Approximating graph-constrained max-cut

An instance of the graph-constrained max-cut (\(\mathsf {GCMC}\)) problem consists of (i) an undirected graph \(G=(V,E)\) and (ii) edge-weights \(c:{V\atopwithdelims ()2} \rightarrow \mathbb {R}_+\) on a complete undirected graph. The objective is to find a subset \(S \subseteq V\) of vertices satisfying some graph-based constraint in G that maximizes the weight \(\sum _{u\in S, v\not \in S} c_{uv}\) of edges in the cut \((S,V{\setminus } S)\). The types of graph constraints we can handle include independent set, vertex cover, dominating set and connectivity. Our main results are for the case when G is a graph with bounded treewidth, where we obtain a \(\frac{1}{2}\)-approximation algorithm. Our algorithm uses an LP relaxation based on the Sherali–Adams hierarchy. It can handle any graph constraint for which there is a dynamic program of a specific form. Using known decomposition results, these imply essentially the same approximation ratio for \(\mathsf {GCMC}\) under constraints such as independent set, dominating set and connectivity on a planar graph G.     

Mid-infrared spectroscopy for detection of Huanglongbing (greening) in citrus leaves

In recent years, Huanglongbing (HLB) also known as citrus greening has greatly affected citrus orchards in Florida. This disease has caused significant economic and production losses costing about $750/acre for HLB management. Early and accurate detection of HLB is a critical management step to control the spread of this disease. This work focuses on the application of mid-infrared spectroscopy for the detection of HLB in citrus leaves. Leaf samples of healthy, nutrient-deficient, and HLB-infected trees were processed in two ways (process-1 and process-2) and analyzed using a rugged, portable mid-infrared spectrometer. Spectral absorbance data from the range of 5.15-10.72 μm (1942-933 cm⁻¹) were preprocessed (baseline correction, negative offset correction, and removal of water absorbance band) and used for data analysis. The first and second derivatives were calculated using the Savitzky-Golay method. The preprocessed raw dataset, first derivatives dataset, and second derivatives dataset were first analyzed by principal component analysis. Then, the selected principal component scores were classified using two classification algorithms, quadratic discriminant analysis (QDA) and k-nearest neighbor (kNN). When the spectral data from leaf samples processed using process-1 were used for data analysis, the kNN-based algorithm yielded higher classification accuracies (especially nutrient-deficient leaf class) than that of the other spectral data (process-2). The performance of the kNN-based algorithm (higher than 95%) was better than the QDA-based algorithm. Moreover, among different types of datasets, preprocessed raw dataset resulted in higher classification accuracies than first and second derivatives datasets. The spectral peak in the region of 9.0-10.5 μm (952-1112 cm⁻¹) was found to be distinctly different between the healthy and HLB-infected leaf samples. This carbohydrate peak could be attributed to the starch accumulation in the HLB-infected citrus leaves. Thus, this study demonstrates the applicability of mid-infrared spectroscopy for HLB detection in citrus.     

An approximation algorithm for vehicle routing with compatibility constraints

We study a multiple-vehicle routing problem with a minimum makespan objective and compatibility constraints. We provide an approximation algorithm and a nearly-matching hardness of approximation result. We also provide computational results on benchmark instances with diverse sizes showing that the proposed algorithm (i) has a good empirical approximation factor, (ii) runs in a short amount of time and (iii) produces solutions comparable to the best feasible solutions found by a direct integer program formulation.     

Comparison of polarized-light propagation in biological tissue and phantoms

We demonstrate significant differences in the propagation of polarized light through biological tissue compared with two common tissue phantoms. Depolarization of linearly and circularly polarized light was measured versus propagation distance by use of two independent measurement techniques. The measurements were performed on adipose and myocardial tissues and on tissue phantoms that consisted of polystyrene microsphere suspensions and Intralipid. The results indicate that, in contrast with results obtained in tissue phantoms, linearly polarized light survives through longer propagation distances than circularly polarized light in biological tissue.     

