A Polynomial Kernel for Diamond-Free Editing

Given a fixed graph H, the H-free editing problem asks whether we can edit at most k edges to make a graph contain no induced copy of H. We obtain a polynomial kernel for this problem when H is a diamond. The incompressibility dichotomy for H being a 3-connected graph and the classical complexity dichotomy suggest that except for H being a complete/empty graph, H-free editing problems admit polynomial kernels only for a few small graphs H. Therefore, we believe that our result is an essential step toward a complete dichotomy on the compressibility of H-free editing. Additionally, we give a cubic-vertex kernel for the diamond-free edge deletion problem, which is far simpler than the previous kernel of the same size for the problem

Infection with a Virulent Strain of Wolbachia Disrupts Genome Wide-Patterns of Cytosine Methylation in the Mosquito Aedes aegypti

BACKGROUND Cytosine methylation is one of several reversible epigenetic modifications of DNA that allow a greater flexibility in the relationship between genotype and phenotype. Methylation in the simplest models dampens gene expression by modifying regions of DNA critical for transcription factor binding. The capacity to methylate DNA is variable in the insects due to diverse histories of gene loss and duplication of DNA methylases. Mosquitoes like Drosophila melanogaster possess only a single methylase, DNMT2. DESCRIPTION Here we characterise the methylome of the mosquito Aedes aegypti and examine its relationship to transcription and test the effects of infection with a virulent strain of the endosymbiont Wolbachia on the stability of methylation patterns. CONCLUSION We see that methylation in the A. aegypti genome is associated with reduced transcription and is most common in the promoters of genes relating to regulation of transcription and metabolism. Similar gene classes are also methylated in aphids and honeybees, suggesting either conservation or convergence of methylation patterns. In addition to this evidence of evolutionary stability, we also show that infection with the virulent wMelPop Wolbachia strain induces additional methylation and demethylation events in the genome. While most of these changes seem random with respect to gene function and have no detected effect on transcription, there does appear to be enrichment of genes associated with membrane function. Given that Wolbachia lives within a membrane-bound vacuole of host origin and retains a large number of genes for transporting host amino acids, inorganic ions and ATP despite a severely reduced genome, these changes might represent an evolved strategy for manipulating the host environments for its own gain. Testing for a direct link between these methylation changes and expression, however, will require study across a broader range of developmental stages and tissues with methods that detect splice variants.This research was supported by The National Health and Medical Research Council of Australia. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Safeguarding the Unseen: a Study on Data Privacy in DeFi Protocols

The financial sector's adoption of technology-driven data analysis has enhanced operational efficiency and revenue generation by leveraging personal sensitive data. However, the inherent characteristics of blockchain hinder decentralized finance (DeFi) from accessing necessary sensitive user data. To address this challenge, we introduce a protocol that both safeguards user privacy and ensures data availability through the incorporation of homomorphic encryption and zero-knowledge-proof techniques in blockchain technology. This novel protocol helps mitigate privacy risks caused by sensitive data leaks while improving the capital efficiency of the DeFi market. Furthermore, we explore the applicability of these privacy-preserving methods in on-chain ecosystems and cross-border financial applications. Our solution contributes to secure, user-centric solutions for DeFi while upholding principles of decentralization and privacy protection