Related papers: Towards the Human Genotope
Being different from deep-learning-based (DL-based) image generation methods, a new image generative model built upon successive subspace learning principle is proposed and named GenHop (an acronym of Generative PixelHop) in this work.…
The polytope containment problem is deciding whether a polytope is a contained within another polytope. This problem is rooted in computational convexity, and arises in applications such as verification and control of dynamical systems. The…
Hive plots are a graph visualization style placing vertices on a set of radial axes emanating from a common center and drawing edges as smooth curves connecting their respective endpoints. In previous work on hive plots, assignment to an…
Marginal polytopes are important geometric objects that arise in statistics as the polytopes underlying hierarchical log-linear models. These polytopes can be used to answer geometric questions about these models, such as determining the…
MOTIVATION: Left ventricular (LV) hypertrophy is a strong predictor of cardiovascular outcomes, but its genetic regulation remains largely unexplained. Conventional phenotyping relies on manual calculation of LV mass and wall thickness, but…
A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to…
Convex hulls are a fundamental geometric tool used in a number of algorithms. As a side-effect of exhaustive tests for an algorithm for which a convex hull computation was the first step, interesting experimental results were found and are…
A spectrahedron is a set defined by a linear matrix inequality. A projection of a spectrahedron is often called a semidefinitely representable set. We show that the convex hull of a finite union of such projections is again a projection of…
Mapping genotypes to phenotypes (G2P) is a fundamental goal in biology. So called PhyloG2P methods are a relatively new set of tools that leverage replicated evolution in phylogenetically independent lineages to identify genomic regions…
Let $2\le k\le d-1$ and let $P$ and $Q$ be two convex polytopes in ${\mathbb E^d}$. Assume that their projections, $P|H$, $Q|H$, onto every $k$-dimensional subspace $H$, are congruent. In this paper we show that $P$ and $Q$ or $P$ and $-Q$…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
A quest to determine the complete sequence of a human DNA from telomere to telomere started three decades ago and was finally completed in 2021. This accomplishment was a result of a tremendous effort of numerous experts who engineered…
A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and…
We study the Hausdorff distance between a random polytope, defined as the convex hull of i.i.d. random points, and the convex hull of the support of their distribution. As particular examples, we consider uniform distributions on convex…
The human genome contains repetitive DNA at different level of sequence length, number and dispersion. Highly repetitive DNA is particularly rich in homo-- and di--nucleotide repeats, while middle repetitive DNA is rich of families of…
3D human pose estimation errors would propagate along the human body topology and accumulate at the end joints of limbs. Inspired by the backtracking mechanism in automatic control systems, we design an Intra-Part Constraint module that…
Classic concepts of genetic (gene) diversity (heterozygosity) such as Nei (1973: PNAS) and Nei and Li (1979: PNAS) nucleotide diversity were defined within the context of populations. Although variations are often measured in population…
We study how to synthesize novel views of human body from a single image. Though recent deep learning based methods work well for rigid objects, they often fail on objects with large articulation, like human bodies. The core step of…
We study the polytopes of affine maps between two polytopes -- the hom-polytopes. The hom-polytope functor has a left adjoint -- tensor product polytopes. The analogy with the category of vector spaces is limited, as we illustrate by a…
Hippocampal neurons track positions of self, others, and gaze direction. However, it is unclear how their respective neural codes differ enough to avoid confusion while allowing for abstraction. We recorded from populations of hippocampal…