Hodge Theory on Metric Spaces

Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We believe that this constitutes a step towards understanding the geometry of vision. The appendix by Anthony Baker provides a separable, compact metric space with infinite dimensional \alpha-scale homology.Comment: appendix by Anthony W. Baker, 48 pages, AMS-LaTeX. v2: final version, to appear in Foundations of Computational Mathematics. Minor changes and addition

Oxidised cosmic acceleration

We give detailed proofs of several new no-go theorems for constructing flat four-dimensional accelerating universes from warped dimensional reduction. These new theorems improve upon previous ones by weakening the energy conditions, by including time-dependent compactifications, and by treating accelerated expansion that is not precisely de Sitter. We show that de Sitter expansion violates the higher-dimensional null energy condition (NEC) if the compactification manifold M is one-dimensional, if its intrinsic Ricci scalar R vanishes everywhere, or if R and the warp function satisfy a simple limit condition. If expansion is not de Sitter, we establish threshold equation-of-state parameters w below which accelerated expansion must be transient. Below the threshold w there are bounds on the number of e-foldings of expansion. If M is one-dimensional or R everywhere vanishing, exceeding the bound implies the NEC is violated. If R does not vanish everywhere on M, exceeding the bound implies the strong energy condition (SEC) is violated. Observationally, the w thresholds indicate that experiments with finite resolution in w can cleanly discriminate between different models which satisfy or violate the relevant energy conditions.Comment: v2: corrections, references adde

Variational description of multi-fluid hydrodynamics: Uncharged fluids

We present a formalism for Newtonian multi-fluid hydrodynamics derived from an unconstrained variational principle. This approach provides a natural way of obtaining the general equations of motion for a wide range of hydrodynamic systems containing an arbitrary number of interacting fluids and superfluids. In addition to spatial variations we use ``time shifts'' in the variational principle, which allows us to describe dissipative processes with entropy creation, such as chemical reactions, friction or the effects of external non-conservative forces. The resulting framework incorporates the generalization of the entrainment effect originally discussed in the case of the mixture of two superfluids by Andreev and Bashkin. In addition to the conservation of energy and momentum, we derive the generalized conservation laws of vorticity and helicity, and the special case of Ertel's theorem for the single perfect fluid. We explicitly discuss the application of this framework to thermally conducting fluids, superfluids, and superfluid neutron star matter. The equations governing thermally conducting fluids are found to be more general than the standard description, as the effect of entrainment usually seems to be overlooked in this context. In the case of superfluid He4 we recover the Landau--Khalatnikov equations of the two-fluid model via a translation to the ``orthodox'' framework of superfluidity, which is based on a rather awkward choice of variables. Our two-fluid model for superfluid neutron star matter allows for dissipation via mutual friction and also ``transfusion'' via beta-reactions between the neutron fluid and the proton-electron fluid.Comment: uses RevTeX 4; 20 pages. To appear in PRD. v2: removed discussion of charged fluids and coupling to electromagnetic fields, which are submitted as a separate paper for a clearer presentation v3: fixed typo in Eq.(9), updated some reference

Young and Intermediate-age Distance Indicators

Distance measurements beyond geometrical and semi-geometrical methods, rely mainly on standard candles. As the name suggests, these objects have known luminosities by virtue of their intrinsic proprieties and play a major role in our understanding of modern cosmology. The main caveats associated with standard candles are their absolute calibration, contamination of the sample from other sources and systematic uncertainties. The absolute calibration mainly depends on their chemical composition and age. To understand the impact of these effects on the distance scale, it is essential to develop methods based on different sample of standard candles. Here we review the fundamental properties of young and intermediate-age distance indicators such as Cepheids, Mira variables and Red Clump stars and the recent developments in their application as distance indicators.Comment: Review article, 63 pages (28 figures), Accepted for publication in Space Science Reviews (Chapter 3 of a special collection resulting from the May 2016 ISSI-BJ workshop on Astronomical Distance Determination in the Space Age

A Corporate Social Entrepreneurship Approach to Market-Based Poverty Reduction

In this article, we aim to conceptualize a market-based approach to poverty reduction from a corporate social entrepreneurship (CSE) perspective. Specifically, we describe some market-based initiatives at the base of the economic pyramid and relate them to the social entrepreneurship literature. We refer to the entrepreneurial activities of multinational corporations that create social value as CSE. We then conceptualize CSE according to the corporate entrepreneurship and social entrepreneurship domains and shed light on how corporations can implement CSE. Finally, by reviewing relevant literature, we propose some of the factors that can stimulate CSE in organizations and some of the benefits companies can gain by implementing CSE

