We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in R m×n , min(m, n) ≤ 2, then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit convexity assumptions on the quasiconvex (polyconvex) envelope.
Previous research suggested that several genetic polymorphisms are associated with increased risk of ischaemic stroke (IS) in young adults. However, the predictive biomarkers of IS in young adults are still unclear. Our aim was to assess the contribution of modifiable and genetic factors in IS in young adults. In total, 40 stroke patients and 40 healthy controls aged 20 to 50 years were recruited. Data on modifiable factors were collected, then participants were genotyped for seven SNPs linked to thrombophilia: ACE rs1799752, PAI-1 rs1799889, APOE rs1412 and rs429358, FV rs6025 and rs1800595, and FII rs62623459. Significantly increased risk factors: hypertension and dyslipidaemia in stroke patients compared with the controls: 50.0 % vs 27.5 % and 75.0 % vs 40.0% (P = 0.039 and P = 0.002, respectively) were observed. Stroke patients compared with controls did not differ in distribution of ACE, APOE, FV, and FII variants. The 4G4G homozygotes of the PAI-1 gene were significantly more prevalent in stroke patients compared to the controls: 42.5 % vs 17.5 %, (P = 0.033). In the group with the small vessel occlusion subtype of stroke, statistically significant overrepresentation of 4G4G homozygotes and frequency of the 4G allele compared with controls: 57.1 % vs 17.5 % and 0.7 vs 0.45 (P = 0.026 and P = 0.03, respectively) were observed. Independent predictors of stroke incident were: dyslipidaemia (OR (95% CI) = 4.2 (1.4–12.4)) and 4G4G genotype (OR (95% CI) = 3.9 (1.1–13.7)). These results confirm the contribution of dyslipidaemia and 4G4G genotype in the increased risk of IS in young Bosnian adults.