135,932 research outputs found
Cutting the d-cube
No full textSome problems concerned with cutting faces of the cube with affine or linear spaces are considered. It is shown that through any d-3 points of Rd there passes a hyperplane which cuts all the facets of the d-cube. Furthermore, it is shown that if m < d - 1 and d' < d - [(m + 1)/3], then no m-dimensional affine subspace of Rd cuts all the d'-dimensional faces of the cube
Multi-Level Sensory Interpretation and Adaptation in a Mobile Cube
No full textSignals from sensors are often analyzed in a sequence of steps, starting with the raw sensor data and eventually ending up with a classification or abstraction of these data. This paper will give a practical example of how the same information can be trained and used to initiate multiple interpretations of the same data on different, application-oriented levels. Crucially, the focus is on expanding embedded analysis software, rather than adding more powerful, but possibly resource-hungry, sensors. Our illustration of this approach involves a tangible input device the shape of a cube that relies exclusively on lowcost accelerometers. The cube supports calibration with user supervision, it can tell which of its sides is on top, give an estimate of its orientation relative to the user, and recognize basic gestures
Property A and CAT(0) cube complexes
No full textProperty A is a non-equivariant analogue of amenability defined for metric spaces. Euclidean spaces and trees are examples of spaces with Property A. Simultaneously generalising these facts, we show that finite-dimensional CAT(0) cube complexes have Property A. We do not assume that the complex is locally finite. We also prove that given a discrete group acting properly on a finite-dimensional CAT(0) cube complex the stabilisers of vertices at infinity are amenable
Flow around a cube in a turbulent boundary layer: LES and experiment
No full textWe present a numerical simulation of flow around a surface mounted cube placed in a turbulent boundary layer which, although representing a typical wind environment, has been specifically tailored to match a series of wind tunnel observations. The simulations were carried out at a Reynolds number, based on the velocity U at the cube height h, of 20,000—large enough that many aspects of the flow are effectively Reynolds number independent. The turbulence intensity was about 18% at the cube height, and the integral length scale was about 0.8 times the cube height h. The Jenson number Je=h/z0, based on the approach flow roughness length z0, was 600, to match the wind tunnel situation. The computational mesh was uniform with a spacing of h/32, aiding rapid convergence of the multigrid solver, and the governing equations were discretised using second-order finite differences within a parallel multiblock environment. The results presented include detailed comparison between measurements and LES computations of both the inflow boundary layer and the flow field around the cube including mean and fluctuating surface pressures. It is concluded that provided properly formulated inflow and surface boundary conditions are used, LES is now a viable tool for use in wind engineering problems concerning flow over isolated bodies. In particular, both mean and fluctuating surface pressures can be obtained with a similar degree of uncertainty as usually associated with wind tunnel modelling
A d-move local permutation routing for the d-cube
No full textAbstractOptimal packet routing algorithms for all binary d-cubes of dimension d ⩽ 7 are presented. The algorithms given are synchronous, offer distributed control, and assume d-port, multiaccepting communication. While the previous best known packet routing algorithm [3]on the 7-cube takes 11 time-units, our algorithm has reduced the worst-case time complexity to the minimum possible of 7 units. We also give an optimal routing algorithm for the ternary 4-cube
On the coverings of the d-cube for d≤6
No full textAbstractA cut of the d-cube is any maximal set of edges that is sliced by a hyperplane, that is, intersecting the interior of the d-cube but avoiding its vertices. A set of k distinct cuts that cover all the edges of the d-cube is called a k-covering. The cut number S(d) of the d-cube is the minimum number of hyperplanes that slice all the edges of the d-cube. Here by applying the geometric structures of the cuts, we prove that there are exactly 13 non-isomorphic 3-coverings for the 3-cube. Moreover, an extended algorithmic approach is given that has the potential to find S(7) by means of largely-distributed computing. As a computational result, we also present a complete enumeration of all 4-coverings of the 4-cube as well as a complete enumeration of all 4-coverings of 78 edges of the 5-cube
Exploring Cube Affordance: Towards Classification of Non-Verbal dynamics of Physical Interfaces For Wearable Computing
No full textAbstract. Current input technologies for wearable computers are difficult to use and learn and can be unreliable. Physical interfaces offer an alternative to traditional input methods. In this paper we propose that developing a well-designed physical interface requires an exploration of the psychological idea of affordance. We present our findings from a design study in which we explore the natural affordance of a cube and suggest possible requirements for the design of graspable cubeshaped physical interfaces as alternative rich-action input device. We expect that such a framework will enhance the precision and usability of devices for wearable and mobile computing
Interconnection networks for parallel and distributed computing
