dataesr/scientific-paragraphs-categorization huggingface dataset:
Biogeographic reconstruction Ancestral presence in the Hajar Mountains. -We conducted an ancestral state reconstruction of mountain occupancy to elucidate first colonization events using the function 'make. simmap' within the R package 'phytools'  (Revell 2012)  in the all Squamate multilocus phylogenetic tree. We assigned the state Hajars/No Hajars to each tip based on current species distribution, selected the most likely model under AIC criteria (all-rates-different; ARD) and ran 1,000 simulations. We used the R packages 'geiger'  (Harmon et al. 2008 ) and 'treeio'  (Wang et al. 2020)  for phylogenetic data manipulation. With this approach, we were able to assess the number of independent reptile colonization events of the Hajar Mountains and the age of each colonization. This also allowed us to differentiate between first colonization followed by within-mountain speciation and independent colonization events within each mountain genus.
Colonization events were considered when a node was present in the Hajar mountains (more than 50% of its state as Hajars), and its parental node was No Hajars. We incorporated uncertainty to the age of colonization by considering a time range instead of a single time point. Such a time range was defined as the branch length between the colonization node and its parental No Hajars node plus the 95% highest posterior density (HPD) interval of both nodes. We trimmed the ancestral state reconstruction results to the deepest node of each mountain genus with the exception of Hemidactylus, for which we only considered the 'arid clade', and Omanosaura, for which we added its sister clade since the whole genus is endemic to the mountain range. Within-mountain biogeographic reconstructions. -We used the R package BioGeoBEARS  (Matzke 2013)  to reconstruct ancestral ranges for each independent colonization event using the SNAPP time-calibrated trees (See above).
We compared the number of observed events with the expected under the inferred model for all biogeographic events together, all vicariance events together, and each event separately, with the goal of identifying specific time intervals where the observed biogeographic history significantly deviates from model expectations. All biogeographic analyses were conducted within the R environment (R Core Team 2021), and we used the packages ggtree (Yu 2020), treeio  (Wang et al. 2020 ) and packages within tidyverse  (Wickham et al. 2019)  for data manipulation and visualization purposes. We also explored the biogeographic patterns and ancestral elevations at the specimen level conducting ancestral state reconstructions for each independent colonization event with the function 'make. simmap' within the R package 'phytools'  (Revell 2012).
Elevation data originated from the Shuttle Radar Topography Mission at a spatial resolution of 1 arc-second (~30 m). For each of the 10 different phylogenetic trees, we selected the most likely model (ER, SYM or ARD) under AIC criteria (Table  S8 ) and ran 1,000 simulations. We then inspected the current range of elevations of each endemic group and compared them to its most recent common ancestor's state. If they differed, we considered it indicative of a 'bottom-up' scenario when the ancestral node presented a lower state, or a 'top-down' scenario when the ancestral node presented a higher state.
Incidence of biogeographic events through time Figure  S56 : Incidence of altitudinal dispersions through time. Downslope (green) and Upslope (pink) migration events recorded at the lineage level. Altitudinal dispersions time-ranges were calculated following the same method as colonization events (See methods). In black surface temperature estimate from the last 20 Myr (extracted from  Hansen et al. 2013). Secondary uplift events in blue  (Hansmann et al. 2017 and Jacobs et al. 2015  respectively from left to right); Hyper-aridity events in Arabia in brown  (Böhme et al. 2021)  with the widest hyper-aridity representing the NADX period. Mio: Miocene; Pli: Pliocene; Ple: Pleistocene; Q: Quaternary. Table  S1 : GenBank accession codes for all species used to reconstruct the Squamata multilocus phylogenetic tree.
and  Gary Feulner  ( Dubai Natural History Group ) for their continuous support. SC is supported by grants  PGC2018-098290-B-I00  ( MCIU /AEI/ FEDER , UE) and  PID2021-128901NB-I00  funded by  MCIN/AEI/ 10. 13039/501100011033  and by  ERDF , A way of making Europe. BB-C was funded by  FPU  grant from  Ministerio de Ciencia, Innovación y Universidades, Spain  ( FPU18/04742 ). AT is supported by  "la Caixa" doctoral fellowship   programme  ( LCF/BQ/DR20/11790007 ). GR was funded by an  FPI  grant from the  Ministerio de Ciencia, Innovación y Universidades, Spain  ( PRE2019-088729 ). PT was funded by  FCT  under the contract  DL57/2016/CP1440/CT0008. JŠ was funded by the  Czech Science Foundation  ( GACR , project number  22-12757S ) and by  Charles University Research Centre  program no. 204069.
