adsabs/AstroCLIMB huggingface dataset:
Paper: Cloud Crushing and Dissipation of Uniformly Driven Adiabatic Turbulence in Circumgalactic Media
Authors: Alex Lv, Lile Wang, Renyue Cen, Luis C. Ho
Figure caption: The density (top) and ﹩{ \mathcal M }﹩ (bottom) power spectra of the four high resolution 2563 runs shown in Figure 6, where Z/Z ⊙ = 0.3 and n = 0.1 cm−3, and ﹩{\dot{\epsilon }}_{i}﹩ being 0.1, 1, 3.0, and 10.0 erg s−1 g−1 from left to right. The bottom row plots the turbulence power spectra during steady-state turbulence, after t  s , 10t s, and 100t s. The cyan colored region represents 1σ across the last 20 outputs of the steady-state turbulence epoch. The top row plots the power spectra from turbulence turnoff up to 100t s, with the color denoting ϵ  k . The value of t  s  is also shown across each of the four runs. Both the top and bottom row plots are smoothed using 5° polynomial splines for visualization purposes.
Paper: Cloud Crushing and Dissipation of Uniformly Driven Adiabatic Turbulence in Circumgalactic Media
Authors: Alex Lv, Lile Wang, Renyue Cen, Luis C. Ho
Figure caption: The full set of dissipation curves for the Z/Z ⊙ = 0.3, n = 0.1 cm−3, and ﹩{\dot{\epsilon }}_{i}=10\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{{\rm{g}}}^{-1}﹩. Across four distinct snapshots t = 0, t  s , 10t  s , 100t  s , the top row plots density slices normalized by n while the middle row plots velocity magnitude. The bottom plot shows five dimensionless dissipation curves over time normalized by t  s : thermal energy (﹩{\epsilon }_{g}/{c}_{s,0}^{2}﹩), kinetic energy (﹩{\epsilon }_{k}/{c}_{s,0}^{2}﹩), clumping factor (C = 〈ρ 2〉/〈ρ〉2 − 1), matter power spectrum linear regime power index (α  δ ), and Mach power spectrum linear regime power index (﹩{\alpha }_{{ \mathcal M }}﹩). The former three quantities are shown on the left y-axis, while the latter two are shown on the right y-axis. The red, green, and cyan dotted lines on the bottom plot corresponding to the boxes of the same color around the slice plots show the times slice plots represent.
Paper: Cloud Crushing and Dissipation of Uniformly Driven Adiabatic Turbulence in Circumgalactic Media
Authors: Alex Lv, Lile Wang, Renyue Cen, Luis C. Ho
Figure caption: Phase plots tracking the temporal evolution of specific thermal (top), specific kinetic energy (bottom) relative to clumping factor. Four 1283 resolution runs are shown, corresponding to Z/Z ⊙ = 0.3, ﹩{\dot{\epsilon }}_{i}=1\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{{\rm{g}}}^{-1}﹩, and n ranging from 0.01 cm−3 to n = 10 cm−3. Similar to Figure 6, stars denote the turbulence driving turnoff time where each curve begins, circular dots denote t  s , 10t s, and 100t s as one moves from the star and along the curve, and squares denote the 100 Myr mark. The black dotted line in the top plot marks the T = 1000 K point.
Paper: Cloud Crushing and Dissipation of Uniformly Driven Adiabatic Turbulence in Circumgalactic Media
Authors: Alex Lv, Lile Wang, Renyue Cen, Luis C. Ho
Figure caption: Comparisons between the power spectra of 1283 (blue), 2563 (orange), and 5123 (green) resolution runs. From top to bottom, we show the turbulence (P  k ), matter (P  δ ), and Mach (﹩{P}_{{ \mathcal M }}﹩) power spectra. All power spectra are normalized via a spatial integral over k  r . P  k  is additionally multiplied by the k 5/3 such that the Kolmogorov power law (dotted lines) is a horizontal line. The initial parameters are Z/Z ⊙ = 0.3, n = 0.1 cm−3, and ﹩{\dot{\epsilon }}_{i}=10\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{{\rm{g}}}^{-1}﹩.
