Fixed-rank matrix factorizations and Riemannian low-rank optimization

Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed-rank matrices. We adopt the geometric framework of optimization on Riemannian quotient manifolds. We study the underlying geometries of several well-known fixed-rank matrix factorizations and then exploit the Riemannian quotient geometry of the search space in the design of a class of gradient descent and trust-region algorithms. The proposed algorithms generalize our previous results on fixed-rank symmetric positive semidefinite matrices, apply to a broad range of applications, scale to high-dimensional problems, and confer a geometric basis to recent contributions on the learning of fixed-rank non-symmetric matrices. We make connections with existing algorithms in the context of low-rank matrix completion and discuss the usefulness of the proposed framework. Numerical experiments suggest that the proposed algorithms compete with state-of-the-art algorithms and that manifold optimization offers an effective and versatile framework for the design of machine learning algorithms that learn a fixed-rank matrix. © 2013 Springer-Verlag Berlin Heidelberg.

Matrix-assisted laser desorption/ionization time-of-flight mass spectrometric analysis of phospholipase A(2) and fibrinolytic enzyme, two enzymes obtained from Chinese Agkistrodon blomhoffii Ussurensis venom

Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) was used to analyze two enzymes, phospholipase AZ and fibrinolytic enzyme isolated from Chinese Agkistrodon blomhoffii Ussurensis venom. Using sinapinic acid as the matrix, positive ion mass spectra of the enzymes were obtained, In addition to the dominant protein [M+H](+) ions, multimeric and multiply charged ions were also observed in the mass spectra, The higher the concentration of the enzymes, the more multiply charged polymer and multimeric ions were detected, Our results indicate that MALDI-TOFMS can provide a rapid and accurate method for molecular weight determination of snake venom enzymes, Mass accuracies of 0.1 and 0.3 % were achieved by analysis of highly dialyzed phospholipase A2 and fibrinolytic enzyme, and these results are much better than those obtained using sodium dodecyl sulfate-palyacrylamide gel electrophoresis. MALDI-TOFMS thus provides a reliable method to determine the purity and molecular weight of these enzymes, which are of potential use as therapeutants, Copyright (C) 1999 John Wiley & Sons, Ltd.

Studies on extracting solutions of endohedral rare-earth metallofullerenes by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

Thirteen extracting solutions of rare-earth metallofullerenes containing La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm and Yb respectively have been investigated by means of matrix-assisted laser desorption/ionization time-of-night, mass spectrometry. The influences of the positive-ion/negative-ion mode, laser intensity, matrix and mass discrimination to the analytical results are studied, based on which the optimal analytical conditions have been determined. The results show that the extracting solutions contain large quantities of rare-earth metallofullerenes brs;des empty fullerenes, On the basis of comparing their relative intensities, the different structure stabilities and solubilities of metallofullerenes with different rare-earth metals encapsulated into the fullerene cages, as well as some possible reasons to those differences, are discussed.

Seasonal and spatial distribution of matrix-bound phosphine and its relationship with the environment in the Changjiang River Estuary, China

Sediment is commonly considered as a source of phosphine, which is a highly toxic and reactive atmospheric trace gas. This study aims to investigate the seasonal and spatial distribution of matrix-bound phosphine (MBP) and its relationship with the environment in the Changjiang River Estuary. A total of 43 surface sediments were collected in four seasons of 2006, and concentrations of MBP and relative environmental factors were analyzed. MBP ranged from 1.93 to 94.86 ng kg(-1) dry weight (dw) with an average concentration of 17.14 ng kg(-1) dw. The concentrations of MBP in the tipper estuary were, higher than those in the lower estuary, which could be attributed to greater pollutant inputs in the upper estuary. The concentrations of MBP also varied with season, with November > August > May > February. Significant correlations existed between MBP and total phosphorus (TP), organic phosphorus (OP), inorganic phosphorus (W), organic carbon (OC), total nitrogen (TN), the grain size, and redox potential (Eh), suggesting that these sedimentary environmental characteristics played an important role in controlling the MBP levels in the sediments. Notably, there were positive linear relationships between the concentrations of soluble reactive phosphorus (SRP), TP, and chlorophyll a (Chl a) in bottom water and MBP in sediments. These relationships might be very complicated and need further exploration. This work is the first comprehensive study of the seasonal and spatial distribution of MBP in sediments and its relationships with environmental factors in a typical estuary, and will lead to deeper understanding of the phosphorus (P) biogeochemical cycle. (C) 2008 Elsevier Ltd. All rights reserved.

