Trace formulas for stochastic evolution operators: Smooth conjugation method

The trace formula for the evolution operator associated with nonlinear stochastic flows with weak additive noise is cast in the path integral formalism. We integrate over the neighborhood of a given saddlepoint exactly by means of a smooth conjugacy, a locally analytic nonlinear change of field variables. The perturbative corrections are transfered to the corresponding Jacobian, which we expand in terms of the conjugating function, rather than the action used in defining the path integral. The new perturbative expansion which follows by a recursive evaluation of derivatives appears more compact than the standard Feynman diagram perturbation theory. The result is a stochastic analog of the Gutzwiller trace formula with the ``hbar'' corrections computed an order higher than what has so far been attainable in stochastic and quantum-mechanical applications.Comment: 16 pages, 1 figure, New techniques and results for a problem we considered in chao-dyn/980703

Beyond the periodic orbit theory

The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. The associated Fredholm determinants are of particularly simple polynomial form. The theory developed suggests an alternative to the conventional periodic orbit theory approach to determining eigenspectra of transfer operators.Comment: 29 pages Latex2

High Macroalgal Cover and Low Coral Recruitment Undermines the Potential Resilience of the World's Southernmost Coral Reef Assemblages

Coral reefs are under increasing pressure from anthropogenic and climate-induced stressors. The ability of reefs to reassemble and regenerate after disturbances (i.e., resilience) is largely dependent on the capacity of herbivores to prevent macroalgal expansion, and the replenishment of coral populations through larval recruitment. Currently there is a paucity of this information for higher latitude, subtropical reefs. To assess the potential resilience of the benthic reef assemblages of Lord Howe Island (31°32′S, 159°04′E), the worlds' southernmost coral reef, we quantified the benthic composition, densities of juvenile corals (as a proxy for coral recruitment), and herbivorous fish communities. Despite some variation among habitats and sites, benthic communities were dominated by live scleractinian corals (mean cover 37.4%) and fleshy macroalgae (20.9%). Live coral cover was higher than in most other subtropical reefs and directly comparable to lower latitude tropical reefs. Juvenile coral densities (0.8 ind.m−2), however, were 5–200 times lower than those reported for tropical reefs. Overall, macroalgal cover was negatively related to the cover of live coral and the density of juvenile corals, but displayed no relationship with herbivorous fish biomass. The biomass of herbivorous fishes was relatively low (204 kg.ha−1), and in marked contrast to tropical reefs was dominated by macroalgal browsing species (84.1%) with relatively few grazing species. Despite their extremely low biomass, grazing fishes were positively related to both the density of juvenile corals and the cover of bare substrata, suggesting that they may enhance the recruitment of corals through the provision of suitable settlement sites. Although Lord Howe Islands' reefs are currently coral-dominated, the high macroalgal cover, coupled with limited coral recruitment and low coral growth rates suggest these reefs may be extremely susceptible to future disturbances

Participatory research in complex marine conservation settings: A review of recent trends and lessons for the future

The conservation of marine ecosystems and species is inherently complex, plagued by social, political, economic and ecological uncertainty. Navigating these challenges to sustain marine systems requires the understanding, consideration and uptake of multiple knowledge systems within decision-making processes. Participatory research approaches, such as knowledge co-production, are advocated given their potential to generate knowledge with those who are most affected by the issue at hand and, based on that knowledge, develop and implement meaningful conservation practices collaboratively. In doing so participatory research is positioned to make marine research more democratic and impactful, and as such, has been a field of growing research enquiry. The aim of this study, therefore, is to synthesise (via a systematic scoping review) the existing literature to generate guidance that can help researchers and practitioners plan and apply participatory research approaches in a complex marine context. Results from systematically identifying and analyzing 337 articles show that the implementation of participatory research approaches are most common in the global north. Participatory research approaches most frequently included representatives from government, industry and civil society (e.g. community groups), while indigenous groups and communities were rarely included. A diversity of participatory research approaches have been used in relation to marine conservation in different settings and at various stages of the participatory process, each with their own challenges and benefits, that can lead to either positive outcomes for actors (e.g. social learning) or negative outcomes (e.g. disempowerment). We draw on our findings to provide guidance for improving the implementation of participatory research approaches in marine conservation such as taking the time to understand context before commencing participatory research approaches, and ensuring transparency with all actors throughout the process. We highlight key implications for researcher and practitioners implementing participatory research approaches including the importance of a diversity of approaches and methods to ensure access, supporting two way communication, addressing power imbalances, and the need to recognise, report on and address pre-existing barriers. Many of these require greater investment in terms of money or personnel, and new funding models are needed with a focus on longevity and sustainability

