Regularity of Wiener-Hopf plus Hankel operators

In this thesis we consider Wiener-Hopf-Hankel operators with Fourier symbols in the class of almost periodic, semi-almost periodic and piecewise almost periodic functions. In the first place, we consider Wiener-Hopf-Hankel operators acting between L2 Lebesgue spaces with possibly different Fourier matrix symbols in the Wiener-Hopf and in the Hankel operators. In the second place, we consider these operators with equal Fourier symbols and acting between weighted Lebesgue spaces Lp(R;w), where 1 < p < 1 and w belongs to a subclass of Muckenhoupt weights. In addition, singular integral operators with Carleman shift and almost periodic coefficients are also object of study. The main purpose of this thesis is to obtain regularity properties characterizations of those classes of operators. By regularity properties we mean those that depend on the kernel and cokernel of the operator. The main techniques used are the equivalence relations between operators and the factorization theory. An invertibility characterization for the Wiener-Hopf-Hankel operators with symbols belonging to the Wiener subclass of almost periodic functions APW is obtained, assuming that a particular matrix function admits a numerical range bounded away from zero and based on the values of a certain mean motion. For Wiener-Hopf-Hankel operators acting between L2-spaces and with possibly different AP symbols, criteria for the semi-Fredholm property and for one-sided and both-sided invertibility are obtained and the inverses for all possible cases are exhibited. For such results, a new type of AP factorization is introduced. Singular integral operators with Carleman shift and scalar almost periodic coefficients are also studied. Considering an auxiliar and simpler operator, and using appropriate factorizations, the dimensions of the kernels and cokernels of those operators are obtained. For Wiener-Hopf-Hankel operators with (possibly different) SAP and PAP matrix symbols and acting between L2-spaces, criteria for the Fredholm property are presented as well as the sum of the Fredholm indices of the Wiener-Hopf plus Hankel and Wiener-Hopf minus Hankel operators. By studying dependencies between different matrix Fourier symbols of Wiener-Hopf plus Hankel operators acting between L2-spaces, results about the kernel and cokernel of those operators are derived. For Wiener-Hopf-Hankel operators acting between weighted Lebesgue spaces, Lp(R;w), a study is made considering equal scalar Fourier symbols in the Wiener-Hopf and in the Hankel operators and belonging to the classes of APp;w, SAPp;w and PAPp;w. It is obtained an invertibility characterization for Wiener-Hopf plus Hankel operators with APp;w symbols. In the cases for which the Fourier symbols of the operators belong to SAPp;w and PAPp;w, it is obtained semi-Fredholm criteria for Wiener-Hopf-Hankel operators as well as formulas for the Fredholm indices of those operators.

Not the outside but the inside matters : functional analysis of Capricious and Tartan during Drosophila tracheal morphogenesis

