Open-closed TQFTs extend Khovanov homology from links to tangles

We use a special kind of 2-dimensional extended Topological Quantum Field Theories (TQFTs), so-called open-closed TQFTs, in order to extend Khovanov homology from links to arbitrary tangles, not necessarily even. For every plane diagram of an oriented tangle, we construct a chain complex whose homology is invariant under Reidemeister moves. The terms of this chain complex are modules of a suitable algebra A such that there is one action of A or A^op for every boundary point of the tangle. We give examples of such algebras A for which our tangle homology theory reduces to the link homology theories of Khovanov, Lee, and Bar-Natan if it is evaluated for links. As a consequence of the Cardy condition, Khovanov's graded theory can only be extended to tangles if the underlying field has finite characteristic. In all cases in which the algebra A is strongly separable, i.e. for Bar-Natan's theory in any characteristic and for Lee's theory in characteristic other than 2, we also provide the required algebraic operation for the composition of oriented tangles. Just as Khovanov's theory for links can be recovered from Lee's or Bar-Natan's by a suitable spectral sequence, we provide a spectral sequence in order to compute our tangle extension of Khovanov's theory from that of Bar-Natan's or Lee's theory. Thus, we provide a tangle homology theory that is locally computable and still strong enough to recover characteristic p Khovanov homology for links.Comment: 56 pages, LaTeX2e with xypic and pstricks macro

Do \u27Off-Site\u27 Adult Businesses Have Secondary Effects? Legal Doctrine, Social Theory, and Empirical Evidence

Recent federal court decisions appear to limit the ability of cities to mitigate the ambient crime risks associated with adult entertainment businesses. In one instance, a court has assumed that criminological theories do not apply to “off-site” adult businesses. After developing the legal doctrine of secondary effects, we demonstrate that the prevailing criminological theory applies to all adult business models. To corroborate the theory, we report the results of a before/after quasi-experiment for an off-site adult business. When an off-site adult business opens, ambient crime risk doubles compared to a control area. As theory predicts, moreover, ambient victimization risk is most acute in night-time hours. The theoretical development and empirical results have obvious implications for the evolving legal doctrine of secondary effects

Global Spinors and Orientable Five-Branes

Fermion fields on an M-theory five-brane carry a representation of the double cover of the structure group of the normal bundle. It is shown that, on an arbitrary oriented Lorentzian six-manifold, there is always an Sp(2) twist that allows such spinors to be defined globally. The vanishing of the arising potential obstructions does not depend on spin structure in the bulk, nor does the six-manifold need to be spin or spin-C. Lifting the tangent bundle to such a generalised spin bundle requires picking a generalised spin structure in terms of certain elements in the integral and modulo-two cohomology of the five-brane world-volume in degrees four and five, respectively.Comment: 18 pages, LaTeX; v2: version to appear in JHE

The Association of Adult Businesses with Secondary Effects: Legal Doctrine, Social Theory, and Empirical Evidence

In the decade since the U.S. Supreme Court’s decision in Alameda Books v. City of Los Angeles, 535 U.S. 425 (2002), the adult entertainment industry has attacked the legal rationale local governments rely upon as the justification for their regulation of adult businesses: that such businesses are associated with so-called negative secondary effects. These attacks have taken a variety of forms, including: trying to subject the studies of secondary effects relied upon by local governments to the Daubert standard for admission of scientific evidence in federal litigation; producing studies that purport to show no association between adult businesses and negative secondary effects in a given jurisdiction; and claims that distinct business models and/or specific local conditions are not associated with the secondary effects demonstrated in the studies relied on by many local governments. In this Article, we demonstrate that, contrary to the industry’s claims, methodologically appropriate studies confirm criminological theory’s prediction that adult businesses are associated with heightened incidences of crime regardless of jurisdiction, business model or location and thus, such studies should have legal and policy effects supporting regulation of adult businesses

Digitally-produced image comparison of three, 90 diopter-equivalent lenses: Subjective and objective findings

