Related papers: Towards the Human Genotope
Understanding humans from photographs has always been a fundamental goal of computer vision. In this thesis we have developed a hierarchy of tools that cover a wide range of topics with the objective of understanding humans from monocular…
GWAS in humans are revealing the genetic architecture of biomedical and anthropomorphic traits, i.e., the frequencies and effect sizes of variants that contribute to heritable variation in a trait. To interpret these findings, we need to…
Adaptation in response to selection on polygenic phenotypes may occur via subtle allele frequencies shifts at many loci. Current population genomic techniques are not well posed to identify such signals. In the past decade, detailed…
Polymers can be modeled as open polygonal paths and their closure generates knots. Knotted proteins detection is currently achieved via high-throughput methods based on a common framework insensitive to the handedness of knots. Here we…
How does the genome encode the form of the organism? What is the nature of this genomic code? Inspired by recent work in machine learning and neuroscience, we propose that the genome encodes a generative model of the organism. In this…
Facets of the convex hull of $n$ independent random vectors chosen uniformly at random from the unit sphere in $\mathbb{R}^d$ are studied. A particular focus is given on the height of the facets as well as the expected number of facets as…
The matching polytope of a graph $G$ is the convex hull of the indicator vectors of the matchings on $G$. We characterize the graphs whose associated matching polytopes are Gorenstein, and then prove that all Gorenstein matching polytopes…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
We consider the bipartite boolean quadric polytope (BQP) with multiple-choice constraints and analyse its combinatorial properties. The well-studied BQP is defined as the convex hull of all quadric incidence vectors over a bipartite graph.…
Recent 2D-to-3D human pose estimation works tend to utilize the graph structure formed by the topology of the human skeleton. However, we argue that this skeletal topology is too sparse to reflect the body structure and suffer from serious…
The prevalence of neutral mutations implies that biological systems typically have many more genotypes than phenotypes. But can the way that genotypes are distributed over phenotypes determine evolutionary outcomes? Answering such questions…
This note defines a complete h-vector for convex polytopes, which extends the already known toric (or mpih) h-vector and has many similar properties. Complete means that it encodes the whole of the flag vector. First we define the concept…
We develop a feature allocation model for inference on genetic tumor variation using next-generation sequencing data. Specifically, we record single nucleotide variants (SNVs) based on short reads mapped to human reference genome and…
Despite recent success on 2D human pose estimation, 3D human pose estimation still remains an open problem. A key challenge is the ill-posed depth ambiguity nature. This paper presents a novel intermediate feature representation named…
When we apply comparative phylogenetic analyses to genome data, it is a well-known problem and challenge that some of given species (or taxa) often have missing genes. In such a case, we have to impute a missing part of a gene tree from a…
Admixture mapping is a popular tool to identify regions of the genome associated with traits in a recently admixed population. Existing methods have been developed primarily for identification of a single locus influencing a dichotomous…
We expand the basic geometric elements of the simplex method to linear programs in locally convex topological vector spaces and provide conditions under which the method converges in value to optimality. This setting generalizes many…
The phenomenon of Human Pose Estimation (HPE) is a problem that has been explored over the years, particularly in computer vision. But what exactly is it? To answer this, the concept of a pose must first be understood. Pose can be defined…
In this work we study a class of random convex sets that "interpolate" between polytopes and zonotopes. These sets arise from considering a $q^{th}$-moment ($q\geq 1$) of an average of order statistics of $1$-dimensional marginals of a…
It is shown how the Beneath-and-Beyond algorithm can be used to yield another proof of the equivalence of V- and H-representations of convex polytopes. In this sense this paper serves as the sketch of an introduction to polytope theory with…