Hopfish algebras

We introduce a notion of "hopfish algebra" structure on an associative algebra, allowing the structure morphisms (coproduct, counit, antipode) to be bimodules rather than algebra homomorphisms. We prove that quasi-Hopf algebras are examples of hopfish algebras. We find that a hopfish structure on the commutative algebra of functions on a finite set G is closely related to a "hypergroupoid" structure on G. The Morita theory of hopfish algebras is also discussed.Comment: 24 page

The Molecular Pathogenesis Of Cerebral Cavernous Malformations

Cerebral cavernous malformation (CCM) is a human genetic, cerebrovascular disease that is caused by loss of function mutations in three non-homologous protein coding genes: KRIT1, CCM2, and PDCD10. These proteins form a heterotrimeric CCM adaptor complex that is required in endothelial cells to prevent disease. How loss of this complex causes disease remains unknown. Here, utilizing a neonatal mouse model of disease, we demonstrate that the CCM complex negatively regulates Mitogen-Activated Protein Kinase Kinase Kinase 3 (MAP3K3 aka MEKK3) signaling in endothelial cells. During disease, loss of the CCM complex results in gain of MEKK3 signaling and pathologic overexpression of downstream target transcription factors Kruppel-like Factor 2 and Kruppel-like factor 4 (KLF2 and KLF4). This endothelial MEKK3-KLF2/4 signaling pathway represents the proximal signaling events that are required for lesion formation. If the CCM complex negatively regulates MEKK3 signaling, what are the upstream activators of MEKK3 in the context of disease? We demonstrate that gram-negative bacterial infection and lipopolysaccharide (LPS) activation of endothelial Toll-like receptor 4 (TLR4) drives MEKK3 signaling to stimulate lesion formation. Commensal bacteria in the gut microbiome produce the vast majority of endogenous LPS. We further show through germ-free and broad-spectrum antibiotic experiments, along with 16S fecal analysis of mice spontaneously resistant to lesion formation, that the gram-negative, bacterial microbiome is a primary driver of lesion formation. These studies reveal that endothelial TLR4—MEKK3—KLF2/4 signaling is required for lesion formation and that inhibition of this pathway may be of therapeutic value for CCM patients. They further demonstrate an unexpected role for the gut microbiome in this cerebrovascular disease and suggest that manipulation of host-microbiome interactions may be a viable therapeutic strategy for this lifelong, progressive disease

Characterization of a novel scaffold for tissue engineering

Thesis (MSD)--Boston University, Goldman School of Dental Medicine, 2006 (Dept. of Biomaterials).Includes bibliography: leaves 93-100.Bone regeneration using degradable scaffolds gives clinicians an alternative approach to the repair of damaged tissue while avoiding the need for a permanent implant. The composition of the scaffold material is vital to the success of bone regeneration. The scaffold material used should display biocompatibility, degradability, mechanical integrity, and osteoconductivity. Scaffolds used in this study were made by the melt molding/particulate leaching technique . The synthetic polymer, poly(DL-lactic-coglycolic acid) (PLGA) was used in this study to construct the three dimensional porous scaffolds. This provided the mechanical integrity for scaffold. Bioactive inorganic element (BIE) was incorporated into the scaffold to promote osteogenesis. NaCl was used as a water soluble porogen to create porosities. The objective of this study was to characterize the mechanical strength and solubility of scaffolds with different compositions of PLGNBIE with varying porosities. Scaffolds were made into cylinders 5mm in diameter by 5mm in height. Compressive strength of the scaffolds was tested using an Instron Universal Testing Machine using the femur bone of rabbits with similar dimensions as controls. Solubility of silicon was tested by electron dispersed x-ray anlysis of scaffolds and Fourier Transforming Infrared Spectroscopy of culture medium used in the incubation of the scaffolds at 37°C. Results of compressive strength test indicate that scaffolds with at least 60% PLGA by weight and with no more than 50% porosity has comparable compressive strength to rabbit bone. Scaffolds with more BIE released more silicon as measured by SiOH bond compared to scaffolds with less BIE. Scaffolds with 50% porosity and 50% bioactive inorganic element showed up to 56.6 mg of silicon released into culture medium by 28 days

Self-Organized Criticality in Non-Conserved Systems

The origin of self-organized criticality in a model without conservation law (Olami, Feder, and Christensen, Phys. Rev. Lett. {\bf 68}, 1244 (1992)) is studied. The homogeneous system with periodic boundary condition is found to be periodic and neutrally stable. A change to open boundaries results in the invasion of the interior by a ``self-organized\u27\u27 region. The mechanism for the self-organization is closely related to the synchronization or phase-locking of the individual elements with each other. A simplified model of marginal oscillator locking on a directed lattice is used to explain many of the features in the non-conserved model: in particular, the dependence of the avalanche-distribution exponent on the conservation parameter $\alpha$ is examined