The tubular structures, which transport essential gases, liquids, or cells from one site to another, are shared among various divergent organisms. These highly organized tubular networks include lung, kidney, vasculature and mammary gland in mammals as well as trachea and salivary gland in Drosophila melanogaster. Many questions regarding the tubular morphogenesis cannot be addressed sufficiently by investigating the mammalian organs because their structures are extremely complex and therefore, systematic analyses of genetic and cellular programs guiding the development is not possible. In contrast, the Drosophila tracheal development provides an excellent model system since many molecular markers and powerful tools for genetic manipulations are available. Two mechanisms were shown to be important for the outgrowth of tracheal cells: the FGF signaling pathway and the interaction between the tracheal cells and the surrounding mesodermal cells. The Drosophila FGF ligand encoded by branchless (bnl) is localized in groups of cells near tracheal metameres. The tracheal cells expressing the FGF receptor breathless (btl) respond to these sources of FGF ligand and extend towards them. However, this FGF signaling pathway is not sufficient for the formation of continuous dorsal trunk, the only muticellular tube in tracheal system. Recently, it was found out that single mesodermal cells called bridge-cells are essential for the formation of continuous dorsal trunk as they direct the outgrowth of dorsal trunk cells towards the correct targets. The results in this PhD thesis demonstrate that a cell adhesion molecule Capricious (Caps), which is specifically localized on the surface of bridge-cells, plays an essential role in guiding the outgrowing dorsal trunk cells towards their correct targets. When caps is lacking, some bridge-cells cannot stretch properly towards the adjacent posterior tracheal metameres and thus fail to interconnect the juxtaposing dorsal trunk cells. Consequently, discontinuous dorsal trunks containing interruptions at several positions are formed. On the other hand, when caps is ectopically expressed in the mesodermal cells through a twi-GAL4 driver, these mesodermal cells acquire a guidance function through ectopic caps and misguide the outgrowing dorsal trunk cells in abnormal directions. As a result, disconnected dorsal trunks are formed. These loss- and gain-of-function studies suggest that Caps presumably establishes the cell-to-cell contact between the bridge-cells and the tracheal cells and thereby mediates directly the guidance function of bridge-cells. The most similar protein known to Caps is another cell adhesion molecule called Tartan (Trn). Interestingly, trn is expressed in the mesodermal cells but not in the bridge-cells. When trn is lacking, the outgrowth of not only the dorsal trunks but also the lateral trunks are disrupted. However, in contrast to the ectopic expression of caps, the misexpression of trn does not affect tracheal development. Whereas Trn requires only its extracellular domain to mediate the matrix function, Caps requires both its extracellular and intracellular domains to function as a guidance molecule in the bridge-cells. These observations suggest that Trn functions differently from Caps during tracheal morphogenesis. Presumably, Trn mediates a matrix function of mesodermal cells, which support the tracheal cells to extend efficiently through the surrounding mesodermal tissue. In order to determine which domains dictate the functional specificity of Caps, two hybrid proteins CapsEdTrnId, which contains the Caps extracellular domain and the Trn intracellular domain, and TrnEdCapsId, which consists of the Trn extracellular domain and the Caps intracellular domain, were constructed. Gain of function and rescue experiments with these hybrid proteins suggest on one hand that the extracellular domains of Caps and Trn are functionally redundant and on the other hand that the intracellular domain dictates the functional specificity of Caps. In order to identify putative interactors of Caps, yeast two-hybrid screening was performed. An in vivo interaction assay in yeast suggests that Ras64B interacts specifically with the Caps intracellular domain. In addition, an in vitro binding assay reveals a direct interaction between an inactive form of Ras64B and the Caps intracellular domain. ras64B, which encodes a small GTPase, is expressed in the mesodermal cells concurrently as caps. Finally, a gain-of-function study with the constitutively active Ras64B suggests that Ras64B presumably functions downstream of Caps. All these results suggest consistently that the small GTPase Ras64B binds specifically to the Caps intracellular domain and may thereby mediate the guidance function of Caps.

Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

THE MATRIX ANALYSIS FOR AN OPTICAL FREE-SPACE SWITCHING NETWORK AND AN OPTICAL CROSSOVER NETWORK WITH 4-FUNCTION INTERCHANGE NODES

A matrix analysis for free-space switching networks, such as perfect shuffle-exchange omega, crossover and Banyan is presented. On the basis of matrix analysis, the equivalence of these three switching networks and the route selection between input and output ports are simply explained. Furthermore, an optical crossover switching network, where MQW SEED arrays are used as electrically addressed four-function interchange nodes, is described and the optical crossover interconnection of 64 x 64, and high-speed four-function, interchange nodes is demonstrated in the experiment.

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.

Pole placement method using the system matrix transfer function and sparsity

This paper presents a pole placement method using both the augmented Jacobian and the corresponding system transfer function matrices. From the manipulation of these matrices a straightforward approach results to get the coefficients of a non-linear system, whose solution gives the parameters of the stabilizers that can provide a pre-specified minimum damping to the system. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Extracellular matrix in airway smooth muscle is associated with dynamics of airway function in asthma

