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18:05, 19 October 2022 Gianfranco talk contribs created page Store:Exel14 (Created page with "The expression for can be readily applied to the probabilities and positions as defined above, resulting in the first term given by <center> {| width="80%" | |- | width="33%" | | width="33%" |{{CD1}}<math>\langle x^2(t)\rangle=\sum_{j=1}^{92}P_j(t) x_j^2</math>{{CD2}} | width="33%" align="right" |<math>(8)</math> |} </center> And the second term given by the square of Eq. (4). The second term of <math>\Delta P_x</math> is given by the square of Eq. (5), but the f...")
18:02, 19 October 2022 Gianfranco talk contribs created page Store:Exel13 (Created page with "== Model == Each of the j electrodes is described by an ordered pair (<math>x_j,y_j,z_j</math>) in 3-dimensional space. To complete this analysis, the electrodes were first projected onto the (<math>x,y</math>) plane, removing the depth of the head. Figure 1A shows the locations of each electrode in this 2d-space. Following this projection, the time courses for each of the 92 electrodes were Hilbert transformed and then normalized following the procedure listed using Eq...")
18:01, 19 October 2022 Gianfranco talk contribs created page Store:Exel12 (Created page with "== Methods== === Data acquisition=== Twenty-eight healthy subjects were recruited from The Brain and Mind Institute at the University of Western Ontario, Canada to participate in this study. Informed written consent was acquired prior to testing from all participants. Ethics approval for this study was granted by the Health Sciences Research Ethics Board and the Non-Medical Research Ethics Board of The University of Western Ontario and all research was performed in acco...")
18:00, 19 October 2022 Gianfranco talk contribs created page Store:Exel11 (Created page with "==== Discussion ==== In the current study, we investigated the spatial-extent and the associated transitional properties of neural activity in the brain during active and resting conditions, and whether similar underlying network properties exist. We found that applying the Hilbert transformation to the EEG data and normalizing it (Eq. 2) imposes a probabilistic structure to the EEG signal across the brain (Eq. 3), which we used to identify probability of spatial patter...")
17:59, 19 October 2022 Gianfranco talk contribs created page Store:Exel10 (Created page with "=== Table 2=== {| class="wikitable" !Stimulus !<math>\Delta x\Delta p_x</math> !<math>\Delta y\Delta p_y</math> !<math>\Delta x\Delta p_x</math> !<math>\Delta y\Delta p_y</math> !<math>\Delta x\Delta p_x</math> !<math>\Delta y\Delta p_y</math> !<math>\Delta x\Delta p_x</math> !<math>\Delta y\Delta p_y</math> |- | colspan="1" rowspan="1" |Taken | colspan="1" rowspan="1" |<math display="inline">(7\pm2.1)10^{-1}</math> | colspan="1" rowspan="1" |<math...")
17:59, 19 October 2022 Gianfranco talk contribs created page Store:Exel09 (Created page with "==== Uncertainty principle ==== Despite the confirmation of previous neuroscientific results, and the apparent success of our quasi-quantum model, our research question as posed above remains only half answered. Using this model, we noted differences in the probability distributions and the phase space centroids in rest when compared to task. However, we still sought a parameter from the model that would remain the same in rest and task. To this end, we defined an analo...")
17:58, 19 October 2022 Gianfranco talk contribs created page Store:Exel08 (Created page with "=== Table 1 === Group averages of the centroids. {| class="wikitable" |+ !Stimulus !<math>\langle x\rangle</math> !<math>\langle y\rangle</math> !<math>\langle p_x\rangle</math> !<math>\langle p_y\rangle</math> |- |Taken | colspan="1" rowspan="1" |<math>(-1.4\pm5.8)\times10^{-1}</math> | colspan="1" rowspan="1" |<math>(2.4\pm8.0)\times10^{-1}</math> | colspan="1" rowspan="1" |<math>(-5.8\pm27.0)\times10^{-2}</math> | colspan=...")
17:57, 19 October 2022 Gianfranco talk contribs created page Store:Exel07 (Created page with "===== Phase space ===== We also explored the average-valued phase space of this system. The phase space for each subject was plotted as the average position and momentum along the <math>x</math> direction <math>(\langle x(t)\rangle,\langle p_x(t)\rangle)</math> or as the average position and momentum along the <math>x</math> direction <math>(\langle y(t)\rangle,\langle p_y(t)\rangle)</math>. Figure 2 shows the centroids of the phase space scatter plots for each subject...")
17:55, 19 October 2022 Gianfranco talk contribs created page Store:Exel06 (Created page with "With the same holding true for y. These two equations are how we create our quasi-quantum mechanical analogues. The second equation is an extension of Ehrenfest’s theorem, relating the average momenta of a particle to the time derivative of its average position. Where we have assumed a Hamiltonian with only a spatially dependent potential. Note that as the positions are fixed in space (positions of the electrodes) only the probability changes in time. Throughout this p...")
17:55, 19 October 2022 Gianfranco talk contribs created page Store:Exel05 (Created page with "With <math>i=\sqrt{-1}</math>. We then imposed the normalization condition, <center> {| width="80%" | |- | width="33%" | | width="33%" |{{CD1}}<math>\hat{\Psi}_j(t)= \frac{\Psi_j(t)}{\sqrt{\sum_{j=1}^{92}|\Psi_j|^2}}</math>{{CD2}} | width="33%" align="right" |<math>(2)</math> |} </center> The summation extends to 92, corresponding to the 92 electrodes selected from the original 129 on the head cap (channels removed from the face and neck for this analysis). T...")