Purpose: To evaluate the image quality of retinal structures as obtained by three high plus lenses manufactured by the Yolk company to determine if any of the lens types provided a better quality of digital image. Methods: Digital images of two different patients\u27 left and right optic nerve heads (ONH) and left and right maculae (MAC) were obtained with three high plus lenses in conjunction with a biomicroscope. One of each of the following three lenses were used during the study: 90 Diopter Classic (90D), Super Field (SF) and Digital Wide Field (DWF). A total of 10 optometric physicians, who were faculty of an accredited school of optometry at the time of the study, were then asked to view 30 pairs of simultaneously presented photographs and select the image of higher quality. The paired photographs consisted of images of either the same optic nerve head or same macula of the one specific patient, as taken with two different lenses. Three sets of identical images were randomly presented to screen for left- or righthandedness. The digital images were also evaluated by Adobe Photoshop for color and luminosity values within a defined area. Results: Objective results showed that there was no statistically significant difference between mean color and luminosity of the ONH and MAC images as produced by the 90D, SF and DWF lenses: p = 0.542, p = 0.587, p = 0.232 and p = 0.186. Subjective results were statistically significant for selecting the 90D lens as producing the better ONH image quality 1 (p == 0.041). While not statistically significant (p == 0.165), the subjects followed a similar trend in choosing the 90D lens as having better quality of the MAC images. Conclusions: The 90D lens appears to produce subjectively better quality in digital images of the posterior pole

Validation of the Pulmonary Function System for Use on the International Space Station

Aerobic deconditioning occurs during long duration space flight despite the use of exercise countermeasures (Convertino, 1996). As a part of International Space Station (ISS) medical operations, periodic tests designed to estimate aerobic capacity are performed to track changes in aerobic fitness and to determine the effectiveness of exercise countermeasures. These tests are performed prior to, during, and after missions of greater than 30 days in duration. Crewmembers selected for missions aboard the ISS perform a graded exercise test on a cycle ergometer approximately 270 days prior to their scheduled launch date in order to measure peak oxygen consumption (VO2PK) and peak heart rate (HRpk). Approximately 30 to 45 days prior to launch, crewmembers perform a submaximal cycle ergometer test at work rates set to elicit 25, 50 and 75% of their pre-flight VO2PK. This test, known as the Periodic Fitness Evaluation (PFE), serves as a baseline measure to which subsequent in-and post-flight exercise tests are compared. While onboard the ISS, crewmembers are normally scheduled to perform the PFE beginning with flight day (FD) 14 and every 30 days thereafter. The PFE is also conducted 5 and 30 days following flight. Using PFE data, aerobic fitness is estimated by quantifying the VO2 vs. HR relationship using linear regression and calculating the VO2 that would occur at the crewmember s previously measured HRpk. Currently, for data collected during flight, this technique assumes that the pre- vs. in-flight oxygen consumption per given cycle workload is similar. However, the validity of this assumption is based upon a sparse amount of data collected during the Skylab era (Michel, et al. 1977). The method of using heart rate and cycle ergometer work rates has been used to estimate aerobic fitness in normal gravity (Astrand and Ryhming, 1954; Lee, 1993). Due to spaceflight induced physiological alterations, such as shifts in extracellular fluid (e.g. plasma) volume, this method may not be valid during space flight. In addition, the ergometer onboard ISS is vibration-isolated and moves with the astronaut s application of force into the pedals. The effect of this movement on the VO2 of cycle exercise on ISS has not been quantified

Thermodynamic metrics and optimal paths

A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a Riemannian manifold on the space of thermodynamic states. Within the linear-response regime, this metric structure controls the dissipation of finite-time transformations, and bestows optimal protocols with many useful properties. We discuss the connection to the existing thermodynamic length formalism, and demonstrate the utility of this metric by solving for optimal control parameter protocols in a simple nonequilibrium model.Comment: 5 page

On the integral cohomology of smooth toric varieties

Let $X_\Sigma$ be a smooth, not necessarily compact toric variety. We show that a certain complex, defined in terms of the fan $\Sigma$, computes the integral cohomology of $X_\Sigma$, including the module structure over the homology of the torus. In some cases we can also give the product. As a corollary we obtain that the cycle map from Chow groups to integral Borel-Moore homology is split injective for smooth toric varieties. Another result is that the differential algebra of singular cochains on the Borel construction of $X_\Sigma$ is formal.Comment: 10 page