Infinite-dimensional convex optimization in optimal and robustcontrol theory

Many engineering problems can be shown to be equivalent to solving semidefinite programs (SPs), i.e., convex optimization problems involving linear matrix inequalities (LMIs). Powerful computation tools are available for such problems in the finite-dimensional case. However, the problems arising in optimal and robust control theory are often infinite dimensional, and so adequate computation tools are not available. The key to tackling such problems with finite computation tools is to have a primal-dual formulation of the problem without duality gap. In this paper we study infinite-dimensional SPs and present a lifting technique to recast SPs as parameterized linear programs (LPs). This enables the wealth of theoretical tools available for infinite-dimensional LPs to be extended to infinite-dimensional SPs. In particular, we develop some new sufficient conditions for the lack of a duality gap for infinite-dimensional SPs and give an exact characterization of the primal and dual problems for these cases. Both primal and dual problems are formed as infinite-dimensional SP problems, with finite truncations to each giving upper and lower bounds, respectively, on the exact solution to the infinite-dimensional problem. Thus, these results can form the basis of practical computation schemes for infinite-dimensional problems, which require only finite-dimensional computation tools. To illustrate the power of these tools we apply the results to two previously unsolved optimization problems, namely minimizing the l₁ norm of a closed-loop system subject to bounds on the frequency response magnitude at a finite number of points and/or bounds on the H₂ norm     

The held out wings (how) Drosophila gene encodes a putative RNA-binding protein involved in the control of muscular and cardiac activity

In an attempt to identify genes that are involved in Drosophila embryonic cardiac development, we have cloned and characterized a gene whose function is required late in embryogenesis to control heart rate and muscular activity. This gene has been named held out wings (how) because hypomorphic mutant alleles produce adult animals that have lost their ability to fly and that keep their wings horizontal at a 90 degree angle from the body axis. In contrast to the late phenotype observed in null mutants, the How protein is expressed early in the invaginating mesoderm and this expression is apparently under the control of twist. When the different mesodermal lineages segregate, the expression of How becomes restricted to the myogenic lineage, including the cardioblasts and probably all the myoblasts. Antibodies directed against the protein demonstrate that How is localized to the nucleus. how encodes a protein containing one KH-domain which has been implicated in binding RNA. how is highly related to the mouse quaking gene which plays a role at least in myelination and that could serve to link a signal transduction pathway to the control of mRNA metabolism. The properties of the how gene described herein suggest that this gene participates in the control of expression of as yet unidentified target mRNAs coding for proteins essential to cardiac and muscular activity.     

A process model for active brazing of ceramics: Part II Optimization of brazing conditions and joint properties

In the present investigation, the process model developed in Part I has been applied to evaluate the microstructure and strength evolution during active brazing of ceramics. As a starting point, reaction-layer growth is assumed to occur isothermally with no restrictions in the supply of reactive element. Different kinds of diagrams are then constructed to show how specific process variables (e.g. the heating and cooling period, the limiting layer thickness, and the diffusion mechanism) affect the growth kinetics. It is concluded that the key to improved joint properties lies in control of the reaction-layer thickness through optimization of the brazing conditions, and an illustration of this is given. This revised version was published online in November 2006 with corrections to the Cover Date.     

Spotlight mode SAR stereo technique for height computation

This paper examines the feasibility of extracting three-dimensional (3-D) or topographic information in spotlight mode stereo synthetic aperture radar (SAR). A display of a SAR (intensity) image has two axes: range and cross-range. Elevated scatterers appear closer in range; this phenomenon is called radar image layover. How the height of each scatterer can be computed from the difference in its layover between two images is investigated. This is analogous to computing height from disparity distance (triangulation) in optical stereo. The same procedure can be applied on pixel by pixel basis for terrain elevation mapping. A general expression is derived for the accuracy of the height estimate as a function of the range resolution and the angular difference between the image planes. Accuracy increases as the angle between the image planes increases, but the bright scatterers in one image tend to fade in the other image. This limited angular persistence of radar scatterers is also discussed. Trajectories for data collection are examined that provide near-optimal height estimates while eliminating the scatterer persistency problem.     

Fullerene Reactivity in an Oxygen Plasma

Fullerene reactivity in an oxygen plasma was measured and compared with those determined under the same conditions for a comprehensive set of 50 carbon materials. The possible reasons for the high plasma reactivity of the fullerene sample in an oxygen plasma are discussed.     

