A ring R is uniquely (nil) clean in case for any $a in R$ there exists a uniquely idempotent $ein R$ such that $a-e$ is invertible (nilpotent). Let $C =(A V W B)$ be the Morita Context ring. We determine conditions under which the rings $A,B$ are uniquely (nil) clean. Moreover we show that the center of a uniquely (nil) clean ring is uniquely (nil) clean.

Graph matching is an important problem in machine learning and pattern recognition. Herein, we present theoretical and practical results on the consistency of graph matching for estimating a latent alignment function between the vertex sets of two graphs, as well as subsequent algorithmic implications when the latent alignment is partially observed. In the correlated Erdős-Rényi graph setting, ...

Anti-Kekulé problem is a concept of chemical graph theory precluding the Kekulé structure of molecules. Matching preclusion and conditional matching preclusion were proposed as measures of robustness in the event of edge failure in interconnection networks. It is known that matching preclusion problem on bipartite graphs is NP-complete. In this paper, we mainly prove that anti-Kekulé problem on...

We consider three restrictions on Boolean circuits: bijectivity, consistency and mul-tilinearity. Our main result is that Boolean circuits require exponential size to compute the bipartite perfect matching function when restricted to be (i) bijective or (ii) consistent and multilinear. As a consequence of the lower bound on bijec-tive circuits, we prove an exponential size lower bound for monot...

For geostationary meteorological satellite (GSMS) remote sensing image registration, high computational cost and matching error are the two main challenging problems. To address these issues, this paper proposes a novel algorithm named slope-restricted multi-scale feature matching. In multi-scale feature matching, images are subsampled to different scales. From a small scale to a large scale, t...