On centripetal flows of entities in scale‐free networks with nodes of finite capability

We examine the transmission of entities from the peripheries of scale‐free networks toward their centers when the nodes of the network have finite processing capabilities. We look at varying network utilization, U and find that clogging of the network sets in after a threshold value has been exceeded, and that the congestion sets in at the downstream nodes (those nearer to the collector) having large numbers of upstream neighbors. Investigation of the question of the degree of correlation of several characteristics of scale‐free networks (such as the average path length to the collector <l_(min)> and the average clustering coefficient ) with the dynamics of centripetal flow in them reveals a negative answer: any correlation is indirect and will manifest in the number of producer nodes (which dictate the effective heaviness of the flow) and the interconnectedness of the feeder nodes, those nodes which are immediate neighbors of the collector node. An examination of reinforcement strategies shows dramatic improvements in both the finishing rate, and the average total transmission time, when the more centrally‐placed nodes are reinforced first, showing that the entities spend a large amount of their lifetime waiting in line at those nodes (which constitute the bottlenecks in the network) compared to the nodes in the periphery. Our results reinforce the importance of a network's hubs and their immediate environs, and suggest strategies for prioritizing elements of a network for optimization. © 2014 Wiley Periodicals, Inc. Complexity 21: 283–295, 2015     

Algebraic methods for the solution of linear functional equations

The equation

$$\sum^{n}_ {i=0} a_{i}f(b_{i}x + (1 - b_{i})y) = 0$$

belongs to the class of linear functional equations. The solutions form a linear space with respect to the usual pointwise operations. According to the classical results of the theory they must be generalized polynomials. New investigations have been started a few years ago. They clarified that the existence of non-trivial solutions depends on the algebraic properties of some related families of parameters. The problem is to find the necessary and sufficient conditions for the existence of non-trivial solutions in terms of these kinds of properties. One of the earliest results is due to Z. Daróczy [1]. It can be considered as the solution of the problem in case of n = 2. We are going to take more steps forward by solving the problem in case of n = 3.

     

Stochastic Optimization Problems with CVaR Risk Measure and Their Sample Average Approximation

We provide a refined convergence analysis for the SAA (sample average approximation) method applied to stochastic optimization problems with either single or mixed CVaR (conditional value-at-risk) measures. Under certain regularity conditions, it is shown that any accumulation point of the weak GKKT (generalized Karush-Kuhn-Tucker) points produced by the SAA method is almost surely a weak stationary point of the original CVaR or mixed CVaR optimization problems. In addition, it is shown that, as the sample size increases, the difference of the optimal values between the SAA problems and the original problem tends to zero with probability approaching one exponentially fast.     

A rapid and sensitive liquid chromatography/tandem mass spectrometry method for determination of docetaxel in human plasma

A novel, rapid and sensitive isocratic liquid chromatography/tandem mass spectrometry (LC/MS/MS) method was developed for quantification of docetaxel in human plasma with paclitaxel as internal standard. The high sensitivity and specificity of MS/MS detection enabled the use of a small volume of plasma (0.05 mL) and a simple liquid-liquid extraction procedure. Furthermore, a very short run-time (3 min) fulfilled the need for monitoring plasma levels of docetaxel from large-scale clinical studies. The calibration curve for docetaxel was linear over the range 5-1000 ng/mL with coefficients of correlation >0.999 using only 0.05 mL plasma. The intra- and inter-day precisions (CV) of analysis were <7%, and accuracy ranged from 96 to 110%. The applicability of the method was demonstrated in a pharmacokinetic study of a 1-h infusion of docetaxel with dosages of 75 mg/m(2). Possible conjugated metabolites of docetaxel were not detected in patients' samples.     

Unlabeled trees: Distribution of the maximum degree

Pick a tree uniformly at random from among all unlabeled trees on n vertices, and let X_n be the maximum of the degrees of its vertices. For any fixed integer d, as n→∞, where μ_n = c₁ log n, where {μ_n} : = μ_n – ?μ? denotes the fractional part of μ_n and where c_o, c₁, and η_∞ are knnown constants, givenb approximately by c₀ = 3.262 …, c₁ = 0.9227 …, and η_∞ = 0.3383…. © 1994 John Wiley & Sons, Inc.     

Identification of a serine protease inhibitor homologue in Bird's Nest by an integrated proteomics approach.

For centuries, the edible nests of Collocalia spp. ("Bird's Nests") have been used as a Chinese delicacy that had been claimed to be an effective health-giving tonic. However, clinical studies indicated that in Singapore, Bird's Nest is the most common cause of food-induced anaphylaxis in children, which could lead to potentially life-threatening allergenic reactions. The purpose of this study was to characterize the major allergens in Bird's Nest by using the combined technologies of two-dimensional gel electrophoresis (2-DE), immunochemistry, N-terminal protein sequencing, and mass spectrometry. Results from the immunostaining of the Western blots of the Bird's Nest 2-DE separated proteins with the sera from allergic patients indicated the presence of a major allergen of 66 kDa. Initial searches of the matrix assisted laser desorption/ionization--time of flight--mass spectrometry (MALDI-TOF-MS) tryptic peptide masses of the allergen in the SWISS-PROT and NCBI nonredundant databases revealed that this protein was novel. Based on the partial protein sequence information obtained from N-terminal microsequencing and nanoelectrospray-tandem MS, the 66 kDa immunoreactive allergen was found to be homologous to ovoinhibitor, a Kazal-type serine protease inhibitor, which is one of the dominant allergens found in chicken egg white.     

Separation of kaempferols in Impatients balsamina flowers by capillary electrophoresis with electrochemical detection

Capillary electrophoresis with wall-jet amperometric detection was used to detect kaempferol and its derivatives kaempferol-3-glucoside, kaempferol-3-glucosylrhamnoside and kaempferol-3-(p-coumaroyl)glucoside. The influence of buffer pH on separation was investigated and optimized. With a phosphate buffer at pH 7.5, nearly complete separation of the four kaempferols was achieved according to their different electrophoretic mobilities. The detection potential was also evaluated and optimized. At detection potential of +0.80 V vs. saturated calomel electrode, an amperometric response with high sensitivity and stability was obtained for these four compounds. Detection limit estimated for all the kaempferols examined was less than 1.4 fmol, based on S/N=3. The use of this method for the separation and detection of these compounds present in balsam flowers (Impatiens balsamina) is reported.     

An efficient lactamization of fimbrolides to novel 1,5-dihydropyrrol-2-ones

A new versatile method for the conversion of fimbrolides to the corresponding novel dihydropyrrol-2-ones is described. This new efficient lactamization protocol has the advantage of higher yields and can be used for the synthesis of a series of new dihydropyrrol-2-ones with interesting anti-bacterial properties.     

Polymerization behavior of 1,2,2,6,6-pentamethyl-4-piperidinyl m-isopropenyl-α,α-dimethylbenzyl carbamate

Copolymers of 1,2,2,6,6-pentamethyl-4-piperidinyl m-isopropenyl-α,α-dimethylbenzyl carbamate (CB) with styrene (S) and with methyl methacrylate (MMA) were synthesized using AIBN as initiator. S–CB copolymers made from feed ranging from 0.45–0.94 mole fractions S and MMA-CB copolymers made from feed of 0.34–0.88 mole fractions MMA were used to determine the monomer reactivity ratios r₁ and r₂. The structure of S–CB copolymers was inferred to be mainly of a random nature and in the MMA–CB copolymerization system there is a stronger tendency to form alternating copolymers. © 1993 John Wiley & Sons, Inc.