The brain must coordinate with redundant bodies to perform motion tasks. The aim of the present study is to propose a novel control model that predicts the characteristics of human joint coordination at a behavioral level. To evaluate the joint coordination, an uncontrolled manifold (UCM) analysis that focuses on the trial-to-trial variance of joints has been proposed. The UCM is a nonlinear ma...

Data sets containing multi-manifold structures are ubiquitous in real-world tasks, and effective grouping of such data is an important yet challenging problem. Though there were many studies on this problem, it is not clear on how to design principled methods for the grouping of multiple hybrid manifolds. In this paper, we show that spectral methods are potentially helpful for hybridmanifold cl...

One of the basic problems of Riemannian geometry is the classification of manifolds of positive sectional curvature. The known examples include the spherical space forms which carry constant curvature metrics and the rank 1 symmetric spaces whose canonical metrics have sectional curvatures at each point varying between 1 and 4. In 1951 H.E. Rauch [18] introduced the notion of curvature pinching...

We show that there exist no proper warped product semi-invariant submanifolds in almost paracontact Riemannian manifolds such that totally geodesic submanifold and totally umbilical submanifold of the warped product are invariant and anti-invariant, respectively. Therefore, we consider warped product semi-invariant submanifolds in the form N N⊥×fNT by reversing two factor manifolds NT and N⊥. W...

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

This paper presents a new unified subdivision scheme that is defined over a k-simplicial complex in n-D space with k ≤ 3. We first present a series of definitions to facilitate topological inquiries during the subdivision process. The scheme is derived from the double (k + 1)-directional box splines over k-simplicial domains. Thus, it guarantees a certain level of smoothness in the limit on a r...

While many dimensionality reduction algorithms have been proposed in recent years, most of them are designed for single view data and cannot cope with multi-view data directly. Dimensionality reduction algorithms in recent ten years, both in theory and application have great breakthrough. In the face of dozens, hundreds or even thousands of dimension by dimension reduction to the data from high...

Multi-modality manifold-ranking is recently used successfully in topic-focused multi-document summarization. This approach is based on Bag-Of-Words (BOW) assumption where the pair-wise similarity values between sentences are computed using the standard cosine similarity measure (TF*IDF). However, the major limitation of the TF*IDF approach is that it only retains the frequency of the words and ...

Images are usually associated with multiple labels and comprised of multiple views, due to each image containing several objects (e.g. a pedestrian, bicycle and tree) and multiple visual features (e.g. color, texture and shape). Currently available tools tend to use either labels or features for classification, but both are necessary to describe the image properly. There have been recent succes...

We describe a novel method for real-time, simultaneous multi-view face detection and facial pose estimation. The method employs a convolutional network to map face images to points on a manifold, parametrized by pose, and non-face images to points far from that manifold. This network is trained by optimizing a loss function of three variables: image, pose, and face/non-face label. We test the r...