Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources

In this paper we study a continuous time, optimal stochastic investment problem under limited resources in a market with N firms. The investment processes are subject to a time-dependent stochastic constraint. Rather than using a dynamic programming approach, we exploit the concavity of the profit functional to derive some necessary and sufficient first order conditions for the corresponding Social Planner optimal policy. Our conditions are a stochastic infinite-dimensional generalization of the Kuhn-Tucker Theorem. The Lagrange multiplier takes the form of a nonnegative optional random measure on [0,T] which is flat off the set of times for which the constraint is binding, i.e. when all the fuel is spent. As a subproduct we obtain an enlightening interpretation of the first order conditions for a single firm in Bank (2005). In the infinite-horizon case, with operating profit functions of Cobb-Douglas type, our method allows the explicit calculation of the optimal policy in terms of the `base capacity' process, i.e. the unique solution of the Bank and El Karoui representation problem (2004).Comment: 25 page

Salvage of Exposed Breast Implant Using Capsular Flaps

Objective: Extrusion represents potential complications associated with the use of breast implants. Attempts to salvage the exposed implants are rarely successful when poor tissue coverage or radiotherpy is present and therefore removal of implant and wound healing are mandatory. In these refractory complicated cases the use of capsular flaps can represent a useful tool to save the implant and achieve definitive healing. Methods: Capsular flaps have been performed on 6 patients with implant extrusion and 11 patients with breast contour deformities over the last 6 years. The authors describe an innovative technique using capsular flaps which are harvested from thicker viable tissues and inset in multiple layers into the fistula tract to reinforce the breast envelope and prevent recurrence of implant extrusion. Results: Complete healing and implant salvage were achieved in all patients treated. No major complications occurred and only minor contour deformities, that regressed spontaneously after surgery, were observed for 2 weeks. Conclusions: Although capsular flaps have been previously described to correct breast shape deformities, no previous report has yet suggested its utility in breast implant salvage in case of extrusion. The authors advocate the use of capsular flap to save the exposed breast implant especially when poor tissue coverage is present and other surgical options to save the implant have already failed

Plans for a 10-m Submillimeter-wave Telescope at the South Pole

A 10 meter diameter submillimeter-wave telescope has been proposed for the NSF Amundsen-Scott South Pole Station. Current evidence indicates that the South Pole is the best submillimeter-wave telescope site among all existing or proposed ground-based observatories. Proposed scientific programs place stringent requirements on the optical quality of the telescope design. In particular, reduction of the thermal background and offsets requires an off-axis, unblocked aperture, and the large field of view needed for survey observations requires shaped optics. This mix of design elements is well-suited for large scale (square degree) mapping of line and continuum radiation from submillimeter-wave sources at moderate spatial resolutions (4 to 60 arcsecond beam size) and high sensitivity (milliJansky flux density levels). the telescope will make arcminute angular scale, high frequency Cosmic Microwave Background measurements from the best possible ground-based site, using an aperture which is larger than is currently possible on orbital or airborne platforms. Effective use of this telescope will require development of large (1000 element) arrays of submillimeter detectors which are background-limited when illuminated by antenna temperatures near 50 K.Comment: 12 pages, 3 figure

I.C.E.: a Transportable Atomic Inertial Sensor for Test in Microgravity

We present our the construction of an atom interferometer for inertial sensing in microgravity, as part of the I.C.E. (\textit{Interf\'{e}rom\'{e}trie Coh\'{e}rente pour l'Espace}) collaboration. On-board laser systems have been developed based on fibre-optic components, which are insensitive to mechanical vibrations and acoustic noise, have sub-MHz linewidth, and remain frequency stabilised for weeks at a time. A compact, transportable vacuum system has been built, and used for laser cooling and magneto-optical trapping. We will use a mixture of quantum degenerate gases, bosonic $^{87}$Rb and fermionic $^{40}$K, in order to find the optimal conditions for precision and sensitivity of inertial measurements. Microgravity will be realised in parabolic flights lasting up to 20s in an Airbus. We show that the factors limiting the sensitivity of a long-interrogation-time atomic inertial sensor are the phase noise in reference frequency generation for Raman-pulse atomic beam-splitters and acceleration fluctuations during free fall

Resource-Bound Quantification for Graph Transformation

Graph transformation has been used to model concurrent systems in software engineering, as well as in biochemistry and life sciences. The application of a transformation rule can be characterised algebraically as construction of a double-pushout (DPO) diagram in the category of graphs. We show how intuitionistic linear logic can be extended with resource-bound quantification, allowing for an implicit handling of the DPO conditions, and how resource logic can be used to reason about graph transformation systems