Search results for "discrete [space-time]"
showing 10 items of 2035 documents
Packing colorings of subcubic outerplanar graphs
2018
Given a graph $G$ and a nondecreasing sequence $S=(s_1,\ldots,s_k)$ of positive integers, the mapping $c:V(G)\longrightarrow \{1,\ldots,k\}$ is called an $S$-packing coloring of $G$ if for any two distinct vertices $x$ and $y$ in $c^{-1}(i)$, the distance between $x$ and $y$ is greater than $s_i$. The smallest integer $k$ such that there exists a $(1,2,\ldots,k)$-packing coloring of a graph $G$ is called the packing chromatic number of $G$, denoted $\chi_{\rho}(G)$. The question of boundedness of the packing chromatic number in the class of subcubic (planar) graphs was investigated in several earlier papers; recently it was established that the invariant is unbounded in the class of all sub…
Miscellaneous Graph Preliminaries
2020
Summary This article contains many auxiliary theorems which were missing in the Mizar Mathematical Library [2] to the best of the author’s knowledge. Most of them regard graph theory as formalized in the GLIB series (cf. [8]) and most of them are preliminaries needed in [7] or other forthcoming articles.
"Table 30" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Barrel MS vertex efficiencies (in %) for baryogenesis $\chi \rightarrow \nu b \bar{b}$ benchmark samples ($m_{h}=125$ GeV). The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
"Table 41" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Endcap MS vertex efficiencies (in %) for baryogenesis $\chi \rightarrow \nu b \bar{b}$ benchmark samples ($m_{h}=125$ GeV). The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
"Table 31" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Barrel MS vertex efficiencies (in %) for baryogenesis $\chi \rightarrow cbs$ benchmark samples ($m_{h}=125$ GeV). The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
"Table 33" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Barrel MS vertex efficiencies (in %) for baryogenesis $\chi \rightarrow \tau\tau\nu$ benchmark samples ($m_{h}=125$ GeV). The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
"Table 42" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Endcap MS vertex efficiencies (in %) for baryogenesis $\chi \rightarrow cbs$ benchmark samples ($m_{h}=125$ GeV). The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
"Table 32" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Barrel MS vertex efficiencies (in %) for baryogenesis $\chi \rightarrow lcb$ benchmark samples ($m_{h}=125$ GeV). The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
"Table 43" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Endcap MS vertex efficiencies (in %) for baryogenesis $\chi \rightarrow lcb$ benchmark samples ($m_{h}=125$ GeV). The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.
"Table 24" of "Search for long-lived particles produced in $pp$ collisions at $\sqrt{s}=13$ TeV that decay into displaced hadronic jets in the ATLAS …
2018
Barrel MS vertex efficiencies (in %) for $m_{\Phi}=125$ GeV scalar benchmark samples. The vertex reconstruction efficiency is defined as the fraction of simulated LLP decays in the MS fiducial volume that match a reconstructed vertex ($\Delta R(\textrm{LLP,vertex}) = 0.4$) passing the baseline event selection and satisfying the vertex isolation criteria. A vertex is considered matched to a displaced decay if the vertex is within $\Delta R = 0.4$ of the simulated decay position. The MS vertex efficiency is parameterized as a function of the LLP decay position.