The hierarchical approach to modeling knowledge and common knowledge

One approach to representing knowledge or belief of agents, used by economists and computer scientists, involves an infinite hierarchy of beliefs. Such a hierarchy consists of an agent's beliefs about the state of the world, his beliefs about other agents' beliefs about the world, his beliefs about other agents' beliefs about other agents' beliefs about the world, and so on. (Economists have typically modeled belief in terms of a probability distribution on the uncertainty space. In contrast, computer scientists have modeled belief in terms of a set of worlds, intuitively, the ones the agent considers possible.) We consider the question of when a countably infinite hierarchy completely describes the uncertainty of the agents. We provide various necessary and sufficient conditions for this property. It turns out that the probability-based approach can be viewed as satisfying one of these conditions, which explains why a countable hierarchy suffices in this case. These conditions also show that whether a countable hierarchy suffices may depend on the “richness” of the states in the underlying state space. We also consider the question of whether a countable hierarchy suffices for “interesting” sets of events, and show that the answer depends on the definition of “interesting”.     

Amorphous and crystalline IrO2 thin films as potential stimulation electrode coatings

Amorphous and crystalline iridium oxide thin films with potential use as coating materials for stimulation electrodes were studied. Characterization of these films by cyclic voltammetry and impedance spectroscopy has revealed a considerable decrease in impedance and an increase in charge capacity of iridium oxide thin films after an electrochemical activation process in 0.9% NaCl solution. The surface morphology of these films was studied by scanning electron microscopy. The two types of IrO₂ films were also compared under conditions relevant to applications as stimulation electrodes. The results indicate that amorphous IrO₂ films have significantly higher charge storage capacity and lower impedance than crystalline IrO₂ films. This makes the amorphous films a preferable coating material for stimulation applications.     

Analytic Representation of Volume Flow as a Function of Geometry and Pressure in a Static Physical Model of the Glottis

A static physical model of the larynx (model M5) was used to obtain a large set of volume flows as a function of symmetric glottal geometry and transglottal pressure. The measurements cover ranges of these variables relevant to human phonation. A generalized equation was created to accurately estimate the glottal volume flow given specific glottal geometries and transglottal pressures. Both the data and the generalized formula give insights into the flow behavior for different glottal geometries, especially the contrast between convergent and divergent glottal angles at different glottal diameters. The generalized equation produced a fit to the entire M5 dataset (267 points) with an average accuracy of 3.4%. The accuracy was about seven times better than that of the Ishizaka-Flanagan approach to glottal flow and about four times better than that of a pressure coefficient approach. Thus, for synthesis purposes, the generalized equation presented here should provide more realistic glottal flows (based on steady flow conditions) as suitable inputs to the vocal tract, for given values of transglottal pressure and glottal geometry. Applications of the generalized formula to pulses generated by vocal fold motions typical of those produced by the Ishizaka-Flanagan coupled-oscillator model and the more recent body-cover model of Story and Titze are also included.     

Joint cumulative distribution functions for Dempster–Shafer belief structures using copulas

We first introduce the Dempster–Shafer belief structure and highlight its role in the representation of information about a random variable for which our knowledge of the probabilities is interval-valued. We investigate the formation of the cumulative distribution function (CDF) for these types of variables. It is noted that this is also interval-valued and is expressible in terms of plausibility and belief measures. The class of aggregation operators known as copulas are introduced and a number of their properties are provided. We discuss Sklar’s theorem, which provides for the use of copulas in the formulation of joint CDFs from the marginal CDFs of classic random variables. We then look to extend these ideas to the case of joining the marginal CDFs associated with Dempster–Shafer belief structures. Finally we look at the formulation CDFs obtained from functions of multiple D–S belief structures.     

Financial scenario generation for stochastic multi-stage decision processes as facility location problems

The quality of multi-stage stochastic optimization models as they appear in asset liability management, energy planning, transportation, supply chain management, and other applications depends heavily on the quality of the underlying scenario model, describing the uncertain processes influencing the profit/cost function, such as asset prices and liabilities, the energy demand process, demand for transportation, and the like. A common approach to generate scenarios is based on estimating an unknown distribution and matching its moments with moments of a discrete scenario model. This paper demonstrates that the problem of finding valuable scenario approximations can be viewed as the problem of optimally approximating a given distribution with some distance function. We show that for Lipschitz continuous cost/profit functions it is best to employ the Wasserstein distance. The resulting optimization problem can be viewed as a multi-dimensional facility location problem, for which at least good heuristic algorithms exist. For multi-stage problems, a scenario tree is constructed as a nested facility location problem. Numerical convergence results for financial mean-risk portfolio selection conclude the paper.     

