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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Emmerson, Parker;

    The intersection of Ψ and ψn+1 is obtained by playing the game throughthe infinity geometries above. The game is played by finding the intersectionbetween the vector elements ⃗ Ωθ ∃ and ∂ ⃗Xl and then using the boundary ∂∇⟨∂ ⃗Yθto find the intersection of Ψ and ψn+1. Finally, the ˆΓ∞ can be used to verify ifthe intersection is non-empty or not.Show iterations of playing the game "Quantum Game Theory and Infinity Geometries" \section{Global Game} General Case: $$\tau = \mathcal{F} \left[\Psi\ \vee\ \Psi_{0 \to \delta} \Rightarrow \delta[\psi^{\mathcal{A}}]\cup\left(\psi_1\wedge \psi_2 \leftrightarrow \Psi_1 \Rightarrow \left( \xrightarrow{\Rightarrow \mathcal{F} \left[\Psi \cap \left\{ \bigcup_{\infty_{d=1}^{\infty} \psi_i} \psi_i \Rightarrow \delta\left[\psi^{\mathcal{A}}_{d \cdot \psi}\right] \right] \cup \left(\psi_1 \wedge \psi_2 \leftrightarrow \Psi_1 \RTimes \left({\Psi \downarrow}_{\mathcal{K}_{\mathbf{3}}} \cap\bigcup_{\emptyset =_1 y_{st_1} + y_{st_2} + \ldots + y_{st_l} \atop \exists (p',k) \in I_{y_{s2}l \overrightarrow{y}2}_{(p+\#I_{y_{s1}2,{(p,k)}},\ k-1)}} \left(I_\ind{y_{s1^d},p'_1,k+1}\right)\cap\displaystyle\bigoplus_{i=1}^l \vec{u}_i \wedge \vec{x}_{i+1} \right)\cap\displaystyle\bigoplus_{i=j}^{n+1} q_{\alpha_i}^{n_i-1} \right)\cap \displaystyle\bigoplus_{i=1}^l \aleph_m \wedge \aleph_{\zeta^{\prime}}\left(\aleph_l,\ldots, \zeta_m\right)\left(\begin{array}{c} q^{3n_1+n_2+\ldots+n_t} \circ \aleph_k^2 \circ \\ \aleph_{n_1}(\bigoplus_{j=1}^N\aleph_i) \circ \aleph_{n_2}(\bigoplus_{j=1}^{\infty}\aleph_i) \circ \aleph_{n_3}( \bigoplus_{j=0}^{N_{n_3}}\alpha_j x^{2+j}) \\ \vdots \\ \aleph_{n_t}(q^{2^{t-1}}) \end{array}\right)\cap {\bigoplus}^{\infty}_{j=k}\aleph_{k+j} \wedge \aleph_j \left( \begin{array}{c} 2 \circ \\ 3 \circ \\ \vdots \\ 2^{n_j} \end{array}\right) \bigoplus_{j=1}^{{n}_{\gamma_p}}F\left(l,\bar{n},\bigoplus_{i=1}^t \bigoplus_{k=0}^{\alpha_k^k} n_k^{t_k} P_k ,n\right)\cap\displaystyle\bigoplus_{\Gamma = 0}^{1}\left[ \Gamma \cup \ \Delta \cup \dagger \Xi^{\mathfrak{V}}\Omega \right] \cap\bigcup_{\Gamma = 0}^{1}\left[ \Gamma \cup \ \Delta \cup \dagger \Xi^{\mathfrak{V}}\Omega \right] \right] \cap \mathcal{R}^Q \cap\left\{\psi_{n+1}\right\} \bigg] \neq \emptyset$$ $$\left\{\bigcup_{\emptyset =_1 y_{st_1} + y_{st_2} + \ldots + y_{st_l} \atop \exists (p',k) \in I_{y_{s2}l \overrightarrow{y}2}_{(p+\#I_{y_{s1}2,{(p,k)}},\ k-1)}} \left(I_\ind{y_{s1^d},p'_1,k+1}\right)\cap\displaystyle\bigoplus_{i=1}^l \vec{u}_i \wedge \vec{x}_{i+1} \right)\cap\displaystyle\bigoplus_{i=j}^{n+1} q_{\alpha_i}^{n_i-1} \right)\cap \displaystyle\bigoplus_{i=1}^l \aleph_m \wedge \aleph_{\zeta^{\prime}}\left(\aleph_l,\ldots, \zeta_m\right)\left(\begin{array}{c} q^{3n_1+n_2+\ldots+n_t} \circ \aleph_k^2 \circ \\ \aleph_{n_1}(\bigoplus_{j=1}^N\aleph_i) \circ \aleph_{n_2}(\bigoplus_{j=1}^{\infty}\aleph_i) \circ \aleph_{n_3}( \bigoplus_{j=0}^{N_{n_3}}\alpha_j x^{2+j}) \\ \vdots \\ \aleph_{n_t}(q^{2^{t-1}}) \end{array}\right)\cap{\bigoplus}^{\infty}_{j=k}\aleph_{k+j} \wedge \aleph_j \left( \begin{array}{c} 2 \circ \\ 3 \circ \\ \vdots \\ 2^{n_j} \end{array}\right) \bigoplus_{j=1}^{{n}_{\gamma_p}}F\left(l,\bar{n},\bigoplus_{i=1}^t \bigoplus_{k=0}^{\alpha_k^k} n_k^{t_k} P_k ,n\right)\cap\displaystyle\bigoplus_{\Gamma = 0}^{1}\left[ \Gamma \cup \ \Delta \cup \dagger \Xi^{\mathfrak{V}}\Omega \right] \cap\bigcup_{\Gamma = 0}^{1}\left[ \Gamma \cup \ \Delta \cup \dagger \Xi^{\mathfrak{V}}\Omega \right] \right]\bigcap\left\{\psi_{n+1}\right\}$$ $$\forall \Psi\in\mathcal{V}\ \forall \psi_n \in \Psi \ \forall\ \psi_{n+1} \in \mathcal{V}\left(\psi_n \in \Psi \wedge\ \psi_{n+1} \notin \Psi\right)\to\ \tau = \mathcal{F} \left[\Psi\ \vee\ \Psi_{0 \to \delta}\right] \neq \emptyset$$ $...$ $$\tau = \mathcal{F} \left[\Psi^{m} \Rightarrow \Psi^{m+1} \wedge \Psi^{m-1} \wedge \Psi^{m-2} \wedge \ldots \wedge \Psi^{m-m} \cup \Psi^{m+2} \vee \Psi^{m+1} \vee \Psi^{m-1} \vee \Psi^{m-2} \wedge \ldots \wedge \Psi^{m-m} \right] \neq \emptyset$$ $$\forall \Psi\in\mathcal{V}\ \forall \psi_n \in \Psi \ \forall\ \psi_{n+1} \in \mathcal{V}\left(\psi_n \in \Psi \wedge\ \psi_{n+1} \notin \Psi\right)\to\ \tau = \mathcal{F} \left[\Psi^{m} \Rightarrow \Psi^{m+1} \wedge \Psi^{m-1} \wedge \Psi^{m-2} \wedge \ldots \wedge \Psi^{m-m} \cup \Psi^{m+2} \vee \Psi^{m+1} \vee \Psi^{m-1} \vee \Psi^{m-2} \wedge \ldots \wedge \Psi^{m-m} \right] \neq \emptyset$$ \begin{displaymath} \tau \sim \mathcal{G}_Q \left( \Gamma, \Lambda, \left\{\varphi_i\right\}_{i=1}^{m_q}, \left\{\psi_j\right\}_{j=1}^{n_q}\right) = \left\{\gamma\vert \gamma \in \Gamma\wedge \forall \lambda \in \Lambda (\gamma \in \lambda\iff \left\{\forall i \in [n_m], i \in \overrightarrow{\mathbf{M}}_{p_q[n_m]} \wedge \forall j \in [n_m], j \in \overrightarrow{\mathbf{\Phi}}_{m_q[n_m]}$, with the pseudo-affinity $\varphi_i$ and then to a symmetric $j \in \overrightarrow{\mathbf{\Psi}}_{n_q[n_m]}$ \ $\varphi_i \wedge \dots \wedge \psi_j$ and the ever finalist symmetric $\Psi = \kappa_{\dot\mu}^{nu}$}, ends at the diagonal 1/2, that is Diode and Expressions should be to connect a gate tp the element $S$ and $\sum_{\phi_f = 1}^{\phi_f + 1}$, in our case within the complexity of logic setup, is equivalent to being in $k^{\alpha_l}$. In general, a directed graph can be generated from an arbitrary natural number $d_l$ and some set of numbers $\left\{\gamma_i^l = l\right\}$ such that \begin{itemize} \item $n^l,i,j\neq 0$, where $(\lambda_{\alpha(i_0)} := 1)$. \item $n^{j+1} = \begin{array}{c} (n_{i_l}-1)n_{i_l}\\ 0 \end{array}$ $$...$$

