Beaconless geocast protocols are routing protocols used to send messages in mobile ad-hoc wireless networks, in which the only information available to each node is its own location. Messages get routed in a distributed manner: each node uses local decision rules based on the message source and destination, and its own location. In this paper we analyze six different beaconless geocast protocols, focusing on two relevant 1D scenarios. The selection of protocols reflects the most relevant types of protocols proposed in the literature, including those evaluated in previous computer simulations. We present a formal and structured analysis of the maximum number of messages that a node can receive, for each protocol, in each of the two scenarios. This is a measure of the network load incurred by each protocol. Our analysis, that for some of the protocols requires an involved probabilistic analysis, confirms behaviors that had been observed only through simulations before.

Early energy analyses of agriculture revealed that behind higher labor and land productivity of industrial farming, there was a decrease in energy returns on energy (EROI) invested, in comparison to more traditional organic agricultural systems. Studies on recent trends show that efficiency gains in production and use of inputs have again somewhat improved energy returns. However, most of these agricultural energy studies have focused only on external inputs at the crop level, concealing the important role of internal biomass flows that livestock and forestry recirculate within agroecosystems. Here, we synthesize the results of 82 farm systems in North America and Europe from 1830 to 2012 that for the first time show the changing energy profiles of agroecosystems, including livestock and forestry, with a multi-EROI approach that accounts for the energy returns on external inputs, on internal biomass reuses, and on all inputs invested. With this historical circular bioeconomic approach, we found a general trend towards much lower external returns, little or no increases in internal returns, and almost no improvement in total returns. This “energy trap” was driven by shifts towards a growing dependence of crop production on fossil-fueled external inputs, much more intensive livestock production based on feed grains, less forestry, and a structural disintegration of agroecosystem components by increasingly linear industrial farm managements. We conclude that overcoming the energy trap requires nature-based solutions to reduce current dependence on fossil-fueled external industrial inputs and increase the circularity and complexity of agroecosystems to provide healthier diets with less animal products.

We present the first universal reconfiguration algorithm for transforming a modular robot between any two facet-connected square-grid configurations using pivot moves. More precisely, we show that five extra "helper" modules ("musketeers") suffice to reconfigure the remaining n modules between any two given configurations. Our algorithm uses O(n^2) pivot moves, which is worst-case optimal. Previous reconfiguration algorithms either require less restrictive "sliding" moves, do not preserve facet-connectivity, or for the setting we consider, could only handle a small subset of configurations defined by a local forbidden pattern. Configurations with the forbidden pattern do have disconnected reconfiguration graphs (discrete configuration spaces), and indeed we show that they can have an exponential number of connected components. But forbidding the local pattern throughout the configuration is far from necessary, as we show that just a constant number of added modules (placed to be freely reconfigurable) suffice for universal reconfigurability. We also classify three different models of natural pivot moves that preserve facet-connectivity, and show separations between these models.

We give both efficient algorithms and hardness results for reconfiguring between two connected configurations of modules in the hexagonal grid. The reconfiguration moves that we consider are "pivots", where a hexagonal module rotates around a vertex shared with another module. Following prior work on modular robots, we define two natural sets of hexagon pivoting moves of increasing power: restricted and monkey moves. When we allow both moves, we present the first universal reconfiguration algorithm, which transforms between any two connected configurations using O(n^3) monkey moves. This result strongly contrasts the analogous problem for squares, where there are rigid examples that do not have a single pivoting move preserving connectivity. On the other hand, if we only allow restricted moves, we prove that the reconfiguration problem becomes PSPACE-complete. Moreover, we show that, in contrast to hexagons, the reconfiguration problem for pivoting squares is PSPACE-complete regardless of the set of pivoting moves allowed. In the process, we strengthen the reduction framework of Demaine et al. [FUN'18] that we consider of independent interest.

In a visibility representation of a graph G, the vertices are represented by non-overlapping geometric objects, while the edges are represented as segments that only intersect the geometric objects associated with their end-vertices. Given a set P of n points, an Anchored Visibility Representation of a graph G with n vertices is a visibility representation such that for each vertex v of G, the geometric object representing v contains a point of P. We prove positive and negative results about the existence of anchored visibility representations under various models, both in 2D and in 3D space. We consider the case when the mapping between the vertices and the points is not given and the case when it is only partially given.

