cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.17611/dp/21142186
title: Global ShakeMovie synthetic for April 28, 2023 MW 5.5 IRIAN JAYA REGION, INDONESIA
DOI: 10.17611/dp/21147050
title: Global ShakeMovie synthetic for April 22, 2023 MW 5.5 BANDA SEA
DOI: 10.17611/dp/21149490
title: Global ShakeMovie synthetic for May 01, 2023 MW 5.8 RYUKYU ISLANDS, JAPAN
DOI: 10.15468/dl.6vg2pn
title: Occurrence Download

description: A dataset containing 0 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Dioscorea alata",
 "Country is Dominica",
 "HasCoordinate is true"
 ]
}

 The dataset includes 0 records from 0 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0027473-250811113504898/datasets/export for details.
DOI: 10.17611/dp/21149494
title: Global ShakeMovie synthetic for May 01, 2023 MW 5.6 SOUTH OF FIJI ISLANDS
DOI: 10.17611/dp/21154792
title: Global ShakeMovie synthetic for May 02, 2023 MW 5.5 SAMOA ISLANDS REGION
DOI: 10.17611/dp/21154796
title: Global ShakeMovie synthetic for May 02, 2023 MW 5.5 NEW GUINEA, PAPUA NEW GUINEA
DOI: 10.17611/dp/21157272
title: Global ShakeMovie synthetic for May 03, 2023 MW 5.5 SOUTHERN EAST PACIFIC RISE
DOI: 10.17611/dp/21159700
title: Global ShakeMovie synthetic for May 05, 2023 MW 6.3 NEAR WEST COAST OF HONSHU, JAPAN
DOI: 10.17611/dp/21159704
title: Global ShakeMovie synthetic for May 05, 2023 MW 5.7 OFF E. COAST OF N. ISLAND, N.Z.
DOI: 10.17611/dp/21159708
title: Global ShakeMovie synthetic for May 05, 2023 MW 5.8 NEAR WEST COAST OF HONSHU, JAPAN
DOI: 10.17611/dp/21159712
title: Global ShakeMovie synthetic for May 05, 2023 MW 6.0 HOKKAIDO, JAPAN REGION
DOI: 10.17611/dp/21164440
title: Global ShakeMovie synthetic for May 08, 2023 MW 5.8 SOUTHERN EAST PACIFIC RISE
DOI: 10.17611/dp/21172073
title: Global ShakeMovie synthetic for May 11, 2023 MW 5.8 SOUTHWESTERN RYUKYU ISL., JAPAN
DOI: 10.17611/dp/21172077
title: Global ShakeMovie synthetic for May 11, 2023 MW 5.5 NORTHERN CALIFORNIA
DOI: 10.17611/dp/21179381
title: Global ShakeMovie synthetic for May 14, 2023 MW 5.5 SOUTHEAST OF HONSHU, JAPAN
DOI: 10.17611/dp/21179385
title: Global ShakeMovie synthetic for May 14, 2023 MW 5.8 SOUTHEAST OF HONSHU, JAPAN
DOI: 10.17611/dp/21179389
title: Global ShakeMovie synthetic for May 14, 2023 MW 5.7 SOUTHEAST OF HONSHU, JAPAN
DOI: 10.17611/dp/21185433
title: Global ShakeMovie synthetic for May 16, 2023 MW 5.3 JAN MAYEN ISLAND REGION
DOI: 10.17611/dp/21188675
title: Global ShakeMovie synthetic for May 17, 2023 MW 6.4 GUATEMALA
DOI: 10.17611/dp/21196117
title: Global ShakeMovie synthetic for May 19, 2023 MW 5.8 EASTERN GULF OF ADEN
DOI: 10.17611/dp/21200074
title: Global ShakeMovie synthetic for May 20, 2023 MW 7.2 SOUTHEAST OF LOYALTY ISLANDS
DOI: 10.17611/dp/21200078
title: Global ShakeMovie synthetic for May 20, 2023 MW 6.5 SOUTHEAST OF LOYALTY ISLANDS
DOI: 10.17611/dp/21203660
title: Global ShakeMovie synthetic for May 21, 2023 MW 5.8 TONGA ISLANDS
DOI: 10.17611/dp/21203664
title: Global ShakeMovie synthetic for May 21, 2023 MW 5.7 OFF COAST OF NORTHERN CALIFORNIA
DOI: 10.17611/dp/21203668
title: Global ShakeMovie synthetic for May 21, 2023 MW 5.4 WEST OF MACQUARIE ISLAND
DOI: 10.17611/dp/21203672
title: Global ShakeMovie synthetic for May 21, 2023 MW 5.6 RYUKYU ISLANDS, JAPAN
DOI: 10.17611/dp/21207195
title: Global ShakeMovie synthetic for May 21, 2023 MW 6.8 PRINCE EDWARD ISLANDS REGION
DOI: 10.17611/dp/21207199
title: Global ShakeMovie synthetic for May 21, 2023 MW 6.2 SOLOMON ISLANDS
DOI: 10.17611/dp/21207203
title: Global ShakeMovie synthetic for May 22, 2023 MW 5.3 SOUTHEAST OF LOYALTY ISLANDS
DOI: 10.17611/dp/21213072
title: Global ShakeMovie synthetic for May 24, 2023 MW 5.6 PACIFIC-ANTARCTIC RIDGE
DOI: 10.17611/dp/21213076
title: Global ShakeMovie synthetic for May 24, 2023 MW 6.2 BANDA SEA
DOI: 10.17611/dp/21215748
title: Global ShakeMovie synthetic for May 25, 2023 MW 6.5 PANAMA-COLOMBIA BORDER REGION
DOI: 10.17611/dp/21215752
title: Global ShakeMovie synthetic for May 25, 2023 MW 5.5 SOUTHEAST OF LOYALTY ISLANDS
DOI: 10.17611/dp/21218180
title: Global ShakeMovie synthetic for May 26, 2023 MW 6.2 NEAR EAST COAST OF HONSHU, JAPAN
DOI: 10.17611/dp/21236908
title: Global ShakeMovie synthetic for April 13, 2023 MW 5.3 GULF OF CALIFORNIA
DOI: 10.17611/dp/21236912
title: Global ShakeMovie synthetic for April 14, 2023 MW 7.1 JAVA, INDONESIA
DOI: 10.17182/hepdata.165445.v1/t58
title: "50.a. Scouting dimuon trig eff vs $\mathrm{p_{T}}$ for m = 2.5" of "Strategy and performance of the CMS long-lived particle trigger program in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV"

