A class of models for uncorrelated random variables

We consider the class of multivariate distributions that gives the distribution of the sum of uncorrelated random variables by the product of their marginal distributions. This class is defined by a representation of the assumption of sub-independence, formulated previously in terms of the characteristic function and convolution, as a weaker assumption than independence for derivation of the distribution of the sum of random variables. The new representation is in terms of stochastic equivalence and the class of distributions is referred to as the summable uncorrelated marginals (SUM) distributions. The SUM distributions can be used as models for the joint distribution of uncorrelated random variables, irrespective of the strength of dependence between them. We provide a method for the construction of bivariate SUM distributions through linking any pair of identical symmetric probability density functions. We also give a formula for measuring the strength of dependence of the SUM models. A final result shows that under the condition of positive or negative orthant dependence, the SUM property implies independence.     

On gap functions for nonsmooth multiobjective optimization problems

A set-valued gap function, \(\phi \), existing in the literature for smooth and nonsmooth multiobjective optimization problems is dealt with. It is known that \(0\in \phi (x^*)\) is a sufficient condition for efficiency of a feasible solution \(x^*\), while the converse does not hold. In the current work, the converse of this assertion is proved for properly efficient solutions. Afterwards, to avoid the complexities of set-valued maps some new single-valued gap functions, for nonsmooth multiobjective optimization problems with locally Lipschitz data are introduced. Important properties of the new gap functions are established.     

Template tailoring: Accurate determination of heterozygous alleles using peptide nucleic acid and dideoxyNTP

Measurement of the length of DNA fragments plays a pivotal role in genetic mapping, disease diagnostics, human identification and forensic applications. PCR followed by electrophoresis is used for DNA length measurement of STRs, a process that requires labeled primers and allelic ladders as standards to avoid machine error. Sequencing‐based approaches can be used for STR analysis to eliminate the requirement of labeled primers and allelic ladder. However, the limiting factor with this approach is unsynchronized polymerization in heterozygous sample analysis, in which alleles with different lengths can lead to imbalanced heterozygote peak height ratios. We have developed a rapid DNA length measurement method using peptide nucleic acid and dideoxy dNTPs to “tailor” DNA templates for accurate sequencing to overcome this hurdle. We also devised an accelerated “dyad” pyrosequencing strategy, such that the combined approach can be used as a faster, more accurate alternative to de novo sequencing. Dyad sequencing interrogates two bases at a time by allowing the polymerase to incorporate two nucleotides to DNA template, cutting the analysis time in half. In addition, for the first time, we show the effect of peptide nucleic acid as a blocking probe to stop polymerization, which is essential to analyze the heterozygous samples by sequencing. This approach provides a new platform for rapid and cost‐effective DNA length measurement for STRs and resequencing of small DNA fragments.     

Enhancement of Human γ-Interferon Production in Recombinant <Emphasis Type="Italic">E. coli</Emphasis> Using Batch Cultivation

Development of inexpensive and simple culture media and appropriate induction conditions are always favorable for industry. In this research, chemical composition and stoichiometric data for γ-interferon production and recombinant Escherichia coli growth were used in order to achieve a simple medium and favorable induction conditions. To achieve this goal, the effects of medium composition and induction conditions on the production of γ-interferon were investigated in batch culture of E. coli BL21 (DE3) [pET3a-ifnγ]. These conditions were considered as suitable conditions for the production of γ-interferon: 2.5× M9 medium, supplemented with a mixture of amino acids (milligram per liter), including glutamic acid 215, aspartic acid 250, lysine 160, and phenylalanine 90, and induction at late-log phase (OD₆₀₀ = 4.5). Under these conditions, dry cell weight of 6 ± 0.2 g/l and γ-interferon concentration of 2.15 ± 0.1 g/l were obtained. Later, without changing the concentration ratio of amino acids and glucose, the effect of increase in the primary glucose concentration on productivity of γ-interferon was investigated. It was found that 25 g/l glucose will result in maximum attainable biomass and recombinant human γ-interferon. At improved conditions, a dry cell weight of 14 ± 0.2 g/l, concentration and overall productivity of γ-interferon 4.2 ± 0.1 g/l and 420 ± 10 mg/l h, respectively, were obtained.     

