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Render to Cube Texture Mapping Vertex Colors
"... Figure 1: A complex shading effect decomposed into userdefined modules in Spark. The dashed boxes show the programmable stages of the Direct3D 11 pipeline; the colored boxes show different concerns in the program. Some logical concerns crosscut multiple pipeline stages. In creating complex realti ..."
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Figure 1: A complex shading effect decomposed into userdefined modules in Spark. The dashed boxes show the programmable stages of the Direct3D 11 pipeline; the colored boxes show different concerns in the program. Some logical concerns crosscut multiple pipeline stages. In creating complex realtime shaders, programmers should be able to decompose code into independent, localized modules of their choosing. Current realtime shading languages, however, enforce a fixed decomposition into perpipelinestage procedures. Program concerns at other scales – including those that crosscut multiple pipeline stages – cannot be expressed as reusable modules. We present a shading language, Spark, and its implementation for modern graphics hardware that improves support for separation of concerns into modules. A Spark shader class can encapsulate code that maps to more than one pipeline stage, and can be extended and composed using objectoriented inheritance. In our tests, shaders written in Spark achieve performance within 2 % of HLSL.
Silver Cubes
"... An n × n matrix A is said to be silver if, for i = 1,2,...,n, each symbol in {1,2,...,2n − 1} appears either in the ith row or the ith column of A. The 38th International Mathematical Olympiad asked whether a silver matrix exists with n = 1997. More generally, a silver cube is a triple (K d n,I,c) ..."
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Cited by 3 (0 self)
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,I,c) where I is a maximum independent set in a Cartesian power of the complete graph Kn, and c: V (K d n) → {1,2,...,d(n − 1) + 1} is a vertex colouring where, for v ∈ I, the closed neighbourhood N[v] sees every colour. Silver cubes are related to codes, dominating sets, and those with n a prime power
Unique Sink Orientations of Cubes
 In Proc. 42 nd IEEE Symp. on Foundations of Comput. Sci
, 2001
"... Suppose we are given (the edge graph of) an n dimensional hypercube with its edges oriented so that every face has a unique sink. Such an orientation is called a unique sink orientation, and we are interested in finding the unique sink of the whole cube, when the orientation is given implicitly. Th ..."
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Cited by 27 (2 self)
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. The basic operation available is the socalled vertex evaluation, where we can access an arbitrary vertex of the cube, for which we obtain the orientations of the incident edges.
Hyperplane Arrangements Separating Arbitrary Vertex Classes in nCubes
"... Strictly layered feedforward networks with binary neurons are viewed as maps from the vertex set of an ncube to the vertex set of an lcube. With only one output neuron in principle they can realize any Boolean function on n inputs. We address the problem of determining the necessary and sufficien ..."
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Cited by 1 (0 self)
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Strictly layered feedforward networks with binary neurons are viewed as maps from the vertex set of an ncube to the vertex set of an lcube. With only one output neuron in principle they can realize any Boolean function on n inputs. We address the problem of determining the necessary
Growth series for vertexregular CAT.0 / cube complexes
"... We show that the known formula for the growth series of a rightangled Coxeter group holds more generally for any CAT(0) cube complex whose vertex links all have the same f –polynomial. 20F55, 20F67, 20F69; 05A15 1 ..."
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We show that the known formula for the growth series of a rightangled Coxeter group holds more generally for any CAT(0) cube complex whose vertex links all have the same f –polynomial. 20F55, 20F67, 20F69; 05A15 1
Analysis of Greedy Algorithm for Vertex Covering of Random Graph by Cubes
 COMUPTING AND INFORMATICS
, 2006
"... We study randomly induced subgraphs G of a hypercube. Specifically, we investigate vertex covering of G by cubes. We instantiate a greedy algorithm for this problem from general hypergraph covering algorithm [9], and estimate the length of vertex covering of G. In order to obtain this result, a num ..."
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Cited by 1 (1 self)
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We study randomly induced subgraphs G of a hypercube. Specifically, we investigate vertex covering of G by cubes. We instantiate a greedy algorithm for this problem from general hypergraph covering algorithm [9], and estimate the length of vertex covering of G. In order to obtain this result, a
Measurement of the NonCommon Vertex Error of a Double Corner Cube
"... ABSTRACT The Space Interferometry Mission (SIM) requires the control of the optical path of each interferometer with picometer accuracy. Laser metrology gauges are used to measure the path lengths to the fiiducial corner cubes at the siderostats. Due to the geometry of SIM a single corner cube does ..."
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commonalty of the vertices and correct for the error in orbit. SIM requires that the noncommon vertex error (NCVE) of the double corner cube to be less than 6 µm. The required accuracy for the knowledge of the NCVE is less than 1 µm. This paper explains a method of measuring noncommon vertices of a brassboard double
ON THE SIZE OF A MINIMAL VERTEX COVER IN A RANDOM SUBGRAPH OF THE nCUBE
"... We describe and analyze a construction of a vertex cover (consisting of subcubes) in a random subgraph of the ncube. The main idea of the construction is to select subcubes with minimal intersection into the vertex cover. We estimate the upper bound of such a vertex cover. Our analysis gives a theo ..."
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We describe and analyze a construction of a vertex cover (consisting of subcubes) in a random subgraph of the ncube. The main idea of the construction is to select subcubes with minimal intersection into the vertex cover. We estimate the upper bound of such a vertex cover. Our analysis gives a
FaultFree VertexPancyclicity in Twisted Cubes with Faulty Edges
"... Abstract—The ndimensional twisted cube, denoted by TQ n, a variation of the hypercube, possesses some properties superior to the hypercube. In this paper, we show that every vertex in TQ n lies on a faultfree cycle of every length from 6 to 2 n, even if there are up to n − 2 link faults. We also s ..."
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Abstract—The ndimensional twisted cube, denoted by TQ n, a variation of the hypercube, possesses some properties superior to the hypercube. In this paper, we show that every vertex in TQ n lies on a faultfree cycle of every length from 6 to 2 n, even if there are up to n − 2 link faults. We also
The hyperdeterminant and triangulations of the 4cube
, 2008
"... The hyperdeterminant of format 2 × 2 × 2 × 2isapolynomial of degree 24 in 16 unknowns which has 2894276 terms. We compute the Newton polytope of this polynomial and the secondary polytope of the 4cube. The 87959448 regular triangulations of the 4cube are classified into 25448 Dequivalence class ..."
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Cited by 26 (5 self)
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equivalence classes, one for each vertex of the Newton polytope. The 4cube has 80876 coarsest regular subdivisions, one for each facet of the secondary polytope, but only 268 of them come from the hyperdeterminant.
Results 1  10
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240