Backward Stackelberg Differential Game with Constraints: a Mixed Terminal-Perturbation and Linear-Quadratic Approach

We discuss an open-loop backward Stackelberg differential game involving single leader and single follower. Unlike most Stackelberg game literature, the state to be controlled is characterized by a backward stochastic differential equation (BSDE) for which the terminal- instead initial-condition is specified as a priori; the decisions of leader consist of a static terminal-perturbation and a dynamic linear-quadratic control. In addition, the terminal control is subject to (convex-closed) pointwise and (affine) expectation constraints. Both constraints are arising from real applications such as mathematical finance. For information pattern: the leader announces both terminal and open-loop dynamic decisions at the initial time while takes account the best response of follower. Then, two interrelated optimization problems are sequentially solved by the follower (a backward linear-quadratic (BLQ) problem) and the leader (a mixed terminal-perturbation and backward-forward LQ (BFLQ) problem). Our open-loop Stackelberg equilibrium is represented by some coupled backward-forward stochastic differential equations (BFSDEs) with mixed initial-terminal conditions. Our BFSDEs also involve nonlinear projection operator (due to pointwise constraint) combining with a Karush-Kuhn-Tucker (KKT) system (due to expectation constraint) via Lagrange multiplier. The global solvability of such BFSDEs is also discussed in some nontrivial cases. Our results are applied to one financial example.Comment: 38 page

Spatially Continuous Distributed Fiber Optic Sensing using Optical Carrier Based Microwave Interferometry

This paper reports a spatially continuous distributed fiber optic sensing technique using optical carrier based microwave interferometry (OCMI), in which many optical interferometers with the same or different optical path differences are interrogated in the microwave domain and their locations can be unambiguously determined. The concept is demonstrated using cascaded weak optical reflectors along a single optical fiber, where any two arbitrary reflectors are paired to define a low-finesse Fabry-Perot interferometer. While spatially continuous (i.e., no dark zone), fully distributed strain measurement was used as an example to demonstrate the capability, the proposed concept may also be implemented on other types of waveguide or free-space interferometers and used for distributed measurement of various physical, chemical and biological quantities

Simultaneous Measurement of Temperature and Pressure with Cascaded Extrinsic Fabry-Perot Interferometer and Intrinsic Fabry-Perot Interferometer Sensors

This paper presents an approach for simultaneous measurement of temperature and pressure using miniaturized fiber inline sensors. The approach utilizes the cascaded optical fiber inline intrinsic Fabry-Perot interferometer and extrinsic Fabry-Perot interferometer as temperature and pressure sensing elements, respectively. A CO2 laser was used to create a loss between them to balance their reflection power levels. The multiplexed signals were demodulated using a Fast Fourier transform-based wavelength tracking method. Experimental results showed that the sensing system could measure temperature and pressure unambiguously in a pressure range of 0 to 6.895 x 105 Pa and a temperature range from 20°C to 700°C

Microwave Assisted Reconstruction of Optical Interferograms for Distributed Fiber Optic Sensing

This paper reports a distributed fiber optic sensing technique through microwave assisted separation and reconstruction of optical interferograms in spectrum domain. The approach involves sending a microwave-modulated optical signal through cascaded fiber optic interferometers. The microwave signal was used to resolve the position and reflectivity of each sensor along the optical fiber. By sweeping the optical wavelength and detecting the modulation signal, the optical spectrum of each sensor can be reconstructed. Three cascaded fiber optic extrinsic Fabry-Perot interferometric sensors were used to prove the concept. Their microwave-reconstructed interferogram matched well with those recorded individually using an optical spectrum analyzer. The application in distributed strain measurement has also been demonstrated

How to Face COVID-19 in Ophthalmology Practice

Background: The novel coronavirus pneumonia has attracted considerable attention from the international community. With the spread of outbreaks around the world, the WHO characterized COVID-19 as a pandemic. Methods: Relevant studies in PubMed were searched from January 1, 2020 to April 12, 2020, using the following search strategy: (“novel coronavirus pneumonia†OR “severe acute respiratory syndrome coronavirus 2†OR “coronavirus disease 2019†OR “COVID-19†OR “novel coronavirus pneumoniaâ€) AND (“ophthalmology†OR “ophthalmologist†OR “eye†OR “conjunctiva†OR “conjunctivitis†OR “corneal†OR “keratitisâ€). Results: SARS-CoV-2 can spread through aerosol and is detected in tears of patients with COVID-19 infection. Notably, some infected patients had conjunctivitis, and conjunctivitis was the first symptom in some patients later diagnosed to have COVID-19 infection. This would increase the risk for ophthalmologists through inpatient consultations or regular clinical practice. When dealing with seemingly regular ophthalmic patients, the vigilance of ophthalmologists and associated staff tends to be reduced. Conclusion: Ophthalmologists must continuously update their knowledge regarding COVID-19 and take effective measures to prevent COVID-19 transmission