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In this work, we describe the new command zonotope, which, by resorting to a geometry-based approach, provides a measure of productivity that fully accounts for the existing heterogeneity across firms within the same industry. The method we propose also enables assessment of the extent of multidimensional heterogeneity with applications to fields beyond that of production analysis. Finally, we detail the functioning of the software to perform the related empirical analysis, and we discuss the main computational issues encountered in its development.

Alpha-Theory was introduced in 1995 to provide a simplified version of Robinson’s non-standard analysis which overcomes the technicalities of symbolic logic. The theory has been improved over the years, and recently it has been used also to solve practical problems in a pure numerical way, thanks to the introduction of algorithmic numbers. In this paper, we introduce Alpha-Theory using a novel axiomatic approach oriented towards real-world applications, to avoid the need to master mathematical logic and model theory. To corroborate the strong link of this Alpha-Theory axiomatization and scientific computations, we report numerical illustrative applications never carried out by means of non-standard numbers within a computer, i.e., the computation of the eigenvalues of a non-Archimedean matrix, some computations related to non-Archimedean Markov chains, and the Cholesky factorization of a non-Archimedean matrix. We also highlight the differences between our numerical routines and pure symbolic approaches: as expected, the former scales better when the dimension of the problem increases.

Maritime operations are affected significantly by meteorological and oceanographic (METOC) conditions. The availability of multiple METOC centres able to deliver more accurate forecasts in the near future (2/3 days) is a promising resource toward better operational planning. However, how a specific maritime operation can benefit from such forecasts is not straightforward. A decision support architecture is required to combine METOC forecasts and human knowledge and select the best action from a set of pre-defined actions for the maritime operation. This paper describes a decision support architecture developed at the NATO Undersea Research Centre that is an improvement over a previous version in two ways: i) it exploits forecasts coming from more than one METOC centre, and ii) it exploits uncertainty associated with METOC forecasts. The former allows for the exploitation of different abilities of METOC centres at different conditions. The latter allows for the propagation of input uncertainty on output products (the risks related to each action), thus allowing operators to assess if risks related to different actions are statistically different. Both features increase the robustness of the previous decision support architecture. The effectiveness of the new architecture is demonstrated on an underwater glider surfacing experiment carried out on data collected during a cruise in the Adriatic Sea in 2006.

This paper describes a generic decision support architecture (DSA) for supporting maritime operations. The system's core is a decision support tool (DST), consisting of a risk assessment framework aimed at computing risks related to each action that can be performed on the maritime operation under consideration. In particular, the risks are computed for each action and for each class describing the forecasted condition of the environment (favourable, marginal, and unfavourable), according to their posterior probabilities. A fuzzy classifier is used to estimate such probabilities, starting from the forecast of the environmental variables affecting the operation. A distinctive feature of the implemented DSA is its flexibility: many different types of operations can be handled (amphibious landing, autonomous underwater vehicle (AUV) recovery, etc.) with no architectural change. The architecture has been tested both on synthetic data and on real data, the latter collected during two cruises carried out in Adriatic Sea and Ligurian Sea.