Related papers: Towards the Human Genotope
Haplotypes, the global patterns of DNA sequence variation, have important implications for identifying complex traits. Recently, blocks of limited haplotype diversity have been discovered in human chromosomes, intensifying the research on…
Over the last fifty years, geneticists have made great strides in understanding how our species' evolutionary history gave rise to current patterns of human genetic diversity classically summarized by Lewontin in his 1972 paper, 'The…
We study the convex hull of a set $S\subset \mathbb{R}^n$ defined by three quadratic inequalities. A simple way of generating inequalities valid on $S$ is to take nonnegative linear combinations of the defining inequalities of $S$. We call…
Given a tree $T$, its path polytope is the convex hull of the edge indicator vectors for the paths between any two distinct leaves in $T$. These polytopes arise naturally in polyhedral geometry and applications, such as phylogenetics,…
Background: Haplotypes, the ordered lists of single nucleotide variations that distinguish chromosomal sequences from their homologous pairs, may reveal an individual's susceptibility to hereditary and complex diseases and affect how our…
This paper studies the haplotype assembly problem from an information theoretic perspective. A haplotype is a sequence of nucleotide bases on a chromosome, often conveniently represented by a binary string, that differ from the bases in the…
Consider a random set of points on the unit sphere in $\mathbb{R}^d$, which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polytope, whose boundary approximates the sphere. We focus on the…
The computational problem of inferring the full haplotype of a cell starting from read sequencing data is known as haplotype assembly, and consists in assigning all heterozygous Single Nucleotide Polymorphisms (SNPs) to exactly one of the…
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…
Convex hulls are fundamental objects in computational geometry. In moderate dimensions or for large numbers of vertices, computing the convex hull can be impractical due to the computational complexity of convex hull algorithms. In this…
Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map.…
Representation learning has been essential for graph machine learning tasks such as link prediction, community detection, and network visualization. Despite recent advances in achieving high performance on these downstream tasks, little…
What is a population? This review considers how a population may be defined in terms of understanding the structure of the underlying genetics of the individuals involved. The main approach is to consider statistically identifiable groups…
Let $\mu$ be a probability distribution on $\mathbb{R}^d$ which assigns measure zero to every hyperplane and $S$ a set of points sampled independently from $\mu$. What can be said about the expected combinatorial structure of the convex…
Population structure can be modelled by evolutionary graphs, which can have a substantial, but very subtle influence on the fate of the arising mutants. Individuals are located on the nodes of these graphs, competing with each other to…
To uncover the genetic basis of complex disease, individuals are often measured at a large number of genetic variants (usually SNPs) across the genome. GemTools provides computationally efficient tools for modeling genetic ancestry based on…
The Human Cell Atlas (HCA) will be made up of comprehensive reference maps of all human cells - the fundamental units of life - as a basis for understanding fundamental human biological processes and diagnosing, monitoring, and treating…
This article provides an overview of our joint work on binary polynomial optimization over the past decade. We define the multilinear polytope as the convex hull of the feasible region of a linearized binary polynomial optimization problem.…
In the last few decades, the human allosomes are engrossed in an intensive attention among researchers. The allosomes are now already been sequenced and found there are about 2000 and 78 genes in human X and Y chromosomes respectively. The…
A biconvex polytope is a classical and tropical convex hull of finitely many points. Given a biconvex polytope, for each vertex of it we construct a directed bigraph and a gammoid so that the collection of base polytopes of those gammoids…