University of California, Santa Barbara

About: University of California, Santa Barbara is a education organization based out in Santa Barbara, California, United States. It is known for research contribution in the topics: Population & Laser. The organization has 30281 authors who have published 80852 publications receiving 4626827 citations. The organization is also known as: UC Santa Barbara & UCSB.

Spectral Properties of Dynamical Systems, Model Reduction and Decompositions

Abstract: In this paper we discuss two issues related to model reduction of deterministic or stochastic processes. The first is the relationship of the spectral properties of the dynamics on the attractor of the original, high-dimensional dynamical system with the properties and possibilities for model reduction. We review some elements of the spectral theory of dynamical systems. We apply this theory to obtain a decomposition of the process that utilizes spectral properties of the linear Koopman operator associated with the asymptotic dynamics on the attractor. This allows us to extract the almost periodic part of the evolving process. The remainder of the process has continuous spectrum. The second topic we discuss is that of model validation, where the original, possibly high-dimensional dynamics and the dynamics of the reduced model – that can be deterministic or stochastic – are compared in some norm. Using the “statistical Takens theorem” proven in (Mezic, I. and Banaszuk, A. Physica D, 2004) we argue that comparison of average energy contained in the finite-dimensional projection is one in the hierarchy of functionals of the field that need to be checked in order to assess the accuracy of the projection.

Policy: Classify plastic waste as hazardous

Abstract: Policies for managing plastic debris are outdated and threaten the health of people and wildlife, say Chelsea M. Rochman, Mark Anthony Browne and colleagues.

Pollen limitation of plant reproduction: Ecological and evolutionary causes and consequences

Abstract: Determining whether seed production is pollen limited has been an area of intensive empirical study over the last two decades. Yet current evidence does not allow satisfactory assessment of the causes or consequences of pollen limitation. Here, we critically evaluate existing theory and issues concerning pollen limitation. Our main conclusion is that a change in approach is needed to determine whether pollen limitation reflects random fluctuations around a pollen–resource equilibrium, an adaptation to stochastic pollination environments, or a chronic syndrome caused by an environmental perturbation. We formalize and extend D. Haig and M. Westoby's conceptual model, and illustrate its use in guiding research on the evolutionary consequences of pollen limitation, i.e., whether plants evolve or have evolved to ameliorate pollen limitation. This synthesis also reveals that we are only beginning to understand when and how pollen limitation at the plant level translates into effects on plant population dynamics...