent interest; it is the positive part of the tropical algebraic varie...

This paper discusses a technique for modeling discontinuous physical systems that combines the bond graph energy-ow modeling scheme with a signal-ow modeling scheme augmented with nite state automata. It enables the generation of complex, multi-mode behaviors without violating the energy ow principles imposed by bond graphs. Mode switching is achieved by controlled junctions which can take on o...