Computer-assisted optimization of reversed-phase HPLC isocratic separation of neutral compounds

An appropriate optimization strategy should be used to find a desired resolution or selectivity with a minimum number of experiments in a limited time, which could assure the baseline separation of all target compounds. It was usually realized by means of a specialized computer program. In this paper, mapping optimization method and overlapping resolution mapping were compared for the optimization of a reversed-phase high-performance liquid chromatography (HPLC) isocratic separation of neutral compounds. The calculated resolutions and separation time of 7 to 10 experiments are fitted by different equations, which were used to build a contour plot with a minimum effective resolution and maximum retention time as a function of a mobile phase composition. The balance between resolution and analysis time could be easily realized by the overlapping of the final overlapping resolution mapping and analysis time mapping. The validity of the two methods was confirmed by some typical experiments. The models are simple, visual, and common without theoretical arithmetic.     

Overlapping spectra resolution using non-negative matrix factorization

Non-negative matrix factorization (NMF), with the constraints of non-negativity, has been recently proposed for multi-variate data analysis. Because it allows only additive, not subtractive, combinations of the original data, NMF is capable of producing region or parts-based representation of objects. It has been used for image analysis and text processing. Unlike PCA, the resolutions of NMF are non-negative and can be easily interpreted and understood directly. Due to multiple solutions, the original algorithm of NMF [D.D. Lee, H.S. Seung, Nature 401 (1999) 788] is not suitable for resolving chemical mixed signals. In reality, NMF has never been applied to resolving chemical mixed signals. It must be modified according to the characteristics of the chemical signals, such as smoothness of spectra, unimodality of chromatograms, sparseness of mass spectra, etc. We have used the modified NMF algorithm to narrow the feasible solution region for resolving chemical signals, and found that it could produce reasonable and acceptable results for certain experimental errors, especially for overlapping chromatograms and sparse mass spectra. Simulated two-dimensional (2-D) data and real GUJINGGONG alcohol liquor GC-MS data have been resolved soundly by NMF technique. Butyl caproate and its isomeric compound (butyric acid, hexyl ester) have been identified from the overlapping spectra. The result of NMF is preferable to that of Heuristic evolving latent projections (HELP). It shows that NMF is a promising chemometric resolution method for complex samples.     

Folded overlapping variance estimators for simulation

We propose and analyze a new class of estimators for the variance parameter of a steady-state simulation output process. The new estimators are computed by averaging individual estimators from “folded” standardized time series based on overlapping batches composed of consecutive observations. The folding transformation on each batch can be applied more than once to produce an entire set of estimators. We establish the limiting distributions of the proposed estimators as the sample size tends to infinity while the ratio of the sample size to the batch size remains constant. We give analytical and Monte Carlo results showing that, compared to their counterparts computed from nonoverlapping batches, the new estimators have roughly the same bias but smaller variance. In addition, these estimators can be computed with order-of-sample-size work.     

Novel family of prime codes for synchronous optical CDMA

In this paper we have proposed a novel prime spreading sequence family hereby referred to as “new-Modified Prime Code (n-MPC)” for direct-detection synchronous optical code-division multiple-access (OCDMA) networks. The new code has been applied to Overlapping Pulse-Position Modulation (OPPM) CDMA system and the performance of system is evaluated. In addition, we have analyzed the system throughput and also introduced a new interference cancellation technique which significantly improves the bit error probability (BEP) of OPPM-OCDMA systems.     

Self-Affine Sets and Graph-Directed Systems

   Abstract. A self-affine set in R ⁿ is a compact set T with A(T)= ∪ _{d∈ D} (T+d) where A is an expanding n× n matrix with integer entries and D ={d ₁ , d ₂ ,···, d _N } ⊂ Z ⁿ is an N -digit set. For the case N = | det(A)| the set T has been studied in great detail in the context of self-affine tiles. Our main interest in this paper is to consider the case N > | det(A)| , but the theorems and proofs apply to all the N . The self-affine sets arise naturally in fractal geometry and, moreover, they are the support of the scaling functions in wavelet theory. The main difficulty in studying such sets is that the pieces T+d, d∈ D, overlap and it is harder to trace the iteration. For this we construct a new graph-directed system to determine whether such a set T will have a nonvoid interior, and to use the system to calculate the dimension of T or its boundary (if T ^o ≠  ). By using this setup we also show that the Lebesgue measure of such T is a rational number, in contrast to the case where, for a self-affine tile, it is an integer.     