Paper: Cloud Crushing and Dissipation of Uniformly Driven Adiabatic Turbulence in Circumgalactic Media
Authors: Alex Lv, Lile Wang, Renyue Cen, Luis C. Ho
Figure caption: Left: thermal and kinetic dissipation curves' comparisons between the fiducial high resolution 2563 runs (solid line) and lower resolution 1283 counterparts (dashed line). Right: The same dissipation curves for only ﹩{\dot{\epsilon }}_{i}=10\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{{\rm{g}}}^{-1}﹩, with one 5123 resolution run included in black. Z/Z ⊙ = 0.3 and n = 0.1 cm−3 for all runs shown.
Paper: Cloud Crushing and Dissipation of Uniformly Driven Adiabatic Turbulence in Circumgalactic Media
Authors: Alex Lv, Lile Wang, Renyue Cen, Luis C. Ho
Figure caption: The power-law indices of ﹩{P}_{{ \mathcal M }}﹩ (top) and P  δ  (bottom) over time across supersonic 1283 runs. The linear range power laws are separated in ﹩{\dot{\epsilon }}_{i}﹩, and the dissipation range power laws are coagulated and shown in black. The shaded regions represent 1σ.
Paper: Cloud Crushing and Dissipation of Uniformly Driven Adiabatic Turbulence in Circumgalactic Media
Authors: Alex Lv, Lile Wang, Renyue Cen, Luis C. Ho
Figure caption: Density (left) and temperature (right) slice plot comparisons between 5123 (top), 2563 (middle), and 1283 (bottom) resolution. The initial parameters are Z/Z ⊙ = 0.3, n = 0.1 cm−3, and ﹩{\dot{\epsilon }}_{i}=10\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{{\rm{g}}}^{-1}﹩.
Paper: Cloud Crushing and Dissipation of Uniformly Driven Adiabatic Turbulence in Circumgalactic Media
Authors: Alex Lv, Lile Wang, Renyue Cen, Luis C. Ho
Figure caption: The ratio between t cool and t cross at turbulence turnoff vs. the clumping factor 〈ρ 2〉/〈ρ〉2–1 at 100 Myr. Each point represents a supersonic turbulent run, with the color bar and marker colors denoting the normalized thermal energy ﹩{\epsilon }_{g}/{c}_{s,0}^{2}﹩ at 100 Myr. As with previous figures, c  s,0 represents the sound speed at turbulence turnoff.
Paper: Are Long Gamma-Ray Bursts Progenitors to Merging Binary Black Holes?
Authors: Tom Y. Wu, Maya Fishbach
Figure caption: Upper panel: in orange (left axis), the maximum likelihood LGRB rate and its uncertainty from G. Ghirlanda & R. Salvaterra (2022). The LGRB rate peaks at redshift z = 2.6, which corresponds to a lookback time tL = 11.2 Gyr. Red, green, black, and blue dashed curves show the maximum likelihood value of ﹩{{ \mathcal R }}_{{\rm{LGRB}}}﹩ (solid orange line) convolved with power-law delay time distributions with slopes α = 0, −0.5, −1, and −1.5 and ﹩{\tau }_{{\rm{\min }}}=10﹩ Myr. At α = −2, the merger rate is indistinguishable from the LGRB rate on this plot. In purple (right axis) is the BBH merger rate inferred by S. S. Bavera et al. (2022a) up to z = 1, which is similar in shape to the α = − 1, ﹩{\tau }_{{\rm{\min }}}=10﹩ Myr curve (cyan dashed line). The right axis, corresponding to the measured BBH merger rate in purple, is scaled by a factor of around 0.06 relative to the left axis, corresponding to all other lines. Lower panel: same as above, fixing α = −1 and taking different values of ﹩{\tau }_{{\rm{\min }}}﹩ from 10 Myr (blue), 100 Myr (red), and 1 Gyr (green).
Paper: Are Long Gamma-Ray Bursts Progenitors to Merging Binary Black Holes?
Authors: Tom Y. Wu, Maya Fishbach
Figure caption: The BBH merger rate at redshift z = 0 and z = 1, as inferred by S. S. Bavera et al. (2022a) and estimated here with a two-dimensional KDE (green). Contours enclose regions of 50%, 90%, and 98% probability. Blue, red, and purple dashed lines show predictions for the BBH merger rate under different power-law delay time distributions with slope α and ﹩{\tau }_{{\rm{\min }}}=10﹩ Myr, assuming that the progenitor formation rate traces the best-fit LGRB rate from G. Ghirlanda & R. Salvaterra (2022). A delay time distribution with α = −1 (red) crosses the high probability region. The circles, squares, and triangles represent f values (the ratio between the BBH formation rate and the LGRB rate) of 0.1, 0.03, and 0.01.