A probabilistic index for completely positive maps and an application

Gohm, Rolf, (2003) 'A probabilistic index for completely positive maps and an application', Journal of Operator Theory 54(2) pp.339-361 RAE2008

Integrin-mediated interactions with extracellular matrix proteins for nucleus pulposus cells of the human intervertebral disc.

The extracellular matrix (ECM) of the human intervertebral disc is rich in molecules that interact with cells through integrin-mediated attachments. Porcine nucleus pulposus (NP) cells have been shown to interact with laminin (LM) isoforms LM-111 and LM-511 through select integrins that regulate biosynthesis and cell attachment. Since human NP cells lose many phenotypic characteristics with age, attachment and interaction with the ECM may be altered. Expression of LM-binding integrins was quantified for human NP cells using flow cytometry. The cell-ECM attachment mechanism was determined by quantifying cell attachment to LM-111, LM-511, or type II collagen after functionally blocking specific integrin subunits. Human NP cells express integrins β1, α3, and α5, with over 70% of cells positive for each subunit. Blocking subunit β1 inhibited NP cell attachment to all substrates. Blocking subunits α1, α2, α3, and α5 simultaneously, but not individually, inhibits NP cell attachment to laminins. While integrin α6β1 mediated porcine NP cell attachment to LM-111, we found integrins α3, α5, and β1 instead contributed to human NP cell attachment. These findings identify integrin subunits that may mediate interactions with the ECM for human NP cells and could be used to promote cell attachment, survival, and biosynthesis in cell-based therapeutics.

False-positive PCR results linked to administration of seasonal influenza vaccine

False-positive PCR results usually occur as a consequence of specimen-to-specimen or amplicon-to-specimen contamination within the laboratory. Evidence of contamination at time of specimen collection linked to influenza vaccine administration in the same location as influenza sampling is described. Clinical, circumstantial and laboratory evidence was gathered for each of five cases of influenza-like illness (ILI) with unusual patterns of PCR reactivity for seasonal H1N1, H3N2, H1N1 (2009) and influenza B viruses. Two 2010 trivalent influenza vaccines and environmental swabs of a hospital influenza vaccination room were also tested for influenza RNA. Sequencing of influenza A matrix (M) gene amplicons from the five cases and vaccines was undertaken. Four 2009 general practitioner (GP) specimens were seasonal H1N1, H3N2 and influenza B PCR positive. One 2010 GP specimen was H1N1 (2009), H3N2 and influenza B positive. PCR of 2010 trivalent vaccines showed high loads of detectable influenza A and B RNA. Sequencing of the five specimens and vaccines showed greatest homology with the M gene sequence of Influenza A/Puerto Rico/8/1934 H1N1 virus (used in generation of influenza vaccine strains). Environmental swabs had detectable influenza A and B RNA. RNA detection studies demonstrated vaccine RNA still detectable for at least 66 days. Administration of influenza vaccines and clinical sampling in the same room resulted in the contamination with vaccine strains of surveillance swabs collected from patients with ILI. Vaccine contamination should therefore be considered, particularly where multiple influenza virus RNA PCR positive signals (e.g. H1N1, H3N2 and influenza B) are detected in the same specimen.

Turbo-smt: Accelerating coupled sparse matrix-tensor factorizations by 200x

How can we correlate the neural activity in the human brain as it responds to typed words, with properties of these terms (like ‘edible’, ‘fits in hand’)? In short, we want to find latent variables, that jointly explain both the brain activity, as well as the behavioral responses. This is one of many settings of the Coupled Matrix-Tensor Factorization (CMTF) problem.

Can we accelerate any CMTF solver, so that it runs within a few minutes instead of tens of hours to a day, while maintaining good accuracy? We introduce Turbo-SMT, a meta-method capable of doing exactly that: it boosts the performance of any CMTF algorithm, by up to 200x, along with an up to 65 fold increase in sparsity, with comparable accuracy to the baseline.

We apply Turbo-SMT to BrainQ, a dataset consisting of a (nouns, brain voxels, human subjects) tensor and a (nouns, properties) matrix, with coupling along the nouns dimension. Turbo-SMT is able to find meaningful latent variables, as well as to predict brain activity with competitive accuracy.

