Hom Quandles

If $A$ is an abelian quandle and $Q$ is a quandle, the hom set $\mathrm{Hom}(Q,A)$ of quandle homomorphisms from $Q$ to $A$ has a natural quandle structure. We exploit this fact to enhance the quandle counting invariant, providing an example of links with the same counting invariant values but distinguished by the hom quandle structure. We generalize the result to the case of biquandles, collect observations and results about abelian quandles and the hom quandle, and show that the category of abelian quandles is symmetric monoidal closed.Comment: 15 pages; revision 1 removes an incorrect remark; revision 2 corrects some small typos. To appear in J. Knot Theory Ramification

Linking Light Scalar Modes with A Small Positive Cosmological Constant in String Theory

Based on the studies in Type IIB string theory phenomenology, we conjecture that a good fraction of the meta-stable de Sitter vacua in the cosmic stringy landscape tend to have a very small cosmological constant $\Lambda$ when compared to either the string scale $M_S$ or the Planck scale $M_P$, i.e., $\Lambda \ll M_S^4 \ll M_P^4$. These low lying de Sitter vacua tend to be accompanied by very light scalar bosons/axions. Here we illustrate this phenomenon with the bosonic mass spectra in a set of Type IIB string theory flux compactification models. We conjecture that small $\Lambda$ with light bosons is generic among de Sitter solutions in string theory; that is, the smallness of $\Lambda$ and the existence of very light bosons (may be even the Higgs boson) are results of the statistical preference for such vacua in the landscape. We also discuss a scalar field $\phi^3/\phi^4$ model to illustrate how this statistical preference for a small $\Lambda$ remains when quantum loop corrections are included, thus bypassing the radiative instability problem.Comment: 35 pages, 7 figures; added subsection: Finite Temperature and Phase Transitio

Perfusion Cell Seeding and Expansion in Dual Mechanical Stimulation Bioreactor for In Vitro Tissue Development

BACKGROUND: Engineered tissues are an exciting potential source of small diameter vascular grafts due to limited supply and patency of available alternatives. Engineered tissue vascular grafts (ETVGs) will provide physiological function that resembles native arteries and maintain the required mechanical properties as they integrate with host tissue. Mechanical stimulation during incubation encourages proper cell alignment and increases extracellular matrix deposition. The enhanced organization of the engineered tissue leads to improved compliance over synthetic alternatives without sacrificing strength and may lead to better integration in vivo. METHODS: We have developed a bioreactor that mechanically trains grafts during incubation. To test the seeding efficiency of the bioreactor, rat vascular smooth muscle cells (VSMC) were seeded onto electrospun PCL scaffolds by perfusion at various cell concentrations then incubated Page | 15 for 1 week under static conditions. We assessed gross morphology with H&E; collagen with picrosirius red; and VSMC density with DAPI. ETVGs were further evaluated with mechanical testing and scanning electron microscopy to evaluate mechanical and microstructural properties. RESULTS: Cells were successfully seeded evenly onto the luminal surface of electrospun PCL scaffolds. Cells remained viable and continued to proliferate and deposit ECM throughout incubation. CONCLUSIONS: Progress in the ETVG paradigm requires a systematic approach toward better understanding of the cause-effect interplay between implant properties, host reactions, and their modulation with controllable parameters. Future directions involve the assessment of the effects of mechanical training on growth and remodeling of engineered tissues in vitro and subsequent effects on the foreign body response post-implantation in a murine model.https://scholarscompass.vcu.edu/gradposters/1115/thumbnail.jp

4-H Ewe and Lamb Project

June, 1956."University of Missouri College of Agriculture and the United States Department of Agriculture Cooperating"--Page [8].Title from caption