We present a new algorithm that reconfigures between any two edge-connected configurations of n sliding squares within their bounding boxes. The algorithm achieves the reconfiguration by means of Θ(n2) slide moves. A visual simulator and a set of experiments allows us to compare the performance over different shapes, showing that in many practical cases the number of slide moves grows significantly slower than in others as n increases.

We study five existing map construction algorithms, designed and tested with urban vehicle data in mind, and apply them to hiking trajectories with different terrain characteristics. Our main goal is to better understand the existing strategies and their limitations, in order to shed new light into the current challenges for map construction algorithms. We carefully analyze the results obtained by each algorithm focusing on the local details of the generated maps. Our analysis includes the characterization of 10 types of common artifacts, which occur in the results of more than one algorithm, and 7 algorithmic-specific artifacts, which are consequences of different algorithmic strategies. This allows us to extract systematic conclusions about the main challenges to fully automatize the construction of maps from trajectory data, to detect the strengths and weaknesses of the potential different strategies, and to suggest possible ways to design higher-quality map construction methods. We consider that this analysis will be of help for designing new and better methods that perform well in wider and more realistic contexts, not only for road map or hiking reconstruction, but also for other types of trajectory data.

The farthest-color Voronoi diagram (FCVD) is a farthest-site Voronoi structure defined on a family 𝒫 of m point-clusters in the plane, where the total number of points is n. The FCVD finds applications in problems related to color spanning objects and facility location. We identify structural properties of the FCVD, refine its combinatorial complexity bounds, and list conditions under which the diagram has O(n) complexity. We show that the diagram may have complexity (n+m^2) even if clusters have disjoint convex hulls. We present construction algorithms with running times ranging from O(nlog n) , when certain conditions are met, to O((n+s(𝒫 ))log ^3n) in general, where s(P) is a parameter reflecting the number of straddles between pairs of clusters in 𝒫 ( s(P)∈ O(mn) ). A pair of points q_1,q_2∈ Q is said to straddle p_1,p_2∈ P if the line segment q_1q_2 intersects (straddles) the line through p_1,p_2 and the disks through (p_1,p_2,q_1) and (p_1,p_2,q_2) contain no points of P, Q. The complexity of the diagram is shown to be O(n+s(𝒫 )) .

Map construction is the problem of reconstructing a travel network based on trajectory data of entities travelling on the network. While many map construction algorithms reconstruct the global structure of a network well, local features such as location of crossings and turns are generally harder to reconstruct correctly, in particular for noisy and irregularly sampled data. We demonstrate how subtrajectory clustering can be used to construct maps that capture both the global structure and local features well.

The farthest-color Voronoi diagram (FCVD) is a farthest-site Voronoi diagram defined on a family of m clusters (sets) of points in the plane. Its combinatorial complexity in the worst case is Θ(mn), where n is the total number of points. In this paper we give structural properties of the FCVD and list sufficient conditions under which this diagram has O(n) combinatorial complexity. For such cases we present efficient construction algorithms.

Rectangulations are partitions of a square into axis-aligned rectangles. A number of results provide bijections between combinatorial equivalence classes of rectangulations and families of pattern-avoiding permutations. Other results deal with local changes involving a single edge of a rectangulation, referred to as flips, edge rotations, or edge pivoting. Such operations induce a graph on equivalence classes of rectangulations, related to so-called flip graphs on triangulations and other families of geometric partitions. In this note, we consider a family of flip operations on the equivalence classes of diagonal rectangulations, and their interpretation as transpositions in the associated Baxter permutations, avoiding the vincular patterns 3142, 2413 . This complements results from Law and Reading (JCTA, 2012) and provides a complete characterization of flip operations on diagonal rectangulations, in both geometric and combinatorial terms.