No full textParallel computers are generally either shared-memory machines or distributed- memory machines. There are currently technological limitations on shared-memory architectures and so parallel computers utilizing a large number of processors tend tube distributed-memory machines. We are concerned solely with distributed-memory multiprocessors. In such machines, the dominant factor inhibiting faster global computations is inter-processor communication. Communication is dependent upon the topology of the interconnection network, the routing mechanism, the flow control policy, and the method of switching. We are concerned with issues relating to the topology of the interconnection network. The choice of how we connect processors in a distributed-memory multiprocessor is a fundamental design decision. There are numerous, often conflicting, considerations to bear in mind. However, there does not exist an interconnection network that is optimal on all counts and trade-offs have to be made. A multitude of interconnection networks have been proposed with each of these networks having some good (topological) properties and some not so good. Existing noteworthy networks include trees, fat-trees, meshes, cube-connected cycles, butterflies, Möbius cubes, hypercubes, augmented cubes, k-ary n-cubes, twisted cubes, n-star graphs, (n, k)-star graphs, alternating group graphs, de Bruijn networks, and bubble-sort graphs, to name but a few. We will mainly focus on k-ary n-cubes and (n, k)-star graphs in this thesis. Meanwhile, we propose a new interconnection network called augmented k-ary n- cubes. The following results are given in the thesis.1. Let k ≥ 4 be even and let n ≥ 2. Consider a faulty k-ary n-cube Q(^k_n) in which the number of node faults f(_n) and the number of link faults f(_e) are such that f(_n) + f(_e) ≤ 2n - 2. We prove that given any two healthy nodes s and e of Q(^k_n), there is a path from s to e of length at least k(^n) - 2f(_n) - 1 (resp. k(^n) - 2f(_n) - 2) if the nodes s and e have different (resp. the same) parities (the parity of a node Q(^k_n) in is the sum modulo 2 of the elements in the n-tuple over 0, 1, ∙∙∙ , k - 1 representing the node). Our result is optimal in the sense that there are pairs of nodes and fault configurations for which these bounds cannot be improved, and it answers questions recently posed by Yang, Tan and Hsu, and by Fu. Furthermore, we extend known results, obtained by Kim and Park, for the case when n = 2.2. We give precise solutions to problems posed by Wang, An, Pan, Wang and Qu and by Hsieh, Lin and Huang. In particular, we show that Q(^k_n) is bi-panconnected and edge-bipancyclic, when k ≥ 3 and n ≥ 2, and we also show that when k is odd, Q(^k_n) is m-panconnected, for m = (^n(k - 1) + 2k - 6’ / ‘_2), and (k -1) pancyclic (these bounds are optimal). We introduce a path-shortening technique, called progressive shortening, and strengthen existing results, showing that when paths are formed using progressive shortening then these paths can be efficiently constructed and used to solve a problem relating to the distributed simulation of linear arrays and cycles in a parallel machine whose interconnection network is Q(^k_n) even in the presence of a faulty processor.3. We define an interconnection network AQ(^k_n) which we call the augmented k-ary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube Q(^k_n) has a number of attractive properties (in the context of parallel computing). For example, we show that the augmented k-ary n-cube Q(^k_n) - is a Cayley graph (and so is vertex-symmetric); has connectivity 4n - 2, and is such that we can build a set of 4n - 2 mutually disjoint paths joining any two distinct vertices so that the path of maximal length has length at most max{{n- l)k- (n-2), k + 7}; has diameter [(^k) / (_3)] + [(^k - 1) /( _3)], when n = 2; and has diameter at most (^k) / (_4) (n+ 1), for n ≥ 3 and k even, and at most [(^k)/ (_4) (n + 1) + (^n) / (_4), for n ^, for n ≥ 3 and k odd.4. We present an algorithm which given a source node and a set of n - 1 target nodes in the (n, k)-star graph S(_n,k) where all nodes are distinct, builds a collection of n - 1 node-disjoint paths, one from each target node to the source. The collection of paths output from the algorithm is such that each path has length at most 6k - 7, and the algorithm has time complexity O(k(^3)n(^4))
d-cube decompositions of K-n/K-m
No full textNecessary conditions on n, m and d are given for the existence of an edge-disjoint decomposition of K-n\K-m into copies of the graph of a d-dimensional cube. Sufficiency is shown when d = 3 and, in some cases, when d = 2(t). We settle the problem of embedding 3-cube decompositions of K-m into 3-cube decompositions of K-n; where n greater than or equal to m
The Rubik Cube of the Wider Middle East. CEPS Paperback. February 2003
No full textGiven the complexity and severity of the problems involved, this book asserts that a comprehensive regional initiative for the Wider Middle East is called for and proceeds to outline exactly what that would entail. The first-best solution would be the adoption of a convergent strategy towards the Wider Middle East by the EU and US together. The authors argue that a US policy that waged a unilateral war against Iraq and left the Israeli-Arab conflict still festering would mean counterproductive effects for the fight against Al Qaeda and huge damage to Western-Islamic relations as well as to the transatlantic alliance. At the same time, however, the EU must be prepared to strengthen both the ‘carrots’ and the ‘sticks’ in its policies in the region in any case.
The point of the image of Rubik’s Cube is to stress the need for a coherent vision for all three regions of the Wider Middle East (Maghreb, Mashreq and the Gulf), for all three major vectors of policy (politics, economics and security), and for all three major external participants (the US, Europe and the international organisations)
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