arXiv subjects
Publications and source records attributed to Eric Chen.
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Short-read DNA sequencing instruments can yield over 1e+12 bases per run, typically composed of reads 150 bases long. Despite this high throughput, de novo assembly algorithms have difficulty reconstructing contiguous genome sequences using short reads due to both repetitive and difficult-to-sequence regions in these genomes. Some of the short read assembly challenges are mitigated by scaffolding assembled sequences using paired-end reads. However, unresolved sequences in these scaffolds appear as "gaps". Here, we introduce GapPredict, a tool that uses a character-level language model to predict unresolved nucleotides in scaffold gaps. We benchmarked GapPredict against the state-of-the-art gap-filling tool Sealer, and observed that the former can fill 65.6% of the sampled gaps that were left unfilled by the latter, demonstrating the practical utility of deep learning approaches to the gap-filling problem in genome sequence assembly.
We study the Yamabe flow starting from an asymptotically flat manifold $(M^n,g_0)$. We show that the flow converges to an asymptotically flat, scalar flat metric in a weighted global sense if $Y(M,[g_0])>0$, and show that the flow does not converge otherwise. If the scalar curvature is nonnegative and integrable, then the ADM mass at time infinity drops by the limit of the total scalar curvature along the flow.
A magic SET square is a 3 by 3 table of SET cards such that each row, column, diagonal, and anti-diagonal is a set. We allow the following transformations of the square: shuffling features, shuffling values within the features, rotations and reflections of the square. Under these transformations, there are 21 types of magic SET squares. We calculate the number of squares of each type. In addition, we discuss a game of SET tic-tac-toe.
We demonstrate and analyze how deploying non-classical intensity correlations obtained from a monolithic semiconductor quantum photon source can enhance classical target detection systems. This is demonstrated by examining the advantages offered by the utilization of the non-classical correlations in a correlation based target detection protocol. We experimentally demonstrate that under the same condition, the target contrast obtained from the protocol when non-classical correlations are utilized exhibits an improvement of up to 17.79dB over the best classical intensity correlation-based target detection protocol, under 29.69dB channel loss and excess noise 13.40dB stronger than the probe signal. We also assessed how the strong frequency correlations within the non-classical photon pairs can be used to further enhance this protocol.
We prove a curvature pinching result for the Ricci flow on asymptotically flat manifolds: if an asymptotically flat manifold of dimension $n\geq 3$ has scale-invariant integral norm of curvature sufficiently pinched relative to the inverse of its Sobolev constant, then the Ricci flow starting from this manifold exists for all positive times and converges to flat Euclidean space. In particular our result implies that the initial manifold must have been diffeomorphic to $\mathbb{R}^n$.
Zeckendorf's Theorem states that any positive integer can be written uniquely as a sum of non-adjacent Fibonacci numbers. We consider higher-dimensional lattice analogues, where a legal decomposition of a number $n$ is a collection of lattice points such that each point is included at most once. Once a point is chosen, all future points must have strictly smaller coordinates, and the pairwise sum of the values of the points chosen equals $n$. We prove that the distribution of the number of summands in these lattice decompositions converges to a Gaussian distribution in any number of dimensions. As an immediate corollary we obtain a new proof for the asymptotic number of certain lattice paths.
We extend the Caffarelli-Kohn-Nirenberg type partial regularity theory for the steady $5$-dimensional fractional Navier-Stokes equations with external force to the hyperdissipative setting. In our argument we use the methods of Colombo-De Lellis-Massaccesi to apply a blowup procedure adapted from work of Ladyzhenskaya-Seregin.
This is an REU paper written for the University of Chicago REU, summer 2017. The main purpose of this note is to collect some of the many combinatorial models for MV cycles that exist in the literature. In particular, we will investigate MV polytopes, preprojective algebras, crystals, and LS galleries. We also compute explicitly some examples to help elucidate the theory and the connections between these models.
Tripod configurations of plane curves, formed by certain triples of normal lines coinciding at a point, were introduced by Tabachnikov, who showed that $C^2$ closed convex curves possess at least two tripod configurations. Later, Kao and Wang established the existence of tripod configurations for $C^2$ closed locally convex curves. In this paper we generalize these two results, answering a conjecture of Tabachnikov on the existence of tripod configurations for all $C^2$ closed plane curves by proving existence for a generalized notion of tripod configuration. We then demonstrate the existence of the natural extensions of these tripod configurations to the spherical and hyperbolic geometries for a certain class of convex curves, and discuss an analogue of the problem for regular plane polygons.
We answer a question by Niederreiter concerning the enumeration of a class of subspaces of finite dimensional vector spaces over finite fields by proving a conjecture by Ghorpade and Ram.