This paper presents the performance evaluation of eight focus measure operators namely Image CURV (Curvature), GRAE (Gradient Energy), HISE (Histogram Entropy), LAPM (Modified Laplacian), LAPV (Variance of Laplacian), LAPD (Diagonal Laplacian), LAP3 (Laplacian in 3D Window) and WAVS (Sum of Wavelet Coefficients). Statistical matrics such as MSE (Mean Squared Error), PNSR (Peak Signal to Noise R...

ABSTRACT Advances in Nuclear Magnetic Resonance (NMR) spectroscopy is a cornerstone structure elucidation of polycyclic 'cage' scaffolds. Due to the compactness these compounds, much overlap, as well unique through-space and bond NMR interactions are frequently observed. This review serves guide for future derivatives by providing some typical relevant aspects characteristic trends, substituent...

Let C∗ (K) denote the cellular chains on the Stasheff associahedra. We construct an explicit combinatorial diagonal ∆ : C∗(K) → C∗(K)⊗C∗(K); consequently, we obtain an explicit diagonal on the A∞-operad. We apply the diagonal ∆ to define the tensor product of A∞-(co)algebras in maximal generality.

We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance–covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance between two nonoverlapping segments of the high-dimensional random vectors. The tests are applicable (i) when the data dimension is much larger than the sample size...

The canonical structure of the massive gravity in the first order moving frame formalism is studied. We work in the simplified context of translation invariant fields, with mass terms given by general non-derivative interactions, invariant under the diagonal Lorentz group, depending on the moving frame as well as a fixed reference frame. We prove that the only mass terms which give 5 propagatin...

All of the following are covered in detail in the notes for Lecture 1: • The definition of LG, specifically that LG = DG − AG, where DG is a diagonal matrix of degrees and AG is the adjacency matrix of graph G. • The action of LG on a vector x, namely that [LGx]i = deg(i) (xi − average of x on neighbors of i) • The eigenvalues of LG are λ1 ≤ · · · ≤ λn with corresponding eigenvectors v1, . . . ...

• Random Sampling: X are iid uniform from unit sphere in S`. • Random Subspace: S` are spanned by d iid uniform vectors in R. GRAPH CONNECTIVITY What about the second design objective? • Nashihatkon & Hartley nailed that connectivity is NOT a generic property for SSC in general when d ≥ 4. • What about for LRR? Assume random sampling and random subspace, we have: Proposition 1 Under independent...

A new method, namely the Parallel Two-Level Hybrid (PTH) method, is developed to solve tridiagonal systems on parallel computers. PTH is designed based on Parallel Diagonal Dominant (PDD) algorithm. Like PDD, PTH is highly scalable. It provides accurate solutions when PDD may not be applicable and maintains a near PDD performance when the underlying machine ensemble size is large. By controllin...