Paper: Are Long Gamma-Ray Bursts Progenitors to Merging Binary Black Holes?
Authors: Tom Y. Wu, Maya Fishbach
Figure caption: Joint posterior on BBH delay time and formation rate parameters α, ﹩{\tau }_{{\rm{\min }}}﹩, and f. Contours enclose 0.5σ, 1σ, 1.5σ, and 2σ posterior probability regions. Top left: posterior probability density for α, marginalizing over f and ﹩{\tau }_{{\rm{\min }}}﹩ (blue curve, with blue dashed lines denoting 90% HPDI) or fixing ﹩{\tau }_{{\rm{\min }}}=10﹩ Myr (red curve, with red dashed lines denoting 90% HDPI). Center right: posterior probability density for ﹩{\tau }_{{\rm{\min }}}﹩, marginalizing over α and f (blue curve, with dashed lines denoting 90% upper bound). Bottom right: posterior probability density for f, marginalizing over α and ﹩{\tau }_{{\rm{\min }}}﹩ (blue curve, with blue dashed lines denoting 90% HDPI). We assume flat priors over α and ﹩{\tau }_{{\rm{\min }}}﹩ and a flat-in-log prior on f.
Paper: Are Long Gamma-Ray Bursts Progenitors to Merging Binary Black Holes?
Authors: Tom Y. Wu, Maya Fishbach
Figure caption: Same as Figure 3, but using the subpopulation of BBH mergers with χeff > 0.2 rather than the full BBH population, assuming that LGRBs produce spinning BHs. Compared to Figure 3, smaller values of f and more negative values of α are preferred in this case, and large values of ﹩{\tau }_{{\rm{\min }}}﹩ are still disfavored. The rate of BBH mergers with χeff > 0.2 over the measured range 0 < z < 1 is consistent with tracing the best-fit LGRB rate, so we infer steep delay time distributions peaking at our prior boundary α = −2.
Paper: A High-resolution Simulation of Protoplanetary Disk Turbulence Driven by the Vertical Shear Instability
Authors: Karim Shariff, Orkan M. Umurhan
Figure caption: Reynolds stress tensor. Averaging was performed in the period t/T 0 ∈ [54.53, 300.19]. A region of Δr/H 0 ≈ 1 at each radial boundary should be considered contaminated by boundary conditions.
Paper: A High-resolution Simulation of Protoplanetary Disk Turbulence Driven by the Vertical Shear Instability
Authors: Karim Shariff, Orkan M. Umurhan
Figure caption: Shakura–Sunyaev turbulent viscosity parameter α(r) for runs with different resolutions. The straight dashed black line is ﹩\alpha (r)\,=\left[2.0+0.28(r/{H}_{0}-10)\right]\times {10}^{-4}﹩.
Paper: A High-resolution Simulation of Protoplanetary Disk Turbulence Driven by the Vertical Shear Instability
Authors: Karim Shariff, Orkan M. Umurhan
Figure caption: Axisymmetric run at late times. Specific angular momentum profile, j  z  = u  ϕ  r, at the midplane.
Paper: A High-resolution Simulation of Protoplanetary Disk Turbulence Driven by the Vertical Shear Instability
Authors: Karim Shariff, Orkan M. Umurhan
Figure caption: Specific energy spectra (all velocity components included) at different heights averaged over samples in the time interval t/T 0 ∈ [444.6, 479.3] with spacing δ t/T 0 = 0.5; strength of Padé filter ϵ filter = 0.015. (a) With respect to the radial wavenumber, k  r . (b) With respect to the azimuthal wavenumber, m.
Paper: A High-resolution Simulation of Protoplanetary Disk Turbulence Driven by the Vertical Shear Instability
Authors: Karim Shariff, Orkan M. Umurhan
Figure caption: Axisymmetric simulation at t/T 0 = 197.6. This is a late time but is prior to the stationary state. In panel (a), the completely white regions have vorticity values beyond the range shown in the legend.
