Estimating the minimal length of tardos code

Abstract. This paper estimates the minimal length of a binary probabilistic traitor tracing code. We consider the code construction proposed by G. Tardos in 2003, with the symmetric accusation function as improved by B. Skoric et al. The length estimation is based on two pillars. First, we consider the Worst Case Attack that a group of c colluders can lead. This attack minimizes the mutual information between the code sequence of a colluder and the pirated sequence. Second, an algorithm pertaining to the field of rare event analysis is presented in order to estimate the probabilities of error: the probability that an innocent user is framed, and the probabilities that all colluders are missed. Therefore, for a given collusion size, we are able to estimate the minimal length of the code satisfying some error probabilities constraints. This estimation is far lower than the known lower bounds

Testing the Effect of Relative Pollen Productivity on the REVEALS Model: A Validated Reconstruction of Europe-Wide Holocene Vegetation

Reliable quantitative vegetation reconstructions for Europe during the Holocene are crucial to improving our understanding of landscape dynamics, making it possible to assess the past effects of environmental variables and land-use change on ecosystems and biodiversity, and mitigating their effects in the future. We present here the most spatially extensive and temporally continuous pollen-based reconstructions of plant cover in Europe (at a spatial resolution of 1º × 1º) over the Holocene (last 11.7 ka BP) using the "Regional Estimates of VEgetation Abundance from Large Sites" (REVEALS) model. This study has three main aims. First, to present the most accurate and reliable generation of REVEALS reconstructions across Europe so far. This has been achieved by including a larger number of pollen records compared to former analyses, in particular from the Mediterranean area. Second, to discuss methodological issues in the quantification of past land cover by using alternative datasets of relative pollen productivities (RPPs), one of the key input parameters of REVEALS, to test model sensitivity. Finally, to validate our reconstructions with the global forest change dataset. The results suggest that the RPPs.st1 (31 taxa) dataset is best suited to producing regional vegetation cover estimates for Europe. These reconstructions offer a long-term perspective providing unique possibilities to explore spatial-temporal changes in past land cover and biodiversity.This research was funded by the TERRANOVA Project, H2020 Marie Sklodowska-Curie grant agreement no. 81390

Testing the Effect of Relative Pollen Productivity on the REVEALS Model: A Validated Reconstruction of Europe-Wide Holocene Vegetation

Reliable quantitative vegetation reconstructions for Europe during the Holocene are crucial to improving our understanding of landscape dynamics, making it possible to assess the past effects of environmental variables and land-use change on ecosystems and biodiversity, and mitigating their effects in the future. We present here the most spatially extensive and temporally continuous pollen-based reconstructions of plant cover in Europe (at a spatial resolution of 1 degrees x 1 degrees) over the Holocene (last 11.7 ka BP) using the 'Regional Estimates of VEgetation Abundance from Large Sites' (REVEALS) model. This study has three main aims. First, to present the most accurate and reliable generation of REVEALS reconstructions across Europe so far. This has been achieved by including a larger number of pollen records compared to former analyses, in particular from the Mediterranean area. Second, to discuss methodological issues in the quantification of past land cover by using alternative datasets of relative pollen productivities (RPPs), one of the key input parameters of REVEALS, to test model sensitivity. Finally, to validate our reconstructions with the global forest change dataset. The results suggest that the RPPs.st1 (31 taxa) dataset is best suited to producing regional vegetation cover estimates for Europe. These reconstructions offer a long-term perspective providing unique possibilities to explore spatial-temporal changes in past land cover and biodiversity