On non-L2L^2 solutions to the Seiberg-Witten equations

We show that a previous paper of Freund describing a solution to the Seiberg-Witten equations has a sign error rendering it a solution to a related but different set of equations. The non-$L^2$ nature of Freund's solution is discussed and clarified and we also construct a whole class of solutions to the Seiberg-Witten equations.Comment: 8 pages, Te

Causes and correction of dissatisfaction after implantation of presbyopia-correcting intraocular lenses

PURPOSE: The purpose of this study was to assess the causes and possible solutions for patient dissatisfaction after the implantation of presbyopia-correcting intraocular lenses (IOLs). METHODS: This study was a retrospective review of clinical records. All patients who were seen between January 2009 and December 2013 whose primary reason for consultation was dissatisfaction with visual performance after presbyopia-correcting IOL implantation were included in the study. A single treating physician, who determined the most probable cause of dissatisfaction, decided which interventions to pursue following the initial consultation. RESULTS: Data from 74 eyes of 49 patients were analyzed. The most common cause for complaint was blurry or foggy vision both for distance and near (68%). Complaints were most frequently attributed to residual refractive error (57%) and dry eye (35%). The most common interventions pursued were treatment of refractive error with glasses or contact lenses (46%) and treatment for dry eye (24%). Corneal laser vision correction was done in 8% of eyes; 7% required an IOL exchange. After the interventions, 45% of patients had completed resolution of symptoms, 23% of patients were partially satisfied with the results, and 32% remained completely dissatisfied with the final results. CONCLUSION: The most identifiable causes of dissatisfaction after presbyopia-correcting IOL implantation are residual refractive error and dry eye. Most patients can be managed with conservative treatment, though a significant number of patients remained unsatisfied despite multiple measures

In vivo distribution and cytopathology of variants of human immunodeficiency virus type 1 showing restricted sequence variability in the V3 loop

The distribution, cell tropism, and cytopathology in vivo of human immunodeficiency virus (HIV) was investigated in postmortem tissue samples from a series of HIV-infected individuals who died either of complications associated with AIDS or for unrelated reasons while they were asymptomatic. Proviral sequences were detected at a high copy number in lymphoid tissue of both presymptomatic patients and patients with AIDS, whereas significant infection of nonlymphoid tissue such as that from brains, spinal cords, and lungs were confined to those with AIDS. V3 loop sequences from both groups showed highly restricted sequence variability and a low overall positive charge of the encoded amino acid sequence compared with those of standard laboratory isolates of HIV type 1 (HIV-1). The low charge and the restriction in sequence variability were comparable to those observed with isolates showing a non-syncytium-inducing (NSI) and macrophage-tropic phenotype in vitro. All patients were either exclusively infected (six of seven cases) or predominantly infected (one case) with variants with a predicted NSI/macrophage-tropic phenotype, irrespective of the degree of disease progression. p24 antigen was detected by immunocytochemical staining of paraffin-fixed sections in the germinal centers within lymphoid tissue, although little or no antigen was found in areas of lymph node or spleen containing T lymphocytes from either presymptomatic patients or patients with AIDS. The predominant p24 antigen-expressing cells in the lungs and brains of the patients with AIDS were macrophages and microglia (in brains), frequently forming multinucleated giant cells (syncytia) even though the V3 loop sequences of these variants resembled those of NSI isolates in vitro. These studies indicate that lack of syncytium-forming ability in established T-cell lines does not necessarily predict syncytium-forming ability in primary target cells in vivo. Furthermore, variants of HIV with V3 sequences characteristic of NSI/macrophage-tropic isolates form the predominant population in a range of lymphoid and nonlymphoid tissues in vivo, even in patients with AIDS

