The unsatisfiability threshold revisited

The problem of determining the unsatisfiability threshold for random 3-SAT formulas consists in determining the clause to variable ratio that marks the experimentally observed abrupt change from almost surely satisfiable formulas to almost surely unsatisfiable. Up to now, there have been rigorously established increasingly better lower and upper bounds to the actual threshold value. In this paper, we consider the problem of bounding the threshold value from above using methods that, we believe, are of interest on their own right. More specifically, we show how the method of local maximum satisfying truth assignments can be combined with results for the occupancy problem in schemes of random allocation of balls into bins in order to achieve an upper bound for the unsatisfiability threshold less than 4.571. In order to obtain this value, we establish a bound on the q-binomial coefficients (a generalization of the binomial coefficients). No such bound was previously known, despite the extensive literature on q-binomial coefficients. Finally, to prove our result we had to establish certain relations among the conditional probabilities of an event in various probabilistic models for random formulas. It turned out that these relations were considerably harder to prove than the corresponding ones for unconditional probabilities, which were previously known.     

Novel fiber-optic biosensor based on immobilized glutathione S-transferase and sol–gel entrapped bromcresol green for the determination of atrazine

The aim of this work was to investigate, for the first time, the potential of the enzyme glutathione S-transferase I (isoenzyme GST-I) for uses in analytical chemistry. A novel fiber-optic biosensor for the detection and determination of the triazine herbicide atrazine was developed based on maize GST-I expressed in E. coli. The sensing bioactive material was a three-layer mini-sandwich. The enzyme was immobilized on the outer layer that consisted of a hydrophilic polyvinylidenefluoride membrane. This membrane was supported on an inner glass disk by means of an intermediate binder sol–gel layer that incorporated bromcresol green (BCG). The biosensor operated in a static mode at 25 °C and the rate of the enzymatic reaction, using atrazine as a substrate, served as an analytical signal. A calibration curve was obtained for atrazine, with analytically useful concentration range 2.52–125 μM. The sensor detection limit was 0.84 μM. The reproducibility of atrazine sensing was in the order of ±3–5%. The method was successfully applied to the determination of this herbicide in real water samples, without sample preparation steps. Atrazine recovery ranged between 85 and 110%. No interference from other pesticides, such as alachlor and carbaryl was observed in the absence of atrazine. The immobilized enzyme retained about 75% of its original activity after 1 month use. Simply unscrewing the terminal holding ring of the probe and placing a new bioactive sandwich could easily replace a deteriorated mini-sandwich.     

Employment of 4-(1-imidazolyl)phenol as a luminol signal enhancer in a competitive-type chemiluminescence immunoassay and its comparison with the conventional antigen-horseradish peroxidase conjugate-based assay

This study describes the employment of a novel imidazole-substituted phenol [4-(1-imidazolyl)phenol] as a highly potent signal enhancer in a horseradish peroxidase (HRP)-luminol chemiluminescence (CL) immunoassay. This competitive-type immunoassay for the model antigen fentanyl is based on the use of fentanyl polyclonal antibody immobilized on white microtiter plates and a biotinylated bovine serum albumin (BSA)-fentanyl derivative as a tracer. The latter was detected by means of streptavidin labeled with HRP, resulting in the generation of a high-intensity and relatively stable chemiluminescent signal, immediately after the addition of the substrate solution (NOAS). The developed method fulfilled the requirements of accuracy (percentage recovery ranged from 93.8 to 107%) and precision (intra- and inter-assay CVs were 2.5-5.2 and 4.5-11.9%, respectively). Its plasma detection limit (1.05 pg ml⁻¹) was lower than those of previous immunoassays. The novel assay was compared in terms of sensitivity and concentration range with other common HRP substrate systems: luminol-p-iodophenol-H₂O₂ and TMB-H₂O₂. Finally, the described method was compared with an HRP-fentanyl conjugate-based assay, similar to commercially available kits (SKIT), employing the novel substrate solution for both assays and the differences observed were explained by applying previously described models. The detection limit was 4.82 pg ml⁻¹ for SKIT, recovery values were 94.2-105% and intra- and inter-assay CVs were 2.5-5.2 and 4.5-11.9%, respectively. In conclusion, the proposed assay could be utilized for a wide range of molecules and replace the existing enzyme-labeled antigen-based kits.     

L1-optimal estimates for a regression type function in R

Let X₁, X₂, …, X_n be random vectors that take values in a compact set in R^d, d ≥ 1. Let Y₁, Y₂, …, Y_n be random variables (“the responses”) which conditionally on X₁ = x₁, …, X_n = x_n are independent with densities f(y | x_i, θ(x_i)), i = 1, …, n. Assuming that θ lives in a sup-norm compact space Θ_q,d of real valued functions, an optimal L₁-consistent estimator of θ is constructed via empirical measures. The rate of convergence of the estimator to the true parameter θ depends on Kolmogorov's entropy of Θ_q,d.     