Hypogene Calcitization: Evaporite Diagenesis in the Western Delaware Basin

Evaporite calcitization within the Castile Formation of the Delaware Basin is more widespread and diverse than originally recognized. Coupled field and GIS studies have identified more than 1000 individual occurrences of calcitization within the Castile Formation outcrop area, which includes both calcitized masses (limestone buttes) and laterally extensive calcitized horizons (limestone sheets). Both limestone buttes and sheets commonly contain a central brecciated zone that we attribute to hypogene dissolution. Lithologic fabric of calcitized zones ranges from little alteration of original varved laminae to fabrics showing extensive laminae distortion as well as extensive vuggy and open cavernous porosity. Calcitization is most abundant in the western portion of the Castile outcrop region where surface denudation has been greatest. Calcitization often forms linear trends, indicating fluid migration along fractures, but also occurs as dense clusters indicating focused, ascending, hydrocarbon-rich fluids. Native sulfur, secondary tabular gypsum (i.e. selenite) and hypogene caves are commonly associated with clusters of calcitization. This assemblage suggests that calcium sulfate diagenesis within the Castile Formation is dominated by hypogene speleogemesis

Long term outcomes of biomaterial-mediated repair of focal cartilage defects in a large animal model

The repair of focal cartilage defects remains one of the foremost issues in the field of orthopaedics. Chondral defects may arise from a variety of joint pathologies and left untreated, will likely progress to osteoarthritis. Current repair techniques, such as microfracture, result in short-term clinical improvements but have poor long-term outcomes. Emerging scaffold-based repair strategies have reported superior outcomes compared to microfracture and motivate the development of new biomaterials for this purpose. In this study, unique composite implants consisting of a base porous reinforcing component (woven poly(ε-caprolactone)) infiltrated with 1 of 2 hydrogels (self-assembling peptide or thermo-gelling hyaluronan) or bone marrow aspirate were evaluated. The objective was to evaluate cartilage repair with composite scaffold treatment compared to the current standard of care (microfracture) in a translationally relevant large animal model, the Yucatan minipig. While many cartilage-repair studies have shown some success in vivo, most are short term and not clinically relevant. Informed by promising 6-week findings, a 12-month study was carried out and those results are presented here. To aid in comparisons across platforms, several structural and functionally relevant outcome measures were performed. Despite positive early findings, the long-term results indicated less than optimal structural and mechanical results with respect to cartilage repair, with all treatment groups performing worse than the standard of care. This study is important in that it brings much needed attention to the importance of performing translationally relevant long-term studies in an appropriate animal model when developing new clinical cartilage repair approaches

Towards liver-directed gene therapy: Retrovirus-mediated gene transfer into human hepatocytes

Liver-directed gene therapy is being considered in the treatment of inherited metabolic diseases. One approach we are considering is the transplantation of autologous hepatocytes that have been genetically modified with recombinant retroviruses ex vivo. We describe, in this report, techniques for isolating human hepatocytes and efficiently transducing recombinant genes into primary cultures. Hepatocytes were isolated from tissue of four different donors, plated in primary culture, and exposed to recombinant retroviruses expressing either the LacZ reporter gene or the cDNA for rabbit LDL receptor. The efficiency of gene transfer under optimal conditions, as determined by Southern blot analysis, varied from a maximum of one proviral copy per cell to a minimum of 0.1 proviral copy per cell. Cytochemical assays were used to detect expression of the recombinant derived proteins, E. coli β-galactosidase and rabbit LDL receptor. Hepatocytes transduced with the LDL receptor gene expressed levels of receptor protein that exceeded the normal endogenous levels. The ability to isolate and genetically modify human hepatocytes, as described in this report, is an important step towards the development of liver-directed gene therapies in humans.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45540/1/11188_2005_Article_BF01233625.pd

Untangling creativity and art for policy purposes : ethnographic insights on Manchester International Festival and Manchester Day Parade

This paper draws on anthropological fieldwork of a civic parade in Manchester from 2010 to 2012 to argue for engaging with creativity as a process rather than an attribute of a particular sector or individual. It shows how the focus on funding and supporting ‘creative industries’ defined as ‘cinema, television, music, literature, performing arts, heritage and related areas’ actually excludes and diminishes the potential for others to engage with ideas and creative processes. Two major events in Manchester’s cultural calendar – Procession by artist Jeremy Deller, produced by Manchester International Festival and Manchester Day Parade, a council-led civic celebration – both combined community groups with artist input to put large-scale structures and people on the city’s streets. In this ethnographic analysis, I argue that the ‘creativity’ sought from these artists is their adaptive and productive approach to making ideas tangible. By focusing on creativity as a process rather than a character trait, there is even greater potential for stimulating a ‘creative’ city

Empirically-grounded development of legal ontologies: a socio-legal perspective

This paper shows the multiple relationships between empirical data and semantic content in the legal field. One of the well-known problems of ontology construction is the "knowledge acquisition bottleneck problem" pointed out by Edward Feigenbaum and others, many years ago. In the next generation of Semantic Web developments this problem has not been completely solved. It is our con-tention that an accurate description of the legal environment, and well-grounded previous sociological studies may help to face it in a more satisfactory way. This means adopting a user-centered approach for legal ontologies, in what we will call an "iterative and integrated pragmatic circle" involving legal theorists, socio-legal researchers, professional people (lawyers, magistrates, prosecutors…) and com-puter scientists. We put the example of how the ontology of IURISERVICE was built up