12 research outputs found
Eigenfunctions of expected value operators in the Wishart distribution, II
AbstractLet V = (vij) denote the k × k symmetric scatter matrix following the Wishart distribution W(k, n, Σ). The problem posed is to characterize the eigenfunctions of the expectation operators of the Wishart distribution, i.e., those scalar-valued functions f(V) such that (Enf)(V) = λn,kf(V). A finite sequence of polynomial eigenspaces, EP spaces, exists whose direct sum is the space of all homogeneous polynomials. These EP subspaces are invariant and irreducible under the action of the congruence transformation V → T′VT. Each of these EP subspaces contains an orthogonally invariant subspace of dimension one. The number of EP subspaces is determined and eigenvalues are computed. Bi-linear expansions of |I + VA|−n2 and (tr VA)r into eigenfunctions are given. When f(V) is an EP polynomial, then f(V−1) is an EP function. These EP subspaces are identical to the more abstractly defined polynomial subspaces studied by James
Candidate CSPG4 mutations and induced pluripotent stem cell modeling implicate oligodendrocyte progenitor cell dysfunction in familial schizophrenia
Schizophrenia is highly heritable, yet its underlying pathophysiology remains largely unknown. Among the most well-replicated findings in neurobiological studies of schizophrenia are deficits in myelination and white matter integrity; however, direct etiological genetic and cellular evidence has thus far been lacking. Here, we implement a family-based approach for genetic discovery in schizophrenia combined with functional analysis using induced pluripotent stem cells (iPSCs). We observed familial segregation of two rare missense mutations in Chondroitin Sulfate Proteoglycan 4 (CSPG4) (c.391G > A [p.A131T], MAF 7.79 × 10−5 and c.2702T > G [p.V901G], MAF 2.51 × 10−3). The CSPG4A131T mutation was absent from the Swedish Schizophrenia Exome Sequencing Study (2536 cases, 2543 controls), while the CSPG4V901G mutation was nominally enriched in cases (11 cases vs. 3 controls, P = 0.026, OR 3.77, 95% CI 1.05–13.52). CSPG4/NG2 is a hallmark protein of oligodendrocyte progenitor cells (OPCs). iPSC-derived OPCs from CSPG4A131T mutation carriers exhibited abnormal post-translational processing (P = 0.029), subcellular localization of mutant NG2 (P = 0.007), as well as aberrant cellular morphology (P = 3.0 × 10−8), viability (P = 8.9 × 10−7), and myelination potential (P = 0.038). Moreover, transfection of healthy non-carrier sibling OPCs confirmed a pathogenic effect on cell survival of both the CSPG4A131T (P = 0.006) and CSPG4V901G (P = 3.4 × 10−4) mutations. Finally, in vivo diffusion tensor imaging of CSPG4A131T mutation carriers demonstrated a reduction of brain white matter integrity compared to unaffected sibling and matched general population controls (P = 2.2 × 10−5). Together, our findings provide a convergence of genetic and functional evidence to implicate OPC dysfunction as a candidate pathophysiological mechanism of familial schizophrenia
ACO2 homozygous missense mutation associated with complicated hereditary spastic paraplegia
Objective: To identify the clinical characteristics and genetic etiology of a family affected with hereditar