On the path structure of a semimartingale arising from monotone probability theory

Let X be the unique normal martingale such that X_0 = 0 and d[X]_t = (1 - t - X_{t-}) dX_t + dt and let Y_t := X_t + t for all t >= 0; the semimartingale Y arises in quantum probability, where it is the monotone-independent analogue of the Poisson process. The trajectories of Y are examined and various probabilistic properties are derived; in particular, the level set {t >= 0 : Y_t = 1} is shown to be non-empty, compact, perfect and of zero Lebesgue measure. The local times of Y are found to be trivial except for that at level 1; consequently, the jumps of Y are not locally summable

Quantum Feynman-Kac perturbations

We develop fully noncommutative Feynman-Kac formulae by employing quantum stochastic processes. To this end we establish some theory for perturbing quantum stochastic flows on von Neumann algebras by multiplier cocycles. Multiplier cocycles are constructed via quantum stochastic differential equations whose coefficients are driven by the flow. The resulting class of cocycles is characterised under alternative assumptions of separability or Markov regularity. Our results generalise those obtained using classical Brownian motion on the one hand, and results for unitarily implemented flows on the other.Comment: 27 pages. Minor corrections to version 2. To appear in the Journal of the London Mathematical Societ

The convergence of unitary quantum random walks

We give a simple and direct treatment of the convergence of quantum random walks to quantum stochastic operator cocycles, using the semigroup method. The pointwise product of two such quantum random walks is shown to converge to the quantum stochastic Trotter product of the respective limit cocycles. Since such Trotter products themselves reduce to pointwise products when the cocycles inhabit commuting subspaces of the system algebra, this yields an elementary approach to the quantum random walk approximation of the 'tensorisation' of cocycles with common noise dimension space. The repeated quantum interactions model is shown to fit nicely into the convergence scheme described

The cocycle identity holds under stopping

In recent work of the authors, it was shown how to use any finite quantum stop time to stop the CCR flow and its strongly continuous isometric cocycles (Q. J. Math. 65:1145–1164, 2014). The stopped cocycle was shown to satisfy a stopped form of the cocycle identity, valid for deterministic increments of the time used for stopping. Here, a generalization of this identity is obtained, where both cocycle parameters are replaced with finite quantum stop times

Harnessing the diversity of small-scale actors is key to the future of aquatic food systems

Small-scale fisheries and aquaculture (SSFA) provide livelihoods for over 100 million people and sustenance for ~1 billion people, particularly in the Global South. Aquatic foods are distributed through diverse supply chains, with the potential to be highly adaptable to stresses and shocks, but face a growing range of threats and adaptive challenges. Contemporary governance assumes homogeneity in SSFA despite the diverse nature of this sector. Here we use SSFA actor profiles to capture the key dimensions and dynamism of SSFA diversity, reviewing contemporary threats and exploring opportunities for the SSFA sector. The heuristic framework can inform adaptive governance actions supporting the diversity and vital roles of SSFA in food systems, and in the health and livelihoods of nutritionally vulnerable people—supporting their viability through appropriate policies whilst fostering equitable and sustainable food systems.Additional co-authors: Caroline E Ferguson, Nicole Franz, Christopher D. Golden, Benjamin S. Halpern, Lucie Hazen, Christina Hicks, Derek Johnson, Sangeeta Mangubhai, Rosamond L. Naylor, Melba Reantaso, U. Rashid Sumaila, Shakuntala H. Thilsted, Michelle Tigchelaar, Colette C. C. Wabnitz & Wenbo Zhan

Seafood in Food Security: a call for bridging the terrestrial-aquatic divide

The contribution of seafood to global food security is being increasingly highlighted in policy. However, the extent to which such claims are supported in the current food security literature is unclear. This review assesses the extent to which seafood is represented in the recent food security literature, both individually and from a food systems perspective, in combination with terrestrially-based production systems. The results demonstrate that seafood remains under-researched compared to the role of terrestrial animal and plant production in food security. Furthermore, seafood and terrestrial production remain siloed, with very few papers addressing the combined contribution or relations between terrestrial and aquatic systems. We conclude that far more attention is needed to the specific and relative role of seafood in global food security and call for the integration of seafood in a wider interdisciplinary approach to global food system research

Seafood in Food Security: A Call for Bridging the Terrestrial-Aquatic Divide

The contribution of seafood to global food security is being increasingly highlighted in policy. However, the extent to which such claims are supported in the current food security literature is unclear. This review assesses the extent to which seafood is represented in the recent food security literature, both individually and from a food systems perspective, in combination with terrestrially-based production systems. The results demonstrate that seafood remains under-researched compared to the role of terrestrial animal and plant production in food security. Furthermore, seafood and terrestrial production remain siloed, with very few papers addressing the combined contribution or relations between terrestrial and aquatic systems. We conclude that far more attention is needed to the specific and relative role of seafood in global food security and call for the integration of seafood in a wider interdisciplinary approach to global food system research

Interactive Marine Spatial Planning: Siting Tidal Energy Arrays around the Mull of Kintyre

The rapid development of the offshore renewable energy sector has led to an increased requirement for Marine Spatial Planning (MSP) and, increasingly, this is carried out in the context of the ‘ecosystem approach’ (EA) to management. We demonstrate a novel method to facilitate implementation of the EA. Using a real-time interactive mapping device (touch-table) and stakeholder workshops we gathered data and facilitated negotiation of spatial trade-offs at a potential site for tidal renewable energy off the Mull of Kintyre (Scotland). Conflicts between the interests of tidal energy developers and commercial and recreational users of the area were identified, and use preferences and concerns of stakeholders were highlighted. Social, cultural and spatial issues associated with conversion of common pool to private resource were also revealed. The method identified important gaps in existing spatial data and helped to fill these through interactive user inputs. The workshops developed a degree of consensus between conflicting users on the best areas for potential development suggesting that this approach should be adopted during MSP