( ( 4.1 ( ( The ( total population ) ) ( We ( ( ( generate ( ( the population ) ( of ( ( close ( double ( white ( dwarfs ( and ( helium stars ) ) ) ) ) ) ( with ( white ( dwarf companions ) ) ) ) ) ) ) and ) ( ( select ( the ( AM ( CVn ( star progenitors ) ) ) ) ) ( according ( to ( ( the criteria ) ( for ( ( the formation ) ( of ( the ( AM CVn ) ) ) ) ) ) ) ) ) ) ) ) ) ( ( stars ( as ( described above ) ) ) . ) )
(ROOT (S (S (VP (VBG 4.1) (NP (NP (DT The) (JJ total) (NN population)) (SBAR (S (NP (PRP We)) (VP (VP (VB generate) (NP (NP (DT the) (NN population)) (PP (IN of) (NP (NP (JJ close) (JJ double) (JJ white) (NNP dwarfs) (CC and) (NNP helium) (NNS stars)) (PP (IN with) (NP (JJ white) (NN dwarf) (NNS companions))))))) (CC and) (VP (VB select) (NP (DT the) (NNP AM) (NNP CVn) (NN star) (NNS progenitors)) (PP (VBG according) (PP (TO to) (NP (NP (DT the) (NNS criteria)) (PP (IN for) (NP (NP (DT the) (NN formation)) (PP (IN of) (NP (DT the) (NNP AM) (NNP CVn))))))))))))))) (VP (VBZ stars) (SBAR (IN as) (S (VP (VBD described) (ADVP (RB above)))))) (. .)))
4.1 The total population We generate the population of close double white dwarfs and helium stars with white dwarf companions and select the AM CVn star progenitors according to the criteria for the formation of the AM CVn stars as described above.
(ROOT (S (SBAR (WHADVP (WRB When)) (S (NP (DT the) (NNP helium)) (VP (VBZ is) (VP (VBN gone))))) (, ,) (NP (DT the) (NNS stars)) (VP (VBP become) (NP (JJ white) (NNS dwarfs))) (. .)))