Phylogenomic reconstructions. -Maximum likelihood (ML; Figs. S2-S11) and Bayesian inference phylogenies (BI; Figs. S12-S21) yielded similar topologies in all datasets and posterior support (pp > 0. 95) or bootstrap support (bp > 85) was generally recovered in all major clades. The phylogenomic reconstruction of Trachydactylus hajarensis is the only case showing discordances between analyses, probably due to historic gene flow between populations (Burriel-Carranza et al. 2022b).
ADMIXTURE to design and evaluate different tests of non-admixed monophyletic species hypotheses with Bayes Factor Delimitation (BFD* with genomic data;Leaché et al. 2014;    Table S5, datasets 46-57). Bayes factor delimitation is a program that combines genetic data and coalescent methods to compare candidate species delimitation models containing different numbers of species. Within BFD*, for each species delimitation model we estimated a species tree with SNAPP v. 1. 5. 2 (Bryant et al. 2012 ) and conducted a Path sampling algorithm to calculate its marginal likelihood. We then ranked each marginal likelihood and used Bayes factors to determine the best species delimitation model for each independent colonization event (both SNAPP and BFD* were implemented in BEAST2 v. 2. 6. 4; Bouckaert et al.
2019). SNAPP uses a Bayesian multispecies coalescent framework to generate a species tree directly from biallelic markers (SNPs or AFLPs) without estimating gene trees. To avoid model violations (SNAPP assumes no gene flow) we only included non-admixed individuals. Since SNAPP is computationally intensive, we downsampled our datasets selecting 1-3 individuals for each putative species, and added its closest sister species to test for a single species hypothesis. We selected those individuals with the highest coverage. Final datasets contained between 692 and 11,304 uSNPs, and 9,873 c_SNPs and 2,759 c_SNPs in Asaccus and Pristurus rupestris respectively.
64455 58. 16508 58. 16508 58. 16508 57. 87942 57. 79982 57. 35825 57. 70014 57. 72425 57. 68267 56. 89378 57. 19189 57. 14122 57. 14572 57. 16305 56. 22051 59. 46464 14. 65 44. 2 14. 9 43. 46666667 15. 6103 38. 957225 15. 6103 38. 957225 15. 6103 38. 957225 22. 59209 59. 30119 381 96 306 306 306 306 60 60 634 634 428 240 240 268 58 15 51 51 51 21 71 7 1673 2086 2026 564 765 905 1214 1593 946 5 317 2067 1416 794 794 794 Dataset Nº 1 2 492 3 yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes TCGAT CAACC AACCA AACCA GCATG GCATG CGATC CGATC TGCAT TCGAT CAACC TCGAT TGCAT GGTTG GGTTG AACCA TCGAT TGCAT AACCA TCGAT TCGAT GCATG AACCA TGCAT CAACC GCATG CGATC GGTTG AAGGA TGCAT TCGAT GCATG GGTTG CAACC TCGAT GGTTG CGATC GCATG Dataset type uSNPs uSNPs AACCA uSNPs 1,291,810 2,763,833 264,248 273,918 405,507 530,829 1,517,002 3,417,708 1,469,286 385,174 3,301,271 2,828,229 2,866,941 2,402,150 1,100,178 1,036,211 2,535,547 1,283,531 2,015,168 1,295,833 2,252,188 3,534,698 3,818,443 2,157,323 3,767,949 3,482,067 1,405,599 2,694,649 3,007,070 1,500,527 1,590,268 1,875,125 1,232,155 1,858,316 2,009,942 2,909,998 5,504,432 4,817,332 Analysis ADMIXTURE 1,289,961 2,759,095 263,880 273,405 405,049 530,003 1,515,848 3,412,076 1,467,696 384,642 3,298,282 2,813,483 2,853,640 2,390,681 1,094,568 1,030,980 2,523,178 1,277,690 2,006,489 1,289,818 2,241,510 3,516,193 3,814,757 2,155,800 3,765,082 3,479,663 1,404,670 2,692,049 3,002,905 1,499,254 1,588,475 1,873,108 1,225,088 1,844,672 1,998,849 2,895,544 5,476,408 4,792,093 ADMIXTURE 2,555,381 2,553,120 ADMIXTURE yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes no yes yes yes yes yes Postprocessing yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes no yes yes yes yes yes filtering 0.