Paper: A High-resolution Simulation of Protoplanetary Disk Turbulence Driven by the Vertical Shear Instability
Authors: Karim Shariff, Orkan M. Umurhan
Figure caption: Turbulent viscosity parameter α 1(r) (in spherical coordinates) as defined by M20; see Equation (46). The lines are for the same cases as in Figure 19. ◯: value from Table 2 of M20. □: value from Table A1 of M20.
Paper: A High-resolution Simulation of Protoplanetary Disk Turbulence Driven by the Vertical Shear Instability
Authors: Karim Shariff, Orkan M. Umurhan
Figure caption: Mean radial mass flux ﹩\dot{m}=2\pi r\overline{\rho {u}_{r}}﹩. (a) Simulation. (b) From Equation (50), a consequence of the Reynolds-averaged angular momentum equation. (c) From Equation (50), after assuming that the Favre-averaged velocity ﹩{\widetilde{u}}_{\phi }﹩ is Keplerian.
Paper: A High-resolution Simulation of Protoplanetary Disk Turbulence Driven by the Vertical Shear Instability
Authors: Karim Shariff, Orkan M. Umurhan
Figure caption: Time history of the volume-averaged perturbation kinetic energy for the axisymmetric run.
Paper: A High-resolution Simulation of Protoplanetary Disk Turbulence Driven by the Vertical Shear Instability
Authors: Karim Shariff, Orkan M. Umurhan
Figure caption: Density field for the axisymmetric simulation at t/T 0 = 197.6.
Paper: The Star Formation History of Nearby Galaxies: A Machine Learning Approach
Authors: Yujiao Yang, Chao Liu, Ming Yang, Yun Zheng,  Hao  Tian
Figure caption: SFHs of eight dwarf galaxies, with galaxy name and the field ID displayed on the title. The red dot line shows the measured initial stellar mass over lookback time; the yellow shadow indicates the random uncertainties and the gray shadow indicates the total uncertainties (sum of random and system uncertainties). The diagonal gray dashed line indicates the mass growth with a constant SFR over time. The blue dot line displays the SFH from D. R. Weisz et al. (2014).
Paper: The Star Formation History of Nearby Galaxies: A Machine Learning Approach
Authors: Yujiao Yang, Chao Liu, Ming Yang, Yun Zheng,  Hao  Tian
Figure caption: Illustration of the goodness of fit. Panels (a) and (b) show the observed CMD and the simulated CMD generated from SFHNet output parameters. The color bar indicates the number of stars in color–magnitude cells. Panel (c) depicts the residual CMD, which equals the observed CMD minus the simulated CMD. Panel (d) shows the residual significance (calculated as the residual of star numbers weighted by the standard deviation of the Poisson distribution).
Paper: The Star Formation History of Nearby Galaxies: A Machine Learning Approach
Authors: Yujiao Yang, Chao Liu, Ming Yang, Yun Zheng,  Hao  Tian
Figure caption: Performance evaluation of branch_par. The upper panels show the distribution of parameters behind the corresponding input HD and the output of branch_par, respectively. Their residual is shown in the lower left panel. The lower right panel shows the projection of parameters over age and metallicity (the blue/red line indicates the input/output value), with the p-values of the two-sided KS test displayed in the title.
Paper: The Star Formation History of Nearby Galaxies: A Machine Learning Approach
Authors: Yujiao Yang, Chao Liu, Ming Yang, Yun Zheng,  Hao  Tian
Figure caption: Illustrate the preprocessing steps applied to dwarf galaxy Ursa Minor. The upper row shows the CMDs before and after removing the Milky Way foreground stars. The black dots are observed stars, and red and blue pluses highlight the foreground stars from TRILEGAL and the removed stars, respectively. Panel (c) shows the CMD before (black dots) and after (red dots) the reddening correction, with the adopted A v displayed in the subtitle. Panel (d) is the HD, with the cell containing the largest number of stars normalized to 1.
Paper: The Star Formation History of Nearby Galaxies: A Machine Learning Approach
Authors: Yujiao Yang, Chao Liu, Ming Yang, Yun Zheng,  Hao  Tian
Figure caption: Illustration of the initial mass of stellar populations over the age–metallicity map, taking Ursa Minor as an example. The three axes are age, metallicity, and initial stellar mass. The blue/red line indicates the projection of mass over the age/metallicity axis.
