Tensor principal component analysis via sum-of
... show how to use SoS to efficiently find sparse vectors planted in random linear subspaces, and the same authors give an algorithm for dictionary learning with strong provable statistical guarantees (Barak et al., 2014a,b). These algorithms, too, proceed by decomposition of an underlying random tenso ...
... show how to use SoS to efficiently find sparse vectors planted in random linear subspaces, and the same authors give an algorithm for dictionary learning with strong provable statistical guarantees (Barak et al., 2014a,b). These algorithms, too, proceed by decomposition of an underlying random tenso ...
Las Vegas algorithms for matrix groups
... bounded by u(G). Also, G contains a subgroup H isomorphic to G1 x G2, where G I is the same kind of classical group as G acting projectively on a vector space of dimension d - 4, and G2 is nontrivial. By Fact 2.5 and the order of IG1 I there is a prime number r dividing lGll and not dividing qi-1 fo ...
... bounded by u(G). Also, G contains a subgroup H isomorphic to G1 x G2, where G I is the same kind of classical group as G acting projectively on a vector space of dimension d - 4, and G2 is nontrivial. By Fact 2.5 and the order of IG1 I there is a prime number r dividing lGll and not dividing qi-1 fo ...
Introduction. This primer will serve as a introduction to Maple 10 and
... use square brackets to create vectors ( a := [ expr] ) and access the components by calling for a[i] ( e.g. a[2]. ) For example: ...
... use square brackets to create vectors ( a := [ expr] ) and access the components by calling for a[i] ( e.g. a[2]. ) For example: ...
Enhanced PDF - Project Euclid
... In [34], Tao and Vu ask the following natural question: what analog of Theorem 1.1 is possible in the case where the matrix is sparse, where entries become more likely to be zero as n increases, instead of entries having the same distribution for all n? One goal of the current paper is to provide an ...
... In [34], Tao and Vu ask the following natural question: what analog of Theorem 1.1 is possible in the case where the matrix is sparse, where entries become more likely to be zero as n increases, instead of entries having the same distribution for all n? One goal of the current paper is to provide an ...
SEQUENTIAL DEFINITIONS OF CONTINUITY FOR REAL
... almost convergence or statistical convergence (these will be discussed below). In all of these investigations, the resulting continuous functions were either precisely the linear functions or precisely the functions which are continuous in the ordinary sense. This paper shows that, as long as the ne ...
... almost convergence or statistical convergence (these will be discussed below). In all of these investigations, the resulting continuous functions were either precisely the linear functions or precisely the functions which are continuous in the ordinary sense. This paper shows that, as long as the ne ...
ONE EXAMPLE OF APPLICATION OF SUM OF SQUARES
... third one is the surprising case of quartic forms in three variables (i.e., the ternary quartic forms where n = 3 and m = 4). 1.1. Univariate polynomials. Since univariate polynomials and forms in two variables are equivalent we will only deal with the first case. Every PSD univariate polynomial is ...
... third one is the surprising case of quartic forms in three variables (i.e., the ternary quartic forms where n = 3 and m = 4). 1.1. Univariate polynomials. Since univariate polynomials and forms in two variables are equivalent we will only deal with the first case. Every PSD univariate polynomial is ...
lecture
... calculates the length of a LCS of two sequences? If two sequences end in the same character, the LCS contains that character If two sequences have a different last character, the length of the LCS is either the length of the LCS we get by dropping the last character from the first sequence, or the l ...
... calculates the length of a LCS of two sequences? If two sequences end in the same character, the LCS contains that character If two sequences have a different last character, the length of the LCS is either the length of the LCS we get by dropping the last character from the first sequence, or the l ...
1 Sets and Set Notation.
... (2) W is closed under addition. That is, for each ~u, ~v ∈ W , we have ~u + ~v ∈ W . (3) W is closed under scalar multiplication. That is, for each c ∈ R and ~u ∈ W , we have c~u ∈ W . Proof. One direction of the proof is trivial: if W is a vector subspace of V , then W satisfies the three condition ...
... (2) W is closed under addition. That is, for each ~u, ~v ∈ W , we have ~u + ~v ∈ W . (3) W is closed under scalar multiplication. That is, for each c ∈ R and ~u ∈ W , we have c~u ∈ W . Proof. One direction of the proof is trivial: if W is a vector subspace of V , then W satisfies the three condition ...
Module Fundamentals
... correspondence between the set of all submodules of M containing N and the set of all submodules of M/N . The inverse of the map is T → π −1 (T ), where π is the canonical map: M → M/N . Proof. The correspondence theorem for groups yields a one-to-one correspondence between additive subgroups of M c ...
... correspondence between the set of all submodules of M containing N and the set of all submodules of M/N . The inverse of the map is T → π −1 (T ), where π is the canonical map: M → M/N . Proof. The correspondence theorem for groups yields a one-to-one correspondence between additive subgroups of M c ...
