Recently modern non-Euclidean structure and motion estimation methods have been incorporated into augmented reality scene tracking and virtual object registration. We present a study of how the choice of projective, affine or Euclidean scene viewing geometry and similarity, affine or homography based object registration affects how accurately a virtual object can be overlaid in scene video from...

Too little mathematics has been written in prose. Thus we prove here, via a fantasy novellette, that locally L-bilipschitz mapping f : X → Y between uniformly Ahlfors q-regular, complete and compact path-metric spaces is an map when simply connected. The motivation for such result arises from studying the asymptotic values of BLD-mappings with empty branch set.

Many real-world networks can be modeled as attributed networks, where nodes are affiliated with attributes. When we implement network embedding, need to face two types of heterogeneous information, namely, structural information and attribute information. The undirected is usually expressed a symmetric adjacency matrix. Network embedding learning utilize the above learn vector representations i...

In the primary visual cortex, the processing of information uses the distribution of orientations in the visual input: neurons react to some orientations in the stimulus more than to others. In many species, orientation preference is mapped in a remarkable way on the cortical surface, and this organization of the neural population seems to be important for visual processing. Now, existing model...

Densely packed and twisted assemblies of filaments are crucial structural motifs in macroscopic materials (cables, ropes, and textiles) as well as synthetic and biological nanomaterials (fibrous proteins). We study the unique and nontrivial packing geometry of this universal material design from two perspectives. First, we show that the problem of twisted bundle packing can be mapped exactly on...

Symmetric positive definite (spd) matrices pervade numerous scientific disciplines, including machine learning and optimization. We consider the key task of measuring distances between two spd matrices; a task that is often nontrivial whenever the distance function must respect the non-Euclidean geometry of spd matrices. Typical non-Euclidean distance measures such as the Riemannian metric δR(X...

Symmetric positive definite (spd) matrices pervade numerous scientific disciplines, including machine learning and optimization. We consider the key task of measuring distances between two spd matrices; a task that is often nontrivial whenever the distance function must respect the non-Euclidean geometry of spd matrices. Typical non-Euclidean distance measures such as the Riemannian metric δR(X...

Of the branches of mathematics, geometry has, from the earliest Hellenic period, been given a curiOZlS position that straddles empirical and exact scien;e. Its standing Os an empirical and approximate science stems from the practical ]1U1'SJlits of artistic drafting. land surveying and measuring in general. From the prominence of vi.sua/ applicatiom, such as figures and constructions in the twe...