5,5′-Di-4-pyridyl-2,2′-(p-phenyl­ene)di-1,3,4-oxadiazole

In the crystal structure of the title compound, C20H12N6O2, the mol­ecules are located on centres of inversion. The complete mol­ecule is almost planar, with a maximum deviation from the mean plane of 0.0657 (1) Å for the O atom. In the crystal, mol­ecules are stacked into columns elongated in the a axis direction. The centroid–centroid distances between the aromatic rings of the mol­ecules within the columns are 3.6406 (1) and 3.6287 (2) Å. Mol­ecules are additionally connected via weak inter­molecular C—H⋯N hydrogen bonding

A method dealing with a large number of correlated traits in a linkage genome scan

We propose a method to perform linkage genome scans for many correlated traits in the Genetic Analysis Workshop 15 (GAW15) data. The proposed method has two steps: first, we use a clustering method to find the tight clusters of the traits and use the first principal component (PC) of the traits in each cluster to represent the cluster; second, we perform a linkage scan for each cluster by using the representative trait of the cluster. The results of applying the method to the GAW15 Problem 1 data indicate that most of the traits in the same cluster have the same regulators, and the representative trait measure, the first PC, can explain a large part of the total variation of all the traits in each cluster. Furthermore, considering one cluster of traits at a time may yield more linkage signals than considering traits individually

(μ-5-Carb­oxy-1H-imidazole-4-carboxyl­ato-κ4 N 1,O 5:N 3,O 4)bis­[amminesilver(I)]

In the title compound, [Ag2(C5H2N2O4)(NH3)2], each of the two AgI atoms is coordinated by two N atoms from an ammonia mol­ecule and a 5-carb­oxy-1H-imidazole-4-carboxyl­ate ligand in an almost linear geometry, and by one carboxyl­ate O atom with a weak inter­action. The Ag atoms are assembled into a linear tetra­mer through Ag⋯Ag inter­actions. Each Ag tetra­mer is linked by four 5-carb­oxy-1H-imidazole-4-carboxyl­ate ligands, forming a puckered chain. The complex involves a strong intra­molecular O—H⋯O hydrogen bond

4-Hydr­oxy-6-[(4-hydr­oxy-1-oxo-1,2-dihydro­phthalazin-6-yl)carbon­yl]phthalazin-1(2H)-one

In the crystal structure of the title compound, C17H10N4O5, the mol­ecules lie on twofold axes (through the ketone bridge C and O atoms). The dihedral angle between the two phthalazine rings is 52.25 (1)°. In the crystal, inter­molecular N—H⋯O and O—H⋯O inter­actions link the mol­ecules

Limited bisimulations for nondeterministic fuzzy transition systems

The limited version of bisimulation, called limited approximate bisimulation, has recently been introduced to fuzzy transition systems (NFTSs). This article extends limited approximate bisimulation to NFTSs, which are more general structures than FTSs, to introduce a notion of $k$-limited $\alpha$-bisimulation by using an approach of relational lifting, where $k$ is a natural number and $\alpha\in[0,1]$. To give the algorithmic characterization, a fixed point characterization of $k$-limited $\alpha$-bisimilarity is first provided. Then $k$-limited $\alpha$-bisimulation vector with $i$-th element being a $(k-i+1)$-limited $\alpha$-bisimulation is introduced to investigate conditions for two states to be $k$-limited $\alpha$-bisimilar, where $1\leq i\leq k+1$. Using these results, an O(2k^2|V|^6\cdot\left|\lra\right|^2) algorithm is designed for computing the degree of similarity between two states, where $|V|$ is the number of states of the NFTS and \left|\lra\right| is the greatest number of transitions from states. Finally, the relationship between $k$-limited $\alpha$-bisimilar and $\alpha$-bisimulation under $\widetilde{S}$ is showed, and by which, a logical characterization of $k$-limited $\alpha$-bisimilarity is provided