Matrix Identity Research Articles

Genetic determinants of hyaloid and retinal vasculature in zebrafish

BackgroundThe retinal vasculature is a capillary network of blood vessels that nourishes the inner retina of most mammals. Developmental abnormalities or microvascular complications in the retinal vasculature result in severe human eye diseases that lead to blindness. To exploit the advantages of zebrafish for genetic, developmental and pharmacological studies of retinal vasculature, we characterised the intraocular vasculature in zebrafish.ResultsWe show a detailed morphological and developmental analysis of the retinal blood supply in zebrafish. Similar to the transient hyaloid vasculature in mammalian embryos, vessels are first found attached to the zebrafish lens at 2.5 days post fertilisation. These vessels progressively lose contact with the lens and by 30 days post fertilisation adhere to the inner limiting membrane of the juvenile retina. Ultrastructure analysis shows these vessels to exhibit distinctive hallmarks of mammalian retinal vasculature. For example, smooth muscle actin-expressing pericytes are ensheathed by the basal lamina of the blood vessel, and vesicle vacuolar organelles (VVO), subcellular mediators of vessel-retinal nourishment, are present. Finally, we identify 9 genes with cell membrane, extracellular matrix and unknown identity that are necessary for zebrafish hyaloid and retinal vasculature development.ConclusionZebrafish have a retinal blood supply with a characteristic developmental and adult morphology. Abnormalities of these intraocular vessels are easily observed, enabling application of genetic and chemical approaches in zebrafish to identify molecular regulators of hyaloid and retinal vasculature in development and disease.

Matrix identities on weighted partial Motzkin paths

We give a combinatorial interpretation of a matrix identity on Catalan numbers and the sequence (1,4,4 2 ,4 3 ,…) which has been derived by Shapiro, Woan and Getu by using Riordan arrays. By giving a bijection between weighted partial Motzkin paths with an elevation line and weighted free Motzkin paths, we find a matrix identity on the number of weighted Motzkin paths and the sequence ( 1 , k , k 2 , k 3 , … ) for k ≥ 2 . By extending this argument to partial Motzkin paths with multiple elevation lines, we give a combinatorial proof of an identity recently obtained by Cameron and Nkwanta. A matrix identity on colored Dyck paths is also given, leading to a matrix identity for the sequence ( 1 , t 2 + t , ( t 2 + t ) 2 , … ) .

398. Extracellular Matrix Identity and Surface Density Alter Transfection by Complexes Delivered from a Cell-Adhesive Substrate

Top of pageAbstract The application of gene delivery to gene therapy, tissue engineering and functional genomics applications requires efficient delivery systems that overcome significant extracellular and intracellular barriers. Substrate-mediated delivery aims to overcome barriers in localized gene transfer by immobilizing preformed DNA complexes in the cellular microenvironment to reduce the amount of DNA delivered, prevent aggregation and distribute vector to adhered cells. We investigated the cellular quantities and distribution of DNA in the cellular population to identify how influencing the interactions between substrate and vector in substrate-mediated delivery enhances either transgene expression or the number of transfected cells. Relative to non-coated substrates, coating of polystyrene substrates with serum proteins yielded enhancement in transgene expression up to 1500 fold for immobilized polyplexes. Increase in total transgene expression paralleled an increase in association of polyplexes with the cells, however increased quantities of DNA associated with cells did not always result in enhanced expression. Substrate coating also increased the number of transfected cells up to 12-fold with both polyplexes and lipoplexes. Coating the substrate with serum proteins increased the number of cells that internalized polyplexes and lipoplexes, better distributing the DNA in the cell population. The identity and density of the extracellular matrix (ECM) component used for substrate coating significantly affects transgene expression. Collagen IV and fibrinogen yielded polyplex expression levels similar to or less than coating by fetal bovine serum (FBS), however, fibronectin coating enhanced gene expression up to 20-fold over FBS coating. Coating the substrate with 6 |[mu]|g/cm2 of fibronectin yielded maximal expression and higher or lower amounts of fibronectin on the surface reduced expression. Enhancement in gene expression did not result from differences in the amount of DNA that bound to the substrate or associated with cells, suggesting that fibronectin enhances intracellular trafficking of polyplexes. For bolus transfection, the identity of the ECM component mediating cell adhesion did not influence gene expression. These studies demonstrate that maximal expression will be obtained when substrates are designed to bind DNA complexes with the appropriate affinity and also stimulate intracellular trafficking of complexes. Understanding the mechanisms in substrate-mediated delivery will enhance the application of gene delivery in vitro and in vivo.

