Shortest Path Problem on a Network with Imprecise Edge Weight

A network with its arc lengths as imprecise number, instead of a real number, namely, interval number and triangular fuzzy number is considered here. Existing ideas on addition and comparison between two imprecise numbers of same type are introduced. To obtain a fuzzy shortest path from a source vertex to all other vertices, a common algorithm is developed which works well on both types of imprecise numbers under consideration. In the proposed algorithm, a decision-maker is to negotiate with the obtained fuzzy shortest paths according to his/her view only when the means are same but the widths are different of the obtained paths. Otherwise, a fuzzy optimal path is obtained to which the decision-maker always satisfies with different grades of satisfaction. All pairs fuzzy shortest paths can be found by repeated use of the proposed algorithm.     

Targeted determination of the early stage SCLC specific biomarker pro-gastrin-releasing peptide (ProGRP) at clinical concentration levels in human serum using LC-MS

Pro-gastrin-releasing peptide (ProGRP) is used as a specific diagnostic marker for small cell lung cancer (SCLC), a rapidly growing neoplasm with high mortality. Our object was to develop an LC-MS method for the detection and quantification of ProGRP in human serum using the specific tryptic digestion product NLLGLIEAK (m/z 485.8 for [M + 2H](2+)). For this purpose the sample pretreatment, clean-up, enrichment, and LC-MS conditions were evaluated. Sample pretreatment was carried out using ACN precipitation to decrease the sample complexity. Although ProGRP (31-98) standards were soluble in 99% ACN, it showed that optimal signal intensities were obtained by adding ACN to the serum in a 1:1 ratio v/v. A simplified tryptic digest protocol was carried out using 100 mM triethanolamine buffer to ensure pH stability during the whole procedure. The simplified protocol also includes omission of reducing and alkylating reagents. Necessary additional sample clean-up was achieved by trapping NLLGLIEAK on a RAM column (ADS-C8) which was back-flushed onto the analytical BioBasic C8 column. Volume of injection, sample enrichment, and column capacity are among the factors optimized to reach a mass LOD of 150 pg on column (OC) ProGRP (31-98). Detection of ProGRP in the serum sample of a patient suffering from SCLC with a clinically relevant concentration shows the potential of the method in diagnosis, prognosis, and monitoring of the disease.     

Aspherical‐Atom Modeling of Coordination Compounds by Single‐Crystal X‐ray Diffraction Allows the Correct Metal Atom To Be Identified

Single‐crystal X‐ray diffraction (XRD) is often considered the gold standard in analytical chemistry, as it allows element identification as well as determination of atom connectivity and the solid‐state structure of completely unknown samples. Element assignment is based on the number of electrons of an atom, so that a distinction of neighboring heavier elements in the periodic table by XRD is often difficult. A computationally efficient procedure for aspherical‐atom least‐squares refinement of conventional diffraction data of organometallic compounds is proposed. The iterative procedure is conceptually similar to Hirshfeld‐atom refinement (Acta Crystallogr. Sect. A­ 2008 , 64, 383–393; IUCrJ. 2014 , 1,61–79), but it relies on tabulated invariom scattering factors (Acta Crystallogr. Sect. B­ 2013 , 69, 91–104) and the Hansen/Coppens multipole model; disordered structures can be handled as well. Five linear‐coordinate 3d metal complexes, for which the wrong element is found if standard independent‐atom model scattering factors are relied upon, are studied, and it is shown that only aspherical‐atom scattering factors allow a reliable assignment. The influence of anomalous dispersion in identifying the correct element is investigated and discussed.     

Probing nuclear surfaces by heavy ion reactions

An analysis of the recently measured ¹⁶O + ²⁶Mg one- and two-proton transfer reaction is given. It is shown that these reactions probe progressively deeper regions of the surface of the two colliding nuclei.