Finite dimensional approximations to Wiener measure and path integral formulas on manifolds

Certain natural geometric approximation schemes are developed for Wiener measure on a compact Riemannian manifold. These approximations closely mimic the informal path integral formulas used in the physics literature for representing the heat semi-group on Riemannian manifolds. The path space is approximated by finite dimensional manifolds consisting of piecewise geodesic paths adapted to partitions $P$ of $[0,1]$. The finite dimensional manifolds of piecewise geodesics carry both an $H^{1}$ and a $L^{2}$ type Riemannian structures $G^i_P$. It is proved that as the mesh of the partition tends to $0$, $$1/Z_P^i e^{- 1/2 E(\sigma)} Vol_{G^i_P}(\sigma) \to \rho_i(\sigma)\nu(\sigma)$$ where $E(\sigma )$ is the energy of the piecewise geodesic path $\sigma$, and for $i=0$ and $1$, $Z_P^i$ is a ``normalization'' constant, $Vol_{G^i_P}$ is the Riemannian volume form relative $G^i_P$, and $\nu$ is Wiener measure on paths on $M$. Here $\rho_1 = 1$ and $$\rho_0 (\sigma) = \exp( -1/6 \int_0^1 Scal(\sigma(s))ds )$$ where $Scal$ is the scalar curvature of $M$. These results are also shown to imply the well know integration by parts formula for the Wiener measure.Comment: 48 pages, latex2e using amsart and amssym

Bringing nature back into cities: urban land environments, indigenous cover and urban restoration

1. The restoration of urban ecosystems is an increasingly important strategy to maintain and enhance indigenous biodiversity as well as reconnecting people to the environment. High levels of endemism, the sensitivity of species that have evolved without humans, and the invasion of exotic species have all contributed to severe depletion of indigenous biodiversity in New Zealand. In this work, we analysed national patterns of urban biodiversity in New Zealand and the contribution that urban restoration can make to maximising and enhancing indigenous biodiversity. 2. We analysed data from two national databases in relation to the 20 largest New Zealand cities. We quantified existing indigenous biodiversity within cities, both within the core built up matrix and in centroid buffer zones of 5, 10 and 20 km around this urban centre. We analysed the type and frequency of land environments underlying cities as indicators of the range of native ecosystems that are (or can potentially be) represented within the broader environmental profile of New Zealand. We identified acutely threatened land environments that are represented within urban and periurban areas and the potential role of cities in enhancing biodiversity from these land environments. 3. New Zealand cities are highly variable in both landform and level of indigenous resource. Thirteen of 20 major land environments in New Zealand are represented in cities, and nearly three-quarters of all acutely threatened land environments are represented within 20 km of city cores nationally. Indigenous land cover is low within urban cores, with less than 2% on average remaining, and fragmentation is high. However, indigenous cover increases to more than 10% on average in the periurban zone, and the size of indigenous remnants also increases. The number of remaining indigenous landcover types also increases from only 5 types within the urban centre, to 14 types within 20 km of the inner urban cores. 4. In New Zealand, ecosystem restoration alone is not enough to prevent biodiversity loss from urban environments, with remnant indigenous cover in the urban core too small (and currently too degraded) to support biodiversity long-term. For some cities, indigenous cover in the periurban zone is also extremely low. This has significant ramifications for the threatened lowland and coastal environments that are most commonly represented in cities. Reconstruction of ecosystems is required to achieve a target of 10% indigenous cover in cities: the addition of land to land banks for this purpose is crucial. Future planning that protects indigenous remnants within the periurban zone is critical to the survival of many species within urban areas, mitigating the homogenisation and depletion of indigenous flora and fauna typical of urbanisation. A national urban biodiversity plan would help city councils address biodiversity issues beyond a local and regional focus, while encouraging predominantly local solutions to restoration challenges, based on the highly variable land environments, ecosystems and patch connectivity present within different urban areas

The institutional determinants of private equity involvement in business groups: The case of Africa

