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

Spectrum of stochastic evolution operators: Local matrix representation approach

A matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulated in terms of local matrix representations of the evolution operator centered on classical periodic orbits. The evaluation of perturbative corrections is easier to implement in this framework than in the standard Feynman diagram perturbation theory. The result are perturbative corrections to a stochastic analog of the Gutzwiller semiclassical spectral determinant computed to several orders beyond what has so far been attainable in stochastic and quantum-mechanical applications.Comment: 7 pages, 2 figures, Third approach to a problem we considered in chao-dyn/9807034 and chao-dyn/981100

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

An Evolving Understanding of Sense of Place in Social-Ecological Systems Research and the Barriers and Enablers to its Measurement

Social-ecological systems (SES) are changing more in the Anthropocene than ever before. With this also comes a change in Sense of Place (SoP), that is, the emotional bond that a person (or group of people) has with a place. This impacts how individuals and groups interact with a place (i.e., their behaviours) and respond to disturbance or change (i.e., their adaptive capacity). To understand how SoP is changing across space and time and to be able to compare this across social-ecological contexts, we must first take stock of how SoP is conceptualised so as to understand how to capture and measure the phenomena in a meaningful way (e.g., to inform policy). Based on in-depth qualitative interviews with leading SoP researchers (n = 17 from 8 countries) this paper aims to identify: (1) the current breadth of theoretical conceptualisations for SoP; (2) the methodologies that have been used to measure SoP in different contexts and settings; and (3) the barriers and (4) enablers to the use of different methodologies. Results show that there has been a change in how SoP has been conceptualised over time, whereby it was traditionally considered as something singular and limited, towards something much more dynamic. Results also show that diverse methods (both quantitative and qualitative) have been used to measure SoP, but the choice of method is often a result of resource constraints that limit research design. These findings suggest that broader collaboration among stakeholders and increased interdisciplinarity would undoubtedly lead to improved outcomes in our understanding of SoP, specifically how it is changing in response to anthropogenic pressures, and how the results can be integrated into policy and practice to support environment conservation and management. It is hoped these findings can help establish a community of practice around how we conceptualise SoP, and hence understand it, to create space for methodological integration and shared learnings as a field

Hopf's last hope: spatiotemporal chaos in terms of unstable recurrent patterns

Spatiotemporally chaotic dynamics of a Kuramoto-Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as accurate guide to the high-dimensional dynamics, and the periodic orbit theory yields several global averages characterizing the chaotic dynamics.Comment: Latex, ioplppt.sty and iopl10.sty, 18 pages, 11 PS-figures, compressed and encoded with uufiles, 170 k

An Introduction to Social Networks for Engaging the Community in Climate Policy

A review of the potential role and importance that social networks can play in engaging the community in climate policy and initiatives. View/download https://www.uts.edu.au/sites/default/files/Cvitanovicetal2014socialnetworksclimatepolicy.pd

An analytic approximation to the Diffusion Coefficient for the periodic Lorentz Gas

An approximate stochastic model for the topological dynamics of the periodic triangular Lorentz gas is constructed. The model, together with an extremum principle, is used to find a closed form approximation to the diffusion coefficient as a function of the lattice spacing. This approximation is superior to the popular Machta and Zwanzig result and agrees well with a range of numerical estimates.Comment: 13 pages, 4 figure

Five organizational features that enable successful interdisciplinary marine research

To generate innovative solutions for marine sustainability challenges, scientists, policymakers, and funders are increasingly calling for interdisciplinary research that transcends disciplinary boundaries. However, challenges associated with doing interdisciplinary research persist and undermine progress toward tackling the complex challenges faced by marine social-ecological systems. One barrier for engaging in effective interdisciplinary research is a lack of understanding about the institutional capacities that support interdisciplinary knowledge production. Based on in-depth qualitative interviews with members of the Centre for Marine Socioecology in Australia, we identify five principles that underpin effective interdisciplinary research organizations. The principles are: (1) support female leadership; (2) forge partnerships outside of academia; (3) develop impact-based performance metrics; (4) focus on long-term funding; and (5) cultivate a visible brand. Going forward, these principles could be used to inform organizational design that transforms institutional barriers into enablers of innovative interdisciplinary research for more sustainable, desirable, and equitable futures

Social network analysis: a primer on engaging communities on climate adaptation in New South Wales, Australia

A network is a group or system of interconnected people or things. Social networks connect people. Those connections provide advantages to members of the network through access to private information, diverse skills and power, which makes the understanding of networks important for the formulation and communication of policy. The Adaptive Communities Node used a network analysis methodology to understand the formal and informal knowledge channels that communicate climate change adaptation policy throughout regional communities (Harman et al, 2016; Harman et al 2015a; Harman et al 2015b). The results of case studies in these communities (centred on Shoalhaven, Bega and Orange) have been published through the UTS:ISF NSW Adaptation Research Hub (https://www.uts.edu.au/research-and-teaching/our-research/institute-sustainable-futures/our-research/climate-change/nsw). This primer serves as a companion document to those reports