6ind -0. 4gen 0. 6ind -0. 4gen yes yes 0. 6ind -0. 4gen no no no no no no no no no no no no no no no no no no no no no yes yes no yes yes no no no no yes no no no no no yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes no yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes no yes yes yes yes yes specifications Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Analysis K/reps/cv 1-8/15/15 1-8/15/15 Present study yes Present study 1-10/15/15 nº of individuals 12 9 32 Dataset length (bp) 16,890 1,453 12,476 nº of loci 16,890 1,453 12,476 nº of SNPs 16,890 1,453 12,476 Missingness (%) 13.
cyanura BFD2 O. cyanura BFD2 O. cyanura BFD2 O. jayakari BFD2 O. jayakari BFD2 O. jayakari BFD2 P. rupestris BFD4 P. rupestris BFD4 P. rupestris BFD4 P. rupestris BFD4 P. rupestris BFD4 P. rupestris BFD4 P. orlovi BFD1 P. orlovi BFD1 P. orlovi BFD1 P. orlovi BFD1 P. orlovi BFD1 P. orlovi BFD1 Dataset SPM001367 CN849 CN761 UAE48 S1872 CN3763 S7547 CN4010 CN4157 S7193 S7509 S7510 S2135 CN3918 CN3949 CN666 CN722 CN236 name 25. 09451 26. 04752 26. 04855 22. 62028 22. 81421 22. 93540 22. 76619 22. 81610 22. 82222 22. 82532 22. 82554 22. 82554 23. 06196 23. 06904 23. 06904 23. 14979 23. 14979 23. 17412 56. 06695 56. 23209 56. 23218 59. 09306 59. 25336 59. 13093 59. 03366 59. 07300 59. 04351 59. 11173 59. 08568 59. 08568 57. 13044 57. 47324 57. 47324 56. 89423 56. 89423 57. 03432 351 274 238 647 33 128 1320 1748 1690 1601 1692 1692 591 648 648 564 564 1116 Dataset Nº yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes AACCA AAGGA GCATG CAACC AAGGA AACCA TCGAT TCGAT CAACC GGTTG AAGGA CGATC CGATC AAGGA TGCAT CAACC AAGGA AACCA Dataset type 1,231,229 1,586,429 708,167 3,947,030 3,197,761 1,933,485 1,529,319 570,245 59,357 1,484,465 2,032,750 2,081,219 1,184,798 6,527,794 3,543,898 2,574,657 3,371,419 2,771,713 Analysis 1,230,896 1,586,277 708,108 3,946,359 3,197,453 1,933,233 1,520,614 567,166 59,047 1,475,566 2,021,619 2,070,050 1,182,660 6,511,691 3,536,911 2,570,247 3,362,309 2,766,601 yes yes no yes yes yes yes no no yes yes yes yes yes yes yes yes yes Postprocessing yes yes no yes yes yes yes no no yes yes yes yes yes yes yes yes yes filtering no yes no yes yes no no no no no no no no yes yes no yes no yes yes no yes yes yes yes no no yes yes yes yes yes yes yes yes yes specifications Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study trees/ bs Present study subs model/starting nº of individuals Dataset length (bp) nº of loci nº of SNPs Missingness (%) RESULTS LACERTOIDEA Lacertidae LACERTOIDEA Lacertidae GEKKOTA Sphaerodactylidae Pristurus rupestris sp2 Omanosaura jayakari Omanosaura jayakari GEKKOTA Sphaerodactylidae Pristurus rupestris sp2 GEKKOTA Phyllodactylidae Ptyodactylus orlovi GEKKOTA Phyllodactylidae Ptyodactylus orlovi ML_Asaccus.
