Fair Allocation of goods and chores -- Tutorial and Survey of Recent Results

Fair resource allocation is an important problem in many real-world scenarios, where resources such as goods and chores must be allocated among agents. In this survey, we delve into the intricacies of fair allocation, focusing specifically on the challenges associated with indivisible resources. We define fairness and efficiency within this context and thoroughly survey existential results, algorithms, and approximations that satisfy various fairness criteria, including envyfreeness, proportionality, MMS, and their relaxations. Additionally, we discuss algorithms that achieve fairness and efficiency, such as Pareto Optimality and Utilitarian Welfare. We also study the computational complexity of these algorithms, the likelihood of finding fair allocations, and the price of fairness for each fairness notion. We also cover mixed instances of indivisible and divisible items and investigate different valuation and allocation settings. By summarizing the state-of-the-art research, this survey provides valuable insights into fair resource allocation of indivisible goods and chores, highlighting computational complexities, fairness guarantees, and trade-offs between fairness and efficiency. It serves as a foundation for future advancements in this vital field

Electrochemical Behavior of Titanium and Its Alloys as Dental Implants in Normal Saline

The electrochemical behavior of pure titanium and titanium alloys in a simulated body fluid (normal saline solution) has been tested, and the results have been reported. The significance of the results for dental use has been discussed. The tests also serve as a screening test for the best alloy system for more comprehensive long-term investigations

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Not AvailableDry root rot (Rhizoctonia bataticola) is an important disease of lentils (Lens culinaris Medik.).To gain an insight into the molecular aspects of host-pathogen interactions, the RNA-seq approach was used in lentils following inoculation with R.bataticola. The RNA-Seq has generated >450 million high-quality reads (HQRs) and nearly 96.97% were properly aligned to the reference genome. Very high similarity in FPKM (fragments per kilobase of exon per million mapped fragments) values (R > 0.9) among biological replicates showed the consistency of the RNA-Seq results. The study revealed various DEGs (differentially expressed genes) that were associated with changes in phenolic compounds, transcription factors (TFs), antioxidants, receptor kinases, hormone signals which corresponded to the cell wall modification enzymes, defense-related metabolites, and jasmonic acid (JA)/ethylene (ET) pathways. Gene ontology (GO) categorization also showed similar kinds of significantly enriched similar GO terms. Interestingly, of the total unigenes (42,606), 12,648 got assembled and showed significant hit with Rhizoctonia species. String analysis also revealed the role of various disease responsive proteins viz., LRR family proteins, LRR-RLKs, protein kinases, etc. in the host-pathogen interaction. Insilico validation analysis was performed using Genevestigator® and DEGs belonging to six major defense-response groups viz., defense-related enzymes, disease responsive genes, hormones, kinases, PR (pathogenesis related) proteins, and TFs were validated. For the first time some key miRNA targets viz. miR156, miR159, miR167, miR169, and miR482 were identified from the studied transcriptome, which may have some vital role in Rhizoctonia-based responses in lentils. The study has revealed the molecular mechanisms of the lentil/R.bataticola interactions and also provided a theoretical approach for the development of lentil genotypes resistant to R.bataticolaNot Availabl