Publications (14)
A genetic variant near olfactory receptor genes influences cilantro preference
Nicholas Eriksson, Shirley Wu, Chuong B. Do +5
The leaves of the Coriandrum sativum plant, known as cilantro or coriander, are widely used in many cuisines around the world. However, far from being a benign culinary herb, cilan…
Genome-wide analysis points to roles for extracellular matrix remodeling, the visual cycle, and neuronal development in myopia
Amy K. Kiefer, Joyce Y. Tung, Chuong B. Do +4
Myopia, or nearsightedness, is the most common eye disorder, resulting primarily from excess elongation of the eye. The etiology of myopia, although known to be complex, is poorly…
Polyhedral conditions for the nonexistence of the MLE for hierarchical log-linear models
Nicholas Eriksson, Stephen E. Fienberg, Alessandro Rinaldo +1
We provide a polyhedral description of the conditions for the existence of the maximum likelihood estimate (MLE) for a hierarchical log-linear model. The MLE exists if and only if…
Apollonian Circle Packings: Number Theory II. Spherical and Hyperbolic Packings
Nicholas Eriksson, Jeffrey C. Lagarias
Apollonian circle packings arise by repeatedly filling the interstices between mutually tangent circles with further tangent circles. In Euclidean space it is possible for every ci…
Viral population estimation using pyrosequencing
Nicholas Eriksson, Lior Pachter, Yumi Mitsuya +6
The diversity of virus populations within single infected hosts presents a major difficulty for the natural immune response as well as for vaccine design and antiviral drug therapy…
Metric learning for phylogenetic invariants
Nicholas Eriksson, Yuan Yao
We introduce new methods for phylogenetic tree quartet construction by using machine learning to optimize the power of phylogenetic invariants. Phylogenetic invariants are polynomi…
Markov bases for noncommutative Fourier analysis of ranked data
Persi Diaconis, Nicholas Eriksson
To calibrate Fourier analysis of ranking data by Markov chain Monte Carlo techniques, a set of moves (Markov basis) is needed. We calculate this basis, and use it to provide…
Using invariants for phylogenetic tree construction
Nicholas Eriksson
Phylogenetic invariants are certain polynomials in the joint probability distribution of a Markov model on a phylogenetic tree. Such polynomials are of theoretical interest in the…
Evolution on distributive lattices
Niko Beerenwinkel, Nicholas Eriksson, Bernd Sturmfels
We consider the directed evolution of a population after an intervention that has significantly altered the underlying fitness landscape. We model the space of genotypes as a distr…
Phylogenetic Algebraic Geometry
Nicholas Eriksson, Kristian Ranestad, Bernd Sturmfels +1
Phylogenetic algebraic geometry is concerned with certain complex projective algebraic varieties derived from finite trees. Real positive points on these varieties represent probab…
Conjunctive Bayesian networks
Niko Beerenwinkel, Nicholas Eriksson, Bernd Sturmfels
Conjunctive Bayesian networks (CBNs) are graphical models that describe the accumulation of events which are constrained in the order of their occurrence. A CBN is given by a parti…
Toric ideals of homogeneous phylogenetic models
Nicholas Eriksson
We consider the phylogenetic tree model in which every node of the tree is observed and binary and the transitions are given by the same matrix on each edge of the tree. We are abl…
Inferring Multidimensional Rates of Aging from Cross-Sectional Data
Emma Pierson, Pang Wei Koh, Tatsunori Hashimoto +4
Modeling how individuals evolve over time is a fundamental problem in the natural and social sciences. However, existing datasets are often cross-sectional with each individual obs…
Reducing pervasive false positive identical-by-descent segments detected by large-scale pedigree analysis
Eric Y. Durand, Nicholas Eriksson, Cory Y. McLean
Analysis of genomic segments shared identical-by-descent (IBD) between individuals is fundamental to many genetic applications, from demographic inference to estimating the heritab…