Tur\'an's problem and Ramsey numbers for trees

Let $T_n^1=(V,E_1)$ and $T_n^2=(V,E_2)$ be the trees on $n$ vertices with $V=\{v_0,v_1,\ldots,v_{n-1}\}$, $E_1=\{v_0v_1,\ldots,v_0v_{n-3},v_{n-4}v_{n-2},v_{n-3}v_{n-1}\}$, and $E_2=\{v_0v_1,\ldots,$ $v_0v_{n-3},v_{n-3}v_{n-2}, v_{n-3}v_{n-1}\}$. In this paper, for $p\ge n\ge 5$ we obtain explicit formulas for \ex(p;T_n^1) and \ex(p;T_n^2), where \ex(p;L) denotes the maximal number of edges in a graph of order $p$ not containing $L$ as a subgraph. Let r(G\sb 1, G\sb 2) be the Ramsey number of the two graphs $G_1$ and $G_2$. In this paper we also obtain some explicit formulas for $r(T_m,T_n^i)$, where $i\in\{1,2\}$ and $T_m$ is a tree on $m$ vertices with $\Delta(T_m)\le m-3$.Comment: 21 page

The coexistence of p-wave spin triplet superconductivity and itinerant ferromagnetism

A model for coexistence of p-wave spin-triplet superconductivity (SC) and itinerant ferromagnetism (FM) is presented. The Hamiltonian can be diagonalized by using the so(5) algebraic coherent state. We obtain the coupling equations of the magnetic exchange energy and superconducting gaps through the double-time Green function. It is found that the ferromagnetisation gives rise to the phase transitions of p-wave superconducting states or superfluid of $^{3}He$.Comment: 9 pages, no figure

A Comparative Study of Refusal Speech Acts in Chinese and American English

Refusals are frequently performed in our daily lives, and the speech act of refusals is one significant research topic in Pragmatics. Based on the speech act theory of Austin (1962) and Searle (1969), with the theoretical frame of the politeness theory put forward by Brown and Levinson, This paper presents a comparative study of speech acts of refusal in Chinese and American English (AE). The results show that refusals vary in directness with situations and cultures, just like other speech acts, yet there are some similarities between Chinese and AE. On the one hand, both languages employ the three directness types, namely the direct refusal speech act, ability of negation and indirect refusal speech act, and prefer indirect refusals. The situational variability of directness in both languages follows a similar trend. On the other hand, Americans are more direct than Chinese and Chinese sincere refusals are considered as face-threatening acts, which call for politeness strategies to minimize the negative effects on the addressee(s). Furthermore, Chinese shows the lower degree of situational variation in the use of the three directness types. From all these evidence, we maintain that the cross-linguistic differences are due to basic differences in cultural values, i.e., Americans value individualism and equality, while Chinese value collectivism and social hierarchy. Key words: Refusal Speech Act, Chinese-American, Comparison, Cultural Values Résumé: Dans la vie quotidienne, il nous arrive souvent de refuser les autres. Les actes de discours de refus est aussi une problématique importante dans les recherches de la pragmatique. Selon la théorie des actes de discours d’Austin et de Searle ainsi que le principe de politesse de Brown et de Levinson, l’article présent exécute une étude comparative des actes de discours de refus des Chinois et des Américains. Il existe des points communs entre eux, par exemple, les mêmes caractéristiques des actes de refus : l’utilisation des trois ordres directs dans les actes de discours, à savoir, actes de discours de refus direct, capacité de refus et actes de disours de refus indirect ; la préférence pour les actes de refus indirect ; la tendance d’aliénation semblable du contexte. Mais il se trouve aussi des différences sous l’influence de la culture. Les Américains sont plus directs que les Chinois dans les actes de refus. Les Chinois s’efforcent de miniment l’impact négatif des actes de refus sur l’interlocuteur en utilisant des stratégies de politess, parce que, d’après eux, le refus direct blessent la face de l’autre partie. D’ailleurs, le niveau d’aliénation du contexte du chinois est inférieur à celui de l’anglais américain. Ces écarts sont dûs aux différentes conceptions de la valeur culturelle des deux pays, les Américains préconisent la personnalité et l’égalité alors que les Chinois insistent sur la collectivité et la hiérarchie sociale. Mots-Clés: actes de discours de refus, Chine et Etats-Unis, comparaison, conception de la valeu

A Structural Representation Learning for Multi-relational Networks

Most of the existing multi-relational network embedding methods, e.g., TransE, are formulated to preserve pair-wise connectivity structures in the networks. With the observations that significant triangular connectivity structures and parallelogram connectivity structures found in many real multi-relational networks are often ignored and that a hard-constraint commonly adopted by most of the network embedding methods is inaccurate by design, we propose a novel representation learning model for multi-relational networks which can alleviate both fundamental limitations. Scalable learning algorithms are derived using the stochastic gradient descent algorithm and negative sampling. Extensive experiments on real multi-relational network datasets of WordNet and Freebase demonstrate the efficacy of the proposed model when compared with the state-of-the-art embedding methods

