Adaptive Optimal Scaling of Metropolis-Hastings Algorithms Using the Robbins-Monro Process

We present an adaptive method for the automatic scaling of Random-Walk Metropolis-Hastings algorithms, which quickly and robustly identifies the scaling factor that yields a specified overall sampler acceptance probability. Our method relies on the use of the Robbins-Monro search process, whose performance is determined by an unknown steplength constant. We give a very simple estimator of this constant for proposal distributions that are univariate or multivariate normal, together with a sampling algorithm for automating the method. The effectiveness of the algorithm is demonstrated with both simulated and real data examples. This approach could be implemented as a useful component in more complex adaptive Markov chain Monte Carlo algorithms, or as part of automated software packages

Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian

Based on the technique of integration within an ordered product (IWOP) of operators we introduce the Fresnel operator for converting Caldirola-Kanai Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel operator with the parameters A,B,C,D corresponds to classical optical Fresnel transformation, these parameters are the solution to a set of partial differential equations set up in the above mentioned converting process. In this way the exact wavefunction solution of the Schr\"odinger equation governed by the Caldirola-Kanai Hamiltonian is obtained, which represents a squeezed number state. The corresponding Wigner function is derived by virtue of the Weyl ordered form of the Wigner operator and the order-invariance of Weyl ordered operators under similar transformations. The method used here can be suitable for solving Schr\"odinger equation of other time-dependent oscillators.Comment: 6 pages, 2 figure

Ultrasonic metal sheet thickness measurement without prior wave speed calibration

Conventional ultrasonic mensuration of sample thickness from one side only requires the bulk wave reverberation time and a calibration speed. This speed changes with temperature, stress, and microstructure, limiting thickness measurement accuracy. Often, only one side of a sample is accessible, making in situ calibration impossible. Non-contact ultrasound can generate multiple shear horizontal guided wave modes on one side of a metal plate. Measuring propagation times of each mode at different transducer separations, allows sheet thickness to be calculated to better than 1% accuracy for sheets of at least 1.5 mm thickness, without any calibration

Information of Structures in Galaxy Distribution

We introduce an information-theoretic measure, the Renyi information, to describe the galaxy distribution in space. We discuss properties of the information measure, and demonstrate its relationship with the probability distribution function and multifractal descriptions. Using the First Look Survey galaxy samples observed by the Infrared Array Camera onboard Spitzer Space Telescope, we present measurements of the Renyi information, as well as the counts-in-cells distribution and multifractal properties of galaxies in mid-infrared wavelengths. Guided by multiplicative cascade simulation based on a binomial model, we verify our measurements, and discuss the spatial selection effects on measuring information of the spatial structures. We derive structure scan functions at scales where selection effects are small for the Spitzer samples. We discuss the results, and the potential of applying the Renyi information to measuring other spatial structures.Comment: 25 pages, 8 figures, submitted to ApJ; To appear in The Astrophysical Journal 2006, 644, 678 (June 20th

Representations of linear dual rate system via single SISO LTI filter, conventional sampler and block sampler

In this brief, it is proved that a linear dual-rate system can be represented via a series cascade of: 1) a conventional expander, a single-input single-output (SISO) linear time-invariant (LTI) filter and a block decimator, or 2) a block expander, an SISO LTI filter and a conventional decimator. Hence, incompatible nonuniform filter banks could achieve perfect reconstruction via LTI filters, conventional samplers and block samplers without expanding the input-output dimension of a subsystem of linear dual-rate systems or converting the nonuniform filter banks to uniform filter banks. The main advantage of the proposed representations is to avoid complicated design of the circuit layout caused by connecting subsystems with large input-output dimension or a lot of subsystems togethe

Characterization of the residual stresses in spray-formed steels using neutron diffraction

Neutron diffraction was used to characterize the residual stresses in an as-sprayed tube-shaped steel preform. The measured residual stress distributions were compared with those simulated using finite element method by taking into account the effects of the thermal history, porosity and different phases of the sprayed preform. The porosity was measured using X-ray microcomputed tomography. The study revealed for the first time the correlation between the distribution of porosity and residual stress developed in the as-sprayed preform

Soft power: Power of attraction or confusion?

Despite its popularity soft power remains power of confusion. The paper examines the concept, with a special focus on the nature and sources of soft power. Nye’s notion of soft power is largely ethnocentric and based on the assumption that there is a link between attractiveness and the ability to influence others in international relations. This poses two problems: Firstly, a country has many different actors. Some of them like the attraction and others don’t. Whether the attraction will lead to the ability to influence the policy of the target country depends on which groups in that country find it attractive and how much control they have on policymaking. Secondly, policymaking at the state level is far more complicated than at the personal level; and has different dynamics that emphasise the rational considerations. This leaves little room for emotional elements thus significantly reducing the effect of soft power. Given the nature of soft power being uncontrollable and unpredictable, it would be impossible to wield soft power in any organised and coordinated fashion as Nye suggested. Furthermore, the relationship between two countries is shaped by many complex factors. It is ultimately decided by the geopolitics and strategic interests of nations, in which soft power may play only a limited role. The paper also discusses the link between soft power and nation branding as both concepts are concerned with a nation’s influence on the world stage. Public diplomacy is a subset of nation branding that focuses on the political brand of a nation; whereas nation branding is about how a nation as whole to reshape the international opinions. A successful nation branding campaign will help create a more favourable and lasting image among the international audience thus further enhancing a country’s soft power