PowerPoint PresentationStatistical MechanicsStatistical-Mechanical Engineering?Programming Distributed SystemsGraphical Message-PassingGraphical NetworksSum ProductBethe ApproximationNoise-Locked LoopsLocal SearchGlobal Convex OptimizationSlide 12Avogadro-Scale Engineering:Form and Functionhttp://cba.mit.eduNSF CCR-0122419Statistical MechanicsStatistical MechanicsStatistical MechanicsStatistical Mechanicsmacroscopic stateinternal configurationmicroscopic degrees of freedomStatistical-Mechanical Engineering?Statistical-Mechanical Engineering?Statistical-Mechanical Engineering?Statistical-Mechanical Engineering?macroscopic goalinternal configurationmicroscopic degrees of freedomProgramming Distributed SystemsProgramming Distributed SystemsProgramming Distributed SystemsProgramming Distributed SystemsproblemalgorithmprogramexecutableprotocolmessagesGraphical Message-PassingGraphical Message-PassingGraphical Message-PassingGraphical Message-PassingproblemalgorithmprogramexecutableprotocolmessagesGraphical NetworksGraphical NetworksGraphical NetworksGraphical NetworksSum ProductSum ProductSum ProductSum ProductBelief propagation, …, (Loeliger, …)fnfmxixjinjnjininnimimnixfNxjfxxxnnixffxNfixfifxxmxfxmxmxm\)(\\)()()()()()(trees: exact loops: approximationsBethe ApproximationBethe ApproximationBethe ApproximationBethe Approximation(Jonathan Yedidia)RRRRRRRRbHcHbUcU )()(xifn1nc311 iidc i xiiiiin xnnnnn xnnnninnxbxbdxbxbHxfxbU)(log)()1()(log)()(log)(BetheBethe)(log)()(0)()()(\ifxinfNxnnnnnxxnniii ninxmexfxbbLxbxbHULniniinin(Ben Vigoda)Noise-LockedNoise-LockedLoopsLoopsNoise-LockedNoise-LockedLoopsLoopsCDMA LFSR code acquisitionLocal SearchLocal SearchLocal SearchLocal SearchGlobal Convex OptimizationGlobal Convex OptimizationGlobal Convex OptimizationGlobal Convex OptimizationInterior point solution to a semidefinite program on a relaxed problem(Pablo Parrilo et al.)computer programminglinear programmingsemidefinite programminginteger programmingdynamic progammingtoolpath programmingfault-tolerant programmingdevelopmental
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