Heuristic Search for Approximating One Matrix in Terms of Another Matrix

We study the approximation of a target matrix in terms of several selected columns of another matrix, sometimes called "a dictionary". This approximation problem arises in various domains, such as signal processing, computer vision, and machine learning. An optimal column selection algorithm for the special case where the target matrix has only one column is known since the 1970's, but most previously proposed column selection algorithms for the general case are greedy. We propose the first nontrivial optimal algorithm for the general case, using a heuristic search setting similar to the classical A* algorithm. We also propose practical sub-optimal algorithms in a setting similar to the classical Weighted A* algorithm. Experimental results show that our sub-optimal algorithms compare favorably with the current state-of-the-art greedy algorithms. They also provide bounds on how close their solutions are to the optimal solution.

Separation of no-carrier-added 71,72As from 46 MeV alpha particle irradiated gallium oxide target

No-carrier-added (NCA) 71,72As radionuclides were produced by irradiating gallium oxide target by 46 MeV α-particles. NCA 71,72As was separated from the target matrix by liquid-liquid extraction (LLX) using trioctyl amine (TOA) and tricaprylmethylammonium chloride (aliquat-336) diluted in cyclohexane. The bulk gallium was quantitatively extracted into the organic phase leaving 71,72As in the aqueous phase. Complete separation was observed at 3 M HCl + 0.1 M TOA and 2 M HCl + 0.01 M aliquat-336.

Local low-rank approach to nonlinear matrix completion

This paper deals with a problem of matrix completion in which each column vector of the matrix belongs to a low-dimensional differentiable manifold (LDDM), with the target matrix being high or full rank. To solve this problem, algorithms based on polynomial mapping and matrix-rank minimization (MRM) have been proposed; such methods assume that each column vector of the target matrix is generated as a vector in a low-dimensional linear subspace (LDLS) and mapped to a pth order polynomial and that the rank of a matrix whose column vectors are dth monomial features of target column vectors is deficient. However, a large number of columns and observed values are needed to strictly solve the MRM problem using this method when p is large; therefore, this paper proposes a new method for obtaining the solution by minimizing the rank of the submatrix without transforming the target matrix, so as to obtain high estimation accuracy even when the number of columns is small. This method is based on the assumption that an LDDM can be approximated locally as an LDLS to achieve high completion accuracy without transforming the target matrix. Numerical examples show that the proposed method has a higher accuracy than other low-rank approaches.

Local low-rank approach to nonlinear-matrix completion

This paper deals with a problem of matrix completion in which each column vector of the matrix belongs to a low-dimensional differentiable manifold (LDDM), with the target matrix being high or full rank. To solve this problem, algorithms based on polynomial mapping and matrix-rank minimization (MRM) have been proposed; such methods assume that each column vector of the target matrix is generated as a vector in a low-dimensional linear subspace (LDLS) and mapped to a p-th order polynomial, and that the rank of a matrix whose column vectors are d-th monomial features of target column vectors is defficient. However, a large number of columns and observed values are needed to strictly solve the MRM problem using this method when p is large; therefore, this paper proposes a new method for obtaining the solution by minimizing the rank of the submatrix without transforming the target matrix, so as to obtain high estimation accuracy even when the number of columns is small. This method is based on the assumption that an LDDM can be approximated locally as an LDLS to achieve high completion accuracy without transforming the target matrix. Numerical examples show that the proposed method has a higher accuracy than other low-rank approaches.

Phase retrieval of low-rank matrices by anchored regression

We study the low-rank phase retrieval problem, where our goal is to recover a $d_1\times d_2$ low-rank matrix from a series of phaseless linear measurements. This is a fourth-order inverse problem, as we are trying to recover factors of a matrix that have been observed, indirectly, through some quadratic measurements. We propose a solution to this problem using the recently introduced technique of anchored regression. This approach uses two different types of convex relaxations: we replace the quadratic equality constraints for the phaseless measurements by a search over a polytope and enforce the rank constraint through nuclear norm regularization. The result is a convex program in the space of $d_1 \times d_2$ matrices. We analyze two specific scenarios. In the first, the target matrix is rank-$1$, and the observations are structured to correspond to a phaseless blind deconvolution. In the second, the target matrix has general rank, and we observe the magnitudes of the inner products against a series of independent Gaussian random matrices. In each of these problems, we show that anchored regression returns an accurate estimate from a near-optimal number of measurements given that we have access to an anchor matrix of sufficient quality. We also show how to create such an anchor in the phaseless blind deconvolution problem from an optimal number of measurements and present a partial result in this direction for the general rank problem.

