In this paper, we introduce a penalized version of the geometric mean. In analogy with the Mazziotta Pareto Index, this composite indicator is derived as a product between the geometric mean and a penalization term to account for the unbalance among indicators. The unbalance is measured in terms of the (horizontal) variability of the normalized indicators opportunely scaled and transformed via the Box–Cox function of order zero. The penalized geometric mean is used to compute the penalized Human Development Index (HDI), and a comparison with the geometric mean approach is presented. Data come from the Human Development Data Center for 2019 and refer to the classical three dimensions of HDI. The results show that the new method does not upset the original ranking produced by the HDI but it impacts more on countries with poor performances. The paper has the merit of proposing a new reading of the Mazziotta Pareto Index in terms of the reliability of the arithmetic mean as well as of generalizing this reading to the geometric mean approach.

Forest ecosystems are increasingly subject to disturbances, such as extreme (climate) events, fires and pathological outbreaks, which exert significant (and still poorly quantified) economic impacts, despite their intrinsic resilience. How forest management addresses these challenges will have profound effects on human health, environmental diversity, (ecological and economic) productivity and the ability of forest ecosystems to recovery from exogenous shocks. Assuming forests as ensuring ecosystem services that are vital to society and human well-being, in addition to providing wood material, a better knowledge of forest ecosystems appears a key requirement to delineate a developmental strategy that guarantees environmental protection objectives and achievement of climate and energy targets. In the context of Sustainable Development Goals of the United Nations 2030 Agenda, the information available on forest management practices in Europe still seems not completely suitable to provide a comprehensive overview of ecosystem conditions, their economic value, and their biodiversity. Based on a literature review, the present contribution focuses on recent dynamics of the forestry sector in Europe, delineating the inherent complexity in the environmental-economic nexus. Additionally, the extensive use of a key natural resource such as wood exerts social implications for local districts adapting to ecological change—from climate warming to landscape transformations. In line with earlier studies, our paper confirms the role of the technical-economic dimension of forestry in sustainable development paths of districts and regions, affecting together (i) short-term economic dynamics, (ii) the growth prospects of the sector, (iii) the organization of the supply chain, (iv) the interconnections between companies, and (v) investment strategies at large. One of the major issues is the low reliability of official statistics to provide a coherent picture of the actual status of forest resources. At the same time, forestry practices are pivotal in maintaining habitats and species while increasing the timber production that remains (too) sustainable. This is the policy direction constantly given by the European Commission to stimulate over time public bodies and private (in whose hands is about 60% of European forests) to start virtuous paths in the circular economy with considerable repercussions in terms of additional jobs, recycled materials, mt of CO₂ equivalent avoided, and increase in community added value. In this context, forestry should assure a more ‘holistic’ contribution to sustainable development paths at various spatial scales. This means concentrating on both economic and environmental targets based on the identification of significant (ecological-economic) dimensions that may delineate future lines of investigation and policy intervention, while increasing between member countries and regional authorities.

In this paper we propose a new aggregation method for constructing composite indicators based on a penalization of the power mean. The idea underlying this approach consists in multiplying the power mean by a factor that accounts for the horizontal heterogeneity among indicators while penalizing units with a larger heterogeneity. In line with the minimum loss of information principle, the penalization factor proposed is proven to be linked to the loss of information generated when the indicators are substituted with their power means. As a consequence, the aggregation approach gives rise to the class of penalized power means and the penalized Benefit of the Doubt aggregative approach. Including heterogeneity makes the aggregation approach more suitable for refined rankings. Interestingly, the penalized power mean of order one coincides with the Mazziotta Pareto Index. Some theoretical properties of the penalized power means are proven, thus supporting the Mazziotta Pareto index. An empirical analysis of the Human Development Index in 2019 is presented. Comparisons of the rankings induced by the penalized and non-penalized Benefit of the Doubt and power mean aggregation approaches are shown. There are three main findings: the penalized power means satisfy the properties characterizing weakly monotone aggregation functions; the penalization reduces ranking variations while differentiating units with close means; and the geometric mean provides composite indicators whose ranking is closest to those obtained with power means of different order.

In this paper we consider a furtivity problem in the context of time-dependent three-dimensional acoustic obstacle scattering. The scattering problem for a ‘passive’ obstacle is the following: an incoming acoustic wavepacket is scattered by a bounded simply connected obstacle with locally Lipschitz boundary having a known boundary acoustic impedance. The scattered wave is the solution of an exterior problem for the wave equation. To make the obstacle furtive we leave ‘passive’ obstacles and we consider ‘active’ obstacles, that is obstacles that, when hit by the incoming wavepacket, react with a pressure current circulating on their boundary. The furtivity problem consists of making the acoustic field scattered by the obstacle ‘as small as possible’ by choosing a control function, that is a pressure current on the boundary of the obstacle, in the function space of the admissible controls. It consists of finding the control function that minimizes a cost functional that will be made precise later. ...