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.

Statistical and physical balances in low Rossby number Rayleigh–Bénard convection

Abstract: Rapidly rotating Rayleigh–Benard convection is studied using an asymptotically reduced equation set valid in the limit of low Rossby numbers. Four distinct dynamical regimes are identified: a disordered cellular regime near threshold, a regime of weakly interacting convective Taylor columns at larger Rayleigh numbers, followed for yet larger Rayleigh numbers by a breakdown of the convective Taylor columns into a disordered plume regime characterized by reduced efficiency and finally by geostrophic turbulence. The transitions are quantified by examining the properties of the horizontally and temporally averaged temperature and thermal dissipation rate. The maximum of the thermal dissipation rate is used to define the width of the thermal boundary layer. In contrast to the non-rotating Rayleigh–Benard convection, the temperature drop across this layer decreases monotonically with increasing Rayleigh number and does not saturate. The breakdown of the convective Taylor column regime is attributed to the onset...

The Viewpoint Consistency Constraint

Abstract: The viewpoint consistency constraint requires that the locations of all object features in an image must be consistent with projection from a single viewpoint. The application of this constraint is central to the problem of achieving robust recognition, since it allows the spatial information in an image to be compared with prior knowledge of an object's shape to the full degree of available image resolution. In addition, the constraint greatly reduces the size of the search space during model-based matching by allowing a few initial matches to provide tight constraints for the locations of other model features. Unfortunately, while simple to state, this constraint has seldom been effectively applied in model-based computer vision systems. This paper reviews the history of attempts to make use of the viewpoint consistency constraint and then describes a number of new techniques for applying it to the process of model-based recognition. A method is presented for probabilistically evaluating new potential matches to extend and refine an initial viewpoint estimate. This evaluation allows the model-based verification process to proceed without the expense of backtracking or search. It will be shown that the effective application of the viewpoint consistency constraint, in conjunction with bottom-up image description based upon principles of perceptual organization, can lead to robust three-dimensional object recognition from single gray-scale images.

On a superlinear elliptic equation

Abstract: In this note we establish multiple solutions for a semilinear elliptic equation with superlinear nonlinearility without assuming any symmetry.

Fourier Analysis of Sinusoidally Driven Thalamocortical Relay Neurons and a Minimal Integrate-and-Fire-or-Burst Model

Abstract: We performed intracellular recordings of relay neurons from the lateral geniculate nucleus of a cat thalamic slice preparation. We measured responses during both tonic and burst firing modes to sin...