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- Brian R Hunt
- 2006

Data assimilation is an iterative approach to the problem of estimating the state of a dynam-ical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the problem from scratch each time new observations become available, one uses the model to " forecast " the current state,… (More)

- Edward Ott, Brian R Hunt, Istvan Szunyogh, Aleksey V Zimin, Eric J Kostelich, Matteo Corazza +3 others
- 2003

In this paper, we introduce a new, local formulation of the ensemble Kalman Filter approach for atmospheric data assimilation. Our scheme is based on the hypothesis that, when the Earth's surface is divided up into local regions of moderate size, vectors of the forecast uncertainties in such regions tend to lie in a subspace of much lower dimension than… (More)

- Brian R Hunt, Vadim Yu Kaloshin
- 1999

We consider the image of a fractal set X in a Banach space under typical linear and nonlinear projections π into R N. We prove that when N exceeds twice the box-counting dimension of X, then almost every (in the sense of prevalence) such π is one-to-one on X, and we give an explicit bound on the Hölder exponent of the inverse of the restriction of π to X.… (More)

We study the transition from incoherence to coherence in large networks of coupled phase oscillators. We present various approximations that describe the behavior of an appropriately defined order parameter past the transition and generalize recent results for the critical coupling strength. We find that, under appropriate conditions, the coupling strength… (More)

A statistic, the BV (bred vector) dimension, is introduced to measure the effective local finite-time dimensionality of a spatiotemporally chaotic system. It is shown that the Earth's atmosphere often has low BV dimension, and the implications for improving weather forecasting are discussed.

The largest eigenvalue of the adjacency matrix of networks is a key quantity determining several important dynamical processes on complex networks. Based on this fact, we present a quantitative, objective characterization of the dynamical importance of network nodes and links in terms of their effect on the largest eigenvalue. We show how our… (More)

Regions in the parameter space of chaotic systems that correspond to stable behavior are often referred to as windows. In this Letter, we elucidate the occurrence of such regions in higher dimensional chaotic systems. We describe the fundamental structure of these windows, and also indicate under what circumstances one can expect to find them. These results… (More)

- M Corazza, E Kalnay, D J Patil, S.-C Yang, R Morss, M Cai +3 others
- 2002

Use of the breeding technique to estimate the structure of the analysis " errors of the day " Abstract. A 3D-variational data assimilation scheme for a quasi-geostrophic channel model (Morss, 1998) is used to study the structure of the background error and its relationship to the corresponding bred vectors. The " true " evolution of the model atmosphere is… (More)

- Brian R Hunt, Vadim Yu Kaloshin
- 1997

We introduce a new potential-theoretic definition of the dimension spectrum D q of a probability measure for q > 1 and explain its relation to prior definitions. We apply this definition to prove that if 1 < q 2 and µ is a Borel probability measure with compact support in R n , then under almost every linear transformation from R n to R m , the q-dimension… (More)

The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a given population are heterogeneous in that their natural frequencies are drawn from a given distribution, and each… (More)