Background: Altered deposition of extracellular matrix (ECM) in the airway smooth muscle (ASM) layer as observed in asthma may influence ASM mechanical properties. We hypothesized that ECM in ASM is associated with airway function in asthma. First, we investigated the difference in ECM expression in ASM between asthma and controls. Second, we examined whether ECM expression is associated with bronchoconstriction and bronchodilation in vivo. Methods: Our cross-sectional study comprised 19 atopic mild asthma patients, 15 atopic and 12 nonatopic healthy subjects. Spirometry, methacholine responsiveness, deep-breath-induced bronchodilation (Delta R-rs) and bronchoscopy with endobronchial biopsies were performed. Positive staining of elastin, collagen I, III and IV, decorin, versican, fibronectin, laminin and tenascin in ASM was quantified as fractional area and mean density. Data were analysed using Pearson's or Spearman's correlation coefficient. Results: Extracellular matrix expression in ASM was not different between asthma and controls. In asthmatics, fractional area and mean density of collagen I and III were correlated with methacholine dose-response slope and DRrs, respectively (r = 0.71, P < 0.01; r = 0.60, P = 0.02). Furthermore, ASM collagen III and laminin in asthma were correlated with FEV1 reversibility (r = -0.65, P = 0.01; r = -0.54, P = 0.04). Conclusion: In asthma, ECM in ASM is related to the dynamics of airway function in the absence of differences in ECM expression between asthma and controls. This indicates that the ASM layer in its full composition is a major structural component in determining variable airways obstruction in asthma.

Molecular characterization of the immune modulatory function of matrix metalloproteinase-7, a factor in the tumour micromilieu

Matrix metalloproteinases are the components of the tumour microenvironment which play a crucial role in tumour progression. Matrix metalloproteinase-7 (MMP-7) is expressed in a variety of tumours and the expression is associated with an aggressive malignant phenotype and poor prognosis. A role for MMP-7 in the immune escape of tumours has been postulated, but the mechanisms are not clearly understood. The present study was focused on identifying physiological inactivators of MMP-7 and also to unravel the mechanisms involved in MMP-7 mediated immune escape. This study shows that human leukocyte elastase (HLE), secreted by polymorphonuclear leukocytes cleaves MMP-7 in the catalytic domain as revealed by N-terminal sequencing. Further analysis demonstrates that the activity of MMP-7 was drastically decreased after HLE treatment in a time and dose dependent manner. MMP-7 induces apoptosis resistance in tumour cells by cleaving CD95 and CD95L. The effect of HLE on MMP-7 mediated apoptosis resistance was analysed. In vitro stimulation of apoptosis by anti-Apo-1 (anti-CD95 antibody) and the chemotherapeutic drug doxorubicin is reduced by MMP-7. Also tumour specific cytotoxic T cells do not effectively kill tumour cells in the presence of MMP-7. This study revealed that HLE abrogates the negative effect of MMP-7 on apoptosis induced by CD95 stimulation, doxorubicin or cytotoxic T cells and restores apoptosis sensitivity of tumour cells. To gain insight into the possible immune modulatory functions of MMP-7, experiments were performed to identify new immune relevant substrates. The human T cell line, Jurkat, was selected for these studies. Hsc70 which is involved in uncoating of clathrin vesicles was found in the supernatants of the MMP-7 treated cells indicating a modulatory role of MMP-7 on endocytosis. Further studies demonstrated that MMP-7 leads to decreased clathrin staining in HEK293, HepG2, Jurkat, CD4+ T cells and dendritic cells. Results also show MMP-7 treatment increased surface expression of cytotoxic T lymphocyte associated protein-4 (CTLA-4) which accumulated due to inhibition of the clathrin mediated internalization in CD4+CD25+ cells.

Should 3K zoom function be used for detection of pneumothorax in cesium iodide/amorphous silicon flat-panel detector radiographs presented on 1K-matrix soft copies?

The purpose of the study was to evaluate observer performance in the detection of pneumothorax with cesium iodide and amorphous silicon flat-panel detector radiography (CsI/a-Si FDR) presented as 1K and 3K soft-copy images. Forty patients with and 40 patients without pneumothorax diagnosed on previous and subsequent digital storage phosphor radiography (SPR, gold standard) had follow-up chest radiographs with CsI/a-Si FDR. Four observers confirmed or excluded the diagnosis of pneumothorax according to a five-point scale first on the 1K soft-copy image and then with help of 3K zoom function (1K monitor). Receiver operating characteristic (ROC) analysis was performed for each modality (1K and 3K). The area under the curve (AUC) values for each observer were 0.7815, 0.7779, 0.7946 and 0.7066 with 1K-matrix soft copies and 0.8123, 0.7997, 0.8078 and 0.7522 with 3K zoom. Overall detection of pneumothorax was better with 3K zoom. Differences between the two display methods were not statistically significant in 3 of 4 observers (p-values between 0.13 and 0.44; observer 4: p = 0.02). The detection of pneumothorax with 3K zoom is better than with 1K soft copy but not at a statistically significant level. Differences between both display methods may be subtle. Still, our results indicate that 3K zoom should be employed in clinical practice.

