Abstract
We present a new type system combining refinement types and the expressiveness of intersection type discipline. The use of such features makes it possible to derive more precise types than in the original refinement system. We have been able to prove several interesting properties for our system (including subject reduction) and developed an inference algorithm, which we proved to be sound.

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Spatial division multiplexing (SDM) is seen as an effective technique to overcome the present limits of fiber capacity and satisfy future bandwidth requirements, by substantially increasing optical transport capacities [1-5]. Similarly to single-mode fiber based modern telecommunication systems, the nonlinear penalties will eventually become the ultimate limiting factor in SDM systems, arising from crosstalk effects in multimode core or few mode fibers, which generate intramodal and intermodal nonlinearities. Here we explore the concept of conjugated twin waves in few mode fibers based SDM optical systems, as a means to overcome these nonlinear impairments and assess the performance of SDM systems for different PCTW configurations and coupling regimes. Our numerical simulation results show that this technique is an effective means to overcome the nonlinear impairments arising in mode division multiplexed systems, improving performance by up to 10 dB, in the strong coupling regime.

Abstract
In this paper we consider the problem of minimizing the waste of textile material in a Portuguese home textile manufacturing company. The company has a vertical structure covering the different production stages of the home textile, from weaving until the finished products. Production planning comprises different decisions: the definition of the widths and lengths of the fabric rolls to be produced, the number of fabric rolls to be used from stock or purchased and the definition of the cutting patterns to be applied to each width of the fabric roll, so that the waste is minimized. We propose a MIP model, solved by a column generation method, to tackle the problem.