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.

C. elegans chromosomes connect to centrosomes by anchoring into the spindle network

Abstract: The mitotic spindle ensures the faithful segregation of chromosomes. Here we combine the first large-scale serial electron tomography of whole mitotic spindles in early C. elegans embryos with live-cell imaging to reconstruct all microtubules in 3D and identify their plus- and minus-ends. We classify them as kinetochore (KMTs), spindle (SMTs) or astral microtubules (AMTs) according to their positions, and quantify distinct properties of each class. While our light microscopy and mutant studies show that microtubules are nucleated from the centrosomes, we find only a few KMTs directly connected to the centrosomes. Indeed, by quantitatively analysing several models of microtubule growth, we conclude that minus-ends of KMTs have selectively detached and depolymerized from the centrosome. In toto, our results show that the connection between centrosomes and chromosomes is mediated by an anchoring into the entire spindle network and that any direct connections through KMTs are few and likely very transient.

Rates and mechanisms of bacterial mutagenesis from maximum-depth sequencing

Abstract: In 1943, Luria and Delbruck used a phage-resistance assay to establish spontaneous mutation as a driving force of microbial diversity. Mutation rates are still studied using such assays, but these can only be used to examine the small minority of mutations conferring survival in a particular condition. Newer approaches, such as long-term evolution followed by whole-genome sequencing, may be skewed by mutational ‘hot’ or ‘cold’ spots. Both approaches are affected by numerous caveats. Here we devise a method, maximum-depth sequencing (MDS), to detect extremely rare variants in a population of cells through error-corrected, high-throughput sequencing. We directly measure locus-specific mutation rates in Escherichia coli and show that they vary across the genome by at least an order of magnitude. Our data suggest that certain types of nucleotide misincorporation occur 10(4)-fold more frequently than the basal rate of mutations, but are repaired in vivo. Our data also suggest specific mechanisms of antibiotic-induced mutagenesis, including downregulation of mismatch repair via oxidative stress, transcription–replication conflicts, and, in the case of fluoroquinolones, direct damage to DNA.

Non-Newtonian Hele-Shaw Flow and the Saffman-Taylor Instability

Abstract: We explore the Saffman-Taylor instability of a gas bubble expanding into a shear thinning liquid in a radial Hele-Shaw cell. Using Darcy{close_quote}s law generalized for non-Newtonian fluids, we perform simulations of the full dynamical problem. The simulations show that shear thinning significantly influences the developing interfacial patterns. Shear thinning can suppress tip splitting, and produce fingers which oscillate during growth and shed side branches. Emergent length scales show reasonable agreement with a general linear stability analysis. {copyright} {ital 1998} {ital The American Physical Society}

Nonparametric forecasting of low-dimensional dynamical systems

Abstract: This paper presents a nonparametric modeling approach for forecasting stochastic dynamical systems on low-dimensional manifolds. The key idea is to represent the discrete shift maps on a smooth basis which can be obtained by the diffusion maps algorithm. In the limit of large data, this approach converges to a Galerkin projection of the semigroup solution to the underlying dynamics on a basis adapted to the invariant measure. This approach allows one to quantify uncertainties (in fact, evolve the probability distribution) for nontrivial dynamical systems with equation-free modeling. We verify our approach on various examples, ranging from an inhomogeneous anisotropic stochastic differential equation on a torus, the chaotic Lorenz three-dimensional model, and the Ni\~no-3.4 data set which is used as a proxy of the El Ni\~no Southern Oscillation.

Learning Theory and Algorithms for Revenue Optimization in Second-Price Auctions with Reserve

Abstract: Second-price auctions with reserve play a critical role for modern search engine and popular online sites since the revenue of these companies often directly de- pends on the outcome of such auctions. The choice of the reserve price is the main mechanism through which the auction revenue can be influenced in these electronic markets. We cast the problem of selecting the reserve price to optimize revenue as a learning problem and present a full theoretical analysis dealing with the complex properties of the corresponding loss function. We further give novel algorithms for solving this problem and report the results of several experiments in both synthetic and real data demonstrating their effectiveness.