Un algoritmo per la scelta dell'origine e della scala nelle routines di tracciamento di grafici

Riassunto Viene proposto un algoritmo che, nelle routine di tracciamento automatico di grafici, opera la scelta della scala (lineare) più conveniente secondo criteri di opportunità non molto dissimili da quelli adottati da Giammo e Dixon-Kronmal. Sostanzialmente si ottiene una migliore utilizzazione dello spazio disponibile con la sola rinuncia al principio per cui l'origine dell'asse debba avere un valore multiplo del fattore di scala.

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Summary This paper provides an efficient computational procedure for providing scales for use in automatic plotting data. The ?reasonable? scale definition used is similar to that of Giammo and of Dixon-Kronmal, but space available for plotting is better utilized.

     

Optical differentiation of geometrical patterns

Two simple optical methods are presented which can perform direct, real-time differentiation of geometrical patterns by shifting. The first one gives uniform shifting in one direction and the resulting moiré fringes are curves of constant partial derivative along the same direction, and the second renders moiré fringes of constant gradient modulus of the function represented by the pattern. Only incoherent light is used with the technique, but applications with coherent light are also envisaged. As an application, the paper presents both types of differentiation of a shadow-moiré pattern.     

The first conversion of primary alkyl halides to nitroalkanes under aqueous medium

Primary nitroalkanes and alpha,omega-dinitroalkanes can be easily obtained in aqueous medium by reaction of the corresponding halo derivatives with silver nitrite. The procedure works well with both alkyl bomide and alkyl iodide and proceeds in satisfactory to good yields even in the presence of other functionalities, minimizing the formation of the undesired alkyl nitrites.     

Selective covalent binding of a positively charged water-soluble benzoheterocycle triosmium cluster to single- and double-stranded DNA

The water-soluble triosmium cluster [Os₃(CO)₉(μ-η²-(4-CHO)C₉H₅N)(μ-H)(P(OCH₂CH₂N(CH₃)₃I)₃)] (4) was tested for its reactivity with plasmid DNA. In contrast to the band retardation previously observed with a related series of positively charged clusters, an intensification and retardation of three discrete bands was observed with increasing cluster concentration. In order to further investigate the apparent modification of DNA by 4, its interaction with a 22-oligomer (sequence 5′-AGT TGT GGT GAC TTT CCC AGG C-3′) was examined. Incubation with this oligonucleotide (pH 7.4 in Tris-HCl buffer and 100 mM NaCl) followed by HPLC analysis revealed the formation of three dose dependent products assigned as covalent modifications at three sites of the oligonucleotide. Incubation of 4 with ³²P-ATP labeled oligonucleotide at the 5′-end followed by treatment with piperidine and comparison with the standard Maxam-Gilbert sequencing protocol products revealed only general background cleavage, indicating that the modification products are piperidine labile and suggesting that the modification involved formation of a Schiff base. An alternative approach was then pursued which involved annealing the 4-oligonucleotide products with their complementary strand and treatment of the resulting duplex DNAwith the exonuclease, Exo III. This assay indicated three exonuclease stops, consistent with the three products observed by HPLC whose electrophoretic mobility approximately matched guanine containing fragments when compared with the Maxam-Gilbert sequencing lanes. Reduction of the 4-oligonucleotide products with borohydride reducing agents, followed by treatment with piperidine, resulted in the formation of one product (by HPLC) with the same electrophoretic mobility as the AGTT fragment based on comparison with the Maxam-Gilbert sequencing lanes. This product most likely results from reduction of an initially formed Schiff base adduct (to the corresponding amine) with the guanine of the TGT fragment of the oligonucleotide, and corresponds to the most stable of the three Schiff base adducts detected by HPLC and by incubation with the exonuclease. The other two products are less stable and competitive reduction of the free aldehyde functionality on the cluster in equilibrium with these adducts precludes their detection after treatment with the reducing agents. The formation of the Schiff base adduct is further corroborated by the model reaction of [Os₃(CO)₁₀(μ-η²-(4-CHO)C₉H₅N)(μ-H)] (4′) with acetylated guanine in nonaqueous solvents where disappearance of the aldehyde resonance and the appearance of several new resonances in the 6-9 ppm region of the ¹H NMR of the reaction mixture is noted.     

The hierarchical backbone of complex networks

Given any complex directed network, a set of acyclic subgraphs can be extracted that will provide valuable information about its hierarchical structure. This Letter presents how the interpretation of the network weight matrix as a transition matrix allows the hierarchical backbone to be identified and characterized in terms of the concepts of hierarchical degree, which expresses the total weights of virtual edges established along successive transitions. The potential of the proposed approach is illustrated with respect to simulated random and preferential-attachment networks as well as real data related to word associations and gene sequencing.     

On shortest path games

A class of cooperative TU-games arising from shortest path problems is introduced and analyzed. Some conditions under which a shortest path game is balanced are obtained. Also an axiomatic characterization of the Shapley value for this class of games is provided.