15 research outputs found
Locked and Unlocked Chains of Planar Shapes
We extend linkage unfolding results from the well-studied case of polygonal
linkages to the more general case of linkages of polygons. More precisely, we
consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are
hinged together sequentially at rotatable joints. Our goal is to characterize
the families of planar shapes that admit locked chains, where some
configurations cannot be reached by continuous reconfiguration without
self-intersection, and which families of planar shapes guarantee universal
foldability, where every chain is guaranteed to have a connected configuration
space. Previously, only obtuse triangles were known to admit locked shapes, and
only line segments were known to guarantee universal foldability. We show that
a surprisingly general family of planar shapes, called slender adornments,
guarantees universal foldability: roughly, the distance from each edge along
the path along the boundary of the slender adornment to each hinge should be
monotone. In contrast, we show that isosceles triangles with any desired apex
angle less than 90 degrees admit locked chains, which is precisely the
threshold beyond which the inward-normal property no longer holds.Comment: 23 pages, 25 figures, Latex; full journal version with all proof
details. (Fixed crash-induced bugs in the abstract.
Profiling social, emotional and behavioural difficulties of children involved in direct and indirect bullying behaviours
Being involved in bullying places a child at risk of poor psychosocial and educational outcomes. This study aimed to examine the profile of behavioural, emotional and social functioning for two subtypes of bullying; direct and indirect (relational). Pupils aged between seven and eleven years old completed sociometric measures of social inclusion and bullying behaviour to identify 192 pupils considered to be involved in either direct, indirect, both or neither types of bullying. These pupils and their teachers completed a battery of assessments relating to behaviour, social competence and self-perception. All bully-groups experienced similar levels of significant social rejection. ‘Direct’ and ‘both’ groups showed the greatest number of behavioural, emotional and social difficulties, while the ‘indirect’ group showed weaknesses in self-perception, but no teacher-rated problems. Understanding the behavioural, emotional and social correlates of bullying is of particular importance for early identification of children at risk of becoming bullies and for developing targeted interventions
Social media for openness and accountability in the public sector: cases in the Greek context
This paper explores the use of government social media for opennessand accountability. The extant literature has
highlighted the benefits of social media use in this context to enhance citizen participation and engagement in
decision-making and policy development, facilitate openness and transparency efforts, and reduce corruption. Yet, there are limited studies that discuss those properties of social media that can afford openness and accountability, and their implications for policy and practise. To address these gaps, a study is conducted in the Greek context using interviews with top managers, policy makers, and relevant stakeholders across five initiatives. We discuss distinct affordances for openness and accountability, and propose their inclusion as building blocks of the national ICT policy for openness and accountability. Finally, we provide the implications of the affordances lens for policy and practise, the limitations of the study and future research avenues
Hinged Dissections Exist
We prove that any finite collection of polygons of equal area has a common hinged dissection.
That is, for any such collection of polygons there exists a chain of polygons hinged at vertices
that can be folded in the plane continuously without self-intersection to form any polygon in
the collection. This result settles the open problem about the existence of hinged dissections
between pairs of polygons that goes back implicitly to 1864 and has been studied extensively
in the past ten years. Our result generalizes and indeed builds upon the result from 1814 that
polygons have common dissections (without hinges). Our proofs are constructive, giving explicit
algorithms in all cases. For two planar polygons whose vertices lie on a rational grid, both the
number of pieces and the running time required by our construction are pseudopolynomial.
This bound is the best possible, even for unhinged dissections. Hinged dissections have possible
applications to reconfigurable robotics, programmable matter, and nanomanufacturing.Massachusetts Institute of Technology/Akamai Presidential FellowshipNational Science Foundation (U.S.) (Graduate Research Fellowship
Path Minima Queries in Dynamic Weighted Trees
Abstract. In the path minima problem on trees each tree edge is assigned a weight and a query asks for the edge with minimum weight on a path between two nodes. For the dynamic version of the problem on a tree, where the edge-weights can be updated, we give comparisonbased and RAM data structures that achieve optimal query time. These structures support inserting a node on an edge, inserting a leaf, and contracting edges. When only insertion and deletion of leaves in a tree are needed, we give two data structures that achieve optimal and significantly lower query times than when updating the edge-weights is allowed. One is a semigroup structure for which the edge-weights are from an arbitrary semigroup and queries ask for the semigroup-sum of the edge-weights on a given path. For the other structure the edge-weights are given in the word RAM. We complement these upper bounds with lower bounds for different variants of the problem.