Classical and consecutive pattern avoidance in rooted forests

Following Anders and Archer, we say that an unordered rooted labeled forest avoids the pattern $\sigma\in\mathcal{S}_k$ if in each tree, each sequence of labels along the shortest path from the root to a vertex does not contain a subsequence with the same relative order as $\sigma$. For each permutation $\sigma\in\mathcal{S}_{k-2}$, we construct a bijection between $n$-vertex forests avoiding $(\sigma)(k-1)k=\sigma(1)\cdots\sigma(k-2)(k-1)k$ and $n$-vertex forests avoiding $(\sigma)k(k-1)=\sigma(1)\cdots\sigma(k-2)k(k-1)$, giving a common generalization of results of West on permutations and Anders--Archer on forests. We further define a new object, the forest-Young diagram, which we use to extend the notion of shape-Wilf equivalence to forests. In particular, this allows us to generalize the above result to a bijection between forests avoiding $\{(\sigma_1)k(k-1), (\sigma_2)k(k-1), \dots, (\sigma_\ell) k(k-1)\}$ and forests avoiding $\{(\sigma_1)(k-1)k, (\sigma_2)(k-1)k, \dots, (\sigma_\ell) (k-1)k\}$ for $\sigma_1, \dots, \sigma_\ell \in \mathcal{S}_{k-2}$. Furthermore, we give recurrences enumerating the forests avoiding $\{123\cdots k\}$, $\{213\}$, and other sets of patterns. Finally, we extend the Goulden--Jackson cluster method to study consecutive pattern avoidance in rooted trees as defined by Anders and Archer. Using the generalized cluster method, we prove that if two length-$k$ patterns are strong-c-forest-Wilf equivalent, then up to complementation, the two patterns must start with the same number. We also prove the surprising result that the patterns $1324$ and $1423$ are strong-c-forest-Wilf equivalent, even though they are not c-Wilf equivalent with respect to permutations.Comment: 39 pages, 11 figure

New Results on Nyldon Words and Nyldon-like Sets

Grinberg defined Nyldon words as those words which cannot be factorized into a sequence of lexicographically nondecreasing smaller Nyldon words. He was inspired by Lyndon words, defined the same way except with "nondecreasing" replaced by "nonincreasing." Charlier, Philibert, and Stipulanti proved that, like Lyndon words, any word has a unique nondecreasing factorization into Nyldon words. They also show that the Nyldon words form a right Lazard set, and equivalently, a right Hall set. In this paper, we provide a new proof of unique factorization into Nyldon words related to Hall set theory and resolve several questions of Charlier et al. In particular, we prove that Nyldon words of a fixed length form a circular code, we prove a result on factorizing powers of words into Nyldon words, and we investigate the Lazard procedure for generating Nyldon words. We show that these results generalize to a new class of Hall sets, of which Nyldon words are an example, that we name "Nyldon-like sets."Comment: 22 pages; generalized many results to Nyldon-like set

Headband technique of reimplantation of a partially amputed finger: a first reported in literature

Background: Reimplantation of a partially amputee finger is a challenging task especially in resource limited country like India. In most of the scenario it lands in total amputation either due to delay in arrival at operative set up or due to lack of plastic surgery facility. Methods: We developed an innovative approach (1st reported in literature) of “headband technique “of reimplantation of such partially amputee fingers and toes. Partially amputee fingers and toes with viability were selected for the operative treatment and for the study. The study was conducted from January 2020 to 2021 with a follow up period for 6 months at our institution. The innovative suturing technique involved a single stitch at the tip of the pulp and rest on adjacent to nail bed securing the neurovascular structures. The patient was in age group of 9 months to 94 years, mostly traumatic injury, with 40 male and 15 female patients. Patients who reported with fully amputee fingers, black escharotic finger were excluded from the study. Results: To our accomplishment out of 55 operated patients, more than 50 have fully recovered. Conclusions: With this simple technique of reimplantation even doctor at PHC’S can save fingers from getting amputed. Our study is with small number of patients; hence we advocate a larger study for to have conclusive evidence for the same

Design, Synthesis and Biological Evaluation of Biphenylamide Derivatives as Hsp90 C-terminal Inhibitors

Modulation of Hsp90 C-terminal function represents a promising therapeutic approach for the treatment of cancer and neurodegenerative diseases. Current drug discovery efforts toward Hsp90 C-terminal inhibition focus on novobiocin, an antibiotic that was transformed into an Hsp90 inhibitor. Based on structural information obtained during the development of novobiocin derivatives and molecular docking studies, scaffolds containing a biphenyl moiety in lieu of the coumarin ring present in novobiocin were identified as new Hsp90 C-terminal inhibitors. Structure-activity relationship studies produced new derivatives that inhibit the proliferation of breast cancer cell lines at nanomolar concentrations, which corresponded directly with Hsp90 inhibition

To Study of Artemisia nilagirica Leaves for their Antithyroid, Oxidative and Antihyperglycemic Properties

The tiny, fragrant shrub Artemisia nilagirica (Clarke) is a member of the Asteraceae family. This plant's leaves and flowering top have been used in traditional medicine as an antimalarial, nerve tonic, and anticancer drug, and there is evidence of anti-leishmanial efficacy. Material and Methods: The plant specimen was obtained from the Ooty district in Tamil Nadu, India, during the month of December. It was subsequently authenticated by NMKRV College for Women, Bengaluru, Karnataka, India. The plant specimens were stored in the herbarium of the NMKRV College for Women, Bengaluru, Karnataka, India. Results: The morphological, microscopic, organoleptic, and other WHO-recommended procedures for standardization were investigated in a powdered sample of Artemisia nilagirica (Clarke) leaf. Phytochemical investigation revealed the existence of numerous elements such as alkaloids, amino acids, carbohydrates, flavonoids, glycosides, terpenoids, steroids, saponins, essential oils, tannins and phenol in diverse extracts. Conclusion: Pharmacognostic and phytochemical analysis of Artemisia nilagirica (Clarke) leaves would be useful for authenticating raw material or crude medication

Reducing stranded assets through early action in the Indian power sector

Cost-effective achievement of the Paris Agreement's long-term goals requires the unanimous phase-out of coal power generation by mid-century. However, continued investments in coal power plants will make this transition difficult. India is one of the major countries with significant under construction and planned increase in coal power capacity. To ascertain the likelihood and consequences of the continued expansion of coal power for India's future mitigation options, we use harmonised scenario results from national and global models along with projections from various government reports. Both these approaches estimate that coal capacity is expected to increase until 2030, along with rapid developments in wind and solar power. However, coal capacity stranding of the order of 133–237 GW needs to occur after 2030 if India were to pursue an ambitious climate policy in line with a well-below 2 °C target. Earlier policy strengthening starting after 2020 can reduce stranded assets (14–159 GW) but brings with it political economy and renewable expansion challenges. We conclude that a policy limiting coal plants to those under construction combined with higher solar targets could be politically feasible, prevent significant stranded capacity, and allow higher mitigation ambition in the future

Erratum: Oral salt and water versus intravenous saline for the prevention of acute kidney injury following contrast-enhanced computed tomography: study protocol for a pilot randomized trial Salmonella blood stream infections in a tertiary care setting in Ghana.

[This corrects the article DOI: 10.1186/s40697-015-0048-7.]