We study a conjecture called “linear rank conjecture” recently raised in (Tsang et al., FOCS’13), which asserts that if many linear constraints are required to lower the degree of a GF(2) polynomial, then the Fourier sparsity (i.e. number of non-zero Fourier coefficients) of the polynomial must be large. We notice that the conjecture implies a surprising phenomenon that if the highest degree mo...

In recent years, the availability of large, complete cluster samples has enabled numerous cosmological parameter inference analyses using number counts. These have provided constraints on cosmic matter density $\Omega_m$ and amplitude fluctuations $\sigma_8$ alternative to those obtained from other standard probes. However, systematics uncertainties, such as mass calibration bias selection effe...

Background: DNA microarray is a useful technology that simultaneously assesses the expression of thousands of genes. It can be utilized for the detection of cancer types and cancer biomarkers. This study aimed to predict blood cancer using leukemia gene expression data and a robust ℓ2,p-norm sparsity-based gene selection method. Materials and Methods: In this descriptive study, the microarray ...

Sufficient number of linear and noisy measurements for exact and approximate sparsity pattern/support set recovery in the high dimensional setting is derived. Although this problem as been addressed in the recent literature, there is still considerable gaps between those results and the exact limits of the perfect support set recovery. To reduce this gap, in this paper, the sufficient con...

— Localizing the sources of electrical activity in the brain from Electroencephalographic (EEG) data is an important tool for non-invasive study of brain dynamics. Generally, the source localization process involves a high-dimensional inverse problem that has an infinite number of solutions and thus requires additional constraints to be considered to have a unique solution. In the context of EE...

Compressed sensing is a new concept in signal processing. Assuming that a signal can be represented or approximated by only a few suitably chosen terms in a frame expansion, compressed sensing allows to recover this signal from much fewer samples than the Shannon-Nyquist theory requires. Many images can be sparsely approximated in expansions of suitable frames as wavelets, curvelets, wave atoms...

Enforcing sparsity constraints has been shown to be an effective and efficient way to obtain state-of-the-art results in regression and classification tasks. Unlike the support vector machine (SVM) the relevance vector machine (RVM) explicitly encodes the criterion of model sparsity as a prior over the model weights. However the lack of an explicit prior structure over the weight variances mean...

This paper proposes an algorithm for satisfying systems of linear equality and inequality constraints with hierarchical strengths or preferences. Basically, it is a numerical method that incrementally obtains the LU decompositions of linear constraint systems. To realize this, it introduces a novel technique for analyzing hierarchical systems of linear constraints. In addition, it improves perf...

In this paper, we address the issue for learning better translation consensus in machine translation (MT) research, and explore the search of translation consensus from similar, rather than the same, source sentences or their spans. Unlike previous work on this topic, we formulate the problem as structured labeling over a much smaller graph, and we propose a novel structured label propagation f...