20301 1440 yes TCGAT 2,795,736 2,792,607 56. 20722 1430 yes CAACC 2,162,077 2,160,963 56. 23472 1478 yes TGCAT 862,403 861,751 56. 23472 1478 yes AACCA 2,426,891 2,424,470 56. 34002 238 yes CGATC 2,497,279 2,485,233 56. 29345 389 yes GGTTG 2,496,766 2,481,743 56. 29380 399 yes GGTTG 2,186,066 2,173,805 55. 96485 431 yes GGTTG 1,928,877 1,917,772 56. 06977 369 yes GGTTG 2,472,741 2,458,538 56. 24138 622 yes GCATG 1,969,603 1,958,374 57. 84420 576 yes AACCA 2,844,138 2,828,632 57. 85322 564 yes TCGAT 1,837,907 1,828,601 59. 30014 198 yes TGCAT 451,507 Dataset Nº Dataset type Analysis 56. 23464 420 yes CAACC 7,966,087 7,955,630 25. 89705 56. 23464 420 yes AACCA 7,759,637 7,747,639 35 c_loci BEAST2 yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes Postprocessing yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes filtering yes yes yes yes 0.
6ind -0. 4gen no yes yes no no no no yes no yes no no no no yes no yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes specifications Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Present study Analysis yes Present study yes Present study Table S7 nº of individuals 126 Dataset length (bp) 37,080 nº of loci 600 nº of SNPs 3,234 Missingness (%) 19. 80 RESULTS - GEKKOTA Sphaerodactylidae Pristurus celerrimus GEKKOTA Sphaerodactylidae Pristurus celerrimus GEKKOTA Sphaerodactylidae Pristurus rupestris sp3 GEKKOTA Sphaerodactylidae Pristurus rupestris sp3 GEKKOTA Phyllodactylidae Ptyodactylus ruusaljibalicus GEKKOTA Phyllodactylidae Ptyodactylus ruusaljibalicus BI_Echis.
10332 0 6098. 09078 3052. 02507 ML BF Rk 14015 Simmap BioGeoBears strength of support 3 1 8. 715731015 BEAST2 BEAST2 BEAST2 BEAST2 BEAST2 BEAST2 Asaccus_montanus specific-priors 0. 7ind -0. 4gen 0. 6ind -0. 4gen 0. 6ind -0. 4gen 0. 7ind -0. 4gen 0. 6ind -0. 4gen 0. 78ind -0. 4gen 2spp: A. montanus vs Outgroup (A. griseonotus) 3spp: A6062. 65421 3083. 86488 Table S7 32 38,859 600 Table S7 24 34,896 600 Table S7 173 39,241 600 Table S7 22 38,798 600 Table S7 72 407,933 6,309 Table S7 47 338,530 5,219 ML BF Rk 7604. 58665 0 strength of support Asaccus_caudivolvulus_margaritae_gardneri specific_priors ML BF Rk Block Elevation Block 2,862 1,967 2,109 18,697 30,079 strength of support 8. 033938921 strength of support 8. 30 2. 05 0. 40 2. 30 22. 40 ------ Dataset name colonization shifts Dataset Nº colonization Dataset type Analysis Postprocessing filtering Analysis specifications nº of individuals Dataset length (bp) nº of loci nº of SNPs Missingness (%) RESULTS Asaccus SNAPP_Asaccus.