Local low-rank approach to nonlinear-matrix completion

This paper deals with a problem of matrix completion in which each column vector of the matrix belongs to a low-dimensional differentiable manifold (LDDM), with the target matrix being high or full rank. To solve this problem, algorithms based on polynomial mapping and matrix-rank minimization (MRM) have been proposed; such methods assume that each column vector of the target matrix is generated as a vector in a low-dimensional linear subspace (LDLS) and mapped to a p-th order polynomial, and that the rank of a matrix whose column vectors are d-th monomial features of target column vectors is deficient. However, a large number of columns and observed values are needed to strictly solve the MRM problem using this method when p is large; therefore, this paper proposes a new method for obtaining the solution by minimizing the rank of the submatrix without transforming the target matrix, so as to obtain high estimation accuracy even when the number of columns is small. This method is based on the assumption that an LDDM can be approximated locally as an LDLS to achieve high completion accuracy without transforming the target matrix. Numerical examples show that the proposed method has a higher accuracy than other low-rank approaches.

THE YKI-CACTUS (IKBα)-JNK AXIS PROMOTES TUMOR GROWTH AND PROGRESSION IN DROSOPHILA

Presence of inflammatory factors in the tumor microenvironment is well known yet their specific role in tumorigenesis is elusive. The core inflammatory pathways are conserved in Drosophila, including the Toll-Like Receptor (TLR) and the Tumor Necrosis Factor (TNF) pathway. We used Drosophila tumor models to study the role of inflammatory factors in tumorigenesis. Specifically, we co-activated oncogenic forms of RasV12 or its major effector Yorkie (Yki3SA) in polarity deficient cells mutant for tumor suppressor gene scribble (scrib) marked by GFP under nubGAL4 or in somatic clones. This system recapitulates the clonal origins of cancer, and shows neoplastic growth, invasion and lethality. We investigated if TLR and TNF pathway affect growth of Yki3SAscribRNAi or RasV12scribRNAi tumors through activation of tumor promoting Jun N-terminal Kinase (JNK) pathway and its target Matrix Metalloprotease1 (MMP1). We report, TLR component, Cactus (Cact) is highly upregulated in Yki3SAscribRNAi or RasV12scribRNAi tumors. Drosophila Cactus (mammalian IKBα) acts as an inhibitor of NFKB signaling that plays key roles in inflammatory and immune response. Here we show an alternative role for Cactus, and by extension cytokine mediated signaling, in tumorigenesis. Downregulating Cact affects both tumor progression and invasion. Interestingly, downregulating TNF receptors in tumor cells did not affect their invasiveness despite reducing JNK activity. Genetic analysis suggested that Cact and JNK are key regulators of tumor progression. Overall, we show that Yki plays a critical role in tumorigenesis by controlling Cact, which in turn, mediates tumor promoting JNK oncogenic signaling in tumor cells.

Entropy-Based Solutions for Ecological Inference Problems: A Composite Estimator

Information-based estimation techniques are becoming more popular in the field of Ecological Inference. Within this branch of estimation techniques, two alternative approaches can be pointed out. The first one is the Generalized Maximum Entropy (GME) approach based on a matrix adjustment problem where the only observable information is given by the margins of the target matrix. An alternative approach is based on a distributionally weighted regression (DWR) equation. These two approaches have been studied so far as completely different streams, even when there are clear connections between them. In this paper we present these connections explicitly. More specifically, we show that under certain conditions the generalized cross-entropy (GCE) solution for a matrix adjustment problem and the GME estimator of a DWR equation differ only in terms of the a priori information considered. Then, we move a step forward and propose a composite estimator that combines the two priors considered in both approaches. Finally, we present a numerical experiment and an empirical application based on Spanish data for the 2010 year.