Thermal degradation of poly(vinyl butyral) in alumina,mullite and silica composites

Thermal degradation of poly(vinyl butyral) (PVB) and its mixtures with alumina, mullite and silica was investigated by non-isothermal thermogravimetry in the temperature range of 323 to 1273 K. The analysis of the data was carried out using a three-dimensional diffusion model. Results showed that the kinetic parameters (activation energy and pre-exponential factor) of the PVB degradation are different for polymer alone, and ceramic/polymer composites. The overall weighted mean apparent activation energy showed an increasing reactivity in the order of PVB<alumina+PVB<mullite+PVB<silica+PVB. This shows that the acidic and basic surface characteristics of the ceramics promote the thermal degradation of PVB and, the more acidic silica affects the degradation more than mullite and alumina. The effect of pellet compression pressure in the range of 4000 to 8000 psig is also investigated.     

Investigation of bending modulus of fiber-reinforced syntactic foams for sandwich and structural applications

Polymer composite foams or syntactic foams containing 0.9, 1.76, 2.54, 3.54 and 4.5 vol% of E-glass short fibers were processed and subjected to a three-point bending test. The results show that the flexural modulus increased with fiber content, with the exception of 1.76% and 3.5% of fibers. This deviation was due to a higher void content for 1.76% and a non-uniform distribution of fibers in the polymer composite foam system for 3.5%. However, in general, the incorporation of chopped strand fibers improved the flexural behavior of the syntactic foam system without much variation in density, thus making the reinforced syntactic foams act as improved core materials for sandwich and other structural applications. Copyright © 2007 John Wiley & Sons, Ltd.     

Fundamental group of locally symmetric varieties

We investigate the fundamental group of a compactified locally symmetric variety after resolution of singularities. We show that it can be any finite group and give examples to show that even for Siegel modular threefolds it can be complicated. We also calculate some cases of special interest, including the fundamental group of the Barth-Nieto space. This article was processed by the author using the Springer-Verlag TEX P Jourlg macro package 1991.     

Variation of the surface stress-charge coefficient of platinum with electrolyte concentration

We report an experimental study of the variation of surface stress with surface charge density for nanoporous Pt immersed in aqueous solutions of NaF of various concentration. As the concentration is reduced, we find initially an increase in the magnitude of the surface stress-charge coefficient, followed by saturation at a value of -1.9 V. Since specific adsorption is expected to be reduced as the solution becomes more dilute, the results support the notion that changes in the bonding at the metal surface play a decisive role in determining the change in the surface stress during double-layer charging.     

X-ray fluorescence method for the determination of rare earths, uranium and thorium in allanites

Summary An X-ray fluorescence (XRF) method for the determination of La, Ce, Pr, Nd, Sm, Gd, Th and U in allanites is described. The estimation limits for different impurity elements are La 0.5–10%, Ce 2–20%, Pr 0.1–2.0%, Nd 0.5–10%, Sm 0.1–2%, Gd 0.1–2.0%, Th 0.2–4% and U 0.2–4%. The sample is diluted in the ratio of 19 by boric acid and double layer pellets are prepared. The precision of the method which varies from 0.2–15% has been determined for every element in each standard. Accuracy of the method is assessed by comparison of the values for rare earth, thorium and uranium content with those obtained by optical emission spectroscopic method and the values for uranium and thorium with those obtained by neutron activation analysis.

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Röntgenfluorescenzmethode zur Bestimmung von Seltenen Erden, Uran und Thorium in Allaniten

Zusammenfassung Das beschriebene Verfahren eignet sich zur Bestimmung von La, Ce, Pr, Nd, Sm Gd, Th und U in Allaniten. Die Bestimmungsgrenzen für die einzelnen Elemente betragen: La 0,5–10%; Ce 2–20%; Pr 0,1–2%; Nd 0,5–10%; Sm 0,1–2%; Gd 0,1–2%; Th 0,2–4%; U 0,2–4%. Die Probe wird mit Borsäure im Verhältnis 19 vermischt und zu Doppelschicht-Tabletten gepreßt. Die Reproduzierbarkeit beträgt 0,2–15% und wurde für jedes Element im jeweiligen Standard bestimmt. Die Richtigkeit des Verfahrens wurde durch Vergleich mit Ergebnissen der Emissionsspektralanalyse (SE, U) sowie der Neutronenaktivierungsanalyse (U, Th) beurteilt.