Chung type strong laws for arrays of random elements and bootstrapping

Let {X_nk } be be an array of rowwise independent random elements in a separable Banach space. Chung type strong laws of large numbers are obtained under various moment conditions on the random elements and geometric type p, 1≤p≤2, conditions on the Banach space. Comparisons with existing results for arrays of random elements are provided to illustrate the strength of these results. The results can be directly applied to show the asymptotic validity of the bootstrap mean and variance for random functions     

Automated registration of sequential breath-hold dynamic contrast-enhanced MR images: a comparison of three techniques

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is increasingly in use as an investigational biomarker of response in cancer clinical studies. Proper registration of images acquired at different time points is essential for deriving diagnostic information from quantitative pharmacokinetic analysis of these data. Motion artifacts in the presence of time-varying intensity due to contrast enhancement make this registration problem challenging. DCE-MRI of chest and abdominal lesions is typically performed during sequential breath-holds, which introduces misregistration due to inconsistent diaphragm positions and also places constraints on temporal resolution vis-à-vis free-breathing. In this work, we have employed a computer-generated DCE-MRI phantom to compare the performance of two published methods, Progressive Principal Component Registration and Pharmacokinetic Model-Driven Registration, with Sequential Elastic Registration (SER) to register adjacent time-sample images using a published general-purpose elastic registration algorithm. In all three methods, a 3D rigid-body registration scheme with a mutual information similarity measure was used as a preprocessing step. The DCE-MRI phantom images were mathematically deformed to simulate misregistration, which was corrected using the three schemes. All three schemes were comparably successful in registering large regions of interest (ROIs) such as muscle, liver, and spleen. SER was superior in retaining tumor volume and shape, and in registering smaller but important ROIs such as tumor core and tumor rim. The performance of SER on clinical DCE-MRI data sets is also presented.     

Phase matching considerations in second harmonic generation from tissues: Effects on emission directionality, conversion efficiency and observed morphology

We present a heuristic treatment which relates SHG image intensities, signal directionality, and observed morphology to the physical structure of collagen and cellulose fibrillar tissues. The SHG creation model is based upon relaxed phase matching conditions which account for dispersion, randomness, and axial momentum contributions from the media, and includes a mathematical treatment which relates SHG conversion efficiency to fibril diameter and packing through the inclusion of potential intensity amplification resultant from quasi-phase matching (QPM). A direct consequence of this theory is that SHG in biological tissues is not strictly a coherent process, and that the forward directed SHG has a longer coherence length than the backward component, Through this treatment, we show that the emission directionality and also conversion efficiency do not arise solely from the fibril size but also depend on packing density and order of the inter-fibril structure. We demonstrate these principles in comparing the SHG response in normal and Osteogenesis Imperfecta (OI) skin. We show that the observed directionality and decreased relative intensity in the diseased state is consistent with phase matching conditions arising from the decreased fibril size and more random assembly. We further use this theory to explain the differences in morphology seen in forward and backward collected SHG in fibrillar tissues (e.g., collagenous and cellulosic). Specifically, we attribute segmented appearance to destructive interference between small fibrils separated by less than the coherence length. We suggest the approach based on relaxed phasematching conditions is general in predicting the SHG response in tissues and may be broadly applicable in interpreting the SHG contrast for diagnostic applications.     

Observation of squeezed light with 10-dB quantum-noise reduction

Squeezing of light's quantum noise requires temporal rearranging of photons. This again corresponds to creation of quantum correlations between individual photons. Squeezed light is a nonclassical manifestation of light with great potential in high-precision quantum measurements, for example, in the detection of gravitational waves [C. M. Caves, Phys. Rev. D 23, 1693 (1981)10.1103/PhysRevD.23.1693]. Equally promising applications have been proposed in quantum communication [H. P. Yuen and J. H. Shapiro, IEEE Trans. Inf. Theory 24, 657 (1978)10.1109/TIT.1978.1055958]. However, after 20 years of intensive research doubts arose whether strong squeezing can ever be realized as required for eminent applications. Here we show experimentally that strong squeezing of light's quantum noise is possible. We reached a benchmark squeezing factor of 10 in power (10 dB). Thorough analysis reveals that even higher squeezing factors will be feasible in our setup.