Continued-fraction expansion of eigenvalues of generalized evolution operators in terms of periodic orbits

A new expansion scheme to evaluate the eigenvalues of the generalized evolution operator (Frobenius-Perron operator) $H_{q}$ relevant to the fluctuation spectrum and poles of the order-$q$ power spectrum is proposed. The ``partition function'' is computed in terms of unstable periodic orbits and then used in a finite pole approximation of the continued fraction expansion for the evolution operator. A solvable example is presented and the approximate and exact results are compared; good agreement is found.Comment: CYCLER Paper 93mar00

Weak noise approach to the logistic map

Using a nonperturbative weak noise approach we investigate the interference of noise and chaos in simple 1D maps. We replace the noise-driven 1D map by an area-preserving 2D map modelling the Poincare sections of a conserved dynamical system with unbounded energy manifolds. We analyze the properties of the 2D map and draw conclusions concerning the interference of noise on the nonlinear time evolution. We apply this technique to the standard period-doubling sequence in the logistic map. From the 2D area-preserving analogue we, in addition to the usual period-doubling sequence, obtain a series of period doubled cycles which are elliptic in nature. These cycles are spinning off the real axis at parameters values corresponding to the standard period doubling events.Comment: 22 pages in revtex and 8 figures in ep

Changes in mangrove cover and exposure to coastal hazards in Kenya

Mangroves are effective carbon sinks, support coastal fisheries and provide wood and non-wood resources to coastal communities. They are threatened by natural and hu-man-induced stresses including over-exploitation, conversion pressures, pollution and climate change. Understanding changes in this important ecosystem is essential to inform the sus-tainable management of mangroves and assess the implications related to the loss of ecosystem services. This study used global remote sensing mangrove forest data to quantify changes in mangrove cover in Kenya between 2010 and 2016 and applied the InVEST coastal vulnerability model to assess the implications concerning the provision of natural coastal protection services in Kenya. Results indicate that the annual rates of mangrove cover loss in Kenya were 0.15% between 2010 and 2016. Currently, 16% of the Kenyan coastline is at higher levels of exposure to coastal hazards but this could increase to 41% if coastal ecosystems (mangroves, corals and seagrasses) are lost. The study further identified that higher rates of mangrove loss are observed in areas at higher risk of exposure in the southern and northern counties of Kwale and Lamu, where monitoring and management efforts should be prioritised

Electron localization by a magnetic vortex

We study the problem of an electron in two dimensions in the presence of a magnetic vortex with a step-like profile. Dependending on the values of the effective mass and gyromagnetic factor of the electron, it may be trapped by the vortex. The bound state spectrum is obtained numerically, and some limiting cases are treated analytically.Comment: 8 pages, latex, 4 figure

Non-integrability of the mixmaster universe

We comment on an analysis by Contopoulos et al. which demonstrates that the governing six-dimensional Einstein equations for the mixmaster space-time metric pass the ARS or reduced Painlev\'{e} test. We note that this is the case irrespective of the value, $I$, of the generating Hamiltonian which is a constant of motion. For $I < 0$ we find numerous closed orbits with two unstable eigenvalues strongly indicating that there cannot exist two additional first integrals apart from the Hamiltonian and thus that the system, at least for this case, is very likely not integrable. In addition, we present numerical evidence that the average Lyapunov exponent nevertheless vanishes. The model is thus a very interesting example of a Hamiltonian dynamical system, which is likely non-integrable yet passes the reduced Painlev\'{e} test.Comment: 11 pages LaTeX in J.Phys.A style (ioplppt.sty) + 6 PostScript figures compressed and uuencoded with uufiles. Revised version to appear in J Phys.

Fractal Weyl laws for chaotic open systems

We present a result relating the density of quantum resonances for an open chaotic system to the fractal dimension of the associated classical repeller. The result is supported by numerical computation of the resonances of the system of n disks on a plane. The result generalizes the Weyl law for the density of states of a closed system to chaotic open systems.Comment: revtex4, 4 pages, 3 figure