Discrete Torsion, AdS/CFT and duality

We analyse D-branes on orbifolds with discrete torsion, extending earlier results. We analyze certain Abelian orbifolds of the type C^3/ \Gamma, where \Gamma is given by Z_m x Z_n, for the most general choice of discrete torsion parameter. By comparing with the AdS/CFT correspondence, we can consider different geometries which give rise to the same physics. This identifies new mirror pairs and suggests new dualities at large N. As a by-product we also get a more geometric picture of discrete torsion.Comment: JHEP format, 6 figure

Resolution of Stringy Singularities by Non-commutative Algebras

In this paper we propose a unified approach to (topological) string theory on certain singular spaces in their large volume limit. The approach exploits the non-commutative structure of D-branes, so the space is described by an algebraic geometry of non-commutative rings. The paper is devoted to the study of examples of these algebras. In our study there is an auxiliary commutative algebraic geometry of the center of the (local) algebras which plays an important role as the target space geometry where closed strings propagate. The singularities that are resolved will be the singularities of this auxiliary geometry. The singularities are resolved by the non-commutative algebra if the local non-commutative rings are regular. This definition guarantees that D-branes have a well defined K-theory class. Homological functors also play an important role. They describe the intersection theory of D-branes and lead to a formal definition of local quivers at singularities, which can be computed explicitly for many types of singularities. These results can be interpreted in terms of the derived category of coherent sheaves over the non-commutative rings, giving a non-commutative version of recent work by M. Douglas. We also describe global features like the Betti numbers of compact singular Calabi-Yau threefolds via global holomorphic sections of cyclic homology classes.Comment: 36 pages, Latex, 5 figures. v2:Reference adde

Target shape dependence in a simple model of receptor-mediated endocytosis and phagocytosis

Phagocytosis and receptor-mediated endocytosis are vitally important particle uptake mechanisms in many cell types, ranging from single-cell organisms to immune cells. In both processes, engulfment by the cell depends critically on both particle shape and orientation. However, most previous theoretical work has focused only on spherical particles and hence disregards the wide-ranging particle shapes occurring in nature, such as those of bacteria. Here, by implementing a simple model in one and two dimensions, we compare and contrast receptor-mediated endocytosis and phagocytosis for a range of biologically relevant shapes, including spheres, ellipsoids, capped cylinders, and hourglasses. We find a whole range of different engulfment behaviors with some ellipsoids engulfing faster than spheres, and that phagocytosis is able to engulf a greater range of target shapes than other types of endocytosis. Further, the 2D model can explain why some nonspherical particles engulf fastest (not at all) when presented to the membrane tip-first (lying flat). Our work reveals how some bacteria may avoid being internalized simply because of their shape, and suggests shapes for optimal drug delivery.Comment: 18 pages, 5 figure

Class Certification and the Substantive Merits

The United States Supreme Court, in its 1974 decision, Eisen v. Carlisle & Jacquelin, held that judges should not conduct a preliminary inquiry into the merits of a suit as part of the decision whether to certify a class. The federal courts have struggled ever since to honor Eisen\u27s bar while still conducting a credible certification analysis-a task complicated by the fact that merits-related factors are often relevant to Rule 23 requirements. The result is a muddled body of case law in which courts tend to certify generously and avoid inquiring into the merits of substantive issues even when those issues are crucial to the certification analysis. This approach creates high social costs by inviting frivolous and weak class action suits. This Article argues that the Eisen rule should be abolished. Trial judges should assess competing evidence, not just allegations, and should evaluate case strength whenever the specific requirements of Rule 23 call for an inquiry into merits-related factors. For example, a party relying on a substantive issue to show commonality or predominance should have to demonstrate a likelihood of success on the issue. The Article also goes further and recommends that judges always conduct a preliminary inquiry into the merits before certifying a class, regardless of whether merits-related factors are directly relevant to a specific requirement of Rule 23. The Article first reviews the history of the Eisen rule and surveys the current state of the law, before turning to a policy analysis of the rule\u27s effects. The policy discussion criticizes the traditional arguments and then offers a systematic evaluation of error and process costs. Error costs must be evaluated in light of the extremely high probability of postcertification settlement. Eisen\u27s liberal approach creates a substantial risk of erroneous certification grants that cannot be corrected later when a case settles. This risk coupled with the high likelihood of settlement invites frivolous and weak class action suits. The result is a serious error-cost problem with regard to certification. At the same time, requiring a merits review at the certification stage increases the risk of erroneous certification denials. But for several reasons this risk is not likely to increase dramatically, and the associated costs are not likely to be large. The net result therefore supports a merits inquiry, and this conclusion remains valid even after process costs are added to the policy mix

Homotopy hyperbolic 3-manifolds are hyperbolic

This paper introduces a rigorous computer-assisted procedure for analyzing hyperbolic 3-manifolds. This procedure is used to complete the proof of several long-standing rigidity conjectures in 3-manifold theory as well as to provide a new lower bound for the volume of a closed orientable hyperbolic 3-manifold

Free personal care for older people : a wider perspective on its costs

The paper comments on the so-called "Free Personal Care (FPC)" policy established in Scotland in 2002. FPC is the legal entitlement of people aged 65 and older, who have been assessed by the council as having personal care needs, to receive services that will assist them in their day-to-day activities. One view is that FPC may not be affordable in its current form because population ageing will increase dramatically the numbers eligible for assistance in the future. This paper discusses ways in which FPC may actually lower the total per-person cost of accommodating Scotland's ageing population

Characterization and Dynamics of Substituted Ruthenacyclobutanes Relevant to the Olefin Cross-Metathesis Reaction

The reaction of the phosphonium alkylidene [(H_(2)IMes)RuCl2═CHP(Cy)_3)]^(+) BF_(4)^− with propene, 1-butene, and 1-hexene at −45 °C affords various substituted, metathesis-active ruthenacycles. These metallacycles were found to equilibrate over extended reaction times in response to decreases in ethylene concentrations, which favored increased populations of α-monosubstituted and α,α′-disubstituted (both cis and trans) ruthenacycles. On an NMR time scale, rapid chemical exchange was found to preferentially occur between the β-hydrogens of the cis and trans stereoisomers prior to olefin exchange. Exchange on an NMR time scale was also observed between the α- and β-methylene groups of the monosubstituted ruthenacycle (H_(2)IMes)Cl_(2)Ru(CHRCH_(2)CH_(2)) (R = CH_3, CH_(2)CH_3, (CH_2)_)_(3)CH_3). EXSY NMR experiments at −87 °C were used to determine the activation energies for both of these exchange processes. In addition, new methods have been developed for the direct preparation of metathesis-active ruthenacyclobutanes via the protonolysis of dichloro(1,3-bis(2,4,6-trimethylphenyl)-2-imidazolidinylidene)(benzylidene) bis(pyridine)ruthenium(II) and its 3-bromopyridine analogue. Using either trifluoroacetic acid or silica-bound toluenesulfonic acid as the proton source, the ethylene-derived ruthenacyclobutane (H_(2)IMes)Cl_(2)Ru(CH_(2)CH_(2)CH_(2)) was observed in up to 98% yield via NMR at −40 °C. On the basis of these studies, mechanisms accounting for the positional and stereochemical exchange within ruthenacyclobutanes are proposed, as well as the implications of these dynamics toward olefin metathesis catalyst and reaction design are described