ELIZA

return kwic search for under out of >500 occurrences
321496 occurrences (No.66 in the rank) during 5 years in the PubMed. [cache]

143) We further identify conditions under which the use of continuum models is justified, and others for which stochastic or discrete effects dominate.

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PMID:24615007 DOI:10.1007/s00285-014-0771-1

2015 Journal of mathematical biology

* Mesoscopic and continuum modelling of angiogenesis.

- Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which processes that include proliferation and cell movement are considered as stochastic events. By studying the dependence of the model on the lattice spacing and the number of cells involved, we are able to derive the deterministic continuum limit of our equations and compare it to similar existing models of angiogenesis. We further identify conditions under which the use of continuum models is justified, and others for which stochastic or discrete effects dominate. We also compare different stochastic models for the movement of endothelial tip cells which have the same macroscopic, deterministic behaviour, but lead to markedly different behaviour in terms of production of new vessel cells.

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(1)95 the	(18)4 these	(35)2 axial	(52)2 of
(2)13 different	(19)3 high	(36)2 censoring	(53)2 optimal
(3)12 a	(20)3 investigation	(37)2 clinical	(54)2 physiological
(4)9 general	(21)3 light	(38)2 consideration	(55)2 pulsatile
(5)8 both	(22)3 local	(39)2 controlled	(56)2 scanning
(6)8 which	(23)3 mechanical	(40)2 current	(57)2 serum-free
(7)7 various	(24)2 null	(41)2 evaluation	(58)2 several
(8)6 conditions	(25)2 12	(42)2 ex	(59)2 simulated
(9)6 curve	(26)2 15	(43)2 extreme	(60)2 specific
(10)6 static	(27)2 2	(44)2 four	(61)2 steady-state
(11)5 and	(28)2 CA	(45)2 hypertensive	(62)2 therapy
(12)4 5	(29)2 CT	(46)2 hypoxia	(63)2 this
(13)4 certain	(30)2 H2O2-induced	(47)2 hypoxic	(64)2 time
(14)4 control	(31)2 UV	(48)2 inflammatory	(65)2 treatment
(15)4 either	(32)2 acute	(49)2 laser	(66)2 ultrasound
(16)4 in	(33)2 additive	(50)2 lateral	(67)2 vertical
(17)4 normal	(34)2 adverse	(51)2 mortality	(68)2 water

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--- WordNet output for under --- =>以下の, (治療, 試練, 刑罰)を受けて, 下部の, の下に, ・・の下に Overview of adj under The adj under has 2 senses (first 2 from tagged texts) 1. (2) nether, under -- (located below or beneath something else; "nether garments"; "the under parts of a machine") 2. (1) under -- (lower in rank, power, or authority; "an under secretary") Overview of adv under The adv under has 8 senses (first 1 from tagged texts) 1. (2) under -- (down to defeat, death, or ruin; "their competitors went under") 2. under -- (through a range downward; "children six and under will be admitted free") 3. under -- (into unconsciousness; "this will put the patient under") 4. under -- (in or into a state of subordination or subjugation; "we must keep our disappointment under") 5. under -- (below some quantity or limit; "fifty dollars or under") 6. under -- (below the horizon; "the sun went under") 7. under -- (down below; "get under quickly!") 8. under, below -- (further down; "see under for further discussion") --- WordNet end ---