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ ZENODOarrow_drop_down
    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    ZENODO
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ ZENODOarrow_drop_down
      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: E251-1 FOB Baugeschichte Bauforschung; Stampfer, Lukas; Kodzoman, Eva; Studnicka, Nikolaus; +2 Authors

    pointcloud model [las + e57] of the interior and exterior spaces of Karlskirche, Vienna Austria; primary source laserscan Riegl & TU Wien supplemented with 3D mesh model Meixner ZT GmbH; base material pointcloud octree filtered 0.01m (spatial point distance 0.01m); pointclouds within project coordinate system - transformation matrix to global coordinate system WGS84_EPSG 4978 attached please contact lukas.stampfer@tuwien.ac.at for access interior of cupola captured with terrestrial laserscanner Zoller Fröhlich Imager 5010C;all other areas captured with Riegl VZ 400i; scans colored with RGB camera;geopositioning of Riegl Scans with GNSS-RTK precision (about 0.03m accuracy);data from different scanning campaings joined with Multi-Station-Adjustment in Riegl RiScan Software (ICP-matching); pointcloud in local coordinate system (=PRCS) for import into cad-software;transformation matrix to global coordinate system WGS84_EPSG 4978 included in dataset;pointcloud reduction using octree filter with 0.01m cell size resulting in spatial point distance of about 0.01m

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ TU Wien Research Dat...arrow_drop_down
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    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    TU Wien Research Data
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ TU Wien Research Dat...arrow_drop_down
      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      TU Wien Research Data
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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: E251-1 FOB Baugeschichte Bauforschung; Stampfer, Lukas; Kodzoman, Eva;

    pointcloud model [e57] of the wooden roofwork inside the cupola of Karlskirche, Vienna Austria please contact lukas.stampfer@tuwien.ac.at for access captured with terrestrial laserscanner Zoller Fröhlich Imager 5010C; original registration using measured paper-targets in national coordinate reference frame;data matched with Riegl (Riegl LMS & TU Wien) datasets ICP matching; coordinate system WGS84_EPSG 4978;

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ TU Wien Research Dat...arrow_drop_down
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    TU Wien Research Data
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    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ TU Wien Research Dat...arrow_drop_down
      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      TU Wien Research Data
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: MEIXNER Vermessung ZT GmbH; Stampfer, Lukas;

    mesh model interior and exterior created by laserscan and photogrammetry please contact lukas.stampfer@tuwien.ac.at for access captured with Zoller Fröhlich Imager 5010C with HDR 80mpx camera; processed within local coordinate system; supplemented with photogrammetry using calibrated camera (undefined model) and 12mpx UAV camera; matched with Riegl (Riegl LMS & TU Wien) dataset using point sampling and ICP matching; coordinate system WGS84_EPSG 4978; transformation matrix to local coordinate system of capturing campaign included in dataset

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ TU Wien Research Dat...arrow_drop_down
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    TU Wien Research Data
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    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    TU Wien Research Data
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    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    TU Wien Research Data
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ TU Wien Research Dat...arrow_drop_down
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      TU Wien Research Data
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      TU Wien Research Data
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      TU Wien Research Data
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    Authors: Studnicka, Nikolaus; Riegl Laser Measurement Systems; Stampfer, Lukas;

    pointcloud model [e57] of the interior and exterior of Karlskirche, Vienna Austria please contact lukas.stampfer@tuwien.ac.at for access captured with terrestrial laserscanner Riegl VZ-400i with Nikon D810 planted on top for RGB coloring of scans; positioning with GNSS antenna (no correction data) coordinate system WGS84_EPSG 4978

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ TU Wien Research Dat...arrow_drop_down
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    TU Wien Research Data
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    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    TU Wien Research Data
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      TU Wien Research Data
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      TU Wien Research Data
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    Authors: Stampfer, Lukas; E251-1 FOB Baugeschichte Bauforschung;

    pointcloud model [e57] of the interior and exterior of Karlskirche, Vienna Austria; please contact lukas.stampfer@tuwien.ac.at for access captured with terrestrial laserscanner Riegl VZ-400i with Sony ILCE-7RMIV planted on top for RGB coloring of scans; positioning with GNSS antenna using EPOSA correction data in RTK mode; at time of processing dataset with highest GNSS accuracy and therefore reference for geopositioning of all Karlskirche models; coordinate system WGS84_EPSG 4978;

