Abstract In identifying biomarkers and molecular profiling of diseases, laser capture microdissection serves as an exceptionally efficient method for isolating disease-specific areas from intricate, varied tissue specimens. These areas must be broken down into manageable pieces that meet specific size and shape requirements for successful extraction. We approach the challenge of constrained shape decomposition by calculating optimal feasible decompositions of simple polygons. Our framework is... In identifying biomarkers and molecular profiling of diseases, laser capture microdissection serves as an exceptionally efficient method for isolating disease-specific areas from intricate, varied tissue specimens. These areas must be broken down into manageable pieces that meet specific size and shape requirements for successful extraction. We approach the challenge of constrained shape decomposition by calculating optimal feasible decompositions of simple polygons. Our framework is based on a skeleton-oriented method and provides analgorithmic structure that supports the integration of different feasibility criteria and optimization objectives. Driven by our application focus, we explore various constraints and analyze the resulting fragmentations. Additionally, we implement our technique on lung tissue samples and demonstrate its benefits over a heuristic decomposition strategy. Read More Read Less

Abstract When dealing with a collection of intervals on the real number line, an interval graph represents these intervals as nodes and their overlaps as edges. Merging pairs of nodes in an interval graph leads to forming a multiple-interval graph. We seek to answer some critical questions with access only to the nodes and edgesof this multiple-interval graph without the original intervals. Is... When dealing with a collection of intervals on the real number line, an interval graph represents these intervals as nodes and their overlaps as edges. Merging pairs of nodes in an interval graph leads to forming a multiple-interval graph. We seek to answer some critical questions with access only to the nodes and edgesof this multiple-interval graph without the original intervals. Is it possible to determine how many intervals are associated with each node? Can we find a path through the nodes of the multiple-interval graph that reflects the sequence of the original intervals? These inquiries are closely tied to linked-read DNA sequencing, where long molecules are labeled with barcodes, and their intersection graph creates an interval graph. Each barcode might represent several molecules, complicating further analysis and correlating with the identification of nodes in the respective interval graph. Addressing these graph-theoretic challenges would enhance the analysis of linked-reads sequencing data by allowing for the conceptual distinction of barcodes into individual molecules and providing a framework for accurately reconstructing the genome through the arrangement of these molecules. In this context, we introduce a framework that accepts any given intersection graph (like the overlap graph of barcodes) and produces a heuristic estimate of the arrangement of the original intervals. Read More Read Less

Abstract Directed Evolution (DE) is a method used in protein engineering that entails multiple cycles of mutagenesis and screening to identify sequences that enhance a specific characteristic (e.g., binding strength to a designated target). However, the fundamental optimization challenge is not fully determined, meaning that alterations to boost the chosen property may negatively impact unmeasured yet significant attributes (e.g., subcellular localization). We aim to tackle... Directed Evolution (DE) is a method used in protein engineering that entails multiple cycles of mutagenesis and screening to identify sequences that enhance a specific characteristic (e.g., binding strength to a designated target). However, the fundamental optimization challenge is not fully determined, meaning that alterations to boost the chosen property may negatively impact unmeasured yet significant attributes (e.g., subcellular localization). We aim to tackle this challenge by integrating a fold-specific regularization component into optimisation. This regularization component steers the search towards designs similar to sequences within the fold family of the protein. We implemented our approach on an extensive collection of protein GB1 mutants, measuring their binding affinities to IgG-Fc. Our findings reveal that the regularized optimization process yields more native-like GB1 sequences while only slightly compromising binding affinity. Specifically, the log-odds of our designs, assessed under a generative model of the GB1 fold family, are approximately 41-45% greater than those achieved without regularization, with merely a 7% reduction in binding affinity. Therefore, our technique successfully balances competing characteristics. Additionally, we show that our active-learning-based method lowers the experimental workload needed to pinpoint optimal GB1 designs by 67%, compared to recent findings from the Arnold lab using the same dataset. Read More Read Less