Acceleration and Stabilization Techniques for the Levenberg-Marquardt Method

In this paper, two techniques are proposed for accelerating and stabilizing the Levenberg-Marquardt (LM) method where its conventional stabilizer matrix (identity matrix) is superseded by (1) a diagonal matrix whose elements are column norms of Jacobian matrix J, or (2) a non-diagonal square root matrix of JTJ. Geometrically, these techniques make constraint conditions of the LM method fitted better to relevant cost function than conventional one. Results of numerical simulations show that proposed techniques are effective when both column norm ratio of J and mutual interactions between arguments of the cost function are large. Especially, the technique (2) introduces a new LM method of damped Gauss-Newton (GN) type which satisfies both properties of global convergence and quadratic convergence by controlling Marquardt factor and can stabilize convergence numerically. Performance of the LMM techniques are compared also with a damped GN method with line search procedure.

Design of FIR Precoders and Equalizers for Broadband MIMO Wireless Channels with Power Constraints

This paper examines the optimum design of FIR precoders or equalizers for multiple-input multiple-output (MIMO) frequency-selective wireless channels. For the case of a left-coprime FIR channel, which arises generically when the number nT of transmit antennas is larger than the number nR of receive antennas, the Bezout matrix identity can be employed to design an FIR MIMO precoder that equalizes exactly the channel at the transmitter. Similarly, for a right-coprime FIR channel, the Bezout identity yields an FIR zero-forcing MIMO equalizer. Unfortunately, Bezout precoders usually increase the transmit power, and Bezout equalizers tend to amplify the noise power. To overcome this problem, we describe in this paper a convex optimization technique for the optimal synthesis of MIMO FIR precoders subject to transmit power constraints, and of MIMO FIR equalizers with output noise power constraints. The synthesis problem reduces to the minimization of a quadratic objective function under convex quadratic inequality constraints, so it can be solved by employing Lagrangian duality. Instead of solving the primal problem, we solve the lower-dimensional dual problem for the Lagrange multipliers. When an FIR MIMO precoder has already been selected, we also describe a technique for adding a vector shaping sequence to the transmitted signal in order to reduce the transmit power. The selection of effective shaping sequences requires a search over a trellis of large dimensionality, which can be accomplished suboptimally by employing reduced-complexity search techniques.

A Matrix Identity on the Schur Complement

This article presents a matrix identity on the Schur complement along with various applications. In particular, it gives a simple and transparent proof for the Crabtree–Haynsworth quotient formula for the Schur complement. Although its proof is straightforward, the identity yields a number of important results that appear to be unrelated.

Controlled release of biocides in solid wood. I. Efficacy against brown rot wood decay fungus (Gloeophyllum trabeum)

AbstractNanoparticles containing the fungicides tebuconazole or chlorothalonil were prepared with median diameters of ∼ 100–250 nm. The nanoparticle matrices were polyvinylpyridine (PVP), copolymers of PVP and styrene (PVP‐co‐St), and blends of PVP and hyperbranched polyesters (HBPs). The isolated nanoparticles were resuspended in water to yield suspensions able to deliver 0.1, 0.2, 0.4, and 0.8 kg fungicide/m3 of wood. Southern yellow pine (SYP) was treated with these suspensions using conventional vacuum‐pressure treatments. Less concentrated suspensions delivered the nanoparticles quantitatively into the SYP while suspensions capable of delivering up to 0.8 kg of the fungicide (the active ingredient or AI) per cubic meter of SYP delivered 0.4–0.7 kg AI/m3, depending on the nanoparticle matrix. The SYP lost less than 5% of its mass after 55 days of exposure to Gloeophyllum trabeum when the tebuconazole content in the SYP reached 0.2 kg/m3, and the matrix identity had little effect on the results. The SYP lost between 3 and 6% of its mass after 55 days of exposure to G. trabeum when the AI was chlorothalonil at a level of ∼ 0.6 kg AI/m3 of wood and was introduced into SYP in nanoparticles with a PVP/HBP matrix, but it lost ∼ 11% of its mass at the same AI levels when the nanoparticle matrix was PVP. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 596–607, 2002

Time-varying threshold integral pulse frequency modulation.

Several methods have been proposed so far for the analysis of the integral pulse frequency modulation (IPFM) model and detecting its corresponding physiological information. Most of these methods rely on the low-pass filtering method to extract the modulating signal of the model. In this paper, we present an entirely new approach based on vector space theory. The new method is developed for a more comprehensive form of the IPFM model, namely the time-varying threshold integral pulse frequency modulation (TVTIPFM) model. The new method decomposes the driving signals of the TVTIPFM model into a series of orthogonal basis functions and constructs a matrix identity through which the input signals can be obtained by a parametric solution. As a particular case, we apply this method to R-R intervals of the SA node to discriminate between its autonomic nervous modulation and the stretch induced effect.

