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Modeling and analyzing the dynamic shape of human motion is a challenging task owing to temporal variations in the shape and multiple sources of observed shape variations such as viewpoint, motion speed, clothing, etc. We present a new framework for dynamic shape analysis based on temporal normalization and factorized shape style analysis. Using a nonlinear generative model with motion manifold embedding in a low-dimensional space, we detect cycles of periodic motion like gait in different views and synthesize temporally-aligned shape sequences from the same type of motion at different speeds. The bilinear analysis of temporally-aligned shape sequences decomposes dynamic motion into time-invariant shape style factors and time-dependent motion factors. We extend the bilinear model into a tensor shape model, a multilinear decomposition of dynamic shape sequences for view-invariant shape style representations. The shape style is a view-invariant, time-invariant, and speed-invariant shape signature and is used as a feature vector for human identification. The shape style can be adapted to new environmental conditions by iterative estimation of style and content factors to reflect new observation conditions. We present the experimental results of gait recognition using the CMU Mobo gait database and the USF gait challenging database.

This paper is concerned with the notion of covariation for Banach space-valued processes. In particular, we introduce a notion of quadratic variation, which is a generalization of the classical restrictive formulation of Métivier and Pellaumail. Our approach is based on the notion of χ-covariation for processes with values in two Banach spaces B₁ and B₂, where χ is a suitable subspace of the dual of the projective tensor product of B₁ and B₂. We investigate some C¹ type transformations for various classes of stochastic processes admitting a χ-quadratic variation and related properties. If 𝕏¹ and 𝕏² admit a χ-covariation, Fⁱ : B_i → ℝ, i = 1, 2 are of class C¹ with some supplementary assumptions, then the covariation of the real processes F¹(𝕏¹) and F²(𝕏²) exist.

A detailed analysis is provided on the so-called window processes. Let X be a real continuous process; the C([-τ, 0])-valued process X(⋅) defined by X_t(y) = X_t+y, where y ∈ [-τ, 0], is called window process. Special attention is given to transformations of window processes associated with Dirichlet and weak Dirichlet processes. Those will constitute a significant Fukushima decomposition for functionals of windows of (weak) Dirichlet processes. As application, we provide a new technique for representing a path-dependent random variable as its expectation plus a stochastic integral with respect to the underlying process.

This paper proposes a novel method for classification using rank-1 tensor projection via regularized regression to directly map tensor example to its corresponding label, which is different from the general procedure of classification on the compact representation of the original data. Action can be naturally considered as a third-order tensor, where the first two dimensions represent the space and the third one is temporal. By applying this method to multi-label action classification based on problem transformation and subset embedding technique, we obtain the comparable results to the state-of-the-art approaches on the popular action datasets Weizmann and KTH. Our experimental results are also considerably robust to the viewpoint changes, the partial occlusion and the irregularities in the motion styles.

Based on tensor analysis and Bell basis measurement, we propose a general method to find proper channel for successful teleportation of an unknown three-qubit state. Instead of starting from "the proper channel" as that of the previous work, we begin from the successful teleportation then trace back to find which channel is proper and why it is proper for successful teleportation. At last, we give the necessary and sufficient condition for three-qubit perfect teleportation. This condition can guide us to design the corresponding channel for realizing the teleportation. Furthermore, the description of teleporting process with the help of tensor analysis is more compact and clear. Our method can also be generalized to find the channel for N-qubit successful teleportation.

The participant attack is the most serious threat for quantum secret-sharing protocols. However, it is only during the transmission of quantum information carriers that attention is paid to this kind of attack in the existing quantum secret-sharing protocols. The security considerations of the secret reconstruction phase of quantum secret-sharing protocols against this kind of attack are neglected. We demonstrate our viewpoint by taking the scheme of Hillery, Buzěk, and Berthiaume (HBB) [Phys. Rev. A59 (1999) 18–29] as an example. By telling a lie in the reconstruction phase, a dishonest participant can easily attain the entire secret key instead of eavesdropping during the transmission awkwardly, whereas the honest one cannot judge whether the dishonest one tells the truth and the obtained secret random key is identical to what the secret distributor owns because of lack of verification mechanism in the HBB protocol. It is not difficult to find that almost all the quantum secret-sharing protocols have such disadvantages. Our viewpoint presented may be useful for the design of other similar protocols.