A Two-Level Quantum Analysis of ERP Data for Mock-Interrogation Trials. Michael Schillaci Jennifer Vendemia Robert Buzan Eric Green

Transcription

1 A Two-Level Quaum Aalysis of ERP Daa for Mock-Ierrogaio Trials Michael Schillaci Jeifer Vedemia Rober Buza Eric Gree

2 Oulie Experimeal Paradigm 4 Low Workload; Sigle Sessio; 39 8 High Workload; Muliple Sessio; 5 Cosrucig a Two-Sae Sysem Two-Level Formalism Chael Kes ad Saes, Respose Saes Two-Level Dyamics Eergy, Probabiliy, Trasiio Raes, Desiy Aalysis Tools Trasiio Raes ad Sae Predicabiliy Corex Variaios ad Load-Swichig Aciviy Time-Course Saisical Sigificace Cogiive Cosrucs Summary ad Coclusio

3 Experimeal Procedure Two-Simulus Paradigm 8 Chaels: 5 Hz Samplig Rae, Verex Referece Kowledge a Simuli: Kowledge of Truh Value, Kowledge of Task Experime 4: Kow Truh Value ad Task a Simulus Experime 8: Kow Oly Truh Value a Simulus

4 Cosrucig a Two-Sae Sysem E E H C ϕ ϕ ψ ψ + ˆ E i e b ϕ h Φ i i C e U e U U ψ ϕ ϕ ψ + Ψ Ψ c C Φ Φ c C E i e a ψ h Ψ Chael-Saes: ime-depede phase ad ampliude Hamiloia: ˆ ˆ U H H + Respose-Saes: liear superposiio of all chael-saes r ψ ψ, v r ϕ ϕ, v Chael-Kes: saioary basis of saes *The base kes are eige-vecors of he free Hamiloia. i.e., E H E H ϕ ϕ ψ ψ ˆ ˆ

5 Eergy ad Frequecy Values *Chael power is he square volage divided by he impedace. i.e., P / / V z [ ] Iegrae chael power o ge eergy: E U, τ V V τ d z, τ V V τ d z Defie frequecies as follows: E α E β h E E δ U h h } h } Fixed by measureme Varies wih perurbaio

6 Two-Level Dyamics Propagaig gives a Schrödiger-like equaio: a e i d db b e i d da i i δ δ Geeral Sae: This yields wo liear, coupled, DE s: I I I U i χ χ h Φ + Ψ χ ˆ e H i I χ χ h *Saes are propagaed i ime usig he full Hamiloia:

7 Trasiio Probabiliies Exac soluios may be wrie i erms of he Rabi Formulae: b a C C si cos δ δ δ δ δ For resoace ω δ we wrie: b p a p C C δ δ si cos *We assume here a pure ruh sar. i.e., a ; b

8 Sae Trasiios Occupaio Values *Thermodyamic eergy icreases wih emperaure: k B T K Trasiio Raes: rae of sae rasiios d Γ a si Γ Sae Occupaio Values: umber of saes available e l b + si ε T k B d d d ε ε kbt C C ε l > ε > ε

9 *Sum of desiies over chaels ad resposes gives % of aciviy. Corical Aciviy C η + η Eergy Desiy: fracioal eergy coribuio for regio η R p E R p E + p E η R p E R p E + p E

10 Aalysis Tools Sum Over Eire Corex: Experime 4 Waveform Aciviy Probabiliy Mai differeces a laer imes Aciviy differeces grealy ehaced Trasiios possible hroughou Eergy Trasiio Rae L Raio Perurbaio drives rasiios Raes average o zero a laer imes Predics high eergy sae as

11 Sae Predicabiliy: Experime 4 *Aciviy-Rae phase discrimiaes sae ad subjec differeces: 3/39 ~ 77 % Plo η vs. Γ : assess how sae rasiios effec TOT aciviy > Good Liar? Bad Liar? > Seady-Sae: rasiios cease; saes idepede

12 Aeio Based Load-Swichig * eocorical ieracio ime, ls, is greaer for decepio. Deermie Miimum FL ad Maximum OR Laecy Load-Swichig Widow is Differece: ls OR max FL mi ls 4 ms ls 64 ms Algorihm: firs FL MI afer OR MAX

13 Workload Effecs *Icreased cogiive workload decreases eocorical ieracio imes. Experime 4 Workload Effecs Durig Mock-Ierrogaio Trials ls 4 ms ls 64 ms 7 6 -Time -Time Experime 8 Day Swichig Widow ms ls 4 ms ls 6 ms 4 8 Day

14 Pracice Effecs *Task pracice decreases eocorical ieracio ime uil subjecs ge bored wih ask. Experime 8: Day : ls 4 ms, 6 ms Day : ls ms, 4 ms Day 3: ls 3 ms, 8 ms Load-Swichig Widow ms Pracice Effecs Durig Mock-Ierrogaio Trials -Time -Time 8 Day 8 Day 8 Day 3 Experim e

15 Aciviy Time-Course Experime 4 Relaive o OR Maximum: TLA mi precedes, FL mi follows Cogiive Time Course for Load-Swichig Durig Mock-Ierrogaio Trials FL-OR TLA-OR FL-OR TLA-OR 4 4 Swicig Time ms Experime 4

16 Workload, Aeio *Timig resuls suppor our cogiive model of decepio. Cogiive Cosrucs Similar Waveform Topology Differe Ieracio Times Exp 4 Regio Waveforms FL TLA OR Saliece, Aeio Memory, Aeio

17 Aciviy Time-Course Experime 8 Pracice Alers Time Course: Day : TLA-OR-FL; : TLA-OR-FL Day : OR-FL-TLA; : OR-FL-TLA Day 3 : OR-FL/TLA; : OR-TLA-FL Cogiive Time-Course for Load-Swichig Durig Repeaed Mock-Ierrogaio Trials FL-OR TLA-OR FL-OR TLA-OR Swichig Time ms Day 8 Day 8 Day 3

18 Facor Loadigs.8 Saisical Sigificace: Experime 4 Weigh arb Time ms Aalysis of Regios ad Decepio: FL3, OR, TLA Resuls: Facor f Resuls: Facor f,39,.687 REG 4.87, p., η f,39, , p., η f,39 DEC,39,.73 REG 9.9, p.4, η DEC* REG , p.3, η.7 Magial Mea Magial Mea Facor Fidigs Regio Facor Fidigs Regio Resuls: Facor 4 f,39,.75 REG.95, p., η.6 Resuls: Facor 5 f,39,.743 REG.9, p., η.8 Resuls: Facor 6 f,39 REG 7.4, p., η.34 Magial Mea Magial Mea Magial Mea Facor 4 Fidigs Regio Facor 5 Fidigs Regio Facor 6 Fidigs Regio

19 Sae Predicabiliy: Experime 8 *Sae eergy ad occupaio reai predicive power wih pracice. Corical Eergy L Raio Aciviy-Rae Phase

20 Summary ad Coclusios Two-Sae Formalism Solid heoreical framework Cogiive aciviy defied i erms of sigal power Accuraely predics sae eergy ad occupaio Cosise assessme of sae dyamics Fidigs Workload decreases corical ieracio ime Pracice alers ime-course Saisical sigificace exceeds expecaio