Opinion Dynamic with agents immigration

We propose a strategy for achieving maximum cooperation in evolutionary games on complex networks. Each individual is assigned a weight that is proportional to the power of its degree, where the exponent alpha is an adjustable parameter that controls the level of diversity among individuals in the network. During the evolution, every individual chooses one of its neighbors as a reference with a probability proportional to the weight of the neighbor, and updates its strategy depending on their payoff difference. It is found that there exists an optimal value of alpha, for which the level of cooperation reaches maximum. This phenomenon indicates that, although high-degree individuals play a prominent role in maintaining the cooperation, too strong influences from the hubs may counterintuitively inhibit the diffusion of cooperation. We provide a physical theory, aided by numerical computations, to explain the emergence of the optimal cooperation. Other pertinent quantities such as the payoff, the cooperator density as a function of the degree, and the payoff distribution, are also investigated. Our results suggest that, in order to achieve strong cooperation on a complex network, individuals should learn more frequently from neighbors with higher degrees, but only to certain extent.Comment: this work was finished in (Dated: April 22, 2011

New algorithm to study the pseudo-Wigner solution of the quark gap equation in the framework of the (2+1)-flavor NJL model

In this paper, we study the pseudo-Wigner solution of the quark gap equation with a recently proposed algorithm in the framework of the (2+1)-flavor Nambu-Jona-Lasinio (NJL) model. We find that for the current quark mass $m_{\rm u,d}=5.5$ MeV and chemical potential $\mu<\mu_{\rm TCP}=272.5$ MeV, the Nambu solution and the positive pseudo-Wigner solution obtained via this algorithm is consistent with the physical solution obtained with the iterative method. Furthermore, the algorithm we used can help to illustrate the evolution of the solutions of the gap equation from the chiral limit to non-chiral limit and gives a prediction where the crossover line is located in the phase diagram for $\mu<272.5$ MeV. In addition, we also study the chiral susceptibilities as well as the loss of solutions for different chemical potentials.Comment: 9 pages, 12 figure

Time-domain global similarity method for automatic data cleaning for multi-channel measurement systems in magnetic confinement fusion devices

To guarantee the availability and reliability of data source in Magnetic Confinement Fusion (MCF) devices, incorrect diagnostic data, which cannot reflect real physical properties of measured objects, should be sorted out before further analysis and study. Traditional data sorting cannot meet the growing demand of MCF research because of the low-efficiency, time-delay, and lack of objective criteria. In this paper, a Time-Domain Global Similarity (TDGS) method based on machine learning technologies is proposed for the automatic data cleaning of MCF devices. Traditional data sorting aims to the classification of original diagnostic data sequences, which are different in both length and evolution properties under various discharge parameters. Hence the classification criteria are affected by many discharge parameters and vary shot by shot. The focus of TDGS method is turned to the physical similarity between data sequences from different channels, which are more essential and independent of discharge parameters. The complexity arisen from real discharge parameters during data cleaning is avoided in the TDGS method by transforming the general data sorting problem into a binary classification problem about the physical similarity between data sequences. As a demonstration of its application to multi-channel measurement systems, the TDGS method is applied to the EAST POlarimeter-INterferomeTer (POINT) system. The optimized performance of the method has reached 0.9871

A Model for the Coexistence of p-wave Superconductivity and Ferroelectricity

A model for the coexistence of p-wave superconductivity (SC) and ferroelectricity (FE) is presented. The Hamiltonian of SC sector and FE sector can be diagonalized by using the $so(5)$ and $h(4)$ algebraic coherent states respectively. We assume a minimal symmetry-allow coupling and simplify the total Hamiltonian through a double mean-field approximation (DMFA). A variational coherent-state (VCS) trial wave-function is applied for the ground state. It is found that the ferroelectricity gives rise to the magnetic field effect of p-wave superconductivity.Comment: 11pages,no figur

Recurrent Squeeze-and-Excitation Context Aggregation Net for Single Image Deraining

Rain streaks can severely degrade the visibility, which causes many current computer vision algorithms fail to work. So it is necessary to remove the rain from images. We propose a novel deep network architecture based on deep convolutional and recurrent neural networks for single image deraining. As contextual information is very important for rain removal, we first adopt the dilated convolutional neural network to acquire large receptive field. To better fit the rain removal task, we also modify the network. In heavy rain, rain streaks have various directions and shapes, which can be regarded as the accumulation of multiple rain streak layers. We assign different alpha-values to various rain streak layers according to the intensity and transparency by incorporating the squeeze-and-excitation block. Since rain streak layers overlap with each other, it is not easy to remove the rain in one stage. So we further decompose the rain removal into multiple stages. Recurrent neural network is incorporated to preserve the useful information in previous stages and benefit the rain removal in later stages. We conduct extensive experiments on both synthetic and real-world datasets. Our proposed method outperforms the state-of-the-art approaches under all evaluation metrics. Codes and supplementary material are available at our project webpage: https://xialipku.github.io/RESCAN .Comment: Accepted by ECC

Thermoelectric-induced unitary Cooper pair splitting efficiency

Thermoelectric effect is exploited to optimize the Cooper pair splitting efficiency in a Y-shaped junction, which consists of two normal leads coupled to an $s$-wave superconductor via double noninteracting quantum dots. Here, utilizing temperature difference rather than bias voltage between the two normal leads, and tuning the two dot levels such that the transmittance of elastic cotunneling process is particle-hole symmetric, we find currents flowing through the normal leads are totally contributed from the splitting of Cooper pairs emitted from the superconductor. Such a unitary splitting efficiency is significantly better than the efficiencies obtained in experiments so far.Comment: 5 pages, 4 figures, accepted by AP