Maha Almohamad, Jayna M Dave, Eric E Calloway, Ruosha Li, Shreela Sharma
Relationship between Food Security, Nutrition Security, and Diabetes: The Role of Supplemental Nutrition Assistance Program Participation
Current developments in nutrition
paper studies average consensus random topologies intermittent links noisy channels consensus noise network links leads biasvariance dilemmarunning consensus long reduces bias final average estimate increases variance present two different compromises tradeoff xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinkai xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinkndi algorithm modifies conventional consensus forcing weights satisfy xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinkpersistencei condition slowly decaying zero xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinkai xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinknci algorithm weights constant consensus run fixed number iterations iota restarted rerun total xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinkpi runs end averages final states xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinkpi runs monte carlo averaging use controlled markov processes stochastic approximation arguments prove almost sure convergence xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinkai xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinkndi finite consensus limit compute explicitly mean square error mse variance consensus limit show xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinkai xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinkndi represents best worldszero bias low varianceat cost slow convergence rate rescaling weights balances variance versus rate bias reduction convergence rate contrast xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinkai xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinknci constant weights converges fast presents different biasvariance tradeoff number iterations iota xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinkpi shorter runs smaller iota lead high bias smaller variance larger number xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinkpi runs average static nonrandom network gaussian noise compute optimal gain xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinkai xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinknci reach shortest number iterations iota xmlnsmmlhttpwwww3org1998mathmathml xmlnsxlinkhttpwwww3org1999xlinkpi high probability 1delta epsiv deltaconsensus epsiv residual bias results hold fairly general assumptions random link failures communication noise