Learning the Kernel Matrix with Semi-Definite Programming

Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the so-called kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space -- classical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semi-definite programming (SDP) techniques. When applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm -- using the labelled part of the data one can learn an embedding also for the unlabelled part. The similarity between test points is inferred from training points and their labels. Importantly, these learning problems are convex, so we obtain a method for learning both the model class and the function without local minima. Furthermore, this approach leads directly to a convex method to learn the 2-norm soft margin parameter in support vector machines, solving another important open problem. Finally, the novel approach presented in the paper is supported by positive empirical results.

Extracellular matrix of the human cyclic corpus luteum

Extracellular matrix regulates many cellular processes likely to be important for development and regression of corpora lutea. Therefore, we identified the types and components of the extracellular matrix of the human corpus luteum at different stages of the menstrual cycle. Two different types of extracellular matrix were identified by electron microscopy; subendothelial basal laminas and an interstitial matrix located as aggregates at irregular intervals between the non-vascular cells. No basal laminas were associated with luteal cells. At all stages, collagen type IV α1 and laminins α5, β2 and γ1 were localized by immunohistochemistry to subendothelial basal laminas, and collagen type IV α1 and laminins α2, α5, β1 and β2 localized in the interstitial matrix. Laminin α4 and β1 chains occurred in the subendothelial basal lamina from mid-luteal stage to regression; at earlier stages, a punctate pattern of staining was observed. Therefore, human luteal subendothelial basal laminas potentially contain laminin 11 during early luteal development and, additionally, laminins 8, 9 and 10 at the mid-luteal phase. Laminin α1 and α3 chains were not detected in corpora lutea. Versican localized to the connective tissue extremities of the corpus luteum. Thus, during the formation of the human corpus luteum, remodelling of extracellular matrix does not result in basal laminas as present in the adrenal cortex or ovarian follicle. Instead, novel aggregates of interstitial matrix of collagen and laminin are deposited within the luteal parenchyma, and it remains to be seen whether this matrix is important for maintaining the luteal cell phenotype.

Homodimerization controls the fibroblast growth factor 9 subfamily's receptor binding and heparan sulfate-dependent diffusion in the extracellular matrix

Uncontrolled fibroblast growth factor (FGF) signaling can lead to human diseases, necessitating multiple layers of self-regulatory control mechanisms to keep its activity in check. Herein, we demonstrate that FGF9 and FGF20 ligands undergo a reversible homodimerization, occluding their key receptor binding sites. To test the role of dimerization in ligand autoinhibition, we introduced structure-based mutations into the dimer interfaces of FGF9 and FGF20. The mutations weakened the ability of the ligands to dimerize, effectively increasing the concentrations of monomeric ligands capable of binding and activating their cognate FGF receptor in vitro and in living cells. Interestingly, the monomeric ligands exhibit reduced heparin binding, resulting in their increased radii of heparan sulfate-dependent diffusion and biologic action, as evidenced by the wider dilation area of ex vivo lung cultures in response to implanted mutant FGF9-loaded beads. Hence, our data demonstrate that homodimerization autoregulates FGF9 and FGF20's receptor binding and concentration gradients in the extracellular matrix. Our study is the first to implicate ligand dimerization as an autoregulatory mechanism for growth factor bioactivity and sets the stage for engineering modified FGF9 subfamily ligands, with desired activity for use in both basic and translational research.

Studies of granulosa cell maturation in dominant and subordinate bovine follicles : novel extracellular matrix focimatrix is co-ordinately regulated with cholesterol side-chain cleavage CYP11A1

During growth of antral ovarian follicles granulosa cells first become associated with a novel type of extracellular matrix, focimatrix, and at larger sizes follicles become either subordinate or dominant. To examine this, bovine subordinate (9.0±s.e.m. 0.4 mm; n=16), partially dominant (12.0±0.6 mm; n=18) and fully dominant (15.0±0.4 mm; n=14) follicles were examined by real time RT-PCR analyses of granulosa cells and by immunohistochemistry of focimatrix. Changes in the expression of FSH receptor, LH receptor, cholesterol side-chain cleavage (CYP11A1), 3β-hydroxysteroid dehydrogenase, aromatase (CYP19A1) and inhibin-α and β-B were observed as expected for follicle sizes examined. After adjusting for size differences, only CYP11A1 was significantly different between the groups, and elevated in dominant follicles. Also after adjusting for differences in size there were no significant differences in expression of focimatrix components collagen type IV α-1 (COL4A1), laminin β-2, nidogen 1 (NID1), and perlecan (HSPG2) or the volume density of NID1 and -2 and HSPG2. The volume density of focimatrix components in laminin 111 was significantly elevated in dominant follicles. Adjusting for analysis of more than one follicle per animal and for multiple correlations, CYP11A1 mRNA levels were highly correlated with the focimatrix genes COL4A1, NID1 and -2 and HSPG2. Thus, focimatrix may potentially regulate CYP11A1 expression, and the regulation of both could be important in follicular dominance.

‘Spotty Dick’ : a research experiment to test design suitability for the use of jewelled spot matrix patterns for UV aware men’s swimwear

The great male Aussie cossie is growing spots. The ‘dick’ tog, as it is colloquially referred to, is linked to Australia’s national identify with overtly masculine bronzed Aussie bodies clothed in this iconic apparel. Yet the reality is our hunger for worshiping the sun and the addiction to a beach lifestyle is tempered by the pragmatic need for neck-to-knee, or more apt head-to-toe, swimwear. Spotty Dick is an irreverent play on male swimwear – it experiments with alternate modes to sheath the body with Lyrca in order to protect it from searing UV’s and at the same time light-heartedly fools around with texture and pattern; to be specific, black Scharovsky crystals, jewelled in spot patterns - jewelled clothing is not characteristically aligned to menswear and even less so to the great Aussie cossie. The crystals form a matrix of spots that attempt to provoke a sense of mischievousness aligned to the Aussie beach larrikin. Ironically, spot patterns are in itself a form of a parody, as prolonged sun exposure ages the skin and sun spots can occur if appropriate sun protection is not used. ‘Spotty Dick’ – a research experiment to test design suitability for the use of jewelled spot matrix patterns for UV aware men’s swimwear. The creative work was paraded at 56 shows, over a 2 week period, and an estimated 50,000 people viewed the work.