The Theory of the Interleaving Distance on Multidimensional Persistence Modules

In 2009, Chazal et al. introduced $\epsilon$-interleavings of persistence modules. $\epsilon$-interleavings induce a pseudometric $d_I$ on (isomorphism classes of) persistence modules, the interleaving distance. The definitions of $\epsilon$-interleavings and $d_I$ generalize readily to multidimensional persistence modules. In this paper, we develop the theory of multidimensional interleavings, with a view towards applications to topological data analysis. We present four main results. First, we show that on 1-D persistence modules, $d_I$ is equal to the bottleneck distance $d_B$. This result, which first appeared in an earlier preprint of this paper, has since appeared in several other places, and is now known as the isometry theorem. Second, we present a characterization of the $\epsilon$-interleaving relation on multidimensional persistence modules. This expresses transparently the sense in which two $\epsilon$-interleaved modules are algebraically similar. Third, using this characterization, we show that when we define our persistence modules over a prime field, $d_I$ satisfies a universality property. This universality result is the central result of the paper. It says that $d_I$ satisfies a stability property generalizing one which $d_B$ is known to satisfy, and that in addition, if $d$ is any other pseudometric on multidimensional persistence modules satisfying the same stability property, then $d\leq d_I$. We also show that a variant of this universality result holds for $d_B$, over arbitrary fields. Finally, we show that $d_I$ restricts to a metric on isomorphism classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in Foundations of Computational Mathematics. 36 page

Review: Consumption-stage food waste reduction interventions - What works and how to design better interventions

Food waste prevention has become an issue of international concern, with Sustainable Development Goal 12.3 aiming to halve per capita global food waste at the retail and consumer levels by 2030. However there is no review that has considered the effectiveness of interventions aimed at preventing food waste in the consumption stages of the food system. This significant gap, if filled, could help support those working to reduce food waste in the developed world, providing knowledge of what interventions are specifically effective at preventing food waste. This paper fills this gap, identifying and summarizing food-waste prevention interventions at the consumption/consumer stage of the supply chain via a rapid review of global academic literature from 2006 to 2017. We identify 17 applied interventions that claim to have achieved food waste reductions. Of these, 13 quantified food waste reductions. Interventions that changed the size or type of plates were shown to be effective (up to 57% food waste reduction) in hospitality environments. Changing nutritional guidelines in schools were reported to reduce vegetable waste by up to 28%, indicating that healthy diets can be part of food waste reduction strategies. Information campaigns were also shown to be effective with up to 28% food waste reduction in a small sample size intervention. Cooking classes, fridge cameras, food sharing apps, advertising and information sharing were all reported as being effective but with little or no robust evidence provided. This is worrying as all these methods are now being proposed as approaches to reduce food waste and, except for a few studies, there is no reproducible quantified evidence to assure credibility or success. To strengthen current results, a greater number of longitudinal and larger sample size intervention studies are required. To inform future intervention studies, this paper proposes a standardised guideline, which consists of: (1) intervention design; (2) monitoring and measurement; (3) moderation and mediation; (4) reporting; (5) systemic effects. Given the importance of food-waste reduction, the findings of this review highlight a significant evidence gap, meaning that it is difficult to make evidence-based decisions to prevent or reduce consumption-stage food waste in a cost-effective manner

Institutional Change and Transition in the Forest Sector of Khabarovsk Krai

Godkänd; 1999; 20080305 (ysko

Sound radiation and sound insulation performances of maritime bulkheads

The research of materials matching low weight and high resistance has always been a key factor in the shipbuilding industry to increase performances and loading capacity. Nowadays, other issues add up to economical convenience, and building quiet ships is important not only for passengers and cabin crew, but also to make harbor areas more comfortable and to respect the aquatic environment. In this context, using sandwich or composite materials must be carefully evaluated and the sound insulation performances must be considered throughout all stages of the design process. This work presents some evaluations about the sound insulation performances of a ribbed fiberglass bulkhead and of a balsa-core sandwich bulkhead. In particular, the bending stiffness and the sound transmission loss obtained by sound transmission suites and mobility measurements are provided. From such measurements it has also been possible to determine the radiation efficiency of the structures, whose optimization is particularly important when a reduction of the noise pollution is required