?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Statistical+mechanics+of+multiple+scales+of+neocortical+interactions&rft.creator=Ingber%2C+Lester&rft.subject=Computational+Neuroscience&rft.subject=Statistical+Models&rft.description=INTRODUCTION+General+philosophy+In+many+complex+systems%2C+as+spatial-temporal+scales+of+observation+are+increased%2C+new+phenomena+arise+by+virtue+of+synergistic+interactions+among+smaller-scale+entities--perhaps+more+properly+labeled+%22quasientities%22--which+serve+to+explain+much+observed+data+in+a+parsimonious%2C+usually+mathematically+aesthetic%2C+fashion.+For+example%2C+in+classical+thermodynamics+of+equilibrium+systems%2C+it+is+possible+to+leap+from+microscopic+molecular+scales+to+macroscopic+scales%2C+to+use+the+macroscopic+concept+of+temperature+to+describe+the+average+kinetic+energy+of+microscopic+molecular+activity%2C+or+to+use+the+macroscopic+concept+of+pressure+to+describe+the+average+rate+of+change+of+momentum+per+unit+area+of+microscopic+molecules+bombarding+the+wall+of+a+cavity.+However%2C+many+complex+systems+are+in+nonequilibrium%2C+being+driven+by+nonlinear+and+stochastic+interactions+of+many+external+and+internal+degrees+of+freedom.+For+these+systems%2C+classical+thermodynamics+typically+does+not+apply.+For+example%2C+the+description+of+weather+and+ocean+patterns%2C+which+attempt+to+include+important+features+such+as+turbulence%2C+rely+on+semiphenomenological+mesoscopic+models%2C+those+in+agreement+with+molecular+theories+but+not+capable+of+being+rigorously+derived+from+them.+Phase+transitions+in+magnetic+systems%2C+and+many+systems+similarly+modeled%2C+require+careful+treatment+of+a+continuum+of+scales+near+critical+points.+In+general%2C+rather+than+having+a+general+theory+of+nonequilibrium+nonlinear+process%2C+there+are+several+overlapping+approaches%2C+typically+geared+to+classes+of+systems%2C+usually+expanding+on+nonlinear+treatments+of+stochastic+systems.+Many+biological+systems+give+rise+to+phenomena+at+overlapping+spatial-temporal+scales.+For+example%2C+the+coiling+of+DNA+is+reasonably+approached+by+blending+microscopic+molecular-dynamics+calculations+with+mesoscopic+diffusion+equations+to+study+angular+winding.+These+approaches+have+been+directed+to+study+electroencephalography+(EEG)%2C+as+well+as+other+biological+systems.+Therefore%2C+it+should+not+be+surprising+that+the+complex+human+brain+supports+many+phenomena+arising+at+different+spatial-temporal+scales.+What+is+perhaps+surprising+is+that+it+seems+possible+to+study+truly+macroscopic+neocortical+phenomena+such+as+EEG+by+appealing+to+a+chain+of+arguments+dealing+with+overlapping+microscopic+and+mesoscopic+scales.+A+series+of+papers+has+developed+this+statistical+mechanics+of+neocortical+interactions+(SMNI).+This+approach+permits+us+to+find+models+of+EEG+whose+variables+and+parameters+are+reasonably+identified+with+ensembles+of+synaptic+and+neuronal+interactions.+This+approach+has+only+recently+been+made+possible+by+developments+in+mathematical+physics+since+the+late+1970s%2C+in+the+field+of+nonlinear+nonequilibrium+statistical+mechanics.+The+origins+of+this+theory+are+in+quantum+and+gravitational+field+theory.&rft.publisher=Oxford+University+Press&rft.contributor=Nunez%2C+Paul+L.&rft.date=1995&rft.type=Book+Chapter&rft.type=NonPeerReviewed&rft.format=application%2Fpostscript&rft.identifier=http%3A%2F%2Fcogprints.org%2F96%2F2%2Fsmni95_scales.ps&rft.identifier=++Ingber%2C+Lester++(1995)+Statistical+mechanics+of+multiple+scales+of+neocortical+interactions.++%5BBook+Chapter%5D+++++&rft.relation=http%3A%2F%2Fcogprints.org%2F96%2F