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Crossover is the process of recombining the genetic features of two parents. For many applications where crossover is applied to permutations, relevant genetic features are pairs of adjacent elements, also called edges in the permutation…
Holographic Predictive Search (HPS) is a novel approach to search-based hologram generation that uses a mathematical understanding of the optical transforms to make informed optimisation decisions. Existing search techniques such as Direct…
Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…
Accurate identification of haplotypes in sequenced human genomes can provide invaluable information about population demography and fine-scale correlations along the genome, thus empowering both population genomic and medical association…
A subset $S$ of vertices of a graph $G$ is called a perfectly matchable set of $G$ if the subgraph induced by $S$ contains a perfect matching. The perfectly matchable set polynomial of $G$, first made explicit by Ohsugi and Tsuchiya, is the…
Phenomics is an emerging branch of modern biology that uses high throughput phenotyping tools to capture multiple environmental and phenotypic traits, often at massive spatial and temporal scales. The resulting high dimensional data…
This paper proposes a Genetic Algorithm based segmentation method that can automatically segment gray-scale images. The proposed method mainly consists of spatial unsupervised grayscale image segmentation that divides an image into regions.…
In a previous work, we gave a metric on the class of semibinary tree-sibling time consistent phylogenetic networks that is computable in polynomial time; in particular, the problem of deciding if two networks of this kind are isomorphic is…
The detection of molecular signatures of selection is one of the major concerns of modern population genetics. A widely used strategy in this context is to compare samples from several populations, and to look for genomic regions with…
Fully Homomorphic Encryption (FHE) is a relatively recent advancement in the field of privacy-preserving technologies. FHE allows for the arbitrary depth computation of both addition and multiplication, and thus the application of…
Reconstruction of family trees, or pedigree reconstruction, for a group of individuals is a fundamental problem in genetics. The problem is known to be NP-hard even for datasets known to only contain siblings. Some recent methods have been…
Finding Boolean functions suitable for cryptographic primitives is a complex combinatorial optimization problem, since they must satisfy several properties to resist cryptanalytic attacks, and the space is very large, which grows super…
Genetic algorithms are high-level heuristic optimization methods which enjoy great popularity thanks to their intuitive description, flexibility, and, of course, effectiveness. The optimization procedure is based on the evolution of…
Feature selection for predictive analytics is the problem of identifying a minimal-size subset of features that is maximally predictive of an outcome of interest. To apply to molecular data, feature selection algorithms need to be scalable…
Perfect Matching-Cut is the problem of deciding whether a graph has a perfect matching that contains an edge-cut. We show that this problem is NP-complete for planar graphs with maximum degree four, for planar graphs with girth five, for…
We show that each member of a broad class of Markovian population models induces a unique stochastic process on the space of genealogies. We construct this genealogy process and derive exact expressions for the likelihood of an observed…
Phylogenetically decisive collections of taxon sets have the property that if trees are chosen for each of their elements, as long as these trees are compatible, the resulting supertree is unique. This means that as long as the trees…
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes…
In this study we introduce a new method to solve the Dynamics Facility Layout Problems (DFLPs). To represent each layout, we use the slicing tree method integrated with our proposed heuristic to obtain promising initial solutions. Then, we…
This paper investigates the influence of genotype size on evolutionary algorithms' performance. We consider genotype compression (where genotype is smaller than phenotype) and expansion (genotype is larger than phenotype) and define…