description: L1T+HLT efficiency of the dimuon scouting trigger as a function of the generator-level subleading muon $\mathrm{p_{T}}$, for HAHM signal events for 2024 conditions. The efficiency is shown for a $m_{Z_D}$ mass of 2.5 GeV, and $c\tau$ values of 1 (purple squares), 10 (blue triangles), and 100 mm (pink circles). The muons are required to have $|\eta|&lt;2.4$ at the generator level.
description: In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022--2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 ${\mathrm{fb}}^{-1}$.
DOI: 10.17182/hepdata.165445.v1/t59
title: "50.b. Scouting dimuon trig eff vs $\mathrm{p_{T}}$ for m = 14" of "Strategy and performance of the CMS long-lived particle trigger program in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV"

description: L1T+HLT efficiency of the dimuon scouting trigger as a function of the generator-level subleading muon $\mathrm{p_{T}}$, for HAHM signal events for 2024 conditions. The efficiency is shown for a $m_{Z_D}$ mass of 14 GeV, and $c\tau$ values of 1 (purple squares), 10 (blue triangles), and 100 mm (pink circles). The muons are required to have $|\eta|&lt;2.4$ at the generator level.
description: In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022--2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 ${\mathrm{fb}}^{-1}$.
DOI: 10.17182/hepdata.165445.v1/t60
title: "51.a. Scouting reconstruction eff vs Lxy for m = 2.5" of "Strategy and performance of the CMS long-lived particle trigger program in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV"