This study examines the governance attributes of post-IPO (initial public offering) retained ownership of private equity in business group constituent firms in contrast to their unaffiliated counterparts, in 202 newly listed firms in 22 emerging African economies. We adopt an actor centred institutional-theoretic perspective in rationalizing institutional voids and the advantages of maintained governance by both business angels (BA) and venture capital (VC) private equity. Our findings reveal private equity retain higher post-IPO ownership in business group constituents compared to unaffiliated firms and that this is inversely moderated in the context of improving institutional quality. Our result adds to the literature on multifocal corporate governance mechanisms

The influence of business groups on board composition in offshore financial multinational enterprises

Based on resource dependence theory we argue for an influence of business groups (BGs) on the board composition of constituent offshore financial multinational enterprises (FMNEs). Using a unique sample of 171 Caribbean FMNEs in an inter-island BG setting, we find BGs’ control in constituent firms to be indicative of the importance of the internal financing and intermediation within the group network. This control leads to a higher proportion of lawyers hired to the boards of directors in BG-constituent firms and supports the argument that lawyers provide skills in complex offshore regulatory frameworks that facilitate BGs’ optimal tax management. Furthermore, we observe that an increased adoption of shareholder rights governance by BG-constituent firms is associated with increased engagement with outside resource providers, increased potential conflicts of interest and hence a need for hiring more lawyers. Our interpretation is that offshore FMNEs have a need for more lawyers, whose legal skill is critical to the competitive advantage of FMNEs.publishedVersio

Determining the stellar masses of submillimetre galaxies: the critical importance of star formation histories

Submillimetre (submm) galaxies are among the most rapidly star-forming and most massive high-redshift galaxies; thus, their properties provide important constraints on galaxy evolution models. However, there is still a debate about their stellar masses and their nature in the context of the general galaxy population. To test the reliability of their stellar mass determinations, we used a sample of simulated submm galaxies for which we derived stellar masses via spectral energy distribution (SED) modelling (with Grasil, Magphys, Hyperz and LePhare) adopting various star formation histories (SFHs). We found that the assumption of SFHs with two independent components leads to the most accurate stellar masses. Exponentially declining SFHs (tau) lead to lower masses (albeit still consistent with the true values), while the assumption of single-burst SFHs results in a significant mass underestimation. Thus, we conclude that studies based on the higher masses inferred from fitting the SEDs of real submm galaxies with double SFHs are most likely to be correct, implying that submm galaxies lie on the high-mass end of the main sequence of star-forming galaxies. This conclusion appears robust to assumptions of whether or not submm galaxies are driven by major mergers, since the suite of simulated galaxies modelled here contains examples of both merging and isolated galaxies. We identified discrepancies between the true and inferred stellar ages (rather than the dust attenuation) as the primary determinant of the success/failure of the mass recovery. Regardless of the choice of SFH, the SED-derived stellar masses exhibit a factor of ~2 scatter around the true value; this scatter is an inherent limitation of the SED modelling due to simplified assumptions. Finally, we found that the contribution of active galactic nuclei does not have any significant impact on the derived stellar masses.Comment: Accepted to A&A. 11 pages, 9 figures, 1 table. V2 main changes: 1) discussion of the stellar age as the main parameter influencing the success of an SED model (Fig. 4, 5, 7); 2) discussion of the age-dust degeneracy (Fig 9); 3) the comparison of real and simulated submm galaxies (Fig 1

Policy and linkages in the application of a one health system for reporting and controlling African trypanosomiasis and other zoonotic diseases in Zambia

The capacity to detect, control and manage emerging and re-emerging zoonotic diseases in Africa has been limited by a lack of utilisation of available reporting structures and policies to support programmes at national and local levels. This study explored the impact of the Zambian government policies on animal and human disease reporting and management and on One Health opportunities. An in-depth review and analysis of strengths, weaknesses, opportunities, and threats in the existing policies and reporting structures in the departments responsible for Veterinary Services, Health, and Wildlife, was conducted. According to our findings, sub-optimal implementation of existing policies related to the control of zoonotic diseases was impacting disease reporting, and reporting structures play an important role in effective and sustainable reporting of zoonotic diseases. Further, the study explored capacities and strategies in trypanosomiasis control as a case study that could prompt effective adoption of a One Health approach, and as such, the study suggests measures that could help to assess the performance of a One Health system in the control of African trypanosomiasis and other zoonotic diseases