The Boundary Equivalence for Rings and Matrix Rings over Them

We study into the question of whether some rings and their associated matrix rings have equal decidability boundaries in the scheme and scheme-alternative hierarchies. Let $$B_H (A;\sigma )$$ be a decidability boundary for an algebraic system 〈 A; σ 〉 w.r.t. the hierarchy H. For a ring R, denote by $$\underline M _n (R)$$ an algebra with universe $$\bigcup\limits_{1 \leqslant k,l \leqslant n} {R^{k \times l} } $$ . On this algebra, define the operations + and ⋅ in such a way as to extend, if necessary, the initial matrices by suitably many zero rows and columns added to the underside and to the right of each matrix, followed by “ordinary” addition and multiplication of the matrices obtained. The main results are collected in Theorems 1-3. Theorem 1 holds that if R is a division or an integral ring, and R has zero or odd characteristic, then the equalities $$\mathcal{B}_S \left( {R; + , \cdot } \right) = \mathcal{B}_S \left( {R^{n \times n} ; + , \cdot } \right){\text{ and }}\mathcal{B}_S \left( {R; + , \cdot ,1} \right) = \mathcal{B}_S \left( {R^{n \times n} ; + , \cdot ,1} \right)$$ hold for any n⩾1. And if R is an arbitrary associative ring with identity then $$\mathcal{B}_S \left( {R; + , \cdot ,1} \right) = \mathcal{B}_S \left( {R^{n \times n} ;\sigma _0 \cup \left\{ {e_{ij} } \right\}} \right)$$ for any n ⩾ 1 and i,j ∈ { 1,..., n}, where e ij is a matrix identity. Theorem 2 maintains that if R is an associative ring with identity then $$\mathcal{B}_S \left( {\underline M _n \left( R \right)} \right) = \mathcal{B}_S \left( {R; + , \cdot } \right)$$ . Theorem 3 proves that $$\mathcal{B}_{SA} \left( {\underline M _n \left( \mathbb{Z} \right)} \right) = \left\{ {\forall \neg \vee ,\exists \neg \wedge ,\forall \exists ,\exists \forall } \right\}$$ for any n ⩾ 1.

How many different parametric cubic curves are there? 2. The "same" game

I'm interested in both the answer to the question in the title and in finding the clearest possible derivation of that answer. My first efforts were very algebra-intensive, but had an aura of concreteness about them. As I played with the question, I came up with more and more elegant ways to ward off the brute-force algebra and make the answer more intuitive without reams of calculation. For these elegant techniques to work, however, I needed to build up a collection of tools (lemmas) that themselves take a little time to explain. One tool is the use of a particular matrix identity, which I review in this article, and which I use to answer the title question: there are three different parametric cubic curves. However, deriving that answer in a clear and obvious manner is still a little way away, but that's OK: the reason I'm doing this is really not so much to answer the question as to build intuition about the algebraic formulas and the geometry that they represent. The journey is the reward.

Exploiting a matrix identity in the computation of the efficient score test for overdispersion in the Poisson regression model

The efficient score test for overdispersion in the Poisson regression model is derived explicitly, and it is shown that by virtue of a particular matrix identity, the test has a surprisingly simple form provided the Poisson regression contains an intercept. It is also pointed out that the test is inherently one-tailed.

A radioimmunoassay for serum estradiol

A radioimmunoassay procedure to measure estradiol levels in human serum was developed using125I labeled estradiol and antiestradiol antibody raised in-house using the estradiol-6-CMO-BSA as the immunogen. Controlled process serum was used to maintain the serum matrix and sample-standard identity. The assay was validated by analysing several (n=40) samples and comparing with established commercial assays. The assay had a sensitivity of 35 pg/mL and a range of 50 pg/mL to 5 ng/mL. The interassay C.V. were between 2 to 10% while the intraassay C.V. were between 2 and 8%. This assay is sensitive enough for monitoring ovulation and hypersecretions in ovarian tumours and was primarily developed to be used as an in-house assay in the local hospitals.

Factors Influencing the Quantitative Determination of Trace Elements in Soils by Glow Discharge Mass Spectrometry

The influence of oxygen content, conducting host matrix, and soil composition on the quantitative determination of trace elements in soils by glow discharge mass spectrometry was examined. Oxygen content and conducting host matrix identity influenced relative sensitivity factors employed in the quantitative interpretation of the glow discharge mass spectra. Soil composition did not influence these relative sensitivity factors. Unknown soils taken from the field were analyzed with the use of a set of relative sensitivity factors obtained from standard soils with certified compositions. The quantitative results from glow discharge mass spectrometry of these unknowns compared favorably with quantitative results from inductively coupled plasma atomic emission spectrometry and laser ablation solid sampling inductively coupled plasma mass spectrometry.