description: Scouting muon reconstruction efficiency of the vertex-constrained (pink circles) and vertex-unconstrained (blue triangles) algorithms as a function of the generator-level $L_{xy}$, for HAHM signal events for 2024 conditions. This efficiency is representative of the reconstruction efficiency of the L2 and L3 HLT muon reconstruction employed in scouting data. The efficiency is shown for $m_{Z_D} = 2.5$ GeV and $c\tau = 100$ mm. The muons are required to have $p_{T} &gt; 15$ GeV and $|\eta| &lt; 2.4$ at the generator level.
description: In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022--2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 ${\mathrm{fb}}^{-1}$.
DOI: 10.17182/hepdata.165445.v1/t61
title: "51.b. Scouting reconstruction eff vs Lxy for m = 14" of "Strategy and performance of the CMS long-lived particle trigger program in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV"

description: Scouting muon reconstruction efficiency of the vertex-constrained (pink circles) and vertex-unconstrained (blue triangles) algorithms as a function of the generator-level $L_{xy}$, for HAHM signal events for 2024 conditions. This efficiency is representative of the reconstruction efficiency of the L2 and L3 HLT muon reconstruction employed in scouting data. The efficiency is shown for $m_{Z_D} = 14$ GeV and $c\tau = 100$ mm. The muons are required to have $p_{T} &gt; 15$ GeV and $|\eta| &lt; 2.4$ at the generator level.
description: In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022--2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 ${\mathrm{fb}}^{-1}$.
DOI: 10.17182/hepdata.165445.v1/t62
title: "52. Scouting resolution vs pt" of "Strategy and performance of the CMS long-lived particle trigger program in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV"

description: The $p_{T}$ resolution of scouting muons with respect to offline muons, as a function of the scouting muon $p_{T}$, for 2024 data events. The root mean square (RMS) of the difference of the scouting muon $p_{T}$ and the offline muon $p_{T}$, divided by the offline muon $p_{T}$, is plotted. The dimuon $\Delta R$ is required to be greater than 0.2, and the scouting muon $p_{T}$ is required to be greater than 3 GeV. The resolution is shown for muons in the barrel (blue filled points) and the endcaps (purple filled triangles) that are reconstructed with both the vertex-unconstrained reconstruction algorithm, as well as for muons in the barrel (red filled squares) and the endcaps (orange unfilled squares) that are reconstructed with the vertex-constrained reconstruction algorithm. A special monitoring data set is used that collects events triggered by a mixture of HLT paths (both scouting and standard triggers) with a very high prescale, in which all information about the muon objects is stored from the offline and scouting reconstruction.
description: In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022--2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 ${\mathrm{fb}}^{-1}$.
DOI: 10.17182/hepdata.165445.v1/t63
title: "56.a. HLT efficiency of DT MDS vs ptmiss" of "Strategy and performance of the CMS long-lived particle trigger program in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV"

description: The HLT efficiency of the DT MDS triggers as a function of $p_T^{miss}$, for simulated $H \to S S \to b\bar{{b}}\,b\bar{{b}}$ events with $m_{H}=125$ GeV, $m_{S}=40$ GeV, and $c\tau_{S}=1$ m, for 2023 conditions. Events are required to have at least one cluster with more than 50 hits.
description: In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022--2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 ${\mathrm{fb}}^{-1}$.
DOI: 10.17182/hepdata.165445.v1/t64
title: "56.b. HLT efficiency of DT MDS vs cluser size" of "Strategy and performance of the CMS long-lived particle trigger program in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV"

description: The HLT efficiency of the DT MDS triggers as a function of cluster size, for simulated $H \to S S \to b\bar{{b}}\,b\bar{{b}}$ events with $m_{H}=125$ GeV, $m_{S}=40$ GeV, and $c\tau_{S}=1$ m, for 2023 conditions. Events are required to have $p_T^{miss}&gt;250$ GeV.
description: In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022--2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 ${\mathrm{fb}}^{-1}$.
DOI: 10.17182/hepdata.165445.v1/t65
title: "58. Muon NoBPTX HLT rate vs number of colliding bunches (2016)" of "Strategy and performance of the CMS long-lived particle trigger program in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV"

