Universal Reconfiguration of Facet-Connected Modular Robots by Pivots: The O(1) Musketeers

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

Constrained generalized Delaunay graphs are plane spanners

We look at generalized Delaunay graphs in the constrained setting by introducing line segments which the edges of the graph are not allowed to cross. Given an arbitrary convex shape C, a constrained Delaunay graph is constructed by adding an edge between two vertices p and q if and only if there exists a homothet of C with p and q on its boundary that does not contain any other vertices visible to p and q. We show that, regardless of the convex shape C used to construct the constrained Delaunay graph, there exists a constant t (that depends on C) such that it is a plane t-spanner of the visibility graph

Schmidt-hammer exposure ages from periglacial patterned ground (sorted circles) in Jotunheimen, Norway, and their interpretative problems

© 2016 Swedish Society for Anthropology and Geography Periglacial patterned ground (sorted circles and polygons) along an altitudinal profile at Juvflya in central Jotunheimen, southern Norway, is investigated using Schmidt-hammer exposure-age dating (SHD). The patterned ground surfaces exhibit R-value distributions with platycurtic modes, broad plateaus, narrow tails, and a negative skew. Sample sites located between 1500 and 1925 m a.s.l. indicate a distinct altitudinal gradient of increasing mean R-values towards higher altitudes interpreted as a chronological function. An established regional SHD calibration curve for Jotunheimen yielded mean boulder exposure ages in the range 6910 ± 510 to 8240 ± 495 years ago. These SHD ages are indicative of the timing of patterned ground formation, representing minimum ages for active boulder upfreezing and maximum ages for the stabilization of boulders in the encircling gutters. Despite uncertainties associated with the calibration curve and the age distribution of the boulders, the early-Holocene age of the patterned ground surfaces, the apparent cessation of major activity during the Holocene Thermal Maximum (HTM) and continuing lack of late-Holocene activity clarify existing understanding of the process dynamics and palaeoclimatic significance of large-scale sorted patterned ground as an indicator of a permafrost environment. The interpretation of SHD ages from patterned ground surfaces remains challenging, however, owing to their diachronous nature, the potential for a complex history of formation, and the influence of local, non-climatic factors

Spanning Properties of Yao and -Graphs in the Presence of Constraints

We present improved upper bounds on the spanning ratio of constrained -graphs with at least 6 cones and constrained Yao-graphs with 5 or at least 7 cones. Given a set of points in the plane, a Yao-graph partitions the plane around each vertex into m disjoint cones, each having aperture = 2p/m, and adds an edge to the closest vertex in each cone. Constrained Yao-graphs have the additional property that no edge properly intersects any of the given line segment constraints. Constrained -graphs are similar to constrained Yao-graphs, but use a different method to determine the closest vertex. We present tight bounds on the spanning ratio of a large family of constrained -graphs. We show that constrained -graphs with 4k + 2 (k ≥ 1 and integer) cones have a tight spanning ratio of 1 + 2sin(/2), where is 2p/(4k + 2). We also present improved upper bounds on the spanning ratio of the other families of constrained -graphs. These bounds match the current upper bounds in the unconstrained setting. We also show that constrained Yao-graphs with an even number of cones (m ≥ 8) have spanning ratio at most 1/(1 - 2sin(/2)) and constrained Yao-graphs with an odd number of cones (m ≥ 5) have spanning ratio at most 1/(1 - 2sin(3/8)). As is the case with constrained -graphs, these bounds match the current upper bounds in the unconstrained setting, which implies that like in the unconstrained setting using more cones can make the spanning ratio worse

