Word Activation Forces Map Word Networks

Words associate with each other in a manner of intricate clusters^1-3^. Yet the brain capably encodes the complex relations into workable networks^4-7^ such that the onset of a word in the brain automatically and selectively activates its associates, facilitating language understanding and generation^8-10^. One believes that the activation strength from one word to another forges and accounts for the latent structures of the word networks. This implies that mapping the word networks from brains to computers^11,12^, which is necessary for various purposes^1,2,13-15^, may be achieved through modeling the activation strengths. However, although a lot of investigations on word activation effects have been carried out^8-10,16-20^, modeling the activation strengths remains open. Consequently, huge labor is required to do the mappings^11,12^. Here we show that our found word activation forces, statistically defined by a formula in the same form of the universal gravitation, capture essential information on the word networks, leading to a superior approach to the mappings. The approach compatibly encodes syntactical and semantic information into sparse coding directed networks, comprehensively highlights the features of individual words. We find that based on the directed networks, sensible word clusters and hierarchies can be efficiently discovered. Our striking results strongly suggest that the word activation forces might reveal the encoding of word networks in the brain

Semidefinite relaxations for semi-infinite polynomial programming

This paper studies how to solve semi-infinite polynomial programming (SIPP) problems by semidefinite relaxation method. We first introduce two SDP relaxation methods for solving polynomial optimization problems with finitely many constraints. Then we propose an exchange algorithm with SDP relaxations to solve SIPP problems with compact index set. At last, we extend the proposed method to SIPP problems with noncompact index set via homogenization. Numerical results show that the algorithm is efficient in practice.Comment: 23 pages, 4 figure

Traveling Wave Solutions of a Reaction-Diffusion Equation with State-Dependent Delay

This paper is concerned with the traveling wave solutions of a reaction-diffusion equation with state-dependent delay. When the birth function is monotone, the existence and nonexistence of monotone traveling wave solutions are established. When the birth function is not monotone, the minimal wave speed of nontrivial traveling wave solutions is obtained. The results are proved by the construction of upper and lower solutions and application of the fixed point theorem

A construction of pooling designs with surprisingly high degree of error correction

It is well-known that many famous pooling designs are constructed from mathematical structures by the "containment matrix" method. In this paper, we propose another method and obtain a family of pooling designs with surprisingly high degree of error correction based on a finite set. Given the numbers of items and pools, the error-tolerant property of our designs is much better than that of Macula's designs when the size of the set is large enough