Tetra-n-butyl­ammonium tricyanido[N-(2-pyridyl­carbon­yl)pyridine-2-carbox­imidato]ferrate(III) dihydrate

In the title compound, (C16H36N)[Fe(C12H8N3O2)(CN)3]·2H2O, the tetra-n-butyl­ammonium ion has a tetra­hedral configuration around the N atom, while the FeIII atom of the tricyanido[N-(2-pyridyl­carbon­yl)pyridine-2-carboximidato]iron(III) anion adopts a distorted octa­hedral geometry. O—H⋯O and O—H⋯N hydrogen bonds link the components in the crystal structure

Evolving Network With Different Edges

We proposed an evolving network model constituted by the same nodes but different edges. The competition between nodes and different links were introduced. Scale free properties have been found in this model by continuum theory. Different network topologies can be generated by some tunable parameters. Simulation results consolidate the prediction.Comment: 14 pages, 9 figures, some contents revised, fluctuation of x degree adde

The First Zagreb Index, Vertex-Connectivity, Minimum Degree And Independent Number in Graphs

Let G be a simple, undirected and connected graph. Defined by M1(G) and RMTI(G) the first Zagreb index and the reciprocal Schultz molecular topological index of G, respectively. In this paper, we determined the graphs with maximal M1 among all graphs having prescribed vertex-connectivity and minimum degree, vertex-connectivity and bipartition, vertex-connectivity and vertex-independent number, respectively. As applications, all maximal elements with respect to RMTI are also determined among the above mentioned graph families, respectively

Scaling the living space: Zipf’s law for traditional courtyard houses in South China

In the traditional feudalistic society of China, there is a characteristic residential pattern of several core families with common ancestors living together in one house, as far as possible. Hence, the habitation of large families and their social dynamic always have a complex function and hierarchical structure. In this article, we consider a courtyard in South China as an example to enable a discussion of the mathematical relationship among the five basic functional spaces in it. Based on Zipf’s law, we find that the distribution of the five types of spaces, from large to small, can be described by the Pareto distribution with a shape parameter close to −1. Moreover, the Zipf parameters of different houses in the same area conform to the double Pareto distribution. This suggests that the size and shape of a residence also follows well-defined scaling laws. Additionally, it indicates that houses, at least traditional Chinese houses, have strong self-organization and self-similarity. It also shows that the power law of the Pareto distribution is applicable not only to the macro scale of the city but also the micro scale of housing

Length is a Curse and a Blessing for Document-level Semantics

In recent years, contrastive learning (CL) has been extensively utilized to recover sentence and document-level encoding capability from pre-trained language models. In this work, we question the length generalizability of CL-based models, i.e., their vulnerability towards length-induced semantic shift. We verify not only that length vulnerability is a significant yet overlooked research gap, but we can devise unsupervised CL methods solely depending on the semantic signal provided by document length. We first derive the theoretical foundations underlying length attacks, showing that elongating a document would intensify the high intra-document similarity that is already brought by CL. Moreover, we found that isotropy promised by CL is highly dependent on the length range of text exposed in training. Inspired by these findings, we introduce a simple yet universal document representation learning framework, LA(SER)$^{3}$: length-agnostic self-reference for semantically robust sentence representation learning, achieving state-of-the-art unsupervised performance on the standard information retrieval benchmark.Comment: Accepted at EMNLP 2023. Our code is publicly available at https://github.com/gowitheflow-1998/LA-SER-cube