Quaternionic Monopoles

We present the simplest non-abelian version of Seiberg-Witten theory: Quaternionic monopoles. These monopoles are associated with Spin^h(4)-structures on 4-manifolds and form finite-dimensional moduli spaces. On a Kahler surface the quaternionic monopole equations decouple and lead to the projective vortex equation for holomorphic pairs. This vortex equation comes from a moment map and gives rise to a new complex-geometric stability concept. The moduli spaces of quaternionic monopoles on Kahler surfaces have two closed subspaces, both naturally isomorphic with moduli spaces of canonically stable holomorphic pairs. These components intersect along Donaldsons instanton space and can be compactified with Seiberg-Witten moduli spaces. This should provide a link between the two corresponding theories. Notes: To appear in CMP The revised version contains more details concerning the Uhlenbeck compactfication of the moduli space of quaternionic monopoles, and possible applications are discussed. Attention ! Due to an ununderstandable mistake, the duke server had replaced all the symbols "=" by "=3D" in the tex-file of the revised version we sent on February, the 2-nd. The command "\def{\ad}" had also been damaged !Comment: LaTeX, 35 page

Khovanov homology is an unknot-detector

We prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence beginning with the reduced Khovanov cohomology and abutting to a knot homology defined using singular instantons. We then show that the latter homology is isomorphic to the instanton Floer homology of the sutured knot complement: an invariant that is already known to detect the unknot.Comment: 124 pages, 13 figure

A note on monopole moduli spaces

We discuss the structure of the framed moduli space of Bogomolny monopoles for arbitrary symmetry breaking and extend the definition of its stratification to the case of arbitrary compact Lie groups. We show that each stratum is a union of submanifolds for which we conjecture that the natural $L^2$ metric is hyperKahler. The dimensions of the strata and of these submanifolds are calculated, and it is found that for the latter, the dimension is always a multiple of four.Comment: 17 pages, LaTe

Nonsingular solutions of Hitchin's equations for noncompact gauge groups

We consider a general ansatz for solving the 2-dimensional Hitchin's equations, which arise as dimensional reduction of the 4-dimensional self-dual Yang-Mills equations, with remarkable integrability properties. We focus on the case when the gauge group G is given by a real form of SL(2,C). For G=SO(2,1), the resulting field equations are shown to reduce to either the Liouville, elliptic sinh-Gordon or elliptic sine-Gordon equations. As opposed to the compact case, given by G=SU(2), the field equations associated with the noncompact group SO(2,1) are shown to have smooth real solutions with nonsingular action densities, which are furthermore localized in some sense. We conclude by discussing some particular solutions, defined on R^2, S^2 and T^2, that come out of this ansatz.Comment: 12 pages, 3 figures. To appear in Nonlinearit

Calorons, Nahm's equations on S^1 and bundles over P^1xP^1

The moduli space of solutions to Nahm's equations of rank (k,k+j) on the circle, and hence, of SU(2) calorons of charge (k,j), is shown to be equivalent to the moduli of holomorphic rank 2 bundles on P^1xP^1 trivialized at infinity with c_2=k and equipped with a flag of degree j along P^1x{0}. An explicit matrix description of these spaces is given by a monad constructio

The Ethics of Corporate Governance

How should corporate directors determine what is the right decision? For at least the past 30 years the debate has raged as to whether shareholder value should take precedence over corporate social responsibility when crucial decisions arise. Directors face pressure, not least from ethical investors, to do the good thing when they seek to make the right choice. Corporate governance theory has tended to look to agency theory and the need of boards to curb excessive executive power to guide directors' decisions. While useful for those purposes, agency theory provides only limited guidance. Supplementing it with the alternatives - stakeholder theory and stewardship theory - tends to put directors in conflict with their legal obligations to work in the interests of shareholders. This paper seeks to reframe the discussion about corporate governance in terms of the ethical debate between consequential, teleological approaches to ethics and idealist, deontological ones, suggesting that directors are - for good reason - more inclined toward utilitarian judgments like those underpinning shareholder value. But the problems with shareholder value have become so great that a different framework is needed: strategic value, with an emphasis on long-term value creation judged from a decidedly utilitarian standpoint