Paper: The Star Formation History of Nearby Galaxies: A Machine Learning Approach
Authors: Yujiao Yang, Chao Liu, Ming Yang, Yun Zheng,  Hao  Tian
Figure caption: Performance evaluation of branch_cmd. Panel (a) shows the input HD; panel (b) is the output of branch_cmd; panel (c) is the residual between the previous two panels. The HD generated from the output parameters is shown in panel (d), and the residual between the input and simulated HD is shown in panel (e).
Paper: The Star Formation History of Nearby Galaxies: A Machine Learning Approach
Authors: Yujiao Yang, Chao Liu, Ming Yang, Yun Zheng,  Hao  Tian
Figure caption: The architecture of SFHNet. The branch_feature includes the input data (the HDs of synthetic galaxies), the main part of EfficientNetV2_S, and the extracted feature layer. The branch_cmd comprises three sets of (Upsampling layer + Convolution layer) combinations; the branch_par includes a global average pooling layer and a fully connected layer, and two sets of (Upsampling layer + Convolution layer) combinations. The activation function SiLU is applied in the entire network.
Paper: The Star Formation History of Nearby Galaxies: A Machine Learning Approach
Authors: Yujiao Yang, Chao Liu, Ming Yang, Yun Zheng,  Hao  Tian
Figure caption: The loss curves for branch_cmd (left panel) and branch_par (right panel). The blue and red lines represent the training set and validation set, respectively.
Paper: Efficient and Accurate Force Replay in Cosmological-baryonic Simulations
Authors: Arpit Arora, Robyn Sanderson, Christopher Regan, Nicolás Garavito-Camargo, Emily Bregou, Nondh Panithanpaisal, Andrew Wetzel, Emily C. Cunningham, Sarah R. Loebman, Adriana Dropulic, Nora Shipp
Figure caption: Preservation of phase-space distribution. Initial sample of all the selected stars (leftmost column), their distribution in the live simulation at “present day” (second from left), and the reconstructed distribution using the TEMP model for orbit integration (third from left). Distributions are shown in the X–Z plane (top row) and for galactocentric distance vs. radial velocity (bottom row). The rightmost column shows the median value of error metric for the initial distribution of sample stars in each bin. Most orbits have errors below 15%, with no angular dependence in the error metric. Errors are larger for particles closer to the center, deep in the disk potential.
Paper: Efficient and Accurate Force Replay in Cosmological-baryonic Simulations
Authors: Arpit Arora, Robyn Sanderson, Christopher Regan, Nicolás Garavito-Camargo, Emily Bregou, Nondh Panithanpaisal, Andrew Wetzel, Emily C. Cunningham, Sarah R. Loebman, Adriana Dropulic, Nora Shipp
Figure caption: Number of periods before “failure” of orbit reconstruction. Failure time is defined as the moment when the instantaneous error in total angular momentum between reconstructed and true values exceeds 100%. It is plotted against integration time (in orbital periods), exclusively for orbits that fail (approximately 10%). The distribution of failure times (red), integration times for orbits that never fail (green), and all the integration times (black) are displayed on the right side. The histogram above the main panel illustrates the fractional integration times for orbits that never failed (green) and those that failed (red), with each bin scaled so that the total across both categories for each bin is 1. Notably, the distribution of failure times appears to be independent of integration time, as indicated by the nearly constant fraction of failures and successes across integration time bins (dashed lines) in the top panel.
Paper: Efficient and Accurate Force Replay in Cosmological-baryonic Simulations
Authors: Arpit Arora, Robyn Sanderson, Christopher Regan, Nicolás Garavito-Camargo, Emily Bregou, Nondh Panithanpaisal, Andrew Wetzel, Emily C. Cunningham, Sarah R. Loebman, Adriana Dropulic, Nora Shipp
Figure caption: Recovery of integrals of motion. Left: reconstructed final energy vs. true final energy. The inset in the top-left corner displays the distribution of the initial energy (green), true final energy (black), and reconstructed final energy (blue). The dashed–dotted line indicates the energy threshold (E tot = 0 (km s–1)2) above which particles are unbound to the main halo. Right: similar to the left panel, but for the total angular momentum (J total). J total exhibits less scatter and tighter correspondence with a stronger one-to-one correlation (black dashed diagonal line) compared to the energy. Approximately 98% of orbits have final angular momentum errors below 100%, and 87% have final energy errors below 100%. Both of the panels have high correlation coefficients (≥0.7) and a p-value greater than 0.5 for the Kolmogorov–Smirnov test, suggesting no significant differences between either of the reconstructed and true distributions.
