Gothic art was developed in western Europe from the second half of the 12th century to the end of the 15th century. The most characteristic Gothic building is the cathedral. Gothic architecture uses well-carved stone ashlars, and its essential elements include the arch. The thrust is transferred by means of external arches (flying buttresses) to external buttresses that end in pinnacles, which accentuates the verticality. The evolution of the flying buttresses should not only be considered as an aesthetic consideration, but also from a constructive point of view as an element of transmission of forces or loads. Thus, one evolves from a beam-type buttress to a simple arch, and finally to a rampant arch. In this work, we study the geometry of the rampant arch to determine which is the optimum from the constructive point of view. The optimum rampant arch obtained is the one with the common tangent to the two arches parallel to the slope line. A computer program was created to determine this optimal rampant arch by means of a numerical or graphical input. It was applied to several well-known and representative cases of Gothic art in France (church of Saint Urbain de Troyes) and Spain (Cathedral of Palma de Mallorca), establishing if they were designs of optimal rampant arches or not.

The dwarf mistletoe, Arceuthobium oxycedri, is found on populations of Juniperus oxycedrus, in central Spain. This species can have negative effects on the physiology of its host, including mortality. Understanding the mechanisms that control its distribution and dispersal is critical to assessing its potential for spread. We assessed dwarf mistletoe distribution within a population of J. oxycedrus, including infected and uninfected host individuals. A new null model of parasitic dispersion was built using two dispersal kernel forms that were simulated with lower and upper envelopes for second-order functions to summarize a point pattern, such as Ripley's K, nearest-neighbour distribution and pair correlation functions. Nine dispersal scenarios were constructed with half-bandwidth kernels (10, 20, 30 m) and initial population of infected trees (P 0 = 05, 10 and 20). These scenarios were compared with the observed pattern and evaluated using the goodnessof-fit test. Significant differences at short distance (r < 10 m) were found between the observed pattern and simulated patterns, corresponding to the range of seed dispersal of the dwarf mistletoe. Interactions between infected and uninfected hosts patterns at all scales were identified, suggesting that A. oxycedri uses other mechanisms in addition to ballistic seed shooting as secondary dispersal agents to spread to distances greater than 20 m. Given that the seed characteristics facilitate dispersal by adhesion, we infer that spread between host individuals is amplified by seed transport by birds or small mammals.

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