User contributions for Gianfranco

10:41, 5 November 2022 diff hist −5,522‎ Store:EEMIen07 ‎ current Tag: Visual edit: Switched
10:41, 5 November 2022 diff hist +5,519‎ N Store:EEMIen08 ‎ 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..."
10:40, 5 November 2022 diff hist +7,958‎ N Store:EEMIen07 ‎ 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..."
10:39, 5 November 2022 diff hist +3,432‎ N Store:EEMIes06 ‎ 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=..."
10:38, 5 November 2022 diff hist +3,432‎ N Store:EEMIde06 ‎ 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=..."
10:38, 5 November 2022 diff hist +3,432‎ N Store:EEMIfr06 ‎ 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=..."
10:38, 5 November 2022 diff hist +3,432‎ N Store:EEMIit06 ‎ 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=..."
10:37, 5 November 2022 diff hist +3,432‎ N Store:EEMIen06 ‎ 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=..." current
10:36, 5 November 2022 diff hist +7,019‎ N Store:EEMIes05 ‎ Created page with "===== In practice ===== 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 paper the m..."
10:36, 5 November 2022 diff hist +7,019‎ N Store:EEMIde05 ‎ Created page with "===== In practice ===== 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 paper the m..."
10:35, 5 November 2022 diff hist +7,019‎ N Store:EEMIfr05 ‎ Created page with "===== In practice ===== 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 paper the m..."
10:35, 5 November 2022 diff hist +7,019‎ N Store:EEMIit05 ‎ Created page with "===== In practice ===== 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 paper the m..."
10:34, 5 November 2022 diff hist +34‎ Store:EEMIen04 ‎ current
10:34, 5 November 2022 diff hist +34‎ Store:EEMIit04 ‎
10:34, 5 November 2022 diff hist +34‎ Store:EEMIfr04 ‎
10:33, 5 November 2022 diff hist +34‎ Store:EEMIde04 ‎
10:33, 5 November 2022 diff hist +34‎ Store:EEMIes04 ‎
10:33, 5 November 2022 diff hist −10‎ Store:EEMIen05 ‎ current
10:17, 5 November 2022 diff hist −20,686‎ Exploring electroencephalography with a model inspired by quantum mechanics ‎
10:17, 5 November 2022 diff hist +7,029‎ N Store:EEMIen05 ‎ 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..."
10:15, 5 November 2022 diff hist +3,637‎ N Store:EEMIes04 ‎ 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...."
10:15, 5 November 2022 diff hist +3,637‎ N Store:EEMIde04 ‎ 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...."
10:15, 5 November 2022 diff hist +3,637‎ N Store:EEMIfr04 ‎ 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...."
10:15, 5 November 2022 diff hist +3,637‎ N Store:EEMIit04 ‎ 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...."
10:14, 5 November 2022 diff hist +3,637‎ N Store:EEMIen04 ‎ 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...."
10:13, 5 November 2022 diff hist +10,014‎ N Store:EEMIes03 ‎ Created page with "Indeed, the same set of structured patterns of neural activity have been found during "active" states, such as, while completing different tasks<ref>Biswal BB, Eldreth DA, Motes MA, Rypma B. Task-dependent individual differences in prefrontal connectivity. Cereb. Cortex. 2010;20:2188–2197. doi: 10.1093/cercor/bhp284. [PMC free article][PubMed] [CrossRef] [Google Scholar]</ref><ref>Fox MD, Raichle ME. Spontaneous fluctuations in brain activity observed with functional m..."
10:13, 5 November 2022 diff hist +10,014‎ N Store:EEMIde03 ‎ Created page with "Indeed, the same set of structured patterns of neural activity have been found during "active" states, such as, while completing different tasks<ref>Biswal BB, Eldreth DA, Motes MA, Rypma B. Task-dependent individual differences in prefrontal connectivity. Cereb. Cortex. 2010;20:2188–2197. doi: 10.1093/cercor/bhp284. [PMC free article][PubMed] [CrossRef] [Google Scholar]</ref><ref>Fox MD, Raichle ME. Spontaneous fluctuations in brain activity observed with functional m..."
10:13, 5 November 2022 diff hist +10,014‎ N Store:EEMIfr03 ‎ Created page with "Indeed, the same set of structured patterns of neural activity have been found during "active" states, such as, while completing different tasks<ref>Biswal BB, Eldreth DA, Motes MA, Rypma B. Task-dependent individual differences in prefrontal connectivity. Cereb. Cortex. 2010;20:2188–2197. doi: 10.1093/cercor/bhp284. [PMC free article][PubMed] [CrossRef] [Google Scholar]</ref><ref>Fox MD, Raichle ME. Spontaneous fluctuations in brain activity observed with functional m..."
10:13, 5 November 2022 diff hist +10,014‎ N Store:EEMIit03 ‎ Created page with "Indeed, the same set of structured patterns of neural activity have been found during "active" states, such as, while completing different tasks<ref>Biswal BB, Eldreth DA, Motes MA, Rypma B. Task-dependent individual differences in prefrontal connectivity. Cereb. Cortex. 2010;20:2188–2197. doi: 10.1093/cercor/bhp284. [PMC free article][PubMed] [CrossRef] [Google Scholar]</ref><ref>Fox MD, Raichle ME. Spontaneous fluctuations in brain activity observed with functional m..."