00 3. 07 0. 00 4. 91 5. 96 3. 54 2. 32 0. 00 3 spp 4 spp 2 spp 3 spp 12 spp 2 spp 3 spp 6 spp BFD_Asaccus_caudivolvulus_Agardneri_Amargaritae. nex BFD_Asaccus_montanus. nex SYM ARD SNAPP_Trachydactylus. vcf Pseudotrapelus Prup ER ER 55 56 DIVALIKE uSNPs uSNPs 57 uSNPs DIVALIKE BFD BFD BFD & SNAPP 0gen 0. 1gen 0. 1gen Table S7 Table S7 Table S7 15 12 12 2,309 1,676 2,147 2,309 1,676 2,147 2,309 1,676 2,147 0. 00 3. 41 4. 23 5. 00 2 spp 4 spp Ptyodactylus Trachidactylus ER ER Dataset name SYM SYM Dataset Nº DIVALIKE Dataset type DIVALIKE Analysis Postprocessing filtering Analysis specifications nº of individuals Dataset length (bp) nº of loci nº of SNPs Missingness (%) RESULTS Best λ A. arnoA. gall. bed 58 uSNPs FEEMS 0. 6ind -0. 2gen - 44 4,415 4,415 4,415 11. 23 1. 83 A. caudA. gard. bed 59 uSNPs FEEMS 0.
The slope of this region, β XY , is independent from other measurable quantities. We can use this property to calibrate SNe Ia accurately and independently of other methods, with sensitivity to different systematic sources of error. It is interesting to explore CMAGIC because in the future, we may be able to use CMAGIC to calibrate SNe Ia lacking data around maximum light. Further, it has been shown that CMAGIC curves may be useful in helping to break the degeneracy between intrinsic color and reddening  (Hoeflich et al. 2017). Conley et al. (2006)  shows that cosmological results from CMAGIC are consistent with the current picture of cosmology, i. e. , an accelerating flat universe with a cosmological constant. Similarly,  Wang et al. (2006)  shows that CMAGIC methods have a Hubble residual rms deviation of approximately 0.
Data Spectra from SNfactory  (Aldering et al. 2002)  were used for this analysis. Details about the SNfactory data set and data reduction can be found in  Saunders et al. (2018)  and  Aldering et al. (2020). After correcting the observed spectra to the restframe, synthetic photometry for each SN was made using BVRI filters from  Bessell & Murphy (2012) , which were calibrated to the Vega system using alpha_lyr_stis_010. fits from the CALSPEC database  (Bohlin et al. 2014 ) (see Appendix A). These filters were chosen for ease of comparison to  Wang et al. (2003). The zero-point for SNfactory data is kept hidden, thus, all magnitudes in this work are the calculated magnitude plus a constant. Cuts were then applied to the data, requiring that observations exist before maximum light, and that a minimum of three observations exist in the linear region in all three types of CMAGIC diagram (see Section 2.
fPCA Fitting Light curves are fit using fPCA, as described by  He et al. (2018). 23 It is advantageous to use PCA methods to fit complex curves, such as light curves, because the result is a parameterization of the curve that is a linear combination of orthogonal PC functions. Therefore, it is straightforward to propagate the errors (See Appendix B). The fitted light curves are used to determine the location of the brightest point in the B band, as well as the change in magnitude between peak B band brightness and 15 days later, Δm 15,B. We use the fits from the light curves to compute the CMAGIC diagram for each SN and color combination. For this analysis, only the first two B-and V-band specific PC components from  He et al. (2018)  are used because these describe the majority of the variation in the light curves, and we found that including the third and fourth components resulted in unphysical fits for some SNe because the data were insufficient to constrain the fit realistically using this method.
The second begins at around 40 days (shown in the left panel of Figure  1 ), although discussion of this region is outside the scope of this study. To fit the first linear region (hereafter "linear region") of the B versus B -V, B -R, and B -I CMAGIC diagrams for each SN, we used Levenberg-Marquardt least squares minimization via mpfit in Python  (Moré 1978; Moré & Wright 1993; Markwardt 2009; Koposov 2017 ). The fits were performed such that χ 2 was fixed to equal the number of degrees of freedom via scaling the errors, with different scalings for the two linear regions. The endpoints of the linear regions in the CMAGIC diagrams for all SNe were determined by visual inspection. SNe with fewer than three observations in the linear region of any of the three diagrams (B -V, B -R, or B -I) were excluded, in order to allow for a minimum of one degree of freedom in all linear fits.