Chemometric quality control of chromatographic purity

It is common practice in chromatographic purity analysis of pharmaceutical manufacturing processes to assess the quality of peak integration combined by visual investigation of the chromatogram. This traditional method of visual chromatographic comparison is simple, but is very subjective, laborious and seldom very quantitative. For high-purity drugs it would be particularly difficult to detect the occurrence of an unknown impurity co-eluting with the target compound, which is present in excess compared to any impurity. We hypothesize that this can be achieved through Multivariate Statistical Process Control (MSPC) based on principal component analysis (PCA) modeling. In order to obtain the lowest detection limit, different chromatographic data preprocessing methods such as time alignment, baseline correction and scaling are applied. Historical high performance liquid chromatography (HPLC) chromatograms from a biopharmaceutical in-process analysis are used to build a normal operation condition (NOC) PCA model. Chromatograms added simulated 0.1% impurities with varied resolutions are exposed to the NOC model and monitored with MSPC charts. This study demonstrates that MSPC based on PCA applied on chromatographic purity analysis is a powerful tool for monitoring subtle changes in the chromatographic pattern, providing clear diagnostics of subtly deviating chromatograms. The procedure described in this study can be implemented and operated as the HPLC analysis runs according to the process analytical technology (PAT) concept aiming for real-time release.     

Four-operand parallel optical computing using shadow-casting technique

Optical shadow-casting (OSC) technique has shown excellent potential for optically implementing two-operand parallel logic gates and array logic operations. The 16 logic functions for two binary patterns (variables) are optically realizable in parallel by properly configuring an array of 2×2 light emitting diodes. In this paper, we propose an enhanced OSC technique for implementing four-operand parallel logic gates. The proposed system is capable of performing 2¹⁶ logic functions by simply programming the switching mode of an array of 4×4 light emitting diodes in the input plane. This leads to an efficient and compact realization scheme when compared to the conventional two-operand OSC system.     

Quantum-inspired space search algorithm (QSSA) for global numerical optimization

This work presents the evolutionary quantum-inspired space search algorithm (QSSA) for solving numerical optimization problems. In the proposed algorithm, the feasible solution space is decomposed into regions in terms of quantum representation. As the search progresses from one generation to the next, the quantum bits evolve gradually to increase the probability of selecting the regions that render good fitness values. Through the inherent probabilistic mechanism, the QSSA initially behaves as a global search algorithm and gradually evolves into a local search algorithm, yielding a good balance between exploration and exploitation. To prevent a premature convergence and to speed up the overall search speed, an overlapping strategy is also proposed. The QSSA is applied to a series of numerical optimization problems. The experiments show that the results obtained by the QSSA are quite competitive compared to those obtained using state-of-the-art IPOP-CMA-ES and QEA.     

Solvent optimization in normal-phase liquid chromatography of selected steroids

Summary Resolution (R_s) is a function of three factors: efficiency, retentivity and selectivity. A procedure for optimization of mobile phase selectivity was demonstrated using a reversed-phase (RP) separation of compounds with various functionalities. In this paper, the same procedure is used with normal bonded-phase (NP) chromatography to develop a separation of structurally similar steroids. The optimization of mobile-phase selectivity provided increased problem-solving capability and decreased the analysis time.A brief summary of this work has been published in September 1981, in the form of a du Pont Application Study.     

Optimal testing strategies in overlapped design process

Testing is an important activity in product development. Past studies, which are developed to determine the optimal scheduling of tests, often focused on single-stage testing of sequential design process. This paper presents an analytical model for the scheduling of tests in overlapped design process, where a downstream stage starts before the completion of upstream testing. We derive optimal stopping rules for upstream and downstream stages’ testing, together with the optimal time elapsed between beginning the upstream tests and beginning the downstream development. We find that the cost function is first convex then concave increasing with respect to upstream testing duration. A one-dimensional search algorithm is then proposed for finding the unique optimum that minimizes the overall cost. Moreover, the impact of different model parameters, such as the problem-solving capacity and opportunity cost, on the optimal solution is discussed. Finally, we compare the testing strategies in overlapped process with those in sequential process, and get some additional results. The methodology is illustrated with a case study at a handset design company.