Plasma-functionalized electrospun matrix for biograft development and cardiac function stabilization.

Cardiac tissue engineering approaches can deliver large numbers of cells to the damaged myocardium and have thus increasingly been considered as a possible curative treatment to counteract the high prevalence of progressive heart failure after myocardial infarction (MI). Optimal scaffold architecture and mechanical and chemical properties, as well as immune- and bio-compatibility, need to be addressed. We demonstrated that radio-frequency plasma surface functionalized electrospun poly(ɛ-caprolactone) (PCL) fibres provide a suitable matrix for bone-marrow-derived mesenchymal stem cell (MSC) cardiac implantation. Using a rat model of chronic MI, we showed that MSC-seeded plasma-coated PCL grafts stabilized cardiac function and attenuated dilatation. Significant relative decreases of 13% of the ejection fraction (EF) and 15% of the fractional shortening (FS) were observed in sham treated animals; respective decreases of 20% and 25% were measured 4 weeks after acellular patch implantation, whereas a steadied function was observed 4 weeks after MSC-patch implantation (relative decreases of 6% for both EF and FS).

Jasmonate-dependent modifications of the pectin matrix during potato development function as a defense mechanism targeted by Dickeya dadantii virulence factors

The plant cell wall constitutes an essential protection barrier against pathogen attack. In addition, cell-wall disruption leads to accumulation of jasmonates (JAs), which are key signaling molecules for activation of plant inducible defense responses. However, whether JAs in return modulate the cell-wall composition to reinforce this defensive barrier remains unknown. The enzyme 13-allene oxide synthase (13-AOS) catalyzes the first committed step towards biosynthesis of JAs. In potato (Solanum tuberosum), there are two putative St13-AOS genes, which we show here to be differentially induced upon wounding. We also determine that both genes complement an Arabidopsis aos null mutant, indicating that they encode functional 13-AOS enzymes. Indeed, transgenic potato plants lacking both St13-AOS genes (CoAOS1/2 lines) exhibited a significant reduction of JAs, a concomitant decrease in wound-responsive gene activation, and an increased severity of soft rot disease symptoms caused by Dickeya dadantii. Intriguingly, a hypovirulent D. dadantii pel strain lacking the five major pectate lyases, which causes limited tissue maceration on wild-type plants, regained infectivity in CoAOS1/2 plants. In line with this, we found differences in pectin methyl esterase activity and cell-wall pectin composition between wild-type and CoAOS1/2 plants. Importantly, wild-type plants had pectins with a lower degree of methyl esterification, which are the substrates of the pectate lyases mutated in the pel strain. These results suggest that, during development of potato plants, JAs mediate modification of the pectin matrix to form a defensive barrier that is counteracted by pectinolytic virulence factors from D. dadantii.

Structure and Function of a Vimentin-associated Matrix Adhesion in Endothelial Cells

The α4 laminin subunit is a component of endothelial cell basement membranes. An antibody (2A3) against the α4 laminin G domain stains focal contact-like structures in transformed and primary microvascular endothelial cells (TrHBMECs and HMVECs, respectively), provided the latter cells are activated with growth factors. The 2A3 antibody staining colocalizes with that generated by αv and β3 integrin antibodies and, consistent with this localization, TrHBMECs and HMVECs adhere to the α4 laminin subunit G domain in an αvβ3-integrin–dependent manner. The αvβ3 integrin/2A3 antibody positively stained focal contacts are recognized by vinculin antibodies as well as by antibodies against plectin. Unusually, vimentin intermediate filaments, in addition to microfilament bundles, interact with many of the αvβ3 integrin-positive focal contacts. We have investigated the function of α4-laminin and αvβ3-integrin, which are at the core of these focal contacts, in cultured endothelial cells. Antibodies against these proteins inhibit branching morphogenesis of TrHBMECs and HMVECs in vitro, as well as their ability to repopulate in vitro wounds. Thus, we have characterized an endothelial cell matrix adhesion, which shows complex cytoskeletal interactions and whose assembly is regulated by growth factors. Our data indicate that this adhesion structure may play a role in angiogenesis.