On the spanning ratio of theta-graphs

We present improved upper bounds on the spanning ratio of a large family of θ-graphs. A θ-graph partitions the plane around each vertex into m disjoint cones, each having aperture θ = 2 π/m. We show that for any integer k ≥ 1, θ-graphs with 4k + 4 cones have spanning ratio at most 1 + 2 sin(θ/2) / (cos(θ/2) - sin(θ/2)). We also show that θ-graphs with 4k + 3 and 4k + 5 cones have spanning ratio at most cos(θ/4) / (cos(θ/2) - sin(3θ/4)). This is a significant improvement on all families of θ-graphs for which exact bounds are not known. For example, the spanning ratio of the θ-graph with 7 cones is decreased from at most 7.5625 to at most 3.5132. We also improve the upper bounds on the competitiveness of the θ-routing algorithm for these graphs to 1 + 2 sin(θ/2) / (cos(θ/2) - sin(θ/2)) on θ-graphs with 4k + 4 cones and to 1 + 2 sin(θ/2)·cos(θ/4) / (cos(θ/2) - sin(3θ/4)) on θ-graphs with 4k + 3 and 4k + 5 cones. For example, the routing ratio of the θ-graph with 7 cones is decreased from at most 7.5625 to at most 4.0490

Inventário masculino dos esquemas de gênero do autoconceito (IMEGA)

O propósito deste artigo foi elaborar e validar o Inventário Masculino dos Esquemas de Gênero do Autoconceito (IMEGA). Baseado nas estruturas fatoriais das escalas masculina e feminina do Inventário dos Esquemas de Gênero do Autoconceito (IEGA), este instrumento avalia os esquemas masculino e feminino do autoconceito dos homens. A amostra utilizada foi composta por estudantes universitários do sexo masculino. Para a validade de construto do IMEGA, foram realizadas análises fatoriais (Principal Axis Factoring - PAF), com rotações oblíquas e ortogonais, para ambas as escalas e análise da consistência interna dos fatores (alfa de Cronbach). Os resultados demonstram que ambas as escalas são compostas por estruturas multifatoriais que se assemelham às estruturas fatoriais do IEGA. Devidamente validado, o IMEGA pode ser utilizado para avaliar os esquemas masculino e feminino do autoconceito de indivíduos do sexo masculino

On Plane Constrained Bounded-Degree Spanners

Let P be a finite set of points in the plane and S a set of non-crossing line segments with endpoints in P. The visibility graph of P with respect to S, denoted (Formula presented.), has vertex set P and an edge for each pair of vertices u, v in P for which no line segment of S properly intersects uv. We show that the constrained half-(Formula presented.)-graph (which is identical to the constrained Delaunay graph whose empty visible region is an equilateral triangle) is a plane 2-spanner of (Formula presented.). We then show how to construct a plane 6-spanner of (Formula presented.) with maximum degree (Formula presented.), where c is the maximum number of segments of S incident to a vertex

The θ5-graph is a spanner

Given a set of points in the plane, we show that the θ-graph with 5 cones is a geometric spanner with spanning ratio at most 50+225≈9.960. This is the first constant upper bound on the spanning ratio of this graph. The upper bound uses a constructive argument that gives a (possibly se

Constrained generalized Delaunay are plane spanners

We look at generalized Delaunay graphs in the constrained setting by introducing line segments which the edges of the graph are not allowed to cross. Given an arbitrary convex shape C, a constrained Delaunay graph is constructed by adding an edge between two vertices p and q if and only if there exists a homothet of C with p and q on its boundary that does not contain any other vertices visible to p and q. We show that, regardless of the convex shape C used to construct the constrained Delaunay graph, there exists a constant t (that depends on C) such that it is a plane t-spanner of the visibility graph. Furthermore, we reduce the upper bound on the spanning ratio for the special case where the empty convex shape is an arbitrary rectangle to 2⋅(2l/s+1), where l and s are the length of the long and short side of the rectangle

Making triangulations 4-connected using flips

We show that any triangulation on n vertices can be transformed into a 4-connected one using at most ⌊(3n - 6)/5⌋ edge flips. We also give an example of a triangulation that requires ⌈(3n-10)/5⌉ flips to be made 4-connected, showing that our bound is tight. Our re- sult implies a new upper bound on the diameter of the flip graph of 5.2n - 24.4, improving on the bound of 6n - 30 by Mori et al. [4]