BUSCADOR RECOLECTA

Wildlife-vehicle collisions on road networks represent a natural problem between human populations and the environment,
that affects wildlife management and raise a risk to the life and safety of car drivers. We propose a statistically principled
method for kernel smoothing of point pattern data on a linear network when the first-order intensity depends on covariates.
In particular, we present a consistent kernel estimator for the first-order intensity function that uses a convenient relationship between the intensity and the density of events location over the network, which also exploits the theoretical
relationship between the original point process on the network and its transformed process through the covariate. We derive
the asymptotic bias and variance of the estimator, and adapt some data-driven bandwidth selectors to estimate the optimal
bandwidth. The performance of the estimator is analysed through a simulation study under inhomogeneous scenarios. We
present a real data analysis on wildlife-vehicle collisions in a region of North-East of Spain., The authors acknowledge the support of the Spanish Ministry of Economy, Industry and Competitivity through Grants MTM2016-76969P, MTM2016-78917-R and MTM2017- 86767-R. J. Mateu is also partially funded by grant UJI-B2018-04.

Statistical analysis of point processes often assumes that the underlying process is isotropic in the sense that its distribution is invariant under rotation. For point processes on ℝ2, some tests based on the K‐ and nearest neighbour orientation functions have been proposed to check such an assumption. However, anisotropy and directional analysis need proper caution when dealing with point processes on linear networks, as the implicit geometry of the network forces particular directions that the points of the pattern have to necessarily meet. In this paper, we adapt such tests to the case of linear networks, and discuss how to use them to detect particular directional preferences, even at some angles that are different from the main angles imposed by the network. Through a simulation study, we check the performance of our proposals under different settings, over a linear network and a dendrite tree, showing that they are able to precisely detect the directional preferences of the points in the pattern, regardless the type of spatial interaction and the geometry of the network. We use our tests to highlight the directional preferences in the spatial distribution of traffic accidents in Barcelona (Spain) during 2019, and in Medellin (Colombia), during 2016., J. Mateu has been partially funded by grants PID2019-107392RB-I00 from the Spanish Ministry of Science, AICO/2019/198 from Generalitat Valenciana, and UJI-B2018-04 from UJI, and C. Comas by grant MTM2017-86767-R from the Spanish Ministry of Science.

The reliability polynomial of a graph gives the probability that a graph remains operational when all its edges could fail independently with a certain fixed probability. In general, the problem of finding uniformly most reliable graphs inside a family of graphs, that is, one graph whose reliability is at least as large as any
other graph inside the family, is very difficult. In this paper, we study this problem in the family of graphs containing a hamiltonian cycle., The authors would like to thank the anonymous referees whose useful comments led to an improvement of the manuscript. Research of the authors was supported in part by grant MTM2017-86767-R (Spanish Ministerio de Ciencia e Innovación)

The Mondrian problem consists of dissecting a square of side length n ∈ N into non-congruent rectangles with natural length sides such that the difference d(n) between the largest and the smallest areas of the rectangles partitioning the square is minimum. In this paper, we compute some bounds on d(n) in terms of the number of rectangles of the square partition. These bounds provide us optimal partitions for some values of n ∈ N. We provide a sequence of square partitions such that d(n)/n2 tends to zero for n large enough. For the case of 'perfect' partitions, that is, with d(n) = 0, we show that, for any fixed powers s1, . . . , sm, a square with side length n = p s1 1 · · · p smm , can have a perfect Mondrian partition only if p1 satisfies a given lower bound. Moreover, if n(x) is the number of side lengths x (with n ≤ x) of squares not having a perfect partition, we prove that its 'density' n(x) x is asymptotic to (log(log(x))2 2 log x , which improves previous results., The research of C. Dalfó and N. López has been partially supported by grant MTM2017-86767-R (Spanish Ministerio de Ciencia e Innovación). The research of C. Dalfó and M. A. Fiol has been partially supported by AGAUR from the Catalan Government under project 2017SGR1087 and by Spanish Ministerio de Ciencia e Innovación from the Spanish Government under project PGC2018-095471-B-I00. The research of the first author has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 734922.

With the clear goal of improving photovoltaic (PV) technology performance towards
nearly-zero energy buildings, a graph theory-based model that characterizes photovoltaic panel
structures is developed. An algorithm to obtain all possible configurations of a given number of
PV panels is presented and the results are exposed for structures using 3 to 7 panels. Two different
classifications of all obtained structures are carried out: the first one regarding the maximum power
they can produce and the second according to their capability to produce energy under a given
probability that the solar panels will fail. Finally, both classifications are considered simultaneously
through the expected value of power production. This creates structures that are, at the same time,
reliable and efficient in terms of production. The parallel associations turn out to be optimal, but
some other less expected configurations prove to be rated high., The authors would like to thank “Ministerio de Economía y Competitividad” and “Ministerio de Ciencia e Innovación” of Spain for the funding (grant reference ENE2016-81040-R and PID2019-111536RB-I00). Research of J. M. Ceresuela was supported by Secretaria d’Universitats i Recerca del Departament d’Empresa i Coneixement de la Generalitat de Catalunya (grant 2020 FISDU 00596). D. Chemisana thanks ”Institució Catalana de Recerca i Estudis Avançats (ICREA)” for the ICREA Acadèmia award. Research of N.López was supported in part by grant MTM2017-86767-R and PID2020-115442RB-I00 (Spanish Ministerio de Ciencia e Innovacion).