Yang-Mills condensate dark energy coupled with matter and radiation

The coincidence problem is studied for the dark energy model of effective Yang-Mills condensate in a flat expanding universe during the matter-dominated stage. The YMC energy $\rho_y(t)$ is taken to represent the dark energy, which is coupled either with the matter, or with both the matter and the radiation components. The effective YM Lagrangian is completely determined by quantum field theory up to 1-loop order. It is found that under very generic initial conditions and for a variety of forms of coupling, the existence of the scaling solution during the early stages and the subsequent exit from the scaling regime are inevitable. The transition to the accelerating stage always occurs around a redshift $z\simeq (0.3\sim 0.5)$. Moreover, when the Yang-Mills condensate transfers energy into matter or into both matter and radiation, the equation of state $w_y$ of the Yang-Mills condensate can cross over -1 around $z\sim 2$, and takes on a current value $\simeq -1.1$. This is consistent with the recent preliminary observations on supernovae Ia. Therefore, the coincidence problem can be naturally solved in the effective YMC dark energy models.Comment: 24 pages, 18 figure

Structure propagation for zero-shot learning

The key of zero-shot learning (ZSL) is how to find the information transfer model for bridging the gap between images and semantic information (texts or attributes). Existing ZSL methods usually construct the compatibility function between images and class labels with the consideration of the relevance on the semantic classes (the manifold structure of semantic classes). However, the relationship of image classes (the manifold structure of image classes) is also very important for the compatibility model construction. It is difficult to capture the relationship among image classes due to unseen classes, so that the manifold structure of image classes often is ignored in ZSL. To complement each other between the manifold structure of image classes and that of semantic classes information, we propose structure propagation (SP) for improving the performance of ZSL for classification. SP can jointly consider the manifold structure of image classes and that of semantic classes for approximating to the intrinsic structure of object classes. Moreover, the SP can describe the constrain condition between the compatibility function and these manifold structures for balancing the influence of the structure propagation iteration. The SP solution provides not only unseen class labels but also the relationship of two manifold structures that encode the positive transfer in structure propagation. Experimental results demonstrate that SP can attain the promising results on the AwA, CUB, Dogs and SUN databases

A derivative formula for the free energy function

We consider bond percolation on the ${\bf Z}^d$ lattice. Let $M_n$ be the number of open clusters in $B(n)=[-n, n]^d$. It is well known that $E_pM_n / (2n+1)^d$ converges to the free energy function $\kappa(p)$ at the zero field. In this paper, we show that $\sigma^2_p(M_n)/(2n+1)^d$ converges to $-(p^2(1-p)+p(1-p)^2)\kappa'(p)$.Comment: 8 pages 1 figur

Interacting Individuals Leading to Zipf's Law

We present a general approach to explain the Zipf's law of city distribution. If the simplest interaction (pairwise) is assumed, individuals tend to form cities in agreement with the well-known statisticsComment: 4 pages 2 figure