Linear and non-linear vibration and frequency response analyses of microcantilevers subjected to tip-sample interaction

Despite their simple structure and design, microcantilevers are receiving increased attention due to their unique sensing and actuation features in many MEMS and NEMS. Along this line, a non-linear distributed-parameters modeling of a microcantilever beam under the influence of a nanoparticle sample is studied in this paper. A long-range Van der Waals force model is utilized to describe the microcantilever-particle interaction along with an inextensibility condition for the microcantilever in order to derive the equations of motion in terms of only one generalized coordinate. Both of these considerations impose strong nonlinearities on the resultant integro-partial equations of motion. In order to provide an understanding of non-linear characteristics of combined microcantilever-particle system, a geometrical function is wisely chosen in such a way that natural frequency of the linear model exactly equates with that of non-linear model. It is shown that both approaches are reasonably comparable for the system considered here. Linear and non-linear equations of motion are then investigated extensively in both frequency and time domains. The simulation results demonstrate that the particle attraction region can be obtained through studying natural frequency of the system consisting of microcantilever and particle. The frequency analysis also proves that the influence of nonlinearities is amplified inside the particle attraction region through bending or shifting the frequency response curves. This is accompanied by sudden changes in the vibration amplitude estimated very closely by the non-linear model, while it cannot be predicted by the best linear model at all.     

From the Klein–Gordon–Zakharov system to a singular nonlinear Schrödinger system

In this paper, we continue our investigation of the high-frequency and subsonic limits of the Klein–Gordon–Zakharov system. Formally, the limit system is the nonlinear Schrödinger equation. However, for some special case of the parameters going to the limits, some new models arise. The main object of this paper is the derivation of those new models, together with convergence of the solutions along the limits.     

Method for clone checking

A new method for simple and fast clone checking is described. We combined the Pyrosequencing technology with a preprogrammed nucleotide dispensation strategy for fast analysis of DNA constructs. To test this method, the N-terminus region of plasmids constructed for the production of recombinant apyrase was analyzed. Of the ten plasmids tested, seven constructs were correct, two constructs showed one base deletion, and one construct showed deletion of a 195 bp fragment. The preprogrammed nucleotide dispensation strategy allowed the identification of the sequence downstream of the deletions. Thus, this method determines both the location and nature of possible artifacts.     

Dynamic 1H NMR Study of Aryl-Nitrogen Single Bond and Carbon-Carbon Double Bond Rotational Energy Barriers in Two Highly Functionalized Pyranopyrimidines

Summary.  The reactive 1:1 intermediate produced in the reaction between 2,6-dimethylphenyl isocyanide and dimethyl acetylenedicarboxylate was trapped by N,N′ -dimethylbarbituric acid to yield the isomeric products dimethyl 7-(2,6-dimethylphenylamino)-1,3-dimethyl-2,4-dioxo-4H-pyrano[3,2-d]pyrimidine-5,6-dicarboxylate and dimethyl (E)-2-((2,6-dimethylphenylamino)-(1,3-dimethyl-2,4,6-trioxo-pyrimidine-5-ylidene)-methyl)-but-2-enedioate in a nearly 1:1 ratio and an overall yield of 85%. Dynamic effects were observed in the ¹H NMR spectra of these compounds and were attributed to restricted rotation around the aryl-nitrogen single bonds and the polarized carbon-carbon double bond. Received September 18, 2000. Accepted (revised) November 22, 2000     

Simultaneous control of false positives and false negatives in multiple hypotheses testing

Multiple hypotheses testing is concerned with appropriately controlling the rate of false positives, false negatives or both when testing several hypotheses simultaneously. Nowadays, the common approach to testing multiple hypotheses calls for controlling the expected proportion of falsely rejected null hypotheses referred to as the false discovery rate (FDR) or suitable measures based on the positive false discovery rate (pFDR). In this paper, we consider the problem of determining levels that both false positives and false negatives can be controlled simultaneously. As our risk function, we use the expected value of the maximum between the proportions of false positives and false negatives, with the expectation being taken conditional on the event that at least one hypothesis is rejected and one is accepted, referred to as hybrid error rate (HER). We then develop, based on HER, an analog of p-value termed as h-value to test the individual hypotheses. The use of the new procedure is illustrated using the well-known public data set by Golub et al. [Molecular classification of cancer: class discovery and class prediction by gene expression monitoring, Science 386 (1999) 531-537] with Affymetrix arrays of patients with acute lymphoic leukemia and acute myeloid leukemia.