相关论文: Towards the Human Genotope

This article studies a large, general class of orthogonal polytopes which we may call "generic orthotopes". These objects emerged from a desire to represent a Coxeter complex by an orthogonal polytope that is particularly nice with respect…

Inference of population structure from genetic data plays an important role in population and medical genetics studies. With the advancement and decreasing cost of sequencing technology, the increasingly available whole genome sequencing…

The human connectome represents a network map of the brain's wiring diagram and the pattern into which its connections are organized is thought to play an important role in cognitive function. The generative rules that shape the topology of…

Gene conversion is a mechanism by which a double-strand break in a DNA molecule is repaired using a homologous DNA molecule as a template. As a result, one gene is 'copied and pasted' onto the other gene. It was recently reported that the…

Correlation of gene histories in the human genome determines the patterns of genetic variation (haplotype structure) and is crucial to understanding genetic factors in common diseases. We derive closed analytical expressions for the…

We study the expected volume of random polytopes generated by taking the convex hull of independent identically distributed points from a given distribution. We show that for log-concave distributions supported on convex bodies, we need at…

We consider two polytopes. The quadratic assignment polytope $QAP(n)$ is the convex hull of the set of tensors $x\otimes x$, $x \in P_n$, where $P_n$ is the set of $n\times n$ permutation matrices. The second polytope is defined as follows.…

We construct genomic predictors for heritable and extremely complex human quantitative traits (height, heel bone density, and educational attainment) using modern methods in high dimensional statistics (i.e., machine learning). Replication…

We identify a set of 575 human genes that are expressed in all conditions tested in a publicly available database of microarray results. Based on this common occurrence, the set is expected to be rich in "housekeeping" genes, showing…

Modern population genetics studies typically involve genome-wide genotyping of individuals from a diverse network of ancestries. An important, unsolved problem is how to formulate and estimate probabilistic models of observed genotypes that…

In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…

We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…

Let $k$ be a positive integer and let $G$ be a graph with $n$ vertices. A connected $k$-subpartition of $G$ is a collection of $k$ pairwise disjoint sets (a.k.a. classes) of vertices in $G$ such that each set induces a connected subgraph.…

Understanding functional organization of genetic information is a major challenge in modern biology. Following the initial publication of the human genome sequence in 2001, advances in high-throughput measurement technologies and efficient…

The multivariate hypergeometric distribution describes sampling without replacement from a discrete population of elements divided into multiple categories. Addressing a gap in the literature, we tackle the challenge of estimating discrete…

The standard convex closed hull of a set is defined as the intersection of all images, under the action of a group of rigid motions, of a half-space containing the given set. In this paper we propose a generalisation of this classical…

The fitness landscape encodes the mapping of genotypes to fitness and provides a succinct representation of possible trajectories followed by an evolving population. Evolutionary accessibility is quantified by the existence of…

A set in the Euclidean plane is said to be biconvex if, for some angle $\theta\in[0,\pi/2)$, all its sections along straight lines with inclination angles $\theta$ and $\theta+\pi/2$ are convex sets (i.e, empty sets or segments).…

The region of entropic vectors is a convex cone that has been shown to be at the core of many fundamental limits for problems in multiterminal data compression, network coding, and multimedia transmission. This cone has been shown to be…

The human thalamus is a brain structure that comprises numerous, highly specific nuclei. Since these nuclei are known to have different functions and to be connected to different areas of the cerebral cortex, it is of great interest for the…