Differential posets and restriction in critical groups

In recent work, Benkart, Klivans, and Reiner defined the critical group of a faithful representation of a finite group $G$, which is analogous to the critical group of a graph. In this paper we study maps between critical groups induced by injective group homomorphisms and in particular the map induced by restriction of the representation to a subgroup. We show that in the abelian group case the critical groups are isomorphic to the critical groups of a certain Cayley graph and that the restriction map corresponds to a graph covering map. We also show that when $G$ is an element in a differential tower of groups, critical groups of certain representations are closely related to words of up-down maps in the associated differential poset. We use this to generalize an explicit formula for the critical group of the permutation representation of the symmetric group given by the second author, and to enumerate the factors in such critical groups.Comment: 18 pages; v2: minor edits and updated reference

Audit of buying patterns of drugs from various pharmacies in Northern India

A study was conducted to gather data regarding drug buying practices in Delhi to compare the same in rural pharmacies in surrounding area. A cross sectional study was conducted as exit interviews using pretested Performa with customers visiting randomly selected pharmacies of Delhi and rural Haryana. Out of 280 consumers interviewed 140 belonged to urban areas and 140 to rural areas. In both areas male and younger consumers are significantly high. Most consumers in both set ups took medication after physician’s prescription in comparison to self medication. Source of information for self medication was media in urban and friends in rural areas. Alteration in brand name was more in rural areas. Antimicrobials and NSAIDs in rural areas and drugs for cardiovascular diseases and oral hypoglycemic drugs in urban areas are major purchased drug groups

Virtual labeling of mitochondria in living cells using correlative imaging and physics-guided deep learning

Mitochondria play a crucial role in cellular metabolism. This paper presents a novel method to visualize mitochondria in living cells without the use of fluorescent markers. We propose a physics-guided deep learning approach for obtaining virtually labeled micrographs of mitochondria from bright-field images. We integrate a microscope’s point spread function in the learning of an adversarial neural network for improving virtual labeling. We show results (average Pearson correlation 0.86) significantly better than what was achieved by state-of-the-art (0.71) for virtual labeling of mitochondria. We also provide new insights into the virtual labeling problem and suggest additional metrics for quality assessment. The results show that our virtual labeling approach is a powerful way of segmenting and tracking individual mitochondria in bright-field images, results previously achievable only for fluorescently labeled mitochondria