description: Rate of the main muon No-BPTX HLT path as a function of the number of colliding bunches, for 2016.
description: In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022--2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 ${\mathrm{fb}}^{-1}$.
DOI: 10.17182/hepdata.165445.v1/t66
title: "58. Muon NoBPTX HLT rate vs number of colliding bunches (2017)" of "Strategy and performance of the CMS long-lived particle trigger program in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV"

description: Rate of the main muon No-BPTX HLT path as a function of the number of colliding bunches, for 2017.
description: In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022--2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 ${\mathrm{fb}}^{-1}$.
DOI: 10.17182/hepdata.165445.v1/t67
title: "58. Muon NoBPTX HLT rate vs number of colliding bunches (2018)" of "Strategy and performance of the CMS long-lived particle trigger program in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV"

description: Rate of the main muon No-BPTX HLT path as a function of the number of colliding bunches, for 2018.
description: In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022--2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 ${\mathrm{fb}}^{-1}$.
DOI: 10.17182/hepdata.165445.v1/t68
title: "58. Muon NoBPTX HLT rate vs number of colliding bunches (2022)" of "Strategy and performance of the CMS long-lived particle trigger program in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV"

description: Rate of the main muon No-BPTX HLT path as a function of the number of colliding bunches, for 2022.
description: In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022--2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 ${\mathrm{fb}}^{-1}$.
DOI: 10.17182/hepdata.165445.v1/t69
title: "58. Muon NoBPTX HLT rate vs number of colliding bunches (2023)" of "Strategy and performance of the CMS long-lived particle trigger program in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV"

description: Rate of the main muon No-BPTX HLT path as a function of the number of colliding bunches, for 2023.
description: In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022--2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 ${\mathrm{fb}}^{-1}$.
DOI: 10.17182/hepdata.165445.v1/t70
title: "58. Muon NoBPTX HLT rate vs number of colliding bunches (2024)" of "Strategy and performance of the CMS long-lived particle trigger program in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV"

description: Rate of the main muon No-BPTX HLT path as a function of the number of colliding bunches, for 2024.
description: In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022--2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 ${\mathrm{fb}}^{-1}$.
DOI: 10.17182/hepdata.165445.v1/t71
title: "61.a. Tracker displaced-jet acceptance vs R (mH=1000, mX=200)" of "Strategy and performance of the CMS long-lived particle trigger program in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV"

description: The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=1000\,\mathrm{GeV}$ and $m_X=200\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.
description: In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022--2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 ${\mathrm{fb}}^{-1}$.
DOI: 10.17182/hepdata.165445.v1/t72
title: "61.a. ECAL delayed-jet acceptance vs R (mH=1000, mX=200)" of "Strategy and performance of the CMS long-lived particle trigger program in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV"

description: The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=1000\,\mathrm{GeV}$ and $m_X=200\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.
description: In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022--2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 ${\mathrm{fb}}^{-1}$.
DOI: 10.17182/hepdata.165445.v1/t73
title: "61.a. HCAL displaced-jet acceptance vs R (mH=1000, mX=200)" of "Strategy and performance of the CMS long-lived particle trigger program in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV"

description: The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=1000\,\mathrm{GeV}$ and $m_X=200\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.
description: In the physics program of the CMS experiment during the CERN LHC Run 3, which started in 2022, the long-lived particle triggers have been improved and extended to expand the scope of the corresponding searches. These dedicated triggers and their performance are described in this paper, using several theoretical benchmark models that extend the standard model of particle physics. The results are based on proton-proton collision data collected with the CMS detector during 2022--2024 at a center-of-mass energy of 13.6 TeV, corresponding to integrated luminosities of up to 123 ${\mathrm{fb}}^{-1}$.