Pseudo generators of spatial transfer operators

Metastable behavior in dynamical systems may be a significant challenge for a simulation based analysis. In recent years, transfer operator based approaches to problems exhibiting metastability have matured. In order to make these approaches computationally feasible for larger systems, various reduction techniques have been proposed: For example, Sch\"utte introduced a spatial transfer operator which acts on densities on configuration space, while Weber proposed to avoid trajectory simulation (like Froyland et al.) by considering a discrete generator. In this manuscript, we show that even though the family of spatial transfer operators is not a semigroup, it possesses a well defined generating structure. What is more, the pseudo generators up to order 4 in the Taylor expansion of this family have particularly simple, explicit expressions involving no momentum averaging. This makes collocation methods particularly easy to implement and computationally efficient, which in turn may open the door for further efficiency improvements in, e.g., the computational treatment of conformation dynamics. We experimentally verify the predicted properties of these pseudo generators by means of two academic examples

Universal recovery maps and approximate sufficiency of quantum relative entropy

The data processing inequality states that the quantum relative entropy between two states $\rho$ and $\sigma$ can never increase by applying the same quantum channel $\mathcal{N}$ to both states. This inequality can be strengthened with a remainder term in the form of a distance between $\rho$ and the closest recovered state $(\mathcal{R} \circ \mathcal{N})(\rho)$, where $\mathcal{R}$ is a recovery map with the property that $\sigma = (\mathcal{R} \circ \mathcal{N})(\sigma)$. We show the existence of an explicit recovery map that is universal in the sense that it depends only on $\sigma$ and the quantum channel $\mathcal{N}$ to be reversed. This result gives an alternate, information-theoretic characterization of the conditions for approximate quantum error correction.Comment: v3: 24 pages, 1 figure, final version published in Annales Henri Poincar\'

Lisières, nouvel élément de compensation écologique

Avec l’ordonnance sur la qualité écologique, la mise en réseau d’écosystèmes proches de la nature est devenue une tâche prioritaire de la compensation écologique. Les lisières riches en espèces sont des éléments de connexion tout à fait appropriés. Les résultats de nos travaux de recherche ont montré que les lisières pouvaient contribuer à renaturer et à diversifier le paysage cultivé. Elles ne produisent que peu de mauvaises herbes (salissement) et n’accroissent pas l’activité des parasites dans les cultures limitrophes davantage que d’autres bordures de champs. En outre, les lisières riches en espèces sont appréciées des promeneurs et des agriculteurs

Prolonged self-paced exercise in the heat - environmental factors affecting performance

In this review we examine how self-paced performance is affected by environmental heat stress factors during cycling time trial performance as well as considering the effects of exercise mode and heat acclimatization. Mean power output during prolonged cycling time trials in the heat (≥30°C) was on average reduced by 15% in the 14 studies that fulfilled the inclusion criteria. Ambient temperature per se was a poor predictor of the integrated environmental heat stress and 2 of the prevailing heat stress indices (WBGT and UTCI) failed to predict the environmental influence on performance. The weighing of wind speed appears to be too low for predicting the effect for cycling in trained acclimatized subjects, where performance may be maintained in outdoor time trials at ambient temperatures as high as 36°C (36°C UTCI; 28°C WBGT). Power output during indoor trials may also be maintained with temperatures up to at least 27°C when humidity is modest and wind speed matches the movement speed generated during outdoor cycling, whereas marked reductions are observed when air movement is minimal. For running, representing an exercise mode with lower movement speed and higher heat production for a given metabolic rate, it appears that endurance is affected even at much lower ambient temperatures. On this basis we conclude that environmental heat stress impacts self-paced endurance performance. However, the effect is markedly modified by acclimatization status and exercise mode, as the wind generated by the exercise (movement speed) or the environment (natural or fan air movement) exerts a strong influence

Redefining ecological engineering in the context of circular economy and sustainable development

In the past decades, the search for a more sustainable way of global development has increased in importance in international politics and economy. A driving force is the continuing degradation of the environment in many areas of the world, often caused or accelerated by population growth and climate change. Sustainable development is seen as key approach to mitigate these processes. It has been defined as “development that meets the needs of the present without compromising the ability of future generations to meet their own needs.” But how can this ambitious goal be achieved in the light of numerous global challenges? Engineering is a very influential human practice and must be addressed in this context. Engineers are crucially involved in design and construction of our built environment and thus in shaping almost its entire development. However, when designing a solution for a given problem, effects caused outside of the system borders are often not considered. If this is combined with a narrowly confined linear problem-solving approach, it is inherently prone to create new environmental challenges. We postulate that the development of a new design paradigm for engineering must be part of the progress towards sustainable development. We think that this new paradigm needs to integrate a sound understanding of ecological principles, processes, and interdependencies as well as thorough system thinking. We call this ecology-inspired approach to engineering “ecological engineering” and redefine it as follows: Ecological Engineering integrates ecological principles, processes, and organisms with existing engineering practice to a holistic approach for problem-solving. In this paper, we explore the historical development of earlier definitions of Ecological Engineering in the light of their underlying value systems. Based on this analysis, we propose a new conceptual approach for Ecological Engineering and define seven principles that point the way towards a future label that can be conferred to Good Ecological Engineering Practice

Nutrient management in aquaponics : comparison of three approaches for cultivating lettuce, mint and mushroom herb

Nutrients that are contained in aquaculture effluent may not supply sufficient levels of nutrients for proper plant development and growth in hydroponics; therefore, they need to be supplemented. To determine the required level of supplementation, three identical aquaponic systems (A, B, and C) and one hydroponic system (D) were stocked with lettuce, mint, and mushroom herbs. The aquaponic systems were stocked with Nile tilapia. System A only received nutrients derived from fish feed; system B received nutrients from fish feed as well as weekly supplements of micronutrients and Fe; system C received the same nutrients as B, with weekly supplements of the macronutrients, P and K; in system D, a hydroponic inorganic solution containing N, Ca, and the same nutrients as system C was added weekly. Lettuce achieved the highest yields in system C, mint in system B, and mushroom herb in systems A and B. The present study demonstrated that the nutritional requirements of the mint and mushroom herb make them suitable for aquaponic farming because they require low levels of supplement addition, and hence little management effort, resulting in minimal cost increases. While the addition of supplements accelerated the lettuce growth (Systems B, C), and even surpassed the growth in hydroponic (System C vs. D), the nutritional quality (polyphenols, nitrate content) was better without supplementation