A Casson-Lin type invariant for links

We define an integer valued invariant for two-component links in S^3 by counting projective SU(2) representations of the link group having non-trivial second Stiefel-Whitney class. We show that our invariant is, up to sign, the linking number of the link. Our construction generalizes that of X.-S. Lin who defined a similar invariant for knots in S^3; his invariant equals half the knot signature.Comment: New set of generators for the braid group in Section

Entropic Bonding in Nanoparticle and Colloidal Systems

Scientists and engineers will create the next generation of materials by precisely controlling their microstructure. One of the most promising and effective methods to control material microstructure is self-assembly, in which the properties of constituent “particles” guide their assembly into the desired structure. Self- assembly mechanisms rely on both inherent interactions between particles and emergent interactions resulting from the collective effects of all particles in the system. These emergent effects are of interest as they provide minimal mechanisms to control self-assembly, and thus can be used in conjunction with other assembly methods to create novel materials. Literature shows that complex phases can be obtained solely from hard, anisotropic particles, which are attracted via an emergent Directional Entropic Force. This thesis shows that this force gives rise to the entropic bond, a mesoscale analog to the chemical bond. In Chapter 3 I investigate the self- assembly of a system from a random tiling into an ordered crystal. Analysis of the emergent directional entropic forces reveal the importance of shape in the final self-assembled system as well as the ability for shape manipulation to control the final self-assembled structure. In Chapter 4, I investigate three-dimensional analogs of two-dimensional systems in Chapter 3, explaining the self-assembly behavior of these systems via understanding of the emergent directional entropic forces. In Chapter 5 I investigate the nature of the entropic bond, investigating two-dimensional systems of hexagonal nanoplatelets. The Entropic bond is quantified, and the ability to manipulate the bonds to produce similar self- assembly behavior to chemically-functionalized nanoparticles is demonstrated. Finally, Chapter 6 investigates the phase transitions of the general class of particle studied in Chapter 5, showing the ability for particle shape to change the type of phase transition present in a system of nanoparticles as well as stabilize phases otherwise not found. As a whole, this work details the nature of the entropic bond and its use in directing the self-assembly of systems of non- interacting anisotropic particles.PHDMaterials Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144096/1/harperic_1.pd

Unveiling Management’s Crystal Ball

The article focuses on the item 303 disclosures of U.S. Securities and Exchange Commission for preventing private securities fraud causes of action by the companies, and mentions reporting companies to disclose information about the companies\u27 plans for the future of their businesses

Food Policy Councils: Lessons Learned

As the food and financial crises bring fresh urgency to concerns over hunger, food access, public health, labor and economic development -- citizens and governments are beginning to connect these issues back to the food system as a whole. Councils are springing up across North America to "connect the dots"1 between the growing number of neighborhood food initiatives and communities forging policies for just, healthy food systems. Food Policy Councils act as both forums for food issues and platforms for coordinated action. The first Food Policy Council started in 1982 in Knoxville, Tennessee. Since then Food Policy Councils have been established at state, local and regional levels across the county. Some have remarkable success stories. Others have failed, disbanded, or spun-off into other service and non-profit organizations.What lessons can be taken from North America's three-decade experiment in formulating local food policy? Food Policy Councils: Lessons Learned is an assessment based on an extensive literature review and testimony from 48 individual interviews with the people most involved in Food Policy Councils

Horror Unmasked: Truth or Fiction?

A review of: A Country Unmasked: Inside South Africa’s Truth and Reconciliation Commission by Alex Boraine. New York: Oxford University Press, 2001. 448pp

Virtual knot groups and almost classical knots

We define a group-valued invariant of virtual knots and relate it to various other group-valued invariants of virtual knots, including the extended group of Silver-Williams and the quandle group of Manturov and Bardakov-Bellingeri. A virtual knot is called almost classical if it admits a diagram with an Alexander numbering, and in that case we show that the group factors as a free product of the usual knot group and Z. We establish a similar formula for mod p almost classical knots, and we use these results to derive obstructions to a virtual knot K being mod p almost classical. Viewed as knots in thickened surfaces, almost classical knots correspond to those that are homologically trivial. We show they admit Seifert surfaces and relate their Alexander invariants to the homology of the associated infinite cyclic cover. We prove the first Alexander ideal is principal, recovering a result first proved by Nakamura et al. using different methods. The resulting Alexander polynomial is shown to satisfy a skein relation, and its degree gives a lower bound for the Seifert genus. We tabulate almost classical knots up to 6 crossings and determine their Alexander polynomials and virtual genus.Comment: 44 page