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.     

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.     

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.     

Study of excretion of ecdysterone in human urine

A study of excretion in human urine of ecdysterone, which is the active component of several over-the-counter supplements such as "Ecdysten", reportedly used by athletes, is presented. The study was performed after oral administration of 20 mg of ecdysterone. The collected urine samples were prepared using the standard screening extraction procedure for the free and conjugated fraction of anabolic steroids, and analyzed by gas chromatography (GC) coupled with quadrupole mass spectrometry (MS) and also with high-resolution mass spectrometry (HRMS). Two ecdysterone metabolites were identified and detected along with unchanged ecdysterone. Accurate mass measurements were made for diagnostic ions, including the molecular ion of the main metabolite of ecdysterone, deoxyecdysone, which, to our knowledge, has not previously been reported in the literature. These accurate mass measurements support the proposed fragmentation scheme.     

Enzymatic fluorimetric determination of the individual bile acids in blood serum

An enzymatic fluorimetric method is described for the determination of total bile acids (cholic acid and deoxycholic acid), primary bile acids (cholic and chen acids and individual bile acids in serum without prior separation of the acids. Total and primary bile acids are determined by equilibrium procedures by conver of the 3α- and 7α-hydroxy bile acids to 3-oxo and 7-oxo bile acids by α-NAD⁺, in the presence of 3α- and 7α-hydroxysteroid dehydrogenase (HSD), respectively, and measurement of the generated NADH fluorimetrically. Chenodeoxycholic acid is determined with 7α-HSD in the presence of cholic and deoxycholic acids by a differential kinetic procedure, and cholic and deoxycholic acids are calculated by difference. Interferents are removed by treatment of serum with Sachrom rein. Only 1.00 ml of serum is required. Low cost, simplicity and reliability are the main features of the method. The recovery of bile acids added to serum averaged 103% (range 83–122%). The method is suitable for routine use in small clinical laboratories.     

Comparative study of pretreatment methods for the determination of metals in atmospheric aerosol by electrothermal atomic absorption spectrometry

A comparative study of pretreatment methods for the determination of 10 elements (As, Cd, Pb, V, Ni, Mn, Cr, Cu, Fe, Al) in atmospheric aerosols by electrothermal atomic absorption spectrometry (ETAAS) was conducted. For the digestion of the particulates collected in filters, six methods were compared using a mixture of HNO₃ and HF with or without the addition of various oxidative agents (HClO₄ or H₂O₂) or acids (HCl). The comparative study was performed using loaded cellulose filter samples, which were digested in Parr bombs and heated in a conventional oven at 170 °C for 5 h. The extraction efficiency and blanks were compared and it was proved that the digestion method using only HNO₃–HF extracted most of the metals and gave the lowest blanks. The HNO₃–HF mixture was selected for the development of an improved microwave digestion method specific for aerosol-loaded filters. The operating parameters were optimized, so that quantitative recovery of the reference materials NIST 1649a urban dust and NIST 1648 urban particulate matter was achieved. The blank of cellulose and teflon filters were also determined and compared. Teflon filters present the lowest blanks for all the elements. The obtained limits of detection for each type of filters were adequate for environmental monitoring purposes. ETAAS instrumental operation was also optimized for the compensation and the elimination of interferences. The temperature optimization was performed for each metal in every type of filter and optimized parameters are proposed for 10 elements.     

Therapeutic potential of phosphoinositide 3-kinase inhibitors

At least one Holy Grail for many academic researchers and pharmaceutical research divisions alike has been to identify therapeutically useful selective PI3K inhibitors. There are several different but closely related PI3Ks which are thought to have distinct biological roles. Until now, however, researchers have been frustrated by poor selectivity of the available pharmacological inhibitors, which are unable to distinguish the different isoforms of PI3K adequately. Fortunately, recently published work gives cause for optimism; there are now several patent specifications published that describe new PI3K inhibitors, including some that are more selective for the delta isoform of PI3K. Given the involvement of PI3Ks in a plethora of biological settings, such isoform-selective inhibitors may have immense potential use for the treatment of patients with inflammatory and autoimmune disorders as well as cancer and cardiovascular diseases.     

Low dose measurement with thick gate oxide MOSFETs

The low dose limit and the accuracy of high sensitivity MOS ionizing radiation dosimeters fabricated at LAAS-CNRS are investigated.