Research Publications (Mathematical and Statistical Sciences)

2016-01-01

Qihua Huang, Yu Jin, Mark A. Lewis

One key issue for theory in stream ecology is how much stream flow can be changed while still maintaining an intact stream ecology, instream flow needs (IFNs); the study of determining IFNs is challenging due to the complex and dynamic nature of the interaction between the stream environment and...

2005

Kouritzin, Michael, Sun, W.

Herein, we analyze an efficient branching particle method for asymptotic solutions to a class of continuous-discrete filtering problems. Suppose that t→Xt is a Markov process and we wish to calculate the measure-valued process t→μt(⋅)≐P{Xt∈⋅|σ{Ytk, tk≤t}}, where tk=kɛ and Ytk is a distorted,...

1992

Kouritzin, Michael, Heunis, A.J.

Let μ be a positive finite Borel measure on the real line R. For t ≥ 0 let et · E1 and E2 denote, respectively, the linear spans in L2(R, μ) of {eisx, s > t} and {eisx, s < 0}. Let θ: R → C such that ∥θ∥ = 1, denote by αt(θ, μ) the angle between θ · et · E1 and E2. The problems considered here...

2015-04-20

Kouritzin, Michael A.

A large class of discrete-time branching particle filters with Bayesian model selection ca-pabilities and effective resampling is introduced in algorithmic form, shown empirically to outperform the popular bootstrap algorithm and analyzed mathematically. The particles interact weakly in the...

2015-09-21

Kouritzin, Michael

2007-01-01

Nisbet, Roger, Anderson, Kurt E., McCauley, Edward, Lewis, Mark A.

Much ecological research involves identifying connections between abiotic forcing and population densities or distributions. We present theory that describes this relationship for populations in media with strong unidirectional flow (e.g., aquatic organisms in streams and rivers). Typically,...

2015-01-01

Ulrike E. Schla¨gel, Mark A. Lewis

Discrete-time random walks and their extensions are common tools for analyzing animal movement data. In these analyses, resolution of temporal discretization is a critical feature. Ideally, a model both mirrors the relevant temporal scale of the biological process of interest and matches the data...

2011-01-01

Lewis, Mark A., Derocher, Andrew E., Auger-Méthé, Marie, St. Clair, C. C.

2011-01-01

Jin, Yu, Lewis, Mark A.

The critical domain size problem determines the size of the region of habitat needed to ensure population persistence. In this paper we address the critical domain size problem for seasonally fluctuating stream environments and determine how large a reach of suitable stream habitat is needed to...

2014-01-01

Yu Jin, Frank M. Hilker, Peter M. Stefer, Mark A. Lewis

A key problem in environmental flow assessment is the explicit linking of the flow regime with ecological dynamics. We present a hybrid modeling approach to couple hydrodynamic and biological processes, focusing on the combined impact of spatial heterogeneity and temporal variability on...