Parallelization of the discrete gradient method of non-smooth optimization and its applications

We investigate parallelization and performance of the discrete gradient method of nonsmooth optimization. This derivative free method is shown to be an effective optimization tool, able to skip many shallow local minima of nonconvex nondifferentiable objective functions. Although this is a sequential iterative method, we were able to parallelize critical steps of the algorithm, and this lead to a significant improvement in performance on multiprocessor computer clusters. We applied this method to a difficult polyatomic clusters problem in computational chemistry, and found this method to outperform other algorithms.

Non-smooth optimization methods for computation of the conditional value-at-risk and portfolio optimization

We examine numerical performance of various methods of calculation of the Conditional Value-at-risk (CVaR), and portfolio optimization with respect to this risk measure. We concentrate on the method proposed by Rockafellar and Uryasev in (Rockafellar, R.T. and Uryasev, S., 2000, Optimization of conditional value-at-risk. Journal of Risk, 2, 21-41), which converts this problem to that of convex optimization. We compare the use of linear programming techniques against a non-smooth optimization method of the discrete gradient, and establish the supremacy of the latter. We show that non-smooth optimization can be used efficiently for large portfolio optimization, and also examine parallel execution of this method on computer clusters.

Cholesterol is necessary both for the toxic effect of Abeta peptides on vascular smooth muscle cells and for Abeta binding to vascular smooth muscle cell membranes

Accumulation of beta amyloid (Aβ) in the brain is central to the pathogenesis of Alzheimer's disease. Aβ can bind to membrane lipids and this binding may have detrimental effects on cell function. In this study, surface plasmon resonance technology was used to study Aβ binding to membranes. Aβ peptides bound to synthetic lipid mixtures and to an intact plasma membrane preparation isolated from vascular smooth muscle cells. Aβ peptides were also toxic to vascular smooth muscle cells. There was a good correlation between the toxic effect of Aβ peptides and their membrane binding. 'Ageing' the Aβ peptides by incubation for 5 days increased the proportion of oligomeric species, and also increased toxicity and the amount of binding to lipids. The toxicities of various Aβ analogs correlated with their lipid binding. Significantly, binding was influenced by the concentration of cholesterol in the lipid mixture. Reduction of cholesterol in vascular smooth muscle cells not only reduced the binding of Aβ to purified plasma membrane preparations but also reduced Aβ toxicity. The results support the view that Aβ toxicity is a direct consequence of binding to lipids in the membrane. Reduction of membrane cholesterol using cholesterol-lowering drugs may be of therapeutic benefit because it reduces Aβ-membrane binding.

PPARγ ligands, 15-deoxy-Δ12,14-prostaglandin J2 and rosiglitazone regulate human cultured airway smooth muscle proliferation through different mechanisms

1. The influence of two peroxisome proliferator-activated receptor γ (PPARγ) ligands, a thiazolidinedione, rosiglitazone (RG) and the prostaglandin D2 metabolite 15-deoxy-Δ12,14-prostaglandin J2 (15d-PGJ2) on the proliferation of human cultured airway smooth muscle (HASM) was examined.

2. The increases in HASM cell number in response to basic fibroblast growth factor (bFGF, 300 pm) or thrombin (0.3 U ml−1) were significantly inhibited by either RG (1–10 μm) or 15d-PGJ2 (1–10 μm). The effects of RG, but not 15d-PGJ2, were reversed by the selective PPARγ antagonist GW9662 (1 μm).

3. Neither RG nor 15d-PGJ2 (10 μm) decreased cell viability, or induced apoptosis, suggesting that the regulation of cell number was due to inhibition of proliferation, rather than increased cell death.

4. Flow-cytometric analysis of HASM cell cycle distribution 24 h after bFGF addition showed that RG prevented the progression of cells from G1 to S phase. In contrast, 15d-PGJ2 caused an increase in the proportion of cells in S phase, and a decrease in G2/M, compared to bFGF alone.

5. Neither RG nor 15d-PGJ2 inhibited ERK phosphorylation measured 6 h post mitogen addition. The bFGF-mediated increase in cyclin D1 protein levels after 8 h was reduced in the presence of 15d-PGJ2, but not RG.

