Self-dual continuous processes

The important application of semi-static hedging in financial markets naturally leads to the notion of conditionally quasi self-dual processes which is, for continuous semimartingales, related to conditional symmetry properties of both their ordinary as well as their stochastic logarithms. We provide a structure result for continuous conditionally quasi self-dual processes. Our main result is to give a characterization of continuous Ocone martingales via a strong version of self-duality.

A continuous-time MILP model for short-term scheduling of make-and-pack production processes

In process industries, make-and-pack production is used to produce food and beverages, chemicals, and metal products, among others. This type of production process allows the fabrication of a wide range of products in relatively small amounts using the same equipment. In this article, we consider a real-world production process (cf. Honkomp et al. 2000. The curse of reality – why process scheduling optimization problems are diffcult in practice. Computers & Chemical Engineering, 24, 323–328.) comprising sequence-dependent changeover times, multipurpose storage units with limited capacities, quarantine times, batch splitting, partial equipment connectivity, and transfer times. The planning problem consists of computing a production schedule such that a given demand of packed products is fulfilled, all technological constraints are satisfied, and the production makespan is minimised. None of the models in the literature covers all of the technological constraints that occur in such make-and-pack production processes. To close this gap, we develop an efficient mixed-integer linear programming model that is based on a continuous time domain and general-precedence variables. We propose novel types of symmetry-breaking constraints and a preprocessing procedure to improve the model performance. In an experimental analysis, we show that small- and moderate-sized instances can be solved to optimality within short CPU times.

Continuous eclogite melting and variable refertilisation in upwelling heterogeneous mantle

Large-scale tectonic processes introduce a range of crustal lithologies into the Earth's mantle. These lithologies have been implicated as sources of compositional heterogeneity in mantle-derived magmas. The model being explored here assumes the presence of widely dispersed fragments of residual eclogite (derived from recycled oceanic crust), stretched and stirred by convection in the mantle. Here we show with an experimental study that these residual eclogites continuously melt during upwelling of such heterogeneous mantle and we characterize the melting reactions and compositional changes in the residue minerals. The chemical exchange between these partial melts and more refractory peridotite leads to a variably metasomatised mantle. Re-melting of these metasomatised peridotite lithologies at given pressures and temperatures results in diverse melt compositions, which may contribute to the observed heterogeneity of oceanic basalt suites. We also show that heterogeneous upwelling mantle is subject to diverse local freezing, hybridization and carbonate-carbon-silicate redox reactions along a mantle adiabat.

Early-Holocene afforestation processes in the lower subalpine belt of the Central Swiss Alps as inferred from macrofossil and pollen records

To reconstruct the vegetation history of the Upper Engadine, continuous sediment cores covering the past 11 800 years from Lej da Champfer and Lej da San Murezzan (Upper Engadine Valley, c. 1800 m a.s.l., southeastern Switzerland) have been analysed for pollen and plant macrofossils. The chronologies of the cores are based on 16 and 22 radiocarbon dates, respectively. The palaeobotanical records of both lakes are in agreement for the Holocene, but remarkable differences exist between the sites during the period 11 100 to 10 500 cal. BP, when Lej da Champfer was affected by re-sedimentation processes. Macrofossil data suggest that Holocene afforestation began at around 11400 cal. BP. A climatic deterioration, the Preboreal Oscillation, stopped and subsequently delayed the establishment of trees until c. 11000 cal. BP, when first Betula, then Pinus sylvestrislmugo, then Larix 300 years later, and finally Pinus cembra expanded within the lake catchment. Treeline was at c. 1500 m during the Younger Dryas (12 542- 11 550 cal. BP) in the Central Alps. Our results, along with other macrofossil studies from the Alps, suggest a nearly simultaneous afforestation (e.g., by Pinus sylvestris in the lower subalpine belt) between 1500 and 2340 m a.s.l. at around 11 400 to 11 300 cal. BP. We suggest that forest-limit species (e.g., Pinus cembra, Larix decidua) could expand faster at today's treeline (c. 2350 m a.s.l.), than 550 m lower. Earlier expansions at higher altitudes probably resulted from reduced competition with low-altitude trees (e.g. Pinus sylvestris) and herbaceous species. Comparison with other proxies such as oxygen isotopes, residual A14C, glacier fluctuations, and alpine climatic cooling phases suggests climatic sensitivity of vegetation during the early Holocene.