Feasible combinatorial matrix theory

We show that the well-known Konig's Min-Max Theorem (KMM), a fundamental result in combinatorial matrix theory, can be proven in the first order theory \LA with induction restricted to $\Sigma_1^B$ formulas. This is an improvement over the standard textbook proof of KMM which requires $\Pi_2^B$ induction, and hence does not yield feasible proofs --- while our new approach does. \LA is a weak theory that essentially captures the ring properties of matrices; however, equipped with $\Sigma_1^B$ induction \LA is capable of proving KMM, and a host of other combinatorial properties such as Menger's, Hall's and Dilworth's Theorems. Therefore, our result formalizes Min-Max type of reasoning within a feasible framework

Biallelic loss-of-function variants in PLD1 cause congenital right-sided cardiac valve defects and neonatal cardiomyopathy

Congenital heart disease is the most common type of birth defect, accounting for one-third of all congenital anomalies. Using whole-exome sequencing of 2718 patients with congenital heart disease and a search in GeneMatcher, we identified 30 patients from 21 unrelated families of different ancestries with biallelic phospholipase D1 (PLD1) variants who presented predominantly with congenital cardiac valve defects. We also associated recessive PLD1 variants with isolated neonatal cardiomyopathy. Furthermore, we established that p.1668F is a founder variant among Ashkenazi Jews (allele frequency of -.2%) and describe the phenotypic spectrum of PLD1-associated congenital heart defects. PLD1 missense variants were overrepresented in regions of the protein critical for catalytic activity, and, correspondingly, we observed a strong reduction in enzymatic activity for most of the mutant proteins in an enzymatic assay. Finally, we demonstrate that PLD1 inhibition decreased endothelial-mesenchymal transition, an established pivotal early step in valvulogenesis. In conclusion, our study provides a more detailed understanding of disease mechanisms and phenotypic expression associated with PLD1 loss of function.Genetics of disease, diagnosis and treatmen