On the sum of the two largest signless Laplacian eigenvalues

Let $G$ be a simple connected graph and let $S_k(G)$ be the sum of the first $k$ largest signless Laplacian eigenvalues of $G$. It was conjectured by Ashraf, Omidi and Tayfeh-Rezaibe in 2013 that $S_k(G)\leq e(G)+\binom{k+1}{2}$ holds for $1\leq k\leq n-1$. They gave a proof for the conjecture when $k = 2$, but applied an incorrect key lemma. Therefore, the conjecture is still open when $k = 2$. In this paper, we prove that $S_2(G)<e(G)+3$ is true for any graphs which also confirm the conjecture when $k = 2$.Comment: 15 pages, 5 figure

Geography and similarity of regional cuisines in China

Food occupies a central position in every culture and it is therefore of great interest to understand the evolution of food culture. The advent of the World Wide Web and online recipe repositories has begun to provide unprecedented opportunities for data-driven, quantitative study of food culture. Here we harness an online database documenting recipes from various Chinese regional cuisines and investigate the similarity of regional cuisines in terms of geography and climate. We found that the geographical proximity, rather than climate proximity is a crucial factor that determines the similarity of regional cuisines. We develop a model of regional cuisine evolution that provides helpful clues to understand the evolution of cuisines and cultures.Comment: 13 pages, 11 figures and 2 table

Influence of Reciprocal links in Social Networks

In this Letter, we empirically study the influence of reciprocal links, in order to understand its role in affecting the structure and function of directed social networks. Experimental results on two representative datesets, Sina Weibo and Douban, demonstrate that the reciprocal links indeed play a more important role than non-reciprocal ones in both spreading information and maintaining the network robustness. In particular, the information spreading process can be significantly enhanced by considering the reciprocal effect. In addition, reciprocal links are largely responsible for the connectivity and efficiency of directed networks. This work may shed some light on the in-depth understanding and application of the reciprocal effect in directed online social networks

Electromagnetic Scattering Laws in Weyl Systems

Wavelength determines the length scale of the cross section when electromagnetic waves are scattered by an electrically small object. The cross section diverges for resonant scattering, and diminishes for non-resonant scattering, when wavelength approaches infinity. This scattering law explains the color of the sky as well as the strength of a mobile phone signal. We show that such wavelength scaling comes from free space's conical dispersion at zero frequency. Emerging Weyl systems, offering similar dispersion at non-zero frequencies, lead to new laws of electromagnetic scattering that allow cross sections to be decoupled from the wavelength limit. Diverging and diminishing cross sections can be realized at any target wavelength in a Weyl system, providing unprecedented ability to tailor the strength of wave-matter interactions for radio-frequency and optical applications

Improving mobility of silicon metal-oxide-semiconductor devices for quantum dots by high vacuum activation annealing

To improve mobility of fabricated silicon metal-oxide-semiconductor (MOS) quantum devices, forming gas annealing is a common method used to mitigate the effects of disorder at the Si/SiO2 interface. However, the importance of activation annealing is usually ignored. Here, we show that a high vacuum environment for implantation activation is beneficial for improving mobility compared to nitrogen atmosphere. Low-temperature transport measurements of Hall bars show that peak mobility can be improved by a factor of two, reaching 1.5 m^2/(Vs) using high vacuum annealing during implantation activation. Moreover, the charge stability diagram of a single quantum dot is mapped, with no visible disturbance caused by disorder, suggesting possibility of fabricating high-quality quantum dots on commercial wafers. Our results may provide valuable insights into device optimization in silicon-based quantum computing.Comment: 13 pages, 4 figure

Collaborative filtering with diffusion-based similarity on tripartite graphs

Collaborative tags are playing more and more important role for the organization of information systems. In this paper, we study a personalized recommendation model making use of the ternary relations among users, objects and tags. We propose a measure of user similarity based on his preference and tagging information. Two kinds of similarities between users are calculated by using a diffusion-based process, which are then integrated for recommendation. We test the proposed method in a standard collaborative filtering framework with three metrics: ranking score, Recall and Precision, and demonstrate that it performs better than the commonly used cosine similarity.Comment: 8 pages, 4 figures, 1 tabl

Dietary Intake of Fatty Acids, Total Cholesterol, and Stomach Cancer in a Chinese Population.

To investigate the associations between dietary fatty acids and cholesterol consumption and stomach cancer (SC), we analyzed data from a population-based case-control study with a total of 1900 SC cases and 6532 controls. Dietary data and other risk or protective factors were collected by face-to-face interviews in Jiangsu Province, China, from 2003 to 2010. Adjusted odds ratios (ORs) and 95% confidence intervals (CIs) were estimated using multiple unconditional logistic regression models and an energy-adjusted method. The joint associations between dietary factors and known risk factors on SC were examined. We observed positive associations between dietary saturated fatty acids (SFAs), monounsaturated fatty acids (MUFAs), and total cholesterol and the development of SC, comparing the highest versus lowest quarters. Increased intakes of dietary SFAs (p-trend = 0.005; aOR, 1.11; 95% CI, 1.01-1.22 with a 7 g/day increase as a continuous variable) and total cholesterol (p-trend &lt; 0.001; aOR, 1.13; 95% CI, 1.06-1.22 with a 250 mg/day increase as a continuous variable) were monotonically associated with elevated odds of developing SC. Our results indicate that dietary SFAs, MUFAs, and total cholesterol are associated with stomach cancer, which might provide a potential dietary intervention for stomach cancer prevention