Tautness for riemannian foliations on non-compact manifolds

For a riemannian foliation $\mathcal{F}$ on a closed manifold $M$, it is known that $\mathcal{F}$ is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form $\kappa_\mu$ (relatively to a suitable riemannian metric $\mu$) is zero. In the transversally orientable case, tautness is equivalent to the non-vanishing of the top basic cohomology group $H^{^{n}}(M/\mathcal{F})$, where n = \codim \mathcal{F}. By the Poincar\'e Duality, this last condition is equivalent to the non-vanishing of the basic twisted cohomology group $H^{^{0}}_{_{\kappa_\mu}}(M/\mathcal{F})$, when $M$ is oriented. When $M$ is not compact, the tautness class is not even defined in general. In this work, we recover the previous study and results for a particular case of riemannian foliations on non compact manifolds: the regular part of a singular riemannian foliation on a compact manifold (CERF).Comment: 18 page

Cohomological tautness for Riemannian foliations

In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation can be characterized cohomologically. We extend this cohomological characterization to a class of foliations which includes the foliated strata of any singular Riemannian foliation of a closed manifold

The persistence landscape and some of its properties

Persistence landscapes map persistence diagrams into a function space, which may often be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map and there is an associated kernel. The main advantage of this summary is that it allows one to apply tools from statistics and machine learning. Furthermore, the mapping from persistence diagrams to persistence landscapes is stable and invertible. We introduce a weighted version of the persistence landscape and define a one-parameter family of Poisson-weighted persistence landscape kernels that may be useful for learning. We also demonstrate some additional properties of the persistence landscape. First, the persistence landscape may be viewed as a tropical rational function. Second, in many cases it is possible to exactly reconstruct all of the component persistence diagrams from an average persistence landscape. It follows that the persistence landscape kernel is characteristic for certain generic empirical measures. Finally, the persistence landscape distance may be arbitrarily small compared to the interleaving distance.Comment: 18 pages, to appear in the Proceedings of the 2018 Abel Symposiu

Modified differentials and basic cohomology for Riemannian foliations

We define a new version of the exterior derivative on the basic forms of a Riemannian foliation to obtain a new form of basic cohomology that satisfies Poincar\'e duality in the transversally orientable case. We use this twisted basic cohomology to show relationships between curvature, tautness, and vanishing of the basic Euler characteristic and basic signature.Comment: 20 pages, references added, minor corrections mad

Crossing media boundaries: adaptations and new media forms of the book

t is necessary to continuously review the definition of the book moving from one bound by its material form to one determined by its function as a means of communication. The book’s social function as the high status vehicle for communicating new ideas and cultural expressions is being challenged by sophisticated systems of conveying meaning in other media. In this article, we report on two projects: electronic book (e-book) publication and reader forum for Nature Mage and the transmedia augmented reality (AR) fiction Sherwood Rise, which investigate these issues. Claudio Pires Franco’s work is based on the adaptation of a source work: Duncan Pile’s Nature Mage. The project aims to develop the book from e-book to a fan-produced enhanced digital book. Through this practice-based research, Franco investigates the definitions and classification of the e and i forms of the book and adaptation in new media; the role of the author in creative collaboration with readers through online forums; the extension of the story world through creative collaboration and reader participation while respecting and safeguarding creative properties. One remove from the traditional book, David Miller’s Sherwood Rise, research the user experience with AR to examine narrative problems and explore new storytelling aesthetics. These new media forms define the outer borders of the book system within which content is formed and moulded, and around which society is shaped

The Total Filmmaker: thinking of screenwriting, directing and editing as one role

As screenwriting continues to establish itself as a discrete discipline in academia, either in alignment with creative writing departments or film and media practice departments, there is a danger that such developments may entrench a distancing of the craft from the cinematic form itself and that such a distancing may ultimately reinforce the screenplay's propensity for dramaturgy and the dramatic, rather than the sensory and experiential of the cinematic. Closely related creative stages in telling cinematic stories include directing and editing and this article seeks to argue, with reference to personal screen practice, that screenwriting, directing and editing are, in fact, three variations of the same thing. The article proposes the notion of the Total Filmmaker who embraces all three aspects of the cinematic storyteller. If the ultimate aim is to create a narrative that fully utilises the unique properties of the cinematic form in telling a story, rather than being dominated by the theatricality of dramatically driven classical narratives. How might one explore the relationship between screenwriting, directing and editing? Can an integrated approach to creating the cinematic blueprint change the way we think of pedagogy and screenwriting

SUpporting well-being through PEeR-Befriending (SUPERB) trial: an exploration of fidelity in peer-befriending for people with aphasia

Assessing the evolution of severely brain-injured patients with disorders of consciousness (DOC) with current tools like the Glasgow Outcome Scale-Extended (GOS-E) remains a challenge. At the bedside, the most reliable diagnostic tool is currently the Coma Recovery Scale-Revised. The CRS-R distinguishes patients with unresponsive wakefulness syndrome (UWS) from patients in minimally conscious state (MCS) and patients who have emerged from MCS (EMCS). This international multi-centric study aims to validate a phone outcome questionnaire (POQ) based on the CRS-R and compare it to the CRS-R performed at the bedside and to the GOS-E which evaluates the level of disability and assigns patient’s in outcomes categories. The POQ will allow clinicians to probe the evolution of patient’s state of consciousness based on caregivers feedback. This research project is part of the International Brain Injury Association, Disorders of Consciousness-Special Interest Group (DOCSIG) and DOCMA consortium

Notes on a paper of Mess

These notes are a companion to the article "Lorentz spacetimes of constant curvature" by Geoffrey Mess, which was first written in 1990 but never published. Mess' paper will appear together with these notes in a forthcoming issue of Geometriae Dedicata.Comment: 26 page