Chronic ischemic cerebral white matter disease is a risk factor for nonfocal neurologic injury after total aortic arch replacement

ObjectiveLeukoaraiosis (chronic ischemic white matter changes) on preoperative brain magnetic resonance imaging is common in patients having aortic arch surgery. This study sought to determine whether it is associated with adverse neurologic outcome in the postoperative period.MethodsData were collected from a retrospective chart review of 142 patients in whom total aortic arch replacement was planned at the Cleveland Clinic between April 2000 and December 2004. All patients had preoperative brain magnetic resonance imaging evaluation. Leukoaraiosis severity was rated semiquantitatively using the Schelten’s scale. Postoperative neurologic injuries were investigated by clinical examination and appropriate neuroimaging. They were stratified as type 1 (focal ischemic stroke) and type 2 (nonfocal neurocognitive changes, generalized seizures) injuries.ResultsThe following were independent predictors of type 1 neurologic injury: age (odds ratio 1.06 [1.01-1.13], P = .02) and moderate to severe aortic atheroma (odds ratio 4.4 [1.4-9.7], P = .012). Total white matter scores (odds ratio 1.16 [1.06-1.27], P = .002) and higher preoperative hemoglobin A1c levels (odds ratio 1.8 [1.00-3.50], P = .05) were significantly associated with type 2 neurologic injuries. Survival was 96%, and 4.2% had persistent focal neurologic deficits at the time of hospital discharge.ConclusionsLeukoaraiosis is a significant independent predictor of nonfocal postoperative neurologic morbidity following aortic arch replacement surgery. Preoperative evaluation with magnetic resonance imaging allows identification of a patient subgroup at risk and implementation of strategies aimed at improving neurologic outcome

Properties of Photon Density Waves in Multiple-Scattering Media

Amplitude-modulated light launched into multiple-scattering media, e.g., tissue, results in the propagation of density waves of diffuse photons. Photon density wave characteristics in turn depend on modulation frequency (ω) and media optical properties. The damped spherical wave solutions to the homogeneous form of the diffusion equation suggest two distinct regimes of behavior: (1) a highfrequency dispersion regime where density wave phase velocity Vp has a ω dependence and (2) a low-frequency domain where Vp is frequency independent. Optical properties are determined for various tissue phantoms by fitting the recorded phase (Φ) and modulation (m) response to simple relations for the appropriate regime. Our results indicate that reliable estimates of tissuelike optical properties can be obtained, particularly when multiple modulation frequencies are employed

Insights into the control and management of human and bovine African Trypanosomiasis in Zambia between 2009 and 2019-a review

Tsetse transmitted trypanosomiasis is a fatal disease commonly known as Nagana in cattle and sleeping sickness in humans. The disease threatens food security and has severe economic impact in Africa including most parts of Zambia. The level of effectiveness of commonly used African trypanosomiasis control methods has been reported in several studies. However, there have been no review studies on African trypanosomiasis control and management conducted in the context of One Health. This paper therefore seeks to fill this knowledge gap. A review of studies that have been conducted on African trypanosomiasis in Zambia between 2009 and 2019, with a focus on the control and management of trypanosomiasis was conducted. A total of 2238 articles were screened, with application of the search engines PubMed, PubMed Central and One Search. Out of these articles, 18 matched the required criteria and constituted the basis for the paper. An in-depth analysis of the 18 articles was conducted to identify knowledge gaps and evidence for best practices. Findings from this review provide stakeholders and health workers with a basis for prioritisation of African trypanosomiasis as an important neglected disease in Zambia and for formulation of One Health strategies for better control and/or management of the disease