Trees with the most subtrees -- an algorithmic approach

When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in applications. The number of subtrees in the extremal cases constitute sequences which are of interest to number theorists. The structures which maximize or minimize the number of subtrees among general trees, binary trees and trees with a given maximum degree have been identified previously. Most recently, results of this nature are generalized to trees with a given degree sequence. In this note, we characterize the trees which maximize the number of subtrees among trees of a given order and degree sequence. Instead of using theoretical arguments, we take an algorithmic approach that explicitly describes the process of achieving an extremal tree from any random tree. The result also leads to some interesting questions and provides insight on finding the trees close to extremal and their numbers of subtrees.Comment: 12 pages, 7 figures; Journal of combinatorics, 201

Bis(2-methoxy­phenolato-κ2 O,O′)copper(II)

In the title compound, [Cu(C7H7O2)2], the asymmetric unit contains one and a half molecules with the central Cu(II) atoms situated on a general position and on a centre of inversion, respectively. Both Cu(II) atoms show a similar slightly distorted square-planar coordination, resulting from four O atoms of two 2-methoxyphenolate anions

Isolation of nematicidal constituents from essential oil of Kaempferia galanga L rhizome and their activity against Heterodera avenae Wollenweber

Purpose: To explore the nematicidal activities of the essential oil of Kaempferia galanga rhizomes and its isolated constituents against Heterodera avenae.Methods: Essential oil of K. galanga rhizomes was obtained by hydrodistillation and characterized by gas chromatography/mass spectrometric (GC/MS) analysis using HP-5MS column. Evaluation of nematicidal toxicity was performed against juveniles (J2) of H. avenae. The bioactive constituent compounds were isolated and identified from the oil based on bioactivity-directed fractionation.Results: Forty-one components were identified and the main components of the essential oil of K. galanga are as follows: ethyl-ρ-methoxy cinnamate (34.79 %), ethyl cinnamate (20.72%), 1,8-cineole (8.96 %), trans-cinnamaldehyde (7.03%) and borneol (5.64 %). The essential oil exhibited nematicidal activity against the cereal cyst nematode with an LC50 value of 91.78 μg/mL. Ethyl cinnamate, ethyl ρ-methoxy cinnamate and trans-cinnamaldehyde (median lethal concentration LC50 = 100.60 μg/ml, 83.04 μg/mL and 94.75 μg/mL, respectively) exhibited stronger nematicidal toxicity than borneol (LC50 = 734.89 μg/mL) and 1,8-cineole (LC50 = 921.21 μg/mL) against the cereal cyst nematode.Conclusion: The results indicate that the essential oil of K. galanga and its isolated constituents have a potential for development into natural nematicides for the control of cereal cyst nematodes.Keywords: Kaempferia galanga, Heterodera avenae, Nematicidal activity, Cereal cyst nematodes, Ethyl cinnamate, Ethyl ρ-methoxy cinnamate, Trans-cinnamaldehyd

2,2′-[(4,6-Dinitro-1,3-phenyl­ene)dioxy]diacetic acid hemihydrate

The skeletons of both independent mol­ecules of the carboxylic acid hemihydrate, C10H8N2O10·0.5H2O, are approximately planar [maximum deviations 0.642 (3) and 0.468 (1) Å]. The deviations arise from the twisting of the nitro groups with respect to the aromatic rings [dihedral angles = 3.24 (2) and 27.01 (1), and 7.87 (1) and 16.37 (2)° in the two molecules]. The crystal structure features inter­molecular O—H⋯O hydrogen bonds, which the link the dicarboxylic acid and water mol­ecules into a supra­molecular layer network

Deep Descriptor Transforming for Image Co-Localization

Reusable model design becomes desirable with the rapid expansion of machine learning applications. In this paper, we focus on the reusability of pre-trained deep convolutional models. Specifically, different from treating pre-trained models as feature extractors, we reveal more treasures beneath convolutional layers, i.e., the convolutional activations could act as a detector for the common object in the image co-localization problem. We propose a simple but effective method, named Deep Descriptor Transforming (DDT), for evaluating the correlations of descriptors and then obtaining the category-consistent regions, which can accurately locate the common object in a set of images. Empirical studies validate the effectiveness of the proposed DDT method. On benchmark image co-localization datasets, DDT consistently outperforms existing state-of-the-art methods by a large margin. Moreover, DDT also demonstrates good generalization ability for unseen categories and robustness for dealing with noisy data.Comment: Accepted by IJCAI 201

A coordination polymer of CdII with benzene-1,3-dicarboxyl­ate and 1,4-bis­[1-(2-pyridylmeth­yl)benzimidazol-2-yl]butane

The title CdII coordination polymer, catena-poly[[{1,4-bis­[1-(2-pyridylmeth­yl)benzimidazol-2-yl]butane}cadmium(II)]-μ-benzene-1,3-dicarboxyl­ato], [Cd(C8H4O4)(C30H28N6)]n, was obtained by reaction of CdCO3, benzene-1,3-dicarboxylic acid (H2btc) and 1,4-bis­[1-(2-pyridylmeth­yl)benzimidazol-2-yl]butane (L). The CdII cation is six-coordinated by an N2O4-donor set. L acts as a bidentate ligand and btc anions link CdII centers into a chain propagating parallel to [010]