6. Although both RG and 15d-PGJ2 can inhibit proliferation of HASM irrespective of the mitogen used, only the antiproliferative effects of RG appear to be PPARγ-dependent. The different antimitogenic mechanisms of 15d-PGJ2 and synthetic ligands for PPARγ may be exploited to optimise the potential for these compounds to inhibit airway remodelling in asthma.

Global non-smooth optimization in robust multivariate regression

Robust regression in statistics leads to challenging optimization problems. Here, we study one such problem, in which the objective is non-smooth, non-convex and expensive to calculate. We study the numerical performance of several derivative-free optimization algorithms with the aim of computing robust multivariate estimators. Our experiences demonstrate that the existing algorithms often fail to deliver optimal solutions. We introduce three new methods that use Powell's derivative-free algorithm. The proposed methods are reliable and can be used when processing very large data sets containing outliers.

Matching objects across the textured-smooth continuum

The problem of 3D object recognition is of immense practical importance, with the last decade witnessing a number of breakthroughs in the state of the art. Most of the previous work has focused on the matching of textured objects using local appearance descriptors extracted around salient image points. The recently proposed bag of boundaries method was the first to address directly the problem of matching smooth objects using boundary features. However, no previous work has attempted to achieve a holistic treatment of the problem by jointly using textural and shape features which is what we describe herein. Due to the complementarity of the two modalities, we fuse the corresponding matching scores and learn their relative weighting in a data specific manner by optimizing discriminative performance on synthetically distorted data. For the textural description of an object we adopt a representation in the form of a histogram of SIFT based visual words. Similarly the apparent shape of an object is represented by a histogram of discretized features capturing local shape. On a large public database of a diverse set of objects, the proposed method is shown to outperform significantly both purely textural and purely shape based approaches for matching across viewpoint variation.

Bacterial attachment on sub-nanometrically smooth titanium substrata

Despite the volume of work that has been conducted on the topic, the role of surface topography in mediating bacterial cell adhesion is not well understood. The primary reason for this lack of understanding is the relatively limited extent of topographical characterisation employed in many studies. In the present study, the topographies of three sub-nanometrically smooth titanium (Ti) surfaces were comprehensively characterised, using nine individual parameters that together describe the height, shape and distribution of their surface features. This topographical analysis was then correlated with the adhesion behaviour of the pathogenic bacteria Staphylococcus aureus and Pseudomonas aeruginosa, in an effort to understand the role played by each aspect of surface architecture in influencing bacterial attachment. While P. aeruginosa was largely unable to adhere to any of the three sub-nanometrically smooth Ti surfaces, the extent of S. aureus cell attachment was found to be greater on surfaces with higher average, RMS and maximum roughness and higher surface areas. The cells also attached in greater numbers to surfaces that had shorter autocorrelation lengths and skewness values that approached zero, indicating a preference for less ordered surfaces with peak heights and valley depths evenly distributed around the mean plane. Across the sub-nanometrically smooth range of surfaces tested, it was shown that S. aureus more easily attached to surfaces with larger features that were evenly distributed between peaks and valleys, with higher levels of randomness. This study demonstrated that the traditionally employed amplitudinal roughness parameters are not the only determinants of bacterial adhesion, and that spatial parameters can also be used to predict the extent of attachment.

A fast non-smooth nonnegative matrix factorization for learning sparse representation

Nonnegative matrix factorization (NMF) is a hot topic in machine learning and data processing. Recently, a constrained version, non-smooth NMF (NsNMF), shows a great potential in learning meaningful sparse representation of the observed data. However, it suffers from a slow linear convergence rate, discouraging its applications to large-scale data representation. In this paper, a fast NsNMF (FNsNMF) algorithm is proposed to speed up NsNMF. In the proposed method, it first shows that the cost function of the derived sub-problem is convex and the corresponding gradient is Lipschitz continuous. Then, the optimization to this function is replaced by solving a proximal function, which is designed based on the Lipschitz constant and can be solved through utilizing a constructed fast convergent sequence. Due to the usage of the proximal function and its efficient optimization, our method can achieve a nonlinear convergence rate, much faster than NsNMF. Simulations in both computer generated data and the real-world data show the advantages of our algorithm over the compared methods.