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We consider the budget allocation problem over bipartite influence model proposed by Alon et al. (Alon et al., 2012). This problem can be viewed as the well-known influence maximization problem with budget constraints. We first show that this problem and its much more general form fall into a general setting; namely the monotone submodular function(More)
We consider a generalization of the submodular cover problem based on the concept of diminishing return property on the integer lattice. We are motivated by real scenarios in machine learning that cannot be captured by (traditional) submodular set functions. We show that the generalized submodular cover problem can be applied to various problems and devise(More)
The problem of maximizing non-negative monotone submodular functions under a certain constraint has been intensively studied in the last decade. In this paper, we address the problem for functions defined over the integer lattice. Suppose that a non-negative monotone submodular function f : Z+ → R+ is given via an evaluation oracle. Assume further that f(More)
A 3D quasiperiodic pattern by projection from an nD lattice can be de®ned by an orthonormal n n lattice matrix which produces basis vectors in pattern space with a prescribed arrangement and basis vectors in perpendicular or test space satisfying the quasicrystallographic condition. A 16 16 lattice matrix is derived which produces basis vectors in pattern(More)
For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace is spanned by rank-1 matrices, the matrices can be obtained by the tensor CP decomposition. For the higher rank case, the situation is not as straightforward. In this work we(More)
As is well known, the smallest possible ratio between the spectral norm and the Frobenius norm of an m× n matrix with m ≤ n is 1/ √ m and is (up to scalar scaling) attained only by matrices having pairwise orthonormal rows. In the present paper, the smallest possible ratio between spectral and Frobenius norms of n1×· · ·×nd tensors of order d, also called(More)