A study of properties of adaptive quadratic grids for three-dimensional near-surface field computations

Curved geometries and the corresponding near-surface fields typically require a large number of linear computational elements. High-order numerical solvers have been primarily used with low-order meshes. There is a need for curved, high-order computational elements. Typical near-surface meshes consist of hexahedral and/or prismatic elements. The present work studies the employment of quadratic meshes that are relatively coarse for field simulations. Directionally quadratic high-order elements are proposed for the near-surface field regions. The quadratic meshes are compared with the conventional low-order ones in terms of accuracy and efficiency. The cases considered include closed surface volume calculations, as well as computation of gradients of several analytic fields. A special method of adaptive local quadratic meshes is proposed and evaluated. Truncation error analysis for quadratic grids yields comparison with the conventional linear hexahedral/prismatic meshes, which are subject to typical distortions such as stretching, skewness, and torsion.     

Convergence theory of extrapolated iterative methods for a certain class of non-symmetric linear systems

Summary A variety of iterative methods considered in [3] are applied to linear algebraic systems of the formAu=b, where the matrixA is consistently ordered [12] and the iteration matrix of the Jacobi method is skew-symmetric. The related theory of convergence is developed and the optimum values of the involved parameters for each considered scheme are determined. It reveals that under the aforementioned assumptions the Extrapolated Successive Underrelaxation method attains a rate of convergence which is clearly superior over the Successive Underrelaxation method [5] when the Jacobi iteration matrix is non-singular.     

An improved high-throughput liquid chromatographic/tandem mass spectrometric method for terbinafine quantification in human plasma, using automated liquid-liquid extraction based on 96-well format plates

A fully automated high-throughput liquid chromatography/tandem mass spectrometry (LC-MS/MS) method was developed for terbinafine quantification in human plasma. The plasma samples were treated by liquid-liquid extraction (LLE) in 2.2 mL 96-deepwell plates. Terbinafine and the internal standard (IS) N-methyl-1-naphthalenemethylamine were extracted from human plasma by LLE, using a mixture of methyl t-butyl ether (MTBE)-hexane (70:30, v/v) as the organic solvent. All liquid transfer steps, including preparation of calibration standards and quality control samples, as well as the addition of the IS, were performed automatically by using robotic liquid handling workstations. After vortexing, centrifugation and freezing, the supernatant organic solvent was evaporated and reconstituted in a small volume of a reconstitution solution. Sample analysis was performed by reversed-phase LC-MS/MS, with positive ion electrospray ionization, using multiple reaction monitoring (MRM). The method had a very short sample preparation time and a chromatographic run time of 2.2 min. It was proved to have excellent sensitivity, specificity, accuracy as well as inter- and intraday precision for the quantification of terbinafine in human plasma. The calibration curve was linear for the range of concentrations 5.0-2000.0 ng/mL. The proposed method was applied to the rapid and reliable determination of terbinafine in a bioequivalence study after per os administration of 250 mg tablet formulations of terbinafine.     

Analysis of monoclonal antibody by a novel CE‐UV/MALDI‐MS interface

mAbs are highly complex proteins that present a wide range of microheterogeneity that requires multiple analytical methods for full structure assessment and quality control. As a consequence, the characterization of mAbs on different levels is particularly product‐ and time‐consuming. CE‐MS couplings, especially to MALDI, appear really attractive methods for the characterization of biological samples. In this work, we report the last instrumental development and performance of the first totally automated off‐line CE‐UV/MALDI‐MS/MS. This interface is based on the removal of the original UV cell of the CE apparatus, modification of the spotting device geometry, and creation of an integrated delivery matrix system. The performance of the method was evaluated with separation of five intact proteins and a tryptic digest mixture of nine proteins. Intact protein application shows the acquisition of electropherograms with high resolution and high repeatability. In the peptide mapping approach, a total number of 154 unique identified peptides were characterized using MS/MS spectra corresponding to average sequence coverage of 64.1%. Comparison with NanoLC/MALDI‐MS/MS showed complementarity at the peptide level with an increase of 42% when using CE/MALDI‐MS coupling. Finally, this work represents the first analysis of intact mAb charge variants by CZE using an MS detection. Moreover, using a peptide mapping approach CE‐UV/MALDI‐MS/MS fragmentation allowed 100% sequence coverage of the light chain and 92% of the heavy chain, and the separation of four major glycosylated peptides and their structural characterization.