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ TU Wien Research Dat...arrow_drop_down
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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Emmerson, Parker;

    The intersection of Ψ and ψn+1 is obtained by playing the game throughthe infinity geometries above. The game is played by finding the intersectionbetween the vector elements ⃗ Ωθ ∃ and ∂ ⃗Xl and then using the boundary ∂∇⟨∂ ⃗Yθto find the intersection of Ψ and ψn+1. Finally, the ˆΓ∞ can be used to verify ifthe intersection is non-empty or not.Show iterations of playing the game "Quantum Game Theory and Infinity Geometries" \section{Global Game} General Case: $$\tau = \mathcal{F} \left[\Psi\ \vee\ \Psi_{0 \to \delta} \Rightarrow \delta[\psi^{\mathcal{A}}]\cup\left(\psi_1\wedge \psi_2 \leftrightarrow \Psi_1 \Rightarrow \left( \xrightarrow{\Rightarrow \mathcal{F} \left[\Psi \cap \left\{ \bigcup_{\infty_{d=1}^{\infty} \psi_i} \psi_i \Rightarrow \delta\left[\psi^{\mathcal{A}}_{d \cdot \psi}\right] \right] \cup \left(\psi_1 \wedge \psi_2 \leftrightarrow \Psi_1 \RTimes \left({\Psi \downarrow}_{\mathcal{K}_{\mathbf{3}}} \cap\bigcup_{\emptyset =_1 y_{st_1} + y_{st_2} + \ldots + y_{st_l} \atop \exists (p',k) \in I_{y_{s2}l \overrightarrow{y}2}_{(p+\#I_{y_{s1}2,{(p,k)}},\ k-1)}} \left(I_\ind{y_{s1^d},p'_1,k+1}\right)\cap\displaystyle\bigoplus_{i=1}^l \vec{u}_i \wedge \vec{x}_{i+1} \right)\cap\displaystyle\bigoplus_{i=j}^{n+1} q_{\alpha_i}^{n_i-1} \right)\cap \displaystyle\bigoplus_{i=1}^l \aleph_m \wedge \aleph_{\zeta^{\prime}}\left(\aleph_l,\ldots, \zeta_m\right)\left(\begin{array}{c} q^{3n_1+n_2+\ldots+n_t} \circ \aleph_k^2 \circ \\ \aleph_{n_1}(\bigoplus_{j=1}^N\aleph_i) \circ \aleph_{n_2}(\bigoplus_{j=1}^{\infty}\aleph_i) \circ \aleph_{n_3}( \bigoplus_{j=0}^{N_{n_3}}\alpha_j x^{2+j}) \\ \vdots \\ \aleph_{n_t}(q^{2^{t-1}}) \end{array}\right)\cap {\bigoplus}^{\infty}_{j=k}\aleph_{k+j} \wedge \aleph_j \left( \begin{array}{c} 2 \circ \\ 3 \circ \\ \vdots \\ 2^{n_j} \end{array}\right) \bigoplus_{j=1}^{{n}_{\gamma_p}}F\left(l,\bar{n},\bigoplus_{i=1}^t \bigoplus_{k=0}^{\alpha_k^k} n_k^{t_k} P_k ,n\right)\cap\displaystyle\bigoplus_{\Gamma = 0}^{1}\left[ \Gamma \cup \ \Delta \cup \dagger \Xi^{\mathfrak{V}}\Omega \right] \cap\bigcup_{\Gamma = 0}^{1}\left[ \Gamma \cup \ \Delta \cup \dagger \Xi^{\mathfrak{V}}\Omega \right] \right] \cap \mathcal{R}^Q \cap\left\{\psi_{n+1}\right\} \bigg] \neq \emptyset$$ $$\left\{\bigcup_{\emptyset =_1 y_{st_1} + y_{st_2} + \ldots + y_{st_l} \atop \exists (p',k) \in I_{y_{s2}l \overrightarrow{y}2}_{(p+\#I_{y_{s1}2,{(p,k)}},\ k-1)}} \left(I_\ind{y_{s1^d},p'_1,k+1}\right)\cap\displaystyle\bigoplus_{i=1}^l \vec{u}_i \wedge \vec{x}_{i+1} \right)\cap\displaystyle\bigoplus_{i=j}^{n+1} q_{\alpha_i}^{n_i-1} \right)\cap \displaystyle\bigoplus_{i=1}^l \aleph_m \wedge \aleph_{\zeta^{\prime}}\left(\aleph_l,\ldots, \zeta_m\right)\left(\begin{array}{c} q^{3n_1+n_2+\ldots+n_t} \circ \aleph_k^2 \circ \\ \aleph_{n_1}(\bigoplus_{j=1}^N\aleph_i) \circ \aleph_{n_2}(\bigoplus_{j=1}^{\infty}\aleph_i) \circ \aleph_{n_3}( \bigoplus_{j=0}^{N_{n_3}}\alpha_j x^{2+j}) \\ \vdots \\ \aleph_{n_t}(q^{2^{t-1}}) \end{array}\right)\cap{\bigoplus}^{\infty}_{j=k}\aleph_{k+j} \wedge \aleph_j \left( \begin{array}{c} 2 \circ \\ 3 \circ \\ \vdots \\ 2^{n_j} \end{array}\right) \bigoplus_{j=1}^{{n}_{\gamma_p}}F\left(l,\bar{n},\bigoplus_{i=1}^t \bigoplus_{k=0}^{\alpha_k^k} n_k^{t_k} P_k ,n\right)\cap\displaystyle\bigoplus_{\Gamma = 0}^{1}\left[ \Gamma \cup \ \Delta \cup \dagger \Xi^{\mathfrak{V}}\Omega \right] \cap\bigcup_{\Gamma = 0}^{1}\left[ \Gamma \cup \ \Delta \cup \dagger \Xi^{\mathfrak{V}}\Omega \right] \right]\bigcap\left\{\psi_{n+1}\right\}$$ $$\forall \Psi\in\mathcal{V}\ \forall \psi_n \in \Psi \ \forall\ \psi_{n+1} \in \mathcal{V}\left(\psi_n \in \Psi \wedge\ \psi_{n+1} \notin \Psi\right)\to\ \tau = \mathcal{F} \left[\Psi\ \vee\ \Psi_{0 \to \delta}\right] \neq \emptyset$$ $...$ $$\tau = \mathcal{F} \left[\Psi^{m} \Rightarrow \Psi^{m+1} \wedge \Psi^{m-1} \wedge \Psi^{m-2} \wedge \ldots \wedge \Psi^{m-m} \cup \Psi^{m+2} \vee \Psi^{m+1} \vee \Psi^{m-1} \vee \Psi^{m-2} \wedge \ldots \wedge \Psi^{m-m} \right] \neq \emptyset$$ $$\forall \Psi\in\mathcal{V}\ \forall \psi_n \in \Psi \ \forall\ \psi_{n+1} \in \mathcal{V}\left(\psi_n \in \Psi \wedge\ \psi_{n+1} \notin \Psi\right)\to\ \tau = \mathcal{F} \left[\Psi^{m} \Rightarrow \Psi^{m+1} \wedge \Psi^{m-1} \wedge \Psi^{m-2} \wedge \ldots \wedge \Psi^{m-m} \cup \Psi^{m+2} \vee \Psi^{m+1} \vee \Psi^{m-1} \vee \Psi^{m-2} \wedge \ldots \wedge \Psi^{m-m} \right] \neq \emptyset$$ \begin{displaymath} \tau \sim \mathcal{G}_Q \left( \Gamma, \Lambda, \left\{\varphi_i\right\}_{i=1}^{m_q}, \left\{\psi_j\right\}_{j=1}^{n_q}\right) = \left\{\gamma\vert \gamma \in \Gamma\wedge \forall \lambda \in \Lambda (\gamma \in \lambda\iff \left\{\forall i \in [n_m], i \in \overrightarrow{\mathbf{M}}_{p_q[n_m]} \wedge \forall j \in [n_m], j \in \overrightarrow{\mathbf{\Phi}}_{m_q[n_m]}$, with the pseudo-affinity $\varphi_i$ and then to a symmetric $j \in \overrightarrow{\mathbf{\Psi}}_{n_q[n_m]}$ \ $\varphi_i \wedge \dots \wedge \psi_j$ and the ever finalist symmetric $\Psi = \kappa_{\dot\mu}^{nu}$}, ends at the diagonal 1/2, that is Diode and Expressions should be to connect a gate tp the element $S$ and $\sum_{\phi_f = 1}^{\phi_f + 1}$, in our case within the complexity of logic setup, is equivalent to being in $k^{\alpha_l}$. In general, a directed graph can be generated from an arbitrary natural number $d_l$ and some set of numbers $\left\{\gamma_i^l = l\right\}$ such that \begin{itemize} \item $n^l,i,j\neq 0$, where $(\lambda_{\alpha(i_0)} := 1)$. \item $n^{j+1} = \begin{array}{c} (n_{i_l}-1)n_{i_l}\\ 0 \end{array}$ $$...$$