Comprehensive profiling and localisation of the matrix metalloproteinases in urothelial carcinoma

The matrix metalloproteinases (MMPs) are endopeptidases which break down the extracellular matrix and regulate cytokine and growth factor activity. Several MMPs have been implicated in the promotion of invasion and metastasis in a broad range of tumours including urothelial carcinoma. In this study, RNA from 132 normal bladder and urothelial carcinoma specimens was profiled for each of the 24 human MMPs, the four endogenous tissue inhibitors of MMPs (TIMPs) and several key growth factors and their receptors using quantitative real time RT-PCR. Laser capture microdissection (LCM) of RNA from 22 tumour and 11 normal frozen sections was performed allowing accurate RNA extraction from either stromal or epithelial compartments. This study confirms the over expression in bladder tumour tissue of well-documented MMPs and highlights a range of MMPs which have not previously been implicated in the development of urothelial cancer. In summary, MMP-2, MT1-MMP and the previously unreported MMP-28 were very highly expressed in tumour samples while MMPs 1, 7, 9, 11, 15, 19 and 23 were highly expressed. There was a significant positive correlation between transcript expression and tumour grade for MMPs 1, 2, 8, 10, 11, 12, 13, 14, 15 and 28 (P < 0.001). At the same confidence interval, TIMP-1 and TIMP-3 also correlated with increasing tumour grade. LCM revealed that most highly expressed MMPs are located primarily within the stromal compartment except MMP-13 which localised to the epithelial compartment. This work forms the basis for further functional studies, which will help to confirm the MMPs as potential diagnostic and therapeutic targets in early bladder cancer.

Discrete Time Inventory Models with/without Positive Service Time

In everyday life different flows of customers to avail some service facility or other at some service station are experienced. In some of these situations, congestion of items arriving for service, because an item cannot be serviced Immediately on arrival, is unavoidable. A queuing system can be described as customers arriving for service, waiting for service if it is not immediate, and if having waited for service, leaving the system after being served. Examples Include shoppers waiting in front of checkout stands in a supermarket, Programs waiting to be processed by a digital computer, ships in the harbor Waiting to be unloaded, persons waiting at railway booking office etc. A queuing system is specified completely by the following characteristics: input or arrival pattern, service pattern, number of service channels, System capacity, queue discipline and number of service stages. The ultimate objective of solving queuing models is to determine the characteristics that measure the performance of the system

Investigations on Stochastic Storage Systems with Positive Service Time

In this thesis the queueing-inventory models considered are analyzed as continuous time Markov chains in which we use the tools such as matrix analytic methods. We obtain the steady-state distributions of various queueing-inventory models in product form under the assumption that no customer joins the system when the inventory level is zero. This is despite the strong correlation between the number of customers joining the system and the inventory level during lead time. The resulting quasi-birth-anddeath (QBD) processes are solved explicitly by matrix geometric methods

Approximate factorization constraint preconditioners for saddle-point matrices

We consider the application of the conjugate gradient method to the solution of large, symmetric indefinite linear systems. Special emphasis is put on the use of constraint preconditioners and a new factorization that can reduce the number of flops required by the preconditioning step. Results concerning the eigenvalues of the preconditioned matrix and its minimum polynomial are given. Numerical experiments validate these conclusions.

Implicit-factorization preconditioning and iterative solvers for regularized saddle-point systems

We consider conjugate-gradient like methods for solving block symmetric indefinite linear systems that arise from saddle-point problems or, in particular, regularizations thereof. Such methods require preconditioners that preserve certain sub-blocks from the original systems but allow considerable flexibility for the remaining blocks. We construct a number of families of implicit factorizations that are capable of reproducing the required sub-blocks and (some) of the remainder. These generalize known implicit factorizations for the unregularized case. Improved eigenvalue clustering is possible if additionally some of the noncrucial blocks are reproduced. Numerical experiments confirm that these implicit-factorization preconditioners can be very effective in practice.

Numerical computation of an analytic singular value decomposition of a matrix valued function

This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.

A Wiener-Hopf type factorization for the exponential functional of Levy processes

For a Lévy process ξ=(ξt)t≥0 drifting to −∞, we define the so-called exponential functional as follows: Formula Under mild conditions on ξ, we show that the following factorization of exponential functionals: Formula holds, where × stands for the product of independent random variables, H− is the descending ladder height process of ξ and Y is a spectrally positive Lévy process with a negative mean constructed from its ascending ladder height process. As a by-product, we generate an integral or power series representation for the law of Iξ for a large class of Lévy processes with two-sided jumps and also derive some new distributional properties. The proof of our main result relies on a fine Markovian study of a class of generalized Ornstein–Uhlenbeck processes, which is itself of independent interest. We use and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual Markov process.