On the Unit Graph of a Noncommutative Ring

Let $R$ be a ring (not necessary commutative) with non-zero identity. The unit graph of $R$, denoted by $G(R)$, is a graph with elements of $R$ as its vertices and two distinct vertices $a$ and $b$ are adjacent if and only if $a+b$ is a unit element of $R$. It was proved that if $R$ is a commutative ring and \fm is a maximal ideal of $R$ such that |R/\fm|=2, then $G(R)$ is a complete bipartite graph if and only if (R, \fm) is a local ring. In this paper we generalize this result by showing that if $R$ is a ring (not necessary commutative), then $G(R)$ is a complete $r$-partite graph if and only if (R, \fm) is a local ring and $r=|R/m|=2^n$, for some $n \in \N$ or $R$ is a finite field. Among other results we show that if $R$ is a left Artinian ring, $2 \in U(R)$ and the clique number of $G(R)$ is finite, then $R$ is a finite ring.Comment: 6 pages. To appear in Algebra Colloquiu

Drug ranking using machine learning systematically predicts the efficacy of anti-cancer drugs

Artificial intelligence and machine learning (ML) promise to transform cancer therapies by accurately predicting the most appropriate therapies to treat individual patients. Here, we present an approach, named Drug Ranking Using ML (DRUML), which uses omics data to produce ordered lists of >400 drugs based on their anti-proliferative efficacy in cancer cells. To reduce noise and increase predictive robustness, instead of individual features, DRUML uses internally normalized distance metrics of drug response as features for ML model generation. DRUML is trained using in-house proteomics and phosphoproteomics data derived from 48 cell lines, and it is verified with data comprised of 53 cellular models from 12 independent laboratories. We show that DRUML predicts drug responses in independent verification datasets with low error (mean squared error < 0.1 and mean Spearman’s rank 0.7). In addition, we demonstrate that DRUML predictions of cytarabine sensitivity in clinical leukemia samples are prognostic of patient survival (Log rank p < 0.005). Our results indicate that DRUML accurately ranks anti-cancer drugs by their efficacy across a wide range of pathologies

Gender classification using 2-D ear images and sparse representation

Gender classification attracted the attention of researchers in computer vision for its use in many applications. Researches have addressed this issue based on facial images. In this paper, we present the first approach for gender classification using 2-D ear images based upon sparse representation. In sparse representation, the training data is used to develop a dictionary based on extracted features. In this work, Gabor filters are used for feature extraction. Classification is achieved by representing the test data using the dictionary based upon the extracted features. Experimental results conducted on the University of Notre Dame (UND) collection J dataset, containing large appearance, pose, and lighting variability, yielded gender classification rate of 89.49%

Ear recognition via sparse representation and Gabor filters

In this paper, we present a fully automated approach for ear recognition based upon sparse representation. In sparse representation, features extracted from the training data of each subject are used to develop a dictionary. In this work, Gabor filters are used for feature extraction. Classification is performed by extracting features from the test data and using the dictionary for representing the test data. The class of the test data is then determined based upon the involvement of the dictionary entries in its representation. Experimental results conducted on the University of Notre Dame (UND) collection G dataset, containing large appearance, pose, and lighting variability, yielded a rank-one recognition rate of 98.46%. The proposed system outperforms the method described in [1], which achieves a recognition rate of 96.88% when evaluated on the same dataset. Moreover, the proposed system was evaluated on a greater number of test images per subject, demonstrating its robustness