17:54, 19 October 2022 Gianfranco talk contribs created page Store:Exel04 (Created page with "=== Results === In this paper, we adapted the probability amplitudes of quantum mechanics to define new metrics for examining EEG data—the ‘average position’ and ‘average momentum’ of the EEG signal. These were constructed from our definition of ‘brain states’ based on the quasi-quantum model. This allowed us to ascertain the frequency with which unique brain regions are entered by the pseudo-wavefunction, as well as explore the average-valued phase space....")
17:53, 19 October 2022 Gianfranco talk contribs created page Store:Exel03 (Created page with "Is there a way to identify the shared neural architecture underlying the cognitive processes associated with rest and active states while also quantifying how these processes diverge from that shared architecture of neural activity? In this paper, we applied mathematical methods analogous to those of quantum mechanics, and the concept of phase space to EEG recorded during rest and movie-watching to extract spatial and transitional properties of dynamic neural activity. Q...")
17:53, 19 October 2022 Gianfranco talk contribs created page Store:Exel02 (Created page with "=== Introduction === An important but outstanding issue in contemporary cognitive neuroscience is understanding the organizational properties of neural activity. For instance, is there a fundamental structure to the spatial–temporal patterns neural brain activity across different conditions? One common approach used to address this question is to examine the brain at “rest”. Measures such as functional connectivity, independent component analysis and graph theoreti...")
17:52, 19 October 2022 Gianfranco talk contribs created page Store:Exel01 (Created page with "== Abstract== An outstanding issue in cognitive neuroscience concerns how the brain is organized across different conditions. For instance, during the resting-state condition, the brain can be clustered into reliable and reproducible networks (e.g., sensory, default, executive networks). Interestingly, the same networks emerge during active conditions in response to various tasks. If similar patterns of neural activity have been found across diverse conditions, and ther...")
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Tau by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Pval by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Psi by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:P-val by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:M by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Krennikov1a by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Krennikov1 by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Khrennikov006 by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Khrennikov005 by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Khrennikov004 by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Khrennikov003 by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Khrennikov002 by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Khrennikov001 by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Imo by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Im by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Hilbert007 by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Hilbert006 by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Hilbert005 by file upload (1 revision)
16:13, 19 October 2022 Gianfranco talk contribs imported Formula:Hilbert004 by file upload (1 revision)
16:12, 19 October 2022 Gianfranco talk contribs imported Formula:Hilbert003 by file upload (1 revision)
16:12, 19 October 2022 Gianfranco talk contribs imported Formula:Hilbert002 by file upload (1 revision)
16:12, 19 October 2022 Gianfranco talk contribs imported Formula:Hilbert001 by file upload (1 revision)
16:12, 19 October 2022 Gianfranco talk contribs imported Formula:H by file upload (1 revision)
16:12, 19 October 2022 Gianfranco talk contribs imported Formula:Delta series by file upload (1 revision)
16:12, 19 October 2022 Gianfranco talk contribs imported Formula:Delta4 by file upload (1 revision)
16:12, 19 October 2022 Gianfranco talk contribs imported Formula:Delta3 by file upload (1 revision)
16:12, 19 October 2022 Gianfranco talk contribs imported Formula:Delta2 by file upload (1 revision)
16:12, 19 October 2022 Gianfranco talk contribs imported Formula:Delta1 by file upload (1 revision)
16:12, 19 October 2022 Gianfranco talk contribs imported Formula:D by file upload (1 revision)
16:12, 19 October 2022 Gianfranco talk contribs imported Formula:C by file upload (1 revision)
16:12, 19 October 2022 Gianfranco talk contribs imported Formula:A-alpha by file upload (1 revision)
16:12, 19 October 2022 Gianfranco talk contribs imported Formula:1 by file upload (1 revision)
16:10, 19 October 2022 Gianfranco talk contribs created page Formula:P-val (Created page with "<math>P-value</math>")
16:09, 19 October 2022 Gianfranco talk contribs created page Formula:Pval (Created page with "<math>P-value</math>")
16:08, 19 October 2022 Gianfranco talk contribs created page Template:Formulist (Created page with "{{!}}- {{!}} [[F:{{{1}}}]] {{!}} {{:F:{{{1}}}}} {{!}} '''<code><nowiki>{{:F:</nowiki>{{{1}}}<nowiki>}}</nowiki></code>'''")
16:08, 19 October 2022 Gianfranco talk contribs created page Aiuto:Elenco formule (Created page with " == Valori caldi== {| |- | {| border="1" cellpadding="8" | |- ! link ! rendering ! codice da inserire |- {{formulist|Pval}} |} | {| border="1" cellpadding="8" | |- ! link ! rendering ! codice da inserire |- {{formulist|P-val}} |} |} == Singole lettere == {| border="1" cellpadding="8" | |- ! link ! rendering ! codice da inserire |- {{Formulist|Khrennikov001}} {{Formulist|Khrennikov002}} {{formulist|C}} {{formulist|D}} {{formulist|H}} {{formulist|Hilbert003}} {{...")

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