Courant Institute of Mathematical Sciences

About: Courant Institute of Mathematical Sciences is a education organization based out in New York, New York, United States. It is known for research contribution in the topics: Nonlinear system & Boundary value problem. The organization has 2414 authors who have published 7759 publications receiving 439773 citations. The organization is also known as: CIMS & New York University Department of Mathematics.

Asymptotic properties of linear field equations in minkowski space

Abstract: The aim of this paper is to derive the uniform asymptotic behavior of solutions to linear field equations in Minkowski space, based on geometric consideration and generalized energy estimates. Our method relies on a systematic use of the invariance properties of the field equations with respect to the conformal group of the Minkowski space and thus departs substantially from the classical method of analyzing the fundamental solution

Numerical Study of the 8-32-Particle Eigenstates of the Pairing Hamiltonian

Abstract: Exact eigenstates of the pairing-force Hamiltonian have been calculated for $2N$ particles in $2N$ equispaced, doubly degenerate single-particle levels for $N=4, 8, 12, \mathrm{and} 16$. The states calculated are the ground state and the first two excited seniority-zero and seniority-two states. These states were calculated for values of the interaction strength that give pairing energies that are typical of nuclear systems. Numerical results are given for the energies and occupation probabilities of these states and are compared with the corresponding results of the Bardeen-Cooper-Schrieffer (BCS) theory. It is shown that the BCS theory is a worse approximation for the larger values of $N$ than it is for the smaller values, with errors as high as 140% (20%) for the excitation energies of the seniority-zero (-two) states. The methods used in the calculation of these states are outlined.

Uniform regularity for the Navier-Stokes equation with Navier boundary condition

Abstract: We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier–Stokes equation with the Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev space and has only one normal derivative bounded in L∞. This allows us to obtain the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument.

Comparing de novo genome assembly: the long and short of it.

Abstract: Recent advances in DNA sequencing technology and their focal role in Genome Wide Association Studies (GWAS) have rekindled a growing interest in the whole-genome sequence assembly (WGSA) problem, thereby, inundating the field with a plethora of new formalizations, algorithms, heuristics and implementations. And yet, scant attention has been paid to comparative assessments of these assemblers' quality and accuracy. No commonly accepted and standardized method for comparison exists yet. Even worse, widely used metrics to compare the assembled sequences emphasize only size, poorly capturing the contig quality and accuracy. This paper addresses these concerns: it highlights common anomalies in assembly accuracy through a rigorous study of several assemblers, compared under both standard metrics (N50, coverage, contig sizes, etc.) as well as a more comprehensive metric (Feature-Response Curves, FRC) that is introduced here; FRC transparently captures the trade-offs between contigs' quality against their sizes. For this purpose, most of the publicly available major sequence assemblers – both for low-coverage long (Sanger) and high-coverage short (Illumina) reads technologies – are compared. These assemblers are applied to microbial (Escherichia coli, Brucella, Wolbachia, Staphylococcus, Helicobacter) and partial human genome sequences (Chr. Y), using sequence reads of various read-lengths, coverages, accuracies, and with and without mate-pairs. It is hoped that, based on these evaluations, computational biologists will identify innovative sequence assembly paradigms, bioinformaticists will determine promising approaches for developing “next-generation” assemblers, and biotechnologists will formulate more meaningful design desiderata for sequencing technology platforms. A new software tool for computing the FRC metric has been developed and is available through the AMOS open-source consortium.

Put‐call symmetry: extensions and applications

Abstract: Classic put-call symmetry relates the prices of puts and calls at strikes on opposite sides of the forward price. We extend put-call symmetry in several directions. Relaxing the assumptions, we generalize to unified local/stochastic volatility models and time-changed Levy processes, under a symmetry condition. Further relaxing the assumptions, we generalize to various asymmetric dynamics. Extending the conclusions, we take an arbitrarily given payoff of European style or single/double/sequential barrier style, and we construct a conjugate European-style claim of equal value, and thereby a semistatic hedge of the given payoff.