El sistema universitario ha ido evolucionando progresivamente hacia una configuración más amplia y equitativa, pero todavía subsisten una serie de desigualdades manifiestas. Además de analizar el importante crecimiento del acceso a la universidad en las últimas décadas, en el presente artículo se analiza si este crecimiento se ha producido o no de forma socialmente equitativa. Por un lado, se aborda si las desigualdades económicas y culturales de partida inciden no sólo en el acceso a la universidad, sino también en la elección de los estudios y en las condiciones de vida estudiantil de los universitarios. Asimismo, al examinar la igualdad de oportunidades en el acceso, el estudio considera también la cuestión desde el punto de vista de la igualdad de género, así como el efecto del incremento sustancial de los precios de las matrículas universitarias, entre otros aspectos. Estas desigualdades en el sistema educativo, pueden comportar no solo efectos en la equidad, sino un mal aprovechamiento del talento de una sociedad.

We propose a new approach for constructing the underlying map from trajectory data. Our algorithm is based on the idea that road segments can be identified as stable subtrajectory clusters in the data. For this, we consider how subtrajectory clusters evolve for varying distance values, and choose stable values for these. In doing so we avoid a global proximity parameter. Within trajectory clusters, we choose representatives, which are combined to form the map. We experimentally evaluate our algorithm on vehicle and hiking tracking data. These experiments demonstrate that our approach can naturally separate roads that run close to each other and can deal with outliers in the data, two issues that are notoriously difficult in road network reconstruction.

Energy balances of farm systems have overlooked the role of energy flows that remain within agro-ecosystems. Yet, such internal flows fulfil important socio-ecological functions, including maintenance of farmers themselves and agro-ecosystem structures. Farming can either give rise to complex landscapes that favour associated biodiversity, or the opposite. This variability can be understood by assessing several types of Energy Returns on Investment (EROI). Applying these measures to a farm system in Catalonia, Spain in 1860 and in 1999, reveals the expected decrease in the ratio of final energy output to total and external inputs. The transition from solar-based to a fossil fuel based agro-ecosystem was further accompanied by an increase in the ratio of final energy output to biomass reused, as well as an absolute increase of Unharvested Phytomass grown in derelict forestland. The study reveals an apparent link between reuse of biomass and the decrease of landscape heterogeneity along with its associated biodiversity. (C) 2016 Elsevier B.V. All rights reserved.

Beaconless geocast protocols are routing protocols used to send messages in mobile ad-hoc wireless networks, in which the only information available to each node is its own location. Packets get routed in a distributed manner: each node uses local decision rules based on the packet source and destination, and its own location. In this paper we analyze some of the most relevant existing protocols in a formal and structured way, focusing on two relevant 1D scenarios.

We present a robust and compact meta-module for edge-hinged modular robot units such as M-TRAN, SuperBot, SMORES, UBot, PolyBot and CKBot, as well as for central-point-hinged ones such as Molecubes and Roombots. Thanks to the rotational degrees of freedom of these units, the novel meta-module is able to expand and contract, as to double/halve its length in each dimension. Moreover, for a large class of edge-hinged robots the proposed meta-module also performs the scrunch/relax and transfer operations required by any tunneling-based reconfiguration strategy, such as those designed for Crystalline and Telecube robots. These results make it possible to apply efficient geometric reconfiguration algorithms to this type of robots. We prove the size of this new meta-module to be optimal. Its robustness and performance substantially improve over previous results.

We present an energy analysis of past and present farm systems aimed to contribute to their sustainability assessment. Looking at agroecosystems as a set of energy loops between nature and society, and adopting a farm-operator standpoint at landscape level to set the system boundaries, enthalpy values of energy carriers are accounted for net Final Produce going outside as well as for Biomass Reused cycling inside, and External Inputs are accounted using embodied values. Human Labour is accounted for the fraction of the energy intake of labouring people devoted to perform farm work, considering the local or external origin of their food basket. In this approach the proportion of internal Biomass Reused becomes a hallmark of organic farm systems that tend to save External Inputs, whereas industrial farming and livestock breeding in feedlots tend to get rid of reuses replacing them with inputs coming from outside. Hence, decomposing the internal or external energy throughputs may bring to light their contrasting sociometabolic profiles. A Catalan case study in 1860 and 1990 is used as a test bench to show how revealing this decomposing analysis may be to plot the energy profiles of farm systems and their possible improvement pathways.