Poset-free Families and Lubell-boundedness

Given a finite poset $P$, we consider the largest size \lanp of a family \F of subsets of $[n]:=\{1,...,n\}$ that contains no subposet $P$. This continues the study of the asymptotic growth of \lanp; it has been conjectured that for all $P$, \pi(P):= \lim_{n\rightarrow\infty} \lanp/\nchn exists and equals a certain integer, $e(P)$. While this is known to be true for paths, and several more general families of posets, for the simple diamond poset \D_2, the existence of $\pi$ frustratingly remains open. Here we develop theory to show that $\pi(P)$ exists and equals the conjectured value $e(P)$ for many new posets $P$. We introduce a hierarchy of properties for posets, each of which implies $\pi=e$, and some implying more precise information about \lanp. The properties relate to the Lubell function of a family \F of subsets, which is the average number of times a random full chain meets \F. We present an array of examples and constructions that possess the properties

First-principles calculations of phase transition, elasticity, and thermodynamic properties for TiZr alloy

tructural transformation, pressure dependent elasticity behaviors, phonon, and thermodynamic properties of the equiatomic TiZr alloy are investigated by using first-principles density-functional theory. Our calculated lattice parameters and equation of state for $\alpha$ and $\omega$ phases as well as the phase transition sequence of $\alpha$$\mathtt{\rightarrow}$$\omega$$\mathtt{\rightarrow}$$\beta$ are consistent well with experiments. Elastic constants of $\alpha$ and $\omega$ phases indicate that they are mechanically stable. For cubic $\beta$ phase, however, it is mechanically unstable at zero pressure and the critical pressure for its mechanical stability is predicted to equal to 2.19 GPa. We find that the moduli, elastic sound velocities, and Debye temperature all increase with pressure for three phases of TiZr alloy. The relatively large $B/G$ values illustrate that the TiZr alloy is rather ductile and its ductility is more predominant than that of element Zr, especially in $\beta$ phase. Elastic wave velocities and Debye temperature have abrupt increase behaviors upon the $\alpha$$\mathtt{\rightarrow}$$\omega$ transition at around 10 GPa and exhibit abrupt decrease feature upon the $\omega$$\mathtt{\rightarrow}$$\beta$ transition at higher pressure. Through Mulliken population analysis, we illustrate that the increase of the \emph{d}-band occupancy will stabilize the cubic $\beta$ phase. Phonon dispersions for three phases of TiZr alloy are firstly presented and the $\beta$ phase phonons clearly indicate its dynamically unstable nature under ambient condition. Thermodynamics of Gibbs free energy, entropy, and heat capacity are obtained by quasiharmonic approximation and Debye model.Comment: 9 pages, 10 figure

Segmentation of ultrasound images of thyroid nodule for assisting fine needle aspiration cytology

The incidence of thyroid nodule is very high and generally increases with the age. Thyroid nodule may presage the emergence of thyroid cancer. The thyroid nodule can be completely cured if detected early. Fine needle aspiration cytology is a recognized early diagnosis method of thyroid nodule. There are still some limitations in the fine needle aspiration cytology, and the ultrasound diagnosis of thyroid nodule has become the first choice for auxiliary examination of thyroid nodular disease. If we could combine medical imaging technology and fine needle aspiration cytology, the diagnostic rate of thyroid nodule would be improved significantly. The properties of ultrasound will degrade the image quality, which makes it difficult to recognize the edges for physicians. Image segmentation technique based on graph theory has become a research hotspot at present. Normalized cut (Ncut) is a representative one, which is suitable for segmentation of feature parts of medical image. However, how to solve the normalized cut has become a problem, which needs large memory capacity and heavy calculation of weight matrix. It always generates over segmentation or less segmentation which leads to inaccurate in the segmentation. The speckle noise in B ultrasound image of thyroid tumor makes the quality of the image deteriorate. In the light of this characteristic, we combine the anisotropic diffusion model with the normalized cut in this paper. After the enhancement of anisotropic diffusion model, it removes the noise in the B ultrasound image while preserves the important edges and local details. This reduces the amount of computation in constructing the weight matrix of the improved normalized cut and improves the accuracy of the final segmentation results. The feasibility of the method is proved by the experimental results.Comment: 15pages,13figure

Combining Traditional Marketing and Viral Marketing with Amphibious Influence Maximization

In this paper, we propose the amphibious influence maximization (AIM) model that combines traditional marketing via content providers and viral marketing to consumers in social networks in a single framework. In AIM, a set of content providers and consumers form a bipartite network while consumers also form their social network, and influence propagates from the content providers to consumers and among consumers in the social network following the independent cascade model. An advertiser needs to select a subset of seed content providers and a subset of seed consumers, such that the influence from the seed providers passing through the seed consumers could reach a large number of consumers in the social network in expectation. We prove that the AIM problem is NP-hard to approximate to within any constant factor via a reduction from Feige's k-prover proof system for 3-SAT5. We also give evidence that even when the social network graph is trivial (i.e. has no edges), a polynomial time constant factor approximation for AIM is unlikely. However, when we assume that the weighted bi-adjacency matrix that describes the influence of content providers on consumers is of constant rank, a common assumption often used in recommender systems, we provide a polynomial-time algorithm that achieves approximation ratio of $(1-1/e-\epsilon)^3$ for any (polynomially small) $\epsilon > 0$. Our algorithmic results still hold for a more general model where cascades in social network follow a general monotone and submodular function.Comment: An extended abstract appeared in the Proceedings of the 16th ACM Conference on Economics and Computation (EC), 201

3-Chloro-N′-[(2-hy­droxy­naphthalen-1-yl)methyl­idene]benzohydrazide

The title compound, C18H13ClN2O2, was prepared by the reaction of 2-hy­droxy-1-naphthaldehyde with 3-chloro­benzohydrazide in methanol. An intra­molecular O—H⋯N hydrogen bond influences the mol­ecular conformation; the benzene ring and naphthyl ring system form a dihedral angle of 17.1 (3)°. In the crystal, inter­molecular N—H⋯O hydrogen bonds link the mol­ecules into chains propagated in [101]