Eliciting and estimating valid subjective probabilities: An experimental investigation of the Exchangeability Method.

Using a laboratory experiment, we investigate whether incentive compatibility affects subjective probabilities elicited via the exchangeability method (EM), an elicitation technique consisting of several chained questions. We hypothesize that subjects who are aware of the chaining strategically behave and provide invalid subjective probabilities, while subjects who are not aware of the chaining state their real beliefs and provide valid subjective probabilities. The validity of subjective probabilities is investigated using de Finetti's notion of coherence, under which probability estimates are valid if and only if they obey all axioms of probability theory.
Four experimental treatments are designed and implemented. Subjects are divided into two initial treatment groups: in the first, they are provided with real monetary incentives, and in the second, they are not. Each group is further sub-divided into two treatment groups, in the first, the chained structure of the experimental design is made clear to the subjects, while, in the second, the chained structure is hidden by randomizing the elicitation questions.
Our results suggest that subjects provided with monetary incentives and randomized questions provide valid subjective probabilities because they are not aware of the chaining which undermines the incentive compatibility of the exchangeability method.

Elastodynamic Modeling and Analysis for an Exechon Parallel Kinematic Machine

As a newly invented parallel kinematic machine (PKM), Exechon has attracted intensive attention from both academic and industrial fields due to its conceptual high performance. Nevertheless, the dynamic behaviors of Exechon PKM have not been thoroughly investigated because of its structural and kinematic complexities. To identify the dynamic characteristics of Exechon PKM, an elastodynamic model is proposed with the substructure synthesis technique in this paper. The Exechon PKM is divided into a moving platform subsystem, a fixed base subsystem and three limb subsystems according to its structural features. Differential equations of motion for the limb subsystem are derived through finite element (FE) formulations by modeling the complex limb structure as a spatial beam with corresponding geometric cross sections. Meanwhile, revolute, universal, and spherical joints are simplified into virtual lumped springs associated with equivalent stiffnesses and mass at their geometric centers. Differential equations of motion for the moving platform are derived with Newton's second law after treating the platform as a rigid body due to its comparatively high rigidity. After introducing the deformation compatibility conditions between the platform and the limbs, governing differential equations of motion for Exechon PKM are derived. The solution to characteristic equations leads to natural frequencies and corresponding modal shapes of the PKM at any typical configuration. In order to predict the dynamic behaviors in a quick manner, an algorithm is proposed to numerically compute the distributions of natural frequencies throughout the workspace. Simulation results reveal that the lower natural frequencies are strongly position-dependent and distributed axial-symmetrically due to the structure symmetry of the limbs. At the last stage, a parametric analysis is carried out to identify the effects of structural, dimensional, and stiffness parameters on the system's dynamic characteristics with the purpose of providing useful information for optimal design and performance improvement of the Exechon PKM. The elastodynamic modeling methodology and dynamic analysis procedure can be well extended to other overconstrained PKMs with minor modifications.

Communication Nonlinearities Techniques for Analysis of Passive Intermodulation

The X-parameter based nonlinear modelling tools have been adopted as the foundation for the advanced methodology
of experimental characterisation and design of passive nonlinear devices. Based upon the formalism of the Xparameters,
it provides a unified framework for co-design of antenna beamforming networks, filters, phase shifters and
other passive and active devices of RF front-end, taking into account the effect of their nonlinearities. The equivalent
circuits of the canonical elements are readily incorporated in the models, thus enabling evaluation of PIM effect on the
performance of individual devices and their assemblies. An important advantage of the presented methodology is its
compatibility with the industry-standard established commercial RF circuit simulator Agilent ADS.
The major challenge in practical implementation of the proposed approach is concerned with experimental retrieval of the X-parameters for canonical passive circuit elements. To our best knowledge commercial PIM testers and practical laboratory test instruments are inherently narrowband and do not allow for simultaneous vector measurements at the PIM and harmonic frequencies. Alternatively, existing nonlinear vector analysers (NVNA) support X-parameter measurements in a broad frequency bands with a range of stimuli, but their dynamic range is insufficient for the PIM characterisation in practical circuits. Further opportunities for adaptation of the X-parameters methodology to the PIM
characterisation of passive devices using the existing test instruments are explored.