COMPOSITION AND COINCIDENCE

Unsupervised Structure Learning: Hierarchical Recursive Composition, Suspicious Coincidence and Competitive Exclusion

We describe a new method for unsupervised structure learning of a hierarchical compositional model (HCM) for deformable objects. The learning is unsupervised in the sense that we are given a training dataset of images containing the object in cluttered backgrounds but we do not know the position or boundary of the object. The structure learning is performed by a bottom-up and top-down process. ...

Coincidence of Material and Mental Elements: Nature and Approache

According to accepted principles of criminal law, whether in written Civil Law system or common law System, the mere existence of material and mental elements of a crime is not suffice, but their coincidence is also required. Only when they coincide in time, it may be said that the crime has occurred and criminal responsibility is completed. Many discussions have been put-forward in legal writi...

Linking and Coincidence Invariants

Given a link map f into a manifold of the form Q = N ×R, when can it be deformed to an “unlinked” position (in some sense, e.g. where its components map to disjoint R-levels)? Using the language of normal bordism theory as well as the path space approach of Hatcher and Quinn we define obstructions ω̃ε(f), ε = + or ε = −, which often answer this question completely and which, in addition, turn ou...

Comorbidity and Coincidence

Coincidence point and common fixed point results via scalarization function

The main purpose of this paper is to obtain sufficient conditions for existence of points of coincidence and common fixed points for three self mappings in $b$-metric spaces. Next, we obtain cone $b$-metric version of these results by using a scalarization function. Our results extend and generalize several well known comparable results in the existing literature.