Extended Kernel Recursive Least Squares Algorithm

This paper presents a kernelized version of the extended recursive least squares (EX-KRLS) algorithm which implements for the first time a general linear state model in reproducing kernel Hilbert spaces (RKHS), or equivalently a general nonlinear state model in the input space. The center piece of this development is a reformulation of the well known extended recursive least squares (EX-RLS) algorithm in RKHS which only requires inner product operations between input vectors, thus enabling the application of the kernel property (commonly known as the kernel trick). The first part of the paper presents a set of theorems that shows the generality of the approach. The EX-KRLS is preferable to 1) a standard kernel recursive least squares (KRLS) in applications that require tracking the state-vector of general linear state-space models in the kernel space, or 2) an EX-RLS when the application requires a nonlinear observation and state models. The second part of the paper compares the EX-KRLS in nonlinear Rayleigh multipath channel tracking and in Lorenz system modeling problem. We show that the proposed algorithm is able to outperform the standard KRLS and EX-RLS in both simulations.     

The separation and concentration of iron from zinc process solutions

In order for solvent-extraction technology to be acceptable in the zinc industry as an alternative to existing jarosite precipitation circuits, iron must be cleanly separated and concentrated into a feed stream suitable for downstream iron by-product recovery. In this article, the use of OPAP, a mixed extractant consisting of mono- and di-octylphenyl phosphoric acids, is described as a potentially suitable extractant to selectively extract Fe(III) from concentrated ZnSO₄(90 g/l zinc)/H₂SO₄(50 g/l) solutions, followed by stripping of Fe(III) with 4–6 N HCl. OPAP was found to exhibit very low solubility/degradation characteristics (similar to D2EHPA) and excellent loading characteristics with minimal zinc and sulfate co-extraction. OPAP seems to have the lowest sulfate carryover than any other extractant previously proposed for iron extraction from strong acidic solutions. In terms of stripping, a 70 g/l Fe(II) (as FeCl₂)/6 N HCl solution was found to be effective in producting 100 g/l total iron in the strip solution. For more information, contact G.P. Demopoulos, McGill University, Department of Mining and Metallurgical Engineering, 3610 University Street, Montreal, QC, Canada H3A 2B2; (514) 398-2046; fax (514) 398-4492; e-mail george@minmet.lan.mcgill.ca.     

A new algorithm for the detection of tool breakage in milling

In this paper a novel signal processing algorithm is presented for the detection of tool breakage using the displacement signal (RORPA). The algorithm extracts information from consecutive revolutions to decrease dependencies on runout conditions and idle noise, creating a much more robust signal for the automatic determination of tool breakage conditions. The algorithm is explained as well as the determination of dynamic thresholds. The thresholds are set using the information regarding the cutting conditions (mean displacement signal and its slope during transient milling). Examples with real data are also presented. A critique of the overall performance and future work incorporating information from x and y channels completes the discussion.     

Vascular endothelial growth factor-C (VEGF-C/VEGF-2) promotes angiogenesis in the setting of tissue ischemia

Recently, vascular endothelial growth factor-C (VEGF-C or VEGF-2) was described as a specific ligand for the endothelial receptor tyrosine kinases VEGFR-2 and VEGFR-3. In vivo data, limited to constitutive overexpression in transgenic mice, have been interpreted as evidence that the growth-promoting effects of VEGF-C are restricted to development of the lymphatic vasculature. The current studies were designed to test the hypothesis that constitutive expression of VEGF-C in adult animals promotes angiogenesis. In vitro, VEGF-C exhibited a dose-dependent mitogenic and chemotactic effect on endothelial cells, particularly for microvascular endothelial cells (72% and 95% potency, respectively, compared with VEGF-A/VEGF-1). VEGF-C stimulated release of nitric oxide from endothelial cells and increased vascular permeability in the Miles assay; the latter effect was attenuated by pretreatment with the nitric oxide synthase inhibitor N(omega)-nitro-L-arginine methyl ester. Both VEGFR-2 and VEGFR-3 receptors were shown to be expressed in human saphenous vein and internal mammary artery. The potential for VEGF-C to promote angiogenesis in vivo was then tested in a rabbit ischemic hindlimb model. Ten days after ligation of the external iliac artery, VEGF-C was administered as naked plasmid DNA (pcVEGF-C; 500 microg) from the polymer coating of an angioplasty balloon (n = 8 each) or as recombinant human protein (rhVEGF-C; 500 microg) by direct intra-arterial infusion. Physiological and anatomical assessments of angiogenesis 30 days later showed evidence of therapeutic angiogenesis for both pcVEGF-C and rhVEGF-C. Hindlimb blood pressure ratio (ischemic/normal) after pcVEGF-C increased to 0.83 +/- 0.03 after pcVEGF-C versus 0.59 +/- 0.04 (P < 0.005) in pGSVLacZ controls and to 0.76 +/- 0.04 after rhVEGF-C versus 0.58 +/- 0.03 (P < 0.01) in control rabbits receiving rabbit serum albumin. Doppler-derived iliac flow reserve was 2.7 +/- 0.1 versus 2.0 +/- 0.2 (P < 0.05) for pcVEGF-C versus LacZ controls and 2.9 +/- 0.3 versus 2.1 +/- 0.2 (P < 0.05) for rhVEGF-C versus albumin controls. Neovascularity was documented by angiography in vivo (angiographic scores: 0.85 +/- 0.05 versus 0.51 +/- 0.02 (P < 0.001) for plasmid DNA and 0.74 +/- 0.08 versus 0.53 +/- 0.03 (P < 0.05) for protein), and capillary density (per mm2) was measured at necropsy (252 +/- 12 versus 183 +/- 10 (P < 0.005) for plasmid DNA and 229 +/- 20 versus 164 +/- 20 (P < 0.05) for protein). In contrast to the results of gene targeting experiments, constitutive expression of VEGF-C in adult animals promotes angiogenesis in the setting of limb ischemia. VEGF-C and its receptors thus constitute an apparently redundant pathway for postnatal angiogenesis and may represent an alternative to VEGF-A for strategies of therapeutic angiogenesis in patients with limb and/or myocardial ischemia.     

Lower and Upper Bounds for Misclassification Probability Based on Renyi's Information

Fano's inequality has proven to be one important result in Shannon's information theory having found applications in numerous proofs of convergence. It also provides us with a lower bound on the symbol error probability in a communication channel, in terms of Shannon's definitions of entropy and mutual information. This result is also significant in that it suggests insights on how the classification performance is influenced by the amount of information transferred through the classifier. We have previously extended Fano's lower bound on the probability of error to a family of lower and upper bounds based on Renyi's definitions of entropy and mutual information. These new bounds however, despite their theoretical appeal, were practically incomputable. In this paper, we present some modifications to these bounds that will allow us to utilize them in practical situations. The significance of these new bounds is threefold: Illustrating a theoretical use of Renyi's definition of information, extending Fano's result to include an upper bound for probability of classification error, and providing insights on how the information transfer through a classifier affects its performance. The performance of the modified bounds is investigated in various numerical examples, including applications to digital communication channels that are designed to point out the major conclusions.