Results 51 to 60 of about 6,019,459 (297)
The Singular Values of Convolutional Layers
CoRR, 2018 We characterize the singular values of the linear transformation associated with a standard 2D multi-channel convolutional layer, enabling their efficient computation. This characterization also leads to an algorithm for projecting a convolutional layer onto an operator-norm ball.
Hanie Sedghi +2 more
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Fast singular value thresholding without singular value decomposition [PDF]
Methods and Applications of Analysis, 2013 We are interested in solving the following minimization problem Dτ (Y ) := arg min X∈Rm×n 1 2 ∥Y −X∥F + τ∥X∥∗, where Y ∈ Rm×n is a given matrix, and ∥ ⋅ ∥F is the Frobenius norm and ∥ ⋅ ∥∗ the nuclear norm. This problem serves as a basic subroutine in many popular numerical schemes for nuclear norm minimization problems, which arise from low rank ...
Cai, Jianfeng, Stanley, Osher
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Modelling stem cell differentiation related processes—A practical overview for biologists
FEBS Letters, EarlyView.Stem cell differentiation is complex and difficult to control experimentally. This review introduces suitable computational modelling approaches that can support stem cell research, from mechanistic ODE and abstract models to multiscale and deep learning methods.
Ricco Zeegelaar +4 more
wiley +1 more source
Optimal Shrinkage of Singular Values [PDF]
IEEE Transactions on Information Theory, 2017 We consider recovery of low-rank matrices from noisy data by shrinkage of singular values, in which a single, univariate nonlinearity is applied to each of the empirical singular values. We adopt an asymptotic framework, in which the matrix size is much larger than the rank of the signal matrix to be recovered, and the signal-to-noise ratio of the low ...
Matan Gavish, David L. Donoho
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Reconstructing enzyme evolution by protein engineering
FEBS Letters, EarlyView.Natural enzyme evolution can be retraced by protein engineering methods such as directed evolution, rational design, and ancestral sequence reconstruction. These approaches reveal how enzymes emerged from ligand‐binding scaffolds, developed varying substrate preferences, formed oligomeric complexes, adapted to environmental changes, and evolved novel ...
Lukas Drexler +2 more
wiley +1 more source
Singular Values of Trilinear Forms [PDF]
Experimental Mathematics, 2001 Let T : H 1 × H 2 × H 3 → C be a trilinear form, where H 1, H 2, H 3 are separable Hilbert spaces. In the hypothesis that at least two of the three spaces are finite dimensional we show that the norm square λ = ∥T∥2 is a root of a certain algebraic equation, usually of very high degree, which we baptize the millennia] equation, because it is an ...
Bo Bernhardsson, Jaak Peetre
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FEBS Letters, EarlyView.The process of internalization of the Shiga toxin A subunit via formation of a complex with the Shiga toxin B subunit, which specifically binds to the Gb3 receptor. The peptide is designed to act as a carrier of drugs into cancer cells. Here, we explored the potential of peptides derived from the catalytic A subunit of Shiga toxin (STxA) to be drug ...
Giulia Opassi +6 more
wiley +1 more source
Finite difference methods for a class of singular two-point boundary value problems [PDF]
, 1984 Twizell, E H
core +7 more sources
A new S-type upper bound for the largest singular value of nonnegative rectangular tensors
Journal of Inequalities and Applications, 2017 By breaking N = { 1 , 2 , … , n } $N=\{1,2,\ldots,n\}$ into disjoint subsets S and its complement, a new S-type upper bound for the largest singular value of nonnegative rectangular tensors is given and proved to be better than some existing ones ...
Jianxing Zhao, Caili Sang
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On the spectrum of noisy blown-up matrices
Special Matrices, 2020 We study the eigenvalues of large perturbed matrices. We consider a pattern matrix P, we blow it up to get a large block-matrix Bn. We can observe only a noisy version of matrix Bn. So we add a random noise Wn to obtain the perturbed matrix An = Bn + Wn.
Fazekas István, Pecsora Sándor
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