منابع مشابه
On the typical rank of real binary forms
We determine the rank of a general real binary form of degree d = 4 and d = 5. In the case d = 5, the possible values of the rank of such general forms are 3, 4, 5. The existence of three typical ranks was unexpected. We prove that a real binary form of degree d with d real roots has rank d.
متن کاملThe (Minimum) Rank of Typical Fooling-Set Matrices
A fooling-set matrix is a square matrix with nonzero diagonal, but at least one in every pair of diagonally opposite entries is 0. Dietzfelbinger et al. ’96 proved that the rank of such a matrix is at least √ n, for a matrix of order n. We ask for the typical minimum rank of a fooling-set matrix: For a fooling-set zerononzero pattern chosen at random, is the minimum rank of a matrix with that z...
متن کاملOn the Typical Rank of Real Closed Fields
In this note we introduce the notion of typical rank for any real closed field R, mimicking the case R = R. We show that the typical ranks are the same if we take a larger real closed field and in particular that for every format (n1, . . . , ns) the typical ranks of tensors of format (n1, . . . , ns) are the same over R and over R. AMS Subject Classification: 14N05
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We introduce a generative model, we call Tensorial Mixture Models (TMMs) based on mixtures of basic component distributions over local structures (e.g. patches in an image) where the dependencies between the local-structures are represented by a ”priors tensor” holding the prior probabilities of assigning a component distribution to each local-structure. In their general form, TMMs are intracta...
متن کاملTensorial Orientation Scores
Orientation scores [7, 10] are representations of images built using filters that only select on orientation (and not on the magnitude of the frequency). Importantly, they allow (easy) reconstruction, making them ideal for use in a filtering pipeline. Traditionally a specific set of orientations has to be chosen, and the response is determined for those orientations. This work introduces an alt...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1985
ISSN: 0024-3795
DOI: 10.1016/0024-3795(85)90070-9