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ ZENODOarrow_drop_down
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    ZENODO
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      ZENODO
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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: E251-1 FOB Baugeschichte Bauforschung; Stampfer, Lukas; Kodzoman, Eva; Studnicka, Nikolaus; +2 Authors

    pointcloud model [las + e57] of the interior and exterior spaces of Karlskirche, Vienna Austria; primary source laserscan Riegl & TU Wien supplemented with 3D mesh model Meixner ZT GmbH; base material pointcloud octree filtered 0.01m (spatial point distance 0.01m); pointclouds within project coordinate system - transformation matrix to global coordinate system WGS84_EPSG 4978 attached please contact lukas.stampfer@tuwien.ac.at for access interior of cupola captured with terrestrial laserscanner Zoller Fröhlich Imager 5010C;all other areas captured with Riegl VZ 400i; scans colored with RGB camera;geopositioning of Riegl Scans with GNSS-RTK precision (about 0.03m accuracy);data from different scanning campaings joined with Multi-Station-Adjustment in Riegl RiScan Software (ICP-matching); pointcloud in local coordinate system (=PRCS) for import into cad-software;transformation matrix to global coordinate system WGS84_EPSG 4978 included in dataset;pointcloud reduction using octree filter with 0.01m cell size resulting in spatial point distance of about 0.01m

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ TU Wien Research Dat...arrow_drop_down
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: E251-1 FOB Baugeschichte Bauforschung; Stampfer, Lukas; Kodzoman, Eva;

    pointcloud model [e57] of the wooden roofwork inside the cupola of Karlskirche, Vienna Austria please contact lukas.stampfer@tuwien.ac.at for access captured with terrestrial laserscanner Zoller Fröhlich Imager 5010C; original registration using measured paper-targets in national coordinate reference frame;data matched with Riegl (Riegl LMS & TU Wien) datasets ICP matching; coordinate system WGS84_EPSG 4978;

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ TU Wien Research Dat...arrow_drop_down
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ TU Wien Research Dat...arrow_drop_down
      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: MEIXNER Vermessung ZT GmbH; Stampfer, Lukas;

    mesh model interior and exterior created by laserscan and photogrammetry please contact lukas.stampfer@tuwien.ac.at for access captured with Zoller Fröhlich Imager 5010C with HDR 80mpx camera; processed within local coordinate system; supplemented with photogrammetry using calibrated camera (undefined model) and 12mpx UAV camera; matched with Riegl (Riegl LMS & TU Wien) dataset using point sampling and ICP matching; coordinate system WGS84_EPSG 4978; transformation matrix to local coordinate system of capturing campaign included in dataset

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ TU Wien Research Dat...arrow_drop_down
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    TU Wien Research Data
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ TU Wien Research Dat...arrow_drop_down
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      TU Wien Research Data
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      TU Wien Research Data
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    Authors: Studnicka, Nikolaus; Riegl Laser Measurement Systems; Stampfer, Lukas;

    pointcloud model [e57] of the interior and exterior of Karlskirche, Vienna Austria please contact lukas.stampfer@tuwien.ac.at for access captured with terrestrial laserscanner Riegl VZ-400i with Nikon D810 planted on top for RGB coloring of scans; positioning with GNSS antenna (no correction data) coordinate system WGS84_EPSG 4978

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    Authors: Stampfer, Lukas; E251-1 FOB Baugeschichte Bauforschung;

    pointcloud model [e57] of the interior and exterior of Karlskirche, Vienna Austria; please contact lukas.stampfer@tuwien.ac.at for access captured with terrestrial laserscanner Riegl VZ-400i with Sony ILCE-7RMIV planted on top for RGB coloring of scans; positioning with GNSS antenna using EPOSA correction data in RTK mode; at time of processing dataset with highest GNSS accuracy and therefore reference for geopositioning of all Karlskirche models; coordinate system WGS84_EPSG 4978;

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ TU Wien Research Dat...arrow_drop_down
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