n (M)} denote its ordered eigenvalues. A.1. Proof of Proposition 1 We will show that the matrix M⇤ specified in Figure 1a satisfies the conditions required by the proposition. It is easy to verify that M⇤ 2 CSST, so that it remains to prove the approximation-theoretic lower bound (4). In order to do so, we require the following auxiliary result: Lemma 1. Consider any matrix M that belongs to CP...

The quantum state of a superconducting transmon qubit inside a three-dimensional cavity is monitored by transmission of a microwave field through the cavity. The information inferred from the measurement record is incorporated in a density matrix ρ_{t}, which is conditioned on probe results until t, and in an auxiliary matrix E_{t}, which is conditioned on probe results obtained after t. Here, ...

Recently, tag recommendation (TR) has become a very hot research topic in data mining and related areas. However, neither co-occurrence based methods which only use the item-tag matrix nor content based methods which only use the item content information can achieve satisfactory performance in real TR applications. Hence, how to effectively combine the item-tag matrix, item content information,...

Starting from the Schild action for membrane, we present an alternative formulation of Matrix Theory. First of all, we construct the Schild action for general bosonic p-brane which is classically equivalent to the Nambu-Goto action for p-brane. Next, based on the constraint obtained from the variational equation for the auxiliary field in the case of p = 2 (membrane), we construct a new matrix ...

Nonnegative matrix factorization (NMF) is a popular technique for pattern recognition, data analysis, and dimensionality reduction, the goal of which is to decompose nonnegative data matrix X into a product of basis matrix A and encoding variable matrix S with both A and S allowed to have only nonnegative elements. In this paper we consider Amari’s α-divergence as a discrepancy measure and rigo...

We study the large N limit of the class of U(N) N = 1 SUSY gauge theories with an adjoint scalar and a superpotential W (Φ). In each of the vacua of the quantum theory, the expectation values 〈TrΦp〉 are determined by a master matrix Φ0 with eigenvalue distribution ρGT (λ). ρGT (λ) is quite distinct from the eigenvalue distribution ρMM (λ) of the corresponding large N matrix model proposed by Di...

Sensitivity analysis attacks aim at estimating a watermark from multiple observations of the detector’s output. Subsequently, the attacker removes the estimated watermark from the watermarked signal. In order to measure the vulnerability of a detector against such attacks, we evaluate the fundamental performance limits for the attacker’s estimation problem. The inverse of the Fisher information...

This paper proposes a fast Minimum-Variance-Distortionless-Response (MVDR) beamforming algorithm for an antenna array for cancellation of multiple interference signals. The proposed algorithm uses Sample-Average Estimate (SAE) of the data covariance matrix and reduces its computational effort by applying the Matrix-Inversion-Lemma (MIL) to its covariance Matrix Inversion (MI) operation. The pro...

Based on a correlation analysis method, a subwaveform threshold retracker is developed and coded in FORTRAN for satellite altimetry to determine the leading edge and retracking gate, and to improve the precision of sea surface heights (SSHs) and gravity anomalies (GAs). Using ERS-1/ERM waveforms, the subwaveform threshold retracker outperforms full-waveform threshold retrackers at the tide gage...

We introduce a dynamic and secondary-memory-based variant of the List of Clusters, which is shown to be competitive with the literature, especially on higher-dimensional spaces, where it outperforms the M-tree in searches and I/Os used for insertions. The basic principles of our design are applicable to other secondary-memory structures.