Equivalence of cubical and simplicial approaches to (∞,n)(\infty,n)-categories

We prove that the marked triangulation functor from the category of marked cubical sets equipped with a model structure for ($n$-trivial, saturated) comical sets to the category of marked simplicial set equipped with a model structure for ($n$-trivial, saturated) complicial sets is a Quillen equivalence. Our proof is based on the theory of cones, previously developed by the first two authors together with Lindsey and Sattler.Comment: 60 pages; v2 improvements to expositio

Experiences of aiding autobiographical memory Using the SenseCam

Human memory is a dynamic system that makes accessible certain memories of events based on a hierarchy of information, arguably driven by personal significance. Not all events are remembered, but those that are tend to be more psychologically relevant. In contrast, lifelogging is the process of automatically recording aspects of one's life in digital form without loss of information. In this article we share our experiences in designing computer-based solutions to assist people review their visual lifelogs and address this contrast. The technical basis for our work is automatically segmenting visual lifelogs into events, allowing event similarity and event importance to be computed, ideas that are motivated by cognitive science considerations of how human memory works and can be assisted. Our work has been based on visual lifelogs gathered by dozens of people, some of them with collections spanning multiple years. In this review article we summarize a series of studies that have led to the development of a browser that is based on human memory systems and discuss the inherent tension in storing large amounts of data but making the most relevant material the most accessible

Cofibration category of digraphs for path homology

We prove that the category of directed graphs and graph maps carries a cofibration category structure in which the weak equivalences are the graph maps inducing isomorphisms on path homology.Comment: 38 pages; comments welcom

Probabilistic Contributing Area Analysis: A GMDSI worked example report

Copyright Flinders UniversityPREFACE The Groundwater Modelling Decision Support Initiative (GMDSI) is an industry-funded and industry-aligned project focused on improving the role that groundwater modelling plays in supporting environmental management and decision-making. Over the life of the project, it will document a number of examples of decision-support groundwater modelling. These documented worked examples will attempt to demonstrate that by following the scientific method, and by employing modern, computer-based approaches to data assimilation, the uncertainties associated with groundwater model predictions can be both quantified and reduced. With realistic confidence intervals associated with predictions of management interest, the risks associated with different courses of management action can be properly assessed before critical decisions are made. GMDSI worked example reports, one of which you are now reading, are deliberately different from other modelling reports. They do not describe all of the nuances of a particular study site. They do not provide every construction and deployment detail of a particular model. In fact, they are not written for modelling specialists at all. Instead, a GMDSI worked example report is written with a broader audience in mind. Its intention is to convey concepts, rather than to record details of model construction. In doing so, it attempts to raise its readers’ awareness of modelling and data-assimilation possibilities that may prove useful in their own groundwater management contexts. The decision-support challenges that are addressed by various GMDSI worked examples include the following: • assessing the reliability of a public water supply; • protection of a groundwater resource from contamination; • estimation of mine dewatering requirements; • assessing the environmental impacts of mining; and • management of aquifers threatened by salt water intrusion. In all cases the approach is the same. Management-salient model predictions are identified. Ways in which model-based data assimilation can be employed to quantify and reduce the uncertainties associated with these predictions are reported. Model design choices are explained in a way that modellers and non-modellers can understand. The authors of GMDSI worked example reports make no claim that the modelling work which they document cannot be improved. As all modellers know, time and resources available for modelling are always limited. The quality of data on which a model relies is always suspect. Modelling choices are always subjective, and are often made differently with the benefit of hindsight. What we do claim, however, is that the modelling work which we report has attempted to implement the scientific method to address challenges that are typical of those encountered on a day-to-day basis in groundwater management worldwide. As stated above, a worked example report purposefully omits many implementation details of the modelling and data assimilation processes that it describes. Its purpose is to demonstrate what can be done, rather than to explain how it is done. Those who are interested in technical details are referred to GMDSI modelling tutorials. A suite of these tutorials has been developed specifically to assist modellers in implementing workflows such as those that are described herein. We thank and acknowledge our collaborators, and GMDSI project funders, for making these reports possible