18,023 research outputs found

    Fixed Boundary Flows

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    We consider the fixed boundary flow with canonical interpretability as principal components extended on the non-linear Riemannian manifolds. We aim to find a flow with fixed starting and ending point for multivariate datasets lying on an embedded non-linear Riemannian manifold, differing from the principal flow that starts from the center of the data cloud. Both points are given in advance, using the intrinsic metric on the manifolds. From the perspective of geometry, the fixed boundary flow is defined as an optimal curve that moves in the data cloud. At any point on the flow, it maximizes the inner product of the vector field, which is calculated locally, and the tangent vector of the flow. We call the new flow the fixed boundary flow. The rigorous definition is given by means of an Euler-Lagrange problem, and its solution is reduced to that of a Differential Algebraic Equation (DAE). A high level algorithm is created to numerically compute the fixed boundary. We show that the fixed boundary flow yields a concatenate of three segments, one of which coincides with the usual principal flow when the manifold is reduced to the Euclidean space. We illustrate how the fixed boundary flow can be used and interpreted, and its application in real data

    Psychological Background of Black as Fashion Color ~A Comparative Study in Japan, China and U.S~

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    On Path Memory in List Successive Cancellation Decoder of Polar Codes

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    Polar code is a breakthrough in coding theory. Using list successive cancellation decoding with large list size L, polar codes can achieve excellent error correction performance. The L partial decoded vectors are stored in the path memory and updated according to the results of list management. In the state-of-the-art designs, the memories are implemented with registers and a large crossbar is used for copying the partial decoded vectors from one block of memory to another during the update. The architectures are quite area-costly when the code length and list size are large. To solve this problem, we propose two optimization schemes for the path memory in this work. First, a folded path memory architecture is presented to reduce the area cost. Second, we show a scheme that the path memory can be totally removed from the architecture. Experimental results show that these schemes effectively reduce the area of path memory.Comment: 5 pages, 6 figures, 2 table

    Refining grain structure and porosity of an aluminium alloy with intensive melt shearing

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    The official published version of the article can be obtained at the link below.Intensive melt shearing was achieved using a twin-screw machine to condition an aluminium alloy prior to solidification. The results show that intensive melt shearing has a significant grain-refining effect. In addition, the intensive melt shearing reduces both the volume fraction and the size of porosity. It can reduce the density index from 10.50% to 2.87% and the average size of porosity in the samples solidified under partial vacuum from around 1 mm to 100 μm.Financial support was obtained from the EPSRC and the Technology Strategy Board
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