Paper: Efficient and Accurate Force Replay in Cosmological-baryonic Simulations
Authors: Arpit Arora, Robyn Sanderson, Christopher Regan, Nicolás Garavito-Camargo, Emily Bregou, Nondh Panithanpaisal, Andrew Wetzel, Emily C. Cunningham, Sarah R. Loebman, Adriana Dropulic, Nora Shipp
Figure caption: Performance of orbit reconstruction over time at different average distances. Left: temporal evolution of relative position error as a function of number of periods passed for each orbit, divided in rows based on the average orbital distance from the center. Distance ranges are indicated in the top-left corner of each row. Right: distribution of relative position error for all orbits at each time step, color-coded by the distance ranges shown on the left. Most errors are within 10% for 2–3 periods across all distance cuts, while orbits with ﹩\tfrac{{\rm{\Delta }}r}{r}(t)\geqslant 1﹩ predominantly occur for orbits closer to the center after 5–6 periods. Additionally, the error trajectories oscillate with orbital phase by nearly an order of magnitude, as is most clearly visible for the longest-period orbits in the bottom-left panel: ﹩\tfrac{{\rm{\Delta }}r}{r}(t)﹩ is higher at pericenter and lower at apocenter. Error trajectories and distributions for bound stars are marked with gray lines (left) and a gray histogram (right).
Paper: Efficient and Accurate Force Replay in Cosmological-baryonic Simulations
Authors: Arpit Arora, Robyn Sanderson, Christopher Regan, Nicolás Garavito-Camargo, Emily Bregou, Nondh Panithanpaisal, Andrew Wetzel, Emily C. Cunningham, Sarah R. Loebman, Adriana Dropulic, Nora Shipp
Figure caption: Variation in performance with different symmetry assumptions across Cartesian axes. Violin plots illustrate the residual distributions between the reconstructed and true forces across different Cartesian axes (first row: X-axis, second row: Y-axis, third row: Z-axis) for DM (green) and stars (orange) within 50 kpc of the galactic center at the present day. The forces are reconstructed using the same symmetry models as in Section 2.3, with various symmetry conditions imposed on the halo and the disk. The notation on the X-axis indicates the symmetry conditions applied on the halo and disk, respectively, following the notation from Table 2. The short-dashed lines represent the 25th and 75th quartiles of the distributions, while the long-dashed line represents the 50th quartile.
Paper: Efficient and Accurate Force Replay in Cosmological-baryonic Simulations
Authors: Arpit Arora, Robyn Sanderson, Christopher Regan, Nicolás Garavito-Camargo, Emily Bregou, Nondh Panithanpaisal, Andrew Wetzel, Emily C. Cunningham, Sarah R. Loebman, Adriana Dropulic, Nora Shipp
Figure caption: Reconstruction of pericenter and apocenter distances. Reconstructed vs. true pericenter distances (left column) and apocenter distances (right column) for the first (top row) and last (bottom row) passages, respectively. Orbits of unbound stars (solid circles) and luminous satellites (diamonds) are color-coded by their orbital period. Most orbits exhibit errors within 10% (shaded gray region around dashed 1:1 line) at the first passage, with higher errors observed closer to the center. Notable discrepancies in the pericenter and apocenter distances, such as those observed at 20 kpc and 80 kpc, respectively, primarily originate from the bound parts of the stream included in the sample (gray open circles; see also Figure 5). By the final passage, pericenter distances in the inner regions have more scatter than apocenter distances, although errors for orbits with pericenter beyond 30 kpc remain within 10%. The insets in each panel plot the distribution of percentage errors between reconstructed and true values for unbound stars. The reconstructed satellite orbits overestimate the last pericenter due to the absence of a dynamical friction prescription in our model.