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O +In O +this O +approach O +, O +statistics B-KEY +, O +concerning O +the O +various O +linguistic O +phenomena O +of O +interest O +, O +are O +gathered O +from O +actual O +linguistic O +data O +and O +used O +to O +estimate O +the O +probabilities O +of O +the O +various O +entities O +that O +are O +generated O +by O +a O +given O +grammar O +, O +e.g. O +, O +derivations O +, O +parse-trees O +and O +sentences O +. O +The O +extension O +of O +grammars O +with O +probabilities O +makes O +it O +possible O +to O +state B-KEY +ambiguity I-KEY +resolution I-KEY +as O +a O +constrained B-KEY +optimization I-KEY +formula I-KEY +, O +which O +aims O +at O +maximizing O +the O +probability O +of O +some O +entity O +that O +the O +grammar O +generates O +given O +the O +input O +-LRB- O +e.g. O +, O +maximum O +probability O +parse-tree O +given O +some O +input O +sentence O +-RRB- O +. O +The O +implementation O +of O +these O +optimization O +formulae O +in O +efficient O +algorithms O +, O +however O +, O +does O +not O +always O +proceed O +smoothly O +. O +In O +this O +paper O +, O +we O +address O +the O +computational B-KEY +complexity I-KEY +of O +ambiguity O +resolution O +under O +various O +kinds O +of O +probabilistic B-KEY +models I-KEY +. O +We O +provide O +proofs O +that O +some O +, O +frequently O +occurring O +problems O +of O +ambiguity O +resolution O +are O +NP-complete O +. O +These O +problems O +are O +encountered O +in O +various O +applications O +, O +e.g. O +, O +language B-KEY +understanding I-KEY +for O +textand O +speech-based O +applications O +. 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O +The O +control O +signals O +of O +the O +power O +switches O +are O +derived O +from O +the O +DC B-KEY +link I-KEY +voltage I-KEY +balance I-KEY +compensator I-KEY +, O +line B-KEY +current I-KEY +controller I-KEY +and O +DC B-KEY +link I-KEY +voltage I-KEY +regulator I-KEY +. O +The O +hysteresis B-KEY +current I-KEY +control I-KEY +scheme I-KEY +is O +employed O +to O +track O +the O +line O +current O +command O +. O +The O +proposed O +control O +scheme O +and O +the O +circuit B-KEY +configuration I-KEY +can O +be O +applied O +to O +the O +active O +power O +filter O +to O +eliminate O +the O +harmonic O +currents O +and O +compensate O +the O +reactive O +power O +generated O +from O +the O +nonlinear O +load O +. O +Analytical O +and O +experimental O +results O +are O +included O +to O +illustrate O +the O +validity O +and O +effectiveness O +of O +the O +proposed O +control O +scheme O + +The O +simulated B-KEY +emergence I-KEY +of O +distributed O +environmental O +control O +in O +evolving B-KEY +microcosms I-KEY +This O +work O +continues O +investigation O +into O +Gaia B-KEY +theory I-KEY +-LRB- O +Lovelock O +, O +The O +ages O +of O +Gaia O +, O +Oxford O +University O +Press O +, O +1995 O +-RRB- O +from O +an O +artificial B-KEY +life I-KEY +perspective O +-LRB- O +Downing O +, O +Proceedings O +of O +the O +7th O +International O +Conference O +on O +Artificial B-KEY +Life I-KEY +, O +p. O +90-99 O +, O +MIT O +Press O +, O +2000 O +-RRB- O +, O +with O +the O +aim O +of O +assessing O +the O +general O +compatibility O +of O +emergent B-KEY +distributed I-KEY +environmental I-KEY +control I-KEY +with O +conventional O +natural B-KEY +selection I-KEY +. O +Our O +earlier O +system O +, O +GUILD O +-LRB- O +Downing O +and O +Zvirinsky O +, O +Artificial B-KEY +Life I-KEY +, O +5 O +, O +p.291-318 O +, O +1999 O +-RRB- O +, O +displayed O +emergent O +regulation O +of O +the O +chemical O +environment O +by O +a O +population O +of O +metabolizing B-KEY +agents I-KEY +, O +but O +the O +chemical B-KEY +model I-KEY +underlying O +those O +results O +was O +trivial O +, O +essentially O +admitting O +all O +possible O +reactions O +at O +a O +single O +energy O +cost O +. O +The O +new O +model O +, O +METAMIC O +, O +utilizes O +abstract O +chemistries O +that O +are O +both O +-LRB- O +a O +-RRB- O +constrained O +to O +a O +small O +set O +of O +legal O +reactions O +, O +and O +-LRB- O +b O +-RRB- O +grounded O +in O +basic O +fundamental O +relationships O +between O +energy O +, O +entropy O +, O +and O +biomass O +synthesis/breakdown O +. O +To O +explore O +the O +general O +phenomena O +of O +emergent B-KEY +homeostasis I-KEY +, O +we O +generate O +100 O +different O +chemistries O +and O +use O +each O +as O +the O +basis O +for O +several O +METAMIC O +runs O +, O +as O +part O +of O +a O +Gaia B-KEY +hunt I-KEY +. O +This O +search O +discovers O +20 O +chemistries O +that O +support O +microbial O +populations O +capable O +of O +regulating O +a O +physical O +environmental O +factor O +within O +their O +growth-optimal O +range O +, O +despite O +the O +extra O +metabolic O +cost O +. O +Case O +studies O +from O +the O +Gaia B-KEY +hunt I-KEY +illustrate O +a O +few O +simple O +mechanisms O +by O +which O +real O +biota O +might O +exploit O +the O +underlying O +chemistry O +to O +achieve O +some O +control O +over O +their O +physical O +environment O +. 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O +The O +theorem O +of O +Mazur O +asserts O +that O +E O +-LRB- O +Q O +-RRB- O +/ O +sub O +tors O +/ O +is O +one O +of O +the O +following O +15 O +groups O +E O +-LRB- O +Q O +-RRB- O +/ O +sub O +tors O +/ O +-LCB- O +Z/mZ O +, O +Z/mZ O +* O +Z/2mZ O +, O +m O +, O += O +1 O +, O +2 O +, O +... O +, O +10 O +, O +12 O +, O +m O += O +1 O +, O +2 O +, O +3 O +, O +4 O +. O +We O +say O +that O +an O +elliptic O +curve O +E O +' O +/ O +Q O +is O +isogenous O +to O +the O +elliptic O +curve O +E O +if O +there O +is O +an O +isogeny O +, O +i.e. O +a O +morphism O +phi O +: O +E O +to O +E O +' O +such O +that O +phi O +-LRB- O +O O +-RRB- O += O +O O +, O +where O +O O +is O +the O +point O +at O +infinity O +. 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