Applications of degree estimate for subalgebras

Let $K$ be a field of positive characteristic and $K$ be the free algebra of rank two over $K$. Based on the degree estimate done by Y.-C. Li and J.-T. Yu, we extend the results of S.J. Gong and J.T. Yu's results: (1) An element $p(x,y)\in K$ is a test element if and only if $p(x,y)$ does not belong to any proper retract of $K$; (2) Every endomorphism preserving the automorphic orbit of a nonconstant element of $K$ is an automorphism; (3) If there exists some injective endomorphism $\phi$ of $K$ such that $\phi(p(x,y))=x$ where $p(x,y)\in K$, then $p(x,y)$ is a coordinate. And we reprove that all the automorphisms of $K$ are tame. Moreover, we also give counterexamples for two conjectures established by Leonid Makar-Limanov, V. Drensky and J.-T. Yu in the positive characteristic case.Comment: 12 page

Gait recognition under carrying condition : a static dynamic fusion method

When an individual carries an object, such as a briefcase, conventional gait recognition algorithms based on average silhouette/Gait Energy Image (GEI) do not always perform well as the object carried may have the potential of being mistakenly regarded as a part of the human body. To solve such a problem, in this paper, instead of directly applying GEI to represent the gait information, we propose a novel dynamic feature template for classification. Based on this extracted dynamic information and some static feature templates (i.e., head part and trunk part), we cast gait recognition on the large USF (University of South Florida) database by adopting a static/dynamic fusion strategy. For the experiments involving carrying condition covariate, significant improvements are achieved when compared with other classic algorithms

Measurable Concurrence of Mixed States

We show that bipartite concurrence for rank-2 mixed states of qubits is written by an observable which can be exactly and directly measurable in experiment by local projective measurements, provided that four copies of the composite quantum system are available. In addition, for a tripartite quantum pure state of qubits, the 3-tangle is also shown to be measurable only by projective measurements on the reduced density matrices of a pair of qubits conditioned on four copies of the state.Comment: 3 page