Infections in patients with cystic fibrosis following lung transplantation

BACKGROUND: There is controversy over whether colonization with drug-resistant organisms is a contraindication to lung transplantation. METHODS: We undertook a retrospective review of the results of lung transplantation for patients with cystic fibrosis (CF) at Duke University Medical Center. RESULTS: As of May 1996, 21 patients with CF underwent bilateral lung transplantation. The first patient died within 24 h of transplantation from sepsis due to Stenotrophomonas maltophilia. Of the remaining 20 patients, 17 (85%) are alive and in stable condition. The three deaths were related primarily to bronchiolitis obliterans at 4 and 18 months in two patients and to cytomegalovirus pneumonitis at 5 months in the other patient. The 17 surviving patients have been followed up for a mean of 13 months (range, 0.5 to 34 months). Most of them were colonized and infected with multidrug-resistant organisms before transplantation. Following transplantation, 11 patients had complications from infections. One patient had bacteremia due to a panresistant Burkholderia cepacia and was treated successfully. Two patients had bacteremia and wound infection due to Burkholderia gladioli, previously thought to be pathogenic only in plants. Both patients were treated successfully. Of the six patients with Aspergillus fumigatus isolated from cultures before transplantation, only one had invasive disease following transplantation and responded to treatment. CONCLUSION: The organisms present before transplantation were not the primary cause of mortality in our patient population. Our findings suggest that lung transplantation should be considered in CF patients infected with multidrug-resistant organisms.     

Determination of a new podophyllotoxin derivative, TOP-53, and its metabolite in rat plasma and urine by high-performance liquid chromatography with electrochemical detection

A high-performance liquid chromatographic method was developed for the determination of a new podophyllotoxin derivative, TOP-53 (I), and TOP-53 glucuronide (II) as its major metabolite in rat plasma and urine. For the analysis of I, the sample was chromatographed on a reversed-phase C18 column with electrochemical detection after consecutive two-step liquid-liquid extractions. Compound II was determined as I after enzymatic hydrolysis of II. This method was validated sufficiently with respect to specificity, accuracy, and precision. The limits of quantitation for both I and II were 2 ng/ml in plasma and 10 ng/ml in urine. The method is thus useful for the pharmacokinetic study of I.     

Relationship between the genomic organization and the overlapping embryonic expression patterns of the zebrafish dlx genes

To understand the relationship between the expression and the genomic organization of the zebrafish dlx genes, we have determined the genomic structure of the dlx2 and dlx4 loci. This led to the identification of the zebrafish dlx1 and dlx6 genes, which are closely linked to dlx2 and dlx4, respectively. Therefore, the inverted convergent configuration of Dlx genes is conserved among vertebrates. Analysis of the expression patterns of dlx1 and dlx6 showed striking similarities to those of dlx2 and dlx4, respectively, the genes to which they are linked. Furthermore, the expression patterns of dlx3 and dlx7, which likely constitute a third pair of convergently transcribed genes, are indistinguishable. Thus, the overlapping expression patterns of linked Dlx genes during embryonic development suggest that they share cis-acting sequences that control their spatiotemporal expression. The evolutionary conservation of the genomic organization and combinatorial expression of Dlx genes in distantly related vertebrates suggest tight control mechanisms that are essential for their function during development.     

Hypercoagulability and chronic atrial fibrillation: the role of markers of thrombin generation

BACKGROUND: We have studied 64 patients with congestive heart failure, half of them also with chronic nonvalvular atrial fibrillation (AF). Patients were also stratified according to a history of prior stroke. METHODS: The generation of thrombin was investigated by means of the molecular markers prothrombin fragment 1 + 2 (F1 + 2) and thrombin-antithrombin III complex (TAT), because AF patients may have a hypercoagulable state. There was only a trend toward higher values of TAT and F1 + 2 for AF patients, while subjects with previous stroke (irrespective of AF) had increased levels of the markers of thrombin generation (TAT stroke+ 18.95 +/- 5.15 vs TAT stroke- 8.34 +/- 2.41; F1 + 2 stroke+ 2.22 +/- 0.29 vs F1 + 2 stroke- 1.32 +/- 0.12). The presence of spontaneous echo contrast (SEC) within left atrium was also investigated in 32 AF patients by transesophageal echocardiography. RESULTS: TAT were significantly higher in subjects (n = 11) with SEC (TAT sec+ 37.5 +/- 13.41 vs TAT sec- 8.7 +/- 2.51, p = 0.008). CONCLUSIONS: Finally, when we grouped into 1) those with both AF and stroke, 2) AF alone, 3) stroke alone and 4) sinus rhythm without stroke, levels of F1 + 2 were higher (and marginally higher TAT) in patients with AF and stroke than in those without stroke, revealing that there is a true clotting activation state in these subjects.