10:12, 5 November 2022 diff hist +10,014‎ N Store:EEMIen03 ‎ Created page with "Indeed, the same set of structured patterns of neural activity have been found during "active" states, such as, while completing different tasks<ref>Biswal BB, Eldreth DA, Motes MA, Rypma B. Task-dependent individual differences in prefrontal connectivity. Cereb. Cortex. 2010;20:2188–2197. doi: 10.1093/cercor/bhp284. [PMC free article][PubMed] [CrossRef] [Google Scholar]</ref><ref>Fox MD, Raichle ME. Spontaneous fluctuations in brain activity observed with functional m..."
10:11, 5 November 2022 diff hist +105‎ Exploring electroencephalography with a model inspired by quantum mechanics ‎
10:10, 5 November 2022 diff hist −4,072‎ Exploring electroencephalography with a model inspired by quantum mechanics ‎ →‎Introduction
10:10, 5 November 2022 diff hist +4,091‎ N Store:EEMIes02 ‎ 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..."
10:10, 5 November 2022 diff hist +4,091‎ N Store:EEMIde02 ‎ 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..."
10:09, 5 November 2022 diff hist +4,091‎ N Store:EEMIfr02 ‎ 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..."
10:09, 5 November 2022 diff hist +4,091‎ N Store:EEMIit02 ‎ 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..."
10:09, 5 November 2022 diff hist +4,091‎ N Store:EEMIen02 ‎ 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..."
10:08, 5 November 2022 diff hist −1,443‎ Exploring electroencephalography with a model inspired by quantum mechanics ‎ →‎Abstract
10:08, 5 November 2022 diff hist +1,462‎ N Store:EEMIes01 ‎ 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..."
10:08, 5 November 2022 diff hist +1,462‎ N Store:EEMIde01 ‎ 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..."
10:08, 5 November 2022 diff hist +1,462‎ N Store:EEMIfr01 ‎ 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..."
10:07, 5 November 2022 diff hist +1,462‎ N Store:EEMIit01 ‎ 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..."
10:07, 5 November 2022 diff hist +1,462‎ N Store:EEMIen01 ‎ 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..." current
10:01, 5 November 2022 diff hist +1,704‎ Exploring electroencephalography with a model inspired by quantum mechanics ‎
02:36, 4 November 2022 diff hist +2,476‎ N Store:FLes06 ‎ Created page with "==Final considerations== Topics that could distract the reader’s attention were, in fact, essential for demonstrating the message. Normally, indeed, when any more or less brilliant mind allows itself to throw a stone into the pond of Science, a shockwave is generated, typical of the period of Kuhn’s extraordinary science, against which most of the members of the international scientific community row. With good faith, we can say that this phenomenon—as regards the..."
02:36, 4 November 2022 diff hist +2,476‎ N Store:FLde06 ‎ Created page with "==Final considerations== Topics that could distract the reader’s attention were, in fact, essential for demonstrating the message. Normally, indeed, when any more or less brilliant mind allows itself to throw a stone into the pond of Science, a shockwave is generated, typical of the period of Kuhn’s extraordinary science, against which most of the members of the international scientific community row. With good faith, we can say that this phenomenon—as regards the..."
02:36, 4 November 2022 diff hist +6,310‎ N Store:FLes05 ‎ Created page with "==Fuzzy set <math>\tilde{A}</math> and membership function <math>\mu_{\displaystyle {\tilde {A}}}(x)</math>== We choose - as a formalism - to represent a fuzzy set with the 'tilde':<math>\tilde{A}</math>. A fuzzy set is a set where the elements have a 'degree' of belonging (consistent with fuzzy logic): some can be included in the set at 100%, others in lower percentages. To mathematically represent this degree of belonging is the function <math>\mu_{\displaystyle {\til..."
02:36, 4 November 2022 diff hist +6,310‎ N Store:FLde05 ‎ Created page with "==Fuzzy set <math>\tilde{A}</math> and membership function <math>\mu_{\displaystyle {\tilde {A}}}(x)</math>== We choose - as a formalism - to represent a fuzzy set with the 'tilde':<math>\tilde{A}</math>. A fuzzy set is a set where the elements have a 'degree' of belonging (consistent with fuzzy logic): some can be included in the set at 100%, others in lower percentages. To mathematically represent this degree of belonging is the function <math>\mu_{\displaystyle {\til..."
02:35, 4 November 2022 diff hist +2,158‎ N Store:FLde04 ‎ Created page with "===Set operators=== Given the whole universe <math>U</math> we indicate with <math>x</math> its generic element so that <math>x \in U</math>; then, we consider two subsets <math>A</math> and <math>B</math> internal to <math>U</math> so that <math>A \subset U</math> and <math>B \subset U</math> {| |left|80px |'''Union:''' represented by the symbol <math>\cup</math>, indicates the union of the two sets <math>A</math> and <math>B</math> <math>(A\cup B..."
02:35, 4 November 2022 diff hist +2,158‎ N Store:FLes04 ‎ Created page with "===Set operators=== Given the whole universe <math>U</math> we indicate with <math>x</math> its generic element so that <math>x \in U</math>; then, we consider two subsets <math>A</math> and <math>B</math> internal to <math>U</math> so that <math>A \subset U</math> and <math>B \subset U</math> {| |left|80px |'''Union:''' represented by the symbol <math>\cup</math>, indicates the union of the two sets <math>A</math> and <math>B</math> <math>(A\cup B..."