The Numerical Solution of the Helmholtz Equation for the Bloodcell Shape: Mars Project

The objective of this research is to investigate numerical solutions of several boundary value problems for the Helmholtz equation for the shape of a Biconcave Disk. The boundary value problems this research mainly focuses on are the Neumann and Robin boundary problems. The Biconcave Disk is a closed, simply connected, bounded shape modi ed from a sphere where the two sides concave toward the center, mapped by a sine curve. There are some numerical issues in this type of analysis; any integration is a ected by the wave number k, because of the oscillatory behavior of the fundamental solution of the Helmholtz equation. This project was funded by NASA RI Space Grant and the NASA EPSCoR Grant for testing of boundary conditions for the Biconcave Disk. This method has already been investigated for the sphere, ellipsoid, superellipsoid, and the oval of cassini. The primary purpose of this research is to extend those known results to the Biconcave Disk with calculating the possibility of this shape acquiring sucient conditions to be part of a spacecraft that might one day land on planet Mars

Minimal Length Maximal Green Sequences and Triangulations of Polygons

We use combinatorics of quivers and the corresponding surfaces to study maximal green sequences of minimal length for quivers of type $\mathbb{A}$. We prove that such sequences have length $n+t$, where $n$ is the number of vertices and $t$ is the number of 3-cycles in the quiver. Moreover, we develop a procedure that yields these minimal length maximal green sequences.Comment: 22 pages, 1 figur

Discovery and Functional Analysis of a Retinitis Pigmentosa Gene, C2ORF71

Retinitis pigmentosa is a genetically heterogeneous group of inherited ocular disorders characterized by progressive photoreceptor cell loss, night blindness, constriction of the visual field, and progressive visual disability. Homozygosity mapping and gene expression studies identified a 2 exon gene, C2ORF71. The encoded protein has no homologs and is highly expressed in the eye, where it is specifically expressed in photoreceptor cells. Two mutations were found in C2ORF71 in human RP patients: A nonsense mutation (p.W253X) in the first exon is likely to be a null allele; the second, a missense mutation (p.I201F) within a highly conserved region of the protein, leads to proteosomal degradation. Bioinformatic and functional studies identified and validated sites of lipid modification within the first three amino acids of the C2ORF71 protein. Using morpholino oligonucleotides to knockdown c2orf71 expression in zebrafish results in visual defects, confirming that C2ORF71 plays an important role in the development of normal vision. Finally, localization of C2ORF71 to primary cilia in cultured cells suggests that the protein is likely to localize to the connecting cilium or outer segment of photoreceptor cells

The gene involved in X-linked agammaglobulinaemia is a member of the src family of protein-tyrosine kinases

X-linked agammaglobulinaemia (XLA) is a human immunodeficiency caused by failure of pre-B cells in the bone marrow to develop into circulating mature B cells. A novel gene has been isolated which maps to the XLA locus, is expressed in B cells, and shows mutations in families with the disorder. The gene is a member of the src family of proto-oncogenes which encode protein-tyrosine kinases. This is, to our knowledge, the first evidence that mutations in a src-related gene are involved in human genetic disease