Weber Correspondence Analysis: The One-Dimensional Case

When designing programs or software for the implementation of Monte Carlo (MC) hypothesis tests, we can save computation time by using sequential stopping boundaries. Such boundaries imply stopping resampling after relatively few replications if the early replications indicate a very large or a very small p value. We study a truncated sequential probability ratio test (SPRT) boundary and provide a tractable algorithm to implement it. We review two properties desired of any MC p value, the validity of the p value and a small resampling risk, where resampling risk is the probability that the accept/reject decision will be different than the decision from complete enumeration. We show how the algorithm can be used to calculate a valid p value and confidence intervals for any truncated SPRT boundary. We show that a class of SPRT boundaries is minimax with respect to resampling risk and recommend a truncated version of boundaries in that class by comparing their resampling risk (RR) to the RR of fixed boundaries with the same maximum resample size. We study the lack of validity of some simple estimators of p values and offer a new, simple valid p value for the recommended truncated SPRT boundary. We explore the use of these methods in a practical example and provide the MChtest R package to perform the methods.     

Sequential resource allocation with constraints: Two-customer case

We study a two-customer sequential resource allocation problem with equity constraint, which is reflected by a max–min objective. For finite discrete demand distribution, we give a sufficient and necessary condition under which the optimal solution has monotonicity property. However, this property never holds with unbounded discrete distribution.     

Well adjusted: Using expediting and cancelation to manage store replenishment inventory for a seasonal good

We consider an inventory problem that can be translated into a two-period newsvendor setting where the day prior to sales, the newsvendor places an initial preliminary order—a semi-binding forecast—with the publisher. At the beginning of the actual day of sales, the newsvendor has a better forecast for the day’s demand: based on knowing the actual content of the paper, he knows whether it will be a high-demand day due to breaking news or a low-demand day due to slow news. He then can revise the preliminary order quantity by expediting additional papers or canceling all or part of the order, but each of these activities has an associated cost.     

Separation between second price auctions with personalized reserves and the revenue optimal auction

When buyer valuations are drawn IID from a known regular distribution, a second price auction with a symmetric reserve price is the revenue-optimal single-item auction. When this distribution is irregular, we provide the first separation result showing that a second price auction with reserves earns at most 0.778 times the revenue of Myerson’s optimal auction, even when the reserves can be asymmetric. Since the lower bound is 0.745 for i.i.d. buyers, our result is nearly tight.     

A modified sequential extraction method for arsenic fractionation in sediments

A modified sequential extraction method was developed to characterize arsenic (As) associated with different solid constituents in surficial deposits (sediments), which are unconsolidated glacial deposits overlying bedrock. Current sequential extraction methods produce a significant amount of unresolved As in the residual fraction, but our proposed scheme can fractionate >90% of the As present in sediments. Sediment samples containing different As concentrations (3–35 μg g⁻¹) were used to assess the developed method. The pooled amount of As recovered from all the fractions using the developed method was similar (83–122%) to the total As extracted by acid digestion. The concentrations of As in different fractions using the developed scheme were comparable (89–106%) to the As fractions obtained by other existing methods. The developed method was also evaluated for the sequential extraction of other metals such as copper (Cu), cobalt (Co), chromium (Cr) and strontium (Sr) in the sediment samples. The pooled concentrations of these four individual metals from all the fractions were similar (96–104%) to their total concentrations extracted by acid digestion. During method development, we used extractants that did not contain chloride to eliminate formation of polyatomic ions of argon chloride (⁴⁰Ar³⁵Cl) that interfered with ⁷⁵As when analyzed using inductively coupled plasma mass spectrometer (ICP-MS). The results suggest that the developed method can reliably be employed for complete As and other metals’ fractionation in sediments using ICP-MS.     