A matrix identity and its applications to equivalent hypotheses in linear models

A matrix identity for the decomposition of sum of squares is considered, and used to convert a general linear hypothesis H in a linear model into an equivalent hypothesis involving only estimable functions. This new approach provides an alternative to the one given by Peixoto (1986, Theorem 2.1). The ‘G-testable’ condition of del Rio (1989, Proposition 1) is then extended to yield a number of necessary and sufficient conditions for testability. The matrix identity is further utilized not only to derive a test statistic for H but also to show that the statistic derived is invariant for testing any hypothesis that is equivalent to H. The results are extended to provide a concise and unified treatment for the inference under a constrained linear model.

On a matrix identity connecting iteration operators associated with a p-cyclic matrix

The successive overrelaxation (SOR) and the symmetric SOR (SSOR) iteration matrices are connected with the Jacobi iteration matrix in case these operators are associated with a ( q, p − q)-generalized consistently ordered matrix through certain matrix identities. The validity of these identities has been proved in the last couple of years. Very recently an analogous matrix identity was shown to hold for the modified SOR (MSOR) and the Jacobi iteration matrices in the particular cases ( p,q) = (2,1), (3,1), and 3,2). It is the main objective of this paper to extend the validity of this identity to cover an entire class or pairs ( p, q). The identity in question is not only of theoretical interest but of practical importance too, since it can be used to show the equivalence of the MSOR and a class of p-step iterative methods for the solution of a linear system whose matrix coefficient possesses the ( q,p − q)-generalized consistently ordered property.

Some recent results on the modified SOR theory

For the solution of the linear system Ax=( I− T) x= c (1), where T is a weakly cyclic of index p⩾2 matrix of a special structure, the block SOR method with different relaxation factors associated with the row blocks of A is considered. First, a well-known relationship connecting the eigenvalue spectra of the block Jacobi matrix T of A and its associated modified SOR (MSOR) matrix is proved for all p⩾3, via an approach due to Varga, Niethammer, and Cai. Next, it is shown that the matrix analogue of the eigenvalue relationship holds at least for p=3. This, together with the facts that the matrix analogue holds true for p=2 and also for any p⩾3, provided all relaxation factors coincide, suggests a more general validity of the aforementioned matrix identity. Then, based on the matrix relationship, an equivalence is established between the MSOR method and a stationary p-parameter p-step iterative one for the solution of (1). So one can study convergence properties and determine optimal parameters of both methods by studying the simpler of the two, that is, the p-step one. Finally, some applications of the theory developed when p=2 are presented, and a brief discussion concerning comparisons of the optimum MSOR and AOR methods in a specific case is given.

A matrix formula for testing linear hypotheses in linear models

A useful matrix identity is verified. The identity is, among other things, applicable to the problem of testing linear hypotheses in linear models, leading to an approach which is equivalent to the one presented by Peixoto, although more straightforward. A simplified proof of a related formula given by Khatri is presented.

A noniterative method for the design of linear robust controllers

A procedure for determining a linear control law which guarantees asymptotic stability for an uncertain system is derived. Using an elementary matrix identity, an alternative proof of the existence of stabilizing control law for the matched case is provided. Bounds for the rates of decay are established, and by using these bounds it is shown that every trajectory of the closed-loop system can be made to decay at a prespecified exponential rate. The technique is simpler to use than existing techniques since it does not require a numerical procedure, but allows the control law to be obtained from some simple formulas. >

On a matrix identity associated with generalized least squares

This note discusses an identity which is useful in the construction of reduced generalized least-squares equations, in the REML method of estimating variance components, and in calculating best linear unbiased predictors. The identity is shown to be a singular form of a better-known matrix relation. Some applications of the result are presented.

A combinatorial interpretation of the inverse kostka matrix

The Kostka matrix K relates the. homogeneous and the Schur bases in the ring of symmetric functions where K λ,μenumerates the number of column strict tableaux of shape λ and type μ. We make use of the Jacobi -Trudi identity to give a combinatorial interpretation for the inverse of the Kostka matrix in terms of certain types of signed rim hook tabloids. Using this interpretation, the matrix identity KK −1=Iis given a purely combinatorial proof. The generalized Jacobi-Trudi identity itself is also shown to admit a combinatorial proof via these rim hook tabloids. A further application of our combinatorial interpretation is a simple rule for the evaluation of a specialization of skew Schur functions that arises in the computation of plethysms.