Avogadro Scale Engineering Form and Function http cba mit edu NSF CCR 0122419 Statistical Mechanics macroscopic state internal configuration microscopic degrees of freedom Statistical Mechanical Engineering macroscopic goal internal configuration microscopic degrees of freedom Programming Distributed Systems problem algorithm program executable protocol messages Graphical Message Passing problem algorithm program executable protocol messages Graphical Networks Sum Product Belief propagation Loeliger fm mxi f n xi xi m f m xi xi f m N xi f n m f n xi xi xn xi trees exact xj fn f n xn m x j fn x j x j N f n xi loops approximations Bethe Approximation Jonathan Yedidia cn 1 U cRU R bR H cR H R bR R U Bethe fn ci 1 d i 1 3 xi H Bethe R bn xn log f n xn n xn n xn bn xn log bn xn 1 d b x log b x L U H b x b x i i i i i xi in i i n i i xn xi L 0 bn xn f n xn e in bn xi N f n in log mxi f n xi n n Noise Locked Loops Ben Vigoda CDMA LFSR code acquisition Local Search Global Convex Optimization Pablo Parrilo et al Interior point solution to a semidefinite program on a relaxed problem computer programming linear programming semidefinite programming integer programming dynamic progamming toolpath programming fault tolerant programming developmental programming programming
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