Hierarchical Model-Based Clustering for Large Datasets

In recent years, hierarchical model-based clustering has provided promising results in a variety of applications. However, its use with large datasets has been hindered by a time and memory complexity that are at least quadratic in the number of observations. To overcome this difficulty, this article proposes to start the hierarchical agglomeration from an efficient classification of the data in many classes rather than from the usual set of singleton clusters. This initial partition is derived from a subgraph of the minimum spanning tree associated with the data. To this end, we develop graphical tools that assess the presence of clusters in the data and uncover observations difficult to classify. We use this approach to analyze two large, real datasets: a multiband MRI image of the human brain and data on global precipitation climatology. We use the real datasets to discuss ways of integrating the spatial information in the clustering analysis. We focus on two-stage methods, in which a second stage of processing using established methods is applied to the output from the algorithm presented in this article, viewed as a first stage.     

Automated capillary electrophoresis with on-line preconcentration by solid phase extraction using a sequential injection manifold and contactless conductivity detection

An extension of a capillary electrophoresis instrument coupled to a sequential injection analysis manifold was developed for automated measurements with on-line solid-phase extraction preconcentration. An in-house built capacitively coupled contactless conductivity detector was employed for sensitive detection with narrow capillaries of 25 μm internal diameter. The system was assembled into standardized 19 in. frames and racks for easy transport and mobile deployment. The system can be left running unattendedly without manual intervention with good operation stability. To demonstrate the application of the system, a method for the determination of four drugs, namely ibuprofen, diclofenac, naproxen and bezafibrate, was developed with enrichment factors of up to several hundreds. Detection of the drug residues down to the nM-scale was found possible and the method was found suitable for the detection of ibuprofen in the waste water of a hospital in Hanoi.     

On-line liquid phase micro-extraction based on drop-in-plug sequential injection lab-at-valve platform for metal determination

A novel automatic on-line liquid phase micro-extraction method based on drop-in-plug sequential injection lab-at-valve (LAV) platform was proposed for metal preconcentration and determination. A flow-through micro-extraction chamber mounted at the selection valve was adopted without the need of sophisticated lab-on-valve components. Coupled to flame atomic absorption spectrometry (FAAS), the potential of this lab-at-valve scheme is demonstrated for trace lead determination in environmental and biological water samples. A hydrophobic complex of lead with ammonium pyrrolidine dithiocarbamate (APDC) was formed on-line and subsequently extracted into an 80 μL plug of chloroform. The extraction procedure was performed by forming micro-droplets of aqueous phase into the plug of the extractant. All critical parameters that affect the efficiency of the system were studied and optimized. The proposed method offered good performance characteristics and high preconcentration ratios. For 10 mL sample consumption an enhancement factor of 125 was obtained. The detection limit was 1.8 μg L⁻¹ and the precision expressed as relative standard deviation (RSD) at 50.0 μg L⁻¹ of lead was 2.9%. The proposed method was evaluated by analyzing certified reference materials and applied for lead determination in natural waters and urine samples.     

Sequential injection methodology for carbon speciation in bathing waters

A sequential injection method (SIA) for carbon speciation in inland bathing waters was developed comprising, in a single manifold, the determination of dissolved inorganic carbon (DIC), free dissolved carbon dioxide (CO₂), total carbon (TC), dissolved organic carbon and alkalinity. The determination of DIC, CO₂ and TC was based on colour change of bromothymol blue (660 nm) after CO₂ diffusion through a hydrophobic membrane placed in a gas diffusion unit (GDU). For the DIC determination, an in-line acidification prior to the GDU was performed and, for the TC determination, an in-line UV photo-oxidation of the sample prior to GDU ensured the conversion of all carbon forms into CO₂. Dissolved organic carbon (DOC) was determined by subtracting the obtained DIC value from the TC obtained value. The determination of alkalinity was based on the spectrophotometric measurement of bromocresol green colour change (611 nm) after reaction with acetic acid. The developed SIA method enabled the determination of DIC (0.24–3.5 mg C L⁻¹), CO₂ (1.0–10 mg C L⁻¹), TC (0.50–4.0 mg C L⁻¹) and alkalinity (1.2–4.7 mg C L⁻¹ and 4.7–19 mg C L⁻¹) with limits of detection of: 9.5 μg C L⁻¹, 20 μg C L⁻¹, 0.21 mg C L⁻¹, 0.32 mg C L⁻¹, respectively. The SIA system was effectively applied to inland bathing waters and the results showed good agreement with reference procedures.