Reconstruction from Periodic Nonlinearities, With Applications to HDR Imaging

We consider the problem of reconstructing signals and images from periodic nonlinearities. For such problems, we design a measurement scheme that supports efficient reconstruction; moreover, our method can be adapted to extend to compressive sensing-based signal and image acquisition systems. Our techniques can be potentially useful for reducing the measurement complexity of high dynamic range (HDR) imaging systems, with little loss in reconstruction quality. Several numerical experiments on real data demonstrate the effectiveness of our approach

From Fault Tree to Credit Risk Assessment: A Case Study

Reliability has been largely applied to industrial systems in order to study the various possibilities of systems’ failure. The goal is to establish the chain of events leading to any system’s failure, namely the top event. Looking for the minimal paths leading to any system’s fault allows for a better control of systems’ safety. To this end, reliability is composed of a static approach (see Ngom et al. [1999] for example) as well as a dynamic approach (see Reory & Andrews [2003] for example). In this paper, we extend the framework stated by Gatfaoui (2003) allowing for the application of fault tree theory to credit risk assessment. The author explains that fault tree is one alternative approach of reliability, which matches default risk analysis in a simple framework. Our extension includes other distributions of probability to model the lifetimes of French firms while studying the related empirical default probabilities. We use mainly, but not exclusively, continuous distributions for which the exponential law used by Gatfaoui (2003) constitutes a particular case. Our results exhibit both the exponential nature of French .rms. lifetimes as well as strong convex and fast decreasing time varying failure rates. Such a feature has some non- negligible impact insofar as it characterizes corresponding credit spreads’ Term structure.credit risk, default probability, failure rate, fault tree, reliability, survival probability

State Estimation in the Cerebellum

An exciting hypothesis about the cerebellum is that its role is one of state estimation—a process that combines afferent copies of motor commands with afferent sensory signals to produce a representation of the current status of the peripheral motor system. Sensory inputs alone cannot provide a perfect state signal because of inevitable delays in their afferent pathways. We have recently reported the effects of transcranial magnetic stimulation (TMS) over the ipsilateral cerebellum as healthy subjects made rapid reaching movements towards visually defined targets (Miall et al. in PLoS Biology 5:2733–2744, 2007). Errors in the initial direction and in the final finger position of this reachto-target movement were consistent with the reaching movements being planned and initiated from an estimated hand position that was about 138 ms out of date. This interval is consistent with estimates of the delays in sensory motor pathways that would inform the central nervous system of the peripheral status. We now report new data using the same paradigm, testing the effects of varying the TMS stimulus train from one, two, or three pulses. We show that the errors in movement are relatively insensitive to the TMS pulse-train duration. The estimated time interval by which the hand position is mislocalized varied by only 12 ms as the TMS train duration increased by 100 ms. Thus, this interval is likely to reflect physiological processes within the cerebellum rather than the TMSstimulus duration. This new evidence supports our earlier claim that the cerebellum is responsible for predictively updating a central state estimate over an interval of about 120–140 ms. Dysfunction of the cerebellum, whether through disease or experimental procedures, leads to motor errors consistent with a loss of knowledge of the true state of the motor system