"Bump" Morphology SNe are distinguishable in the CMAGIC diagram by the presence, or lack, of a luminosity excess relative to the linear region near B max , the maximum magnitude in the B band. We have qualitatively divided our sample into three categories based on visual inspection: those with a bump, those without a bump, and those where it is ambiguous whether or not there is a bump. The last group includes those without enough data in this region to say definitively if there is a "bump" or not, and Note. We correct for the "look-elsewhere effect" by dividing our significance level α = 0. 05 by the number of parameters in this table. Thus, our significance level is α C = 0. 005. The first section shows the results for parameters independent of the bump. The second section shows the results for slope β XY of the linear region of the CMAGIC diagram, which we have shown to be strongly correlated with "bump" size (Figure  2 ).
The green arrow points to the "bump" feature, and the small vertical orange arrow shows a visualization of the definition of ω BV (Equation (  1 )). The right plot does not show a "bump" feature. The filled purple circles are members of the linear region and were therefore used in the linear fits. The open blue circles do not belong to the linear region, and were therefore excluded from the linear fits. The points are labeled by the light-curve phase relative to B max. The solid purple line is the linear fit and the solid blue curve is from the fPCA fit. β BV is the slope of the fit line (purple), and the fit was performed such that χ 2 was fixed to equal the number of degrees of freedom via scaling the errors. Note that for the SN with the bump, data up to approximately 15 days after maximum brightness in the B band (the numbers tracking each data point) stay bluer than those for the SN without a bump.
(2018). correlation between polarization and the velocity gradient for the Si II λ6355 absorption line. We do not include line velocity gradients in this study; thus, it could be a useful parameter to study in this context if the "bump" feature can be connected with asymmetry and polarization. We also emphasize the need to examine asymmetry with 3D models in relation to the "bump" feature. These results would be improved by using a data set with more well-sampled SNe Ia in the window 0-60 days after maximum brightness. We may also apply machine-learning techniques, such as the one used by  Hu et al. (2022) , to fill in gaps in the data. These results may also have implications for SN Ia cosmology. Wang et al. (2003)  shows that the dispersion of standardized magnitudes when using CMAGIC is very small; however, given the results in this work, the dispersion should be reexamined from the perspective of differing CMAGIC diagram morphologies.
Stretch is held constant at x 1 = 1. Figure  10. Left: slope β BV measured from linear fits applied directly to the data compared to β BV measured from a linear fit to a synthetic SALT3 CMAGIC diagram in the same phase window. Right: "bump" size ω BV measured from SALT3 fits and fPCA fits. fPCA ω BV is calculated using β BV from the data rather than a linear fit to the synthetic CMAGIC diagram from the fPCA templates. ρ X,Y is the Pearson correlation coefficient for each plot, and p is the corresponding p-value. F f R , A 1 i i i X i i i 1 1 2 where f (λ i ) is the energy flux at a particular wavelength λ i and R X is the response function for the filter. Then, the variance of F is ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ( )( ) ( ) ( ) å s ls l l l = - l l l = - R. A 2 F i i f X i i i 2 1 2 i 1 2 Individual magnitudes are calculated by ⎜ ⎟ ⎛ ⎝ ⎞ ⎠ ( ) = - m F F 2.
Then, for arbitrary color X -Y, the Jacobian is ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ ( ) ( ) ( ) ( )  l l l = ¶ ¶ ¶ ¶ ¶ ¶ - - - - J m f m f m f , A 6 X Y X Y X Y X Y N 0 1 where N is the last measured wavelength in the spectrum. The ith entry is ( ) ( ) ( )( ) ( )( ) l l l l l l l ¶ ¶ = - - + - - - - A7 m f F R F R 1. 09 1. 09. X Y i X X i i i Y Y i i i 1 1 Then, the covariance matrix is diagonal, and each entry is the spectrum error provided in the data g q m q q , B 1 s s k K s k k 0 1 where q is the phase, m sλ is the peak magnitude, s is the corresponding SN, λ is the corresponding filter, f kλ are the fPCA vectors, and ( ) b l s k are the outputs of the fPCA analysis code  (He et al. 2018). The errorsin the entire light curve can be calculated with σ 2 = JCJ T. The covariance matrix is output from the fPCA analysis code.