Finite mixture analysis of beauty-contest data using generalised beta distributions

This paper introduces a mixture model based on the beta distribution, without preestablishedmeans and variances, to analyze a large set of Beauty-Contest data obtainedfrom diverse groups of experiments (Bosch-Domenech et al. 2002). This model gives a bettert of the experimental data, and more precision to the hypothesis that a large proportionof individuals follow a common pattern of reasoning, described as iterated best reply (degenerate),than mixture models based on the normal distribution. The analysis shows thatthe means of the distributions across the groups of experiments are pretty stable, while theproportions of choices at dierent levels of reasoning vary across groups.

Fusion weld metal solidification:Continuum from weld interface to centerline

We present a brief résumé of the history of solidification research and key factors affecting the solidification of fusion welds. There is a general agreement of the basic solidification theory, albeit differing - even confusing - nomenclatures do exist, and Cases 2 and 3 (the Chalmers' basic boundary conditions for solidification, categorized by Savage as Cases) are variably emphasized. Model Frame, a tool helping to model the continuum of fusion weld solidification from start to end, is proposed. It incorporates the general solidification models, of which the pertinent ones are selected for the actual modeling. The basic models are the main solidification Cases 1…4. These discrete Cases are joined with Sub-Cases: models of Pfann, Flemings and others, bringing needed Sub-Case variables into the model. Model Frame depicts a grain growing from the weld interface to its centerline. Besides modeling, the Model Frame supports education and academic debate. The new mathematical modeling techniques will extend its use into multi-dimensional modeling, introducing new variables and increasing the modeling accuracy. We propose a model: melting/solidification-model (M/S-model) - predicting the solute profile at the start of the solidification of a fusion weld. This Case 3-based Sub-Case takes into account the melting stage, the solute back-diffusion in the solid, and the growth rate acceleration typical to fusion welds. We propose - based on works of Rutter & Chalmers, David & Vitek and our experimental results on copper - that NEGS-EGS-transition is not associated only with cellular-dendritic-transition. Solidification is studied experimentally on pure and doped copper with welding speed range from 0 to 200 cm/min, with one test at 3000 cm/min. Found were only planar and cellular structures, no dendrites - columnar or equiaxed. Cell sub structures: rows of cubic elements we call "cubelettes", "cell-bands" and "micro-cells", as well as an anomalous crack morphology "crack-eye", were detected, as well as microscopic hot crack nucleus we call "grain-lag cracks", caused by a grain slightly lagging behind its neighbors in arrival to the weld centerline. Varestraint test and R-test revealed a change of crack morphologies from centerline cracks to grainand cell boundary cracks with an increasing welding speed. High speed made the cracks invisible to bare eye and hardly detectable with light microscope, while electron microscope often revealed networks of fine micro-cracks.

Efficient estimation using the characteristic function : theory and applications with high frequency data

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Wittgenstein And Labyrinth Of ‘Actual Infinity’: The Critique Of Transfinite Set Theory

In order to explain Wittgenstein’s account of the reality of completed infinity in mathematics, a brief overview of Cantor’s initial injection of the idea into set- theory, its trajectory (including the Diagonal Argument, the Continuum Hypothesis and Cantor’s Theorem) and the philosophic implications he attributed to it will be presented. Subsequently, we will first expound Wittgenstein’s grammatical critique of the use of the term ‘infinity’ in common parlance and its conversion into a notion of an actually existing (completed) infinite ‘set’. Secondly, we will delve into Wittgenstein’s technical critique of the concept of ‘denumerability’ as it is presented in set theory as well as his philosophic refutation of Cantor’s Diagonal Argument and the implications of such a refutation onto the problems of the Continuum Hypothesis and Cantor’s Theorem. Throughout, the discussion will be placed within the historical and philosophical framework of the Grundlagenkrise der Mathematik and Hilbert’s problems.

Continuum Double Exchange Model

We present a continuum model for doped manganites which consist of two species of quantum spin-1 / 2 fermions interacting with classical spin fields. The phase structure at zero temperature turns out to be considerably rich: antiferromagnetic insulator, antiferromagnetic two band conducting, canted two band conducting, canted one band conducting, and ferromagnetic one band conducting phases are identified, all of them being stable against phase separation. There are also regions in the phase diagram where phase separation occurs

Continuum bound states as surface states of a finite periodic system

We discuss the relation between continuum bound states (CBSs) localized on a defect, and surface states of a finite periodic system. We model an experiment of Capasso et al. [F. Capasso, C. Sirtori, J. Faist, D. L. Sivco, S-N. G. Chu, and A. Y. Cho, Nature (London) 358, 565 (1992)] using the transfer-matrix method. We compute the rate for intrasubband transitions from the ground state to the CBS and derive a sum rule. Finally we show how to improve the confinement of a CBS while keeping the energy fixed.

Reduced L_1 level width and Coster-Kronig yields by relaxation and continuum interactions in atomic zinc

Calculations of the level width \gamma( L_1) and the f_12 and f_13 Coster-Kronig yields for atomic zinc have been performed with Dirac-Fock wave functions. For \gamma(L_1), a large deviation between theory and evaluated data exists. We include the incomplete orthogonality of the electron orbitals as well as the interchannel interaction of the decaying states. Orbital relaxation reduces the total rates in all groups of the electron-emission spectrum by about 10-20 %. Different, however, is the effect of the continuum interaction. The L_1-L_23X Coster-Kronig part of the spectrum is definitely reduced in its intensity, whereas the MM and MN spectra are slightly enhanced. This results in a reduction of Coster-Kronig yields, where for medium and heavy elements considerable discrepancies have been found in comparison to relativistic theory. Briefly, we discuss the consequences of our calculations for heavier elements.

Atomistic-continuum modeling of ultrafast laser-induced melting of silicon targets

In this work, we present an atomistic-continuum model for simulations of ultrafast laser-induced melting processes in semiconductors on the example of silicon. The kinetics of transient non-equilibrium phase transition mechanisms is addressed with MD method on the atomic level, whereas the laser light absorption, strong generated electron-phonon nonequilibrium, fast heat conduction, and photo-excited free carrier diffusion are accounted for with a continuum TTM-like model (called nTTM). First, we independently consider the applications of nTTM and MD for the description of silicon, and then construct the combined MD-nTTM model. Its development and thorough testing is followed by a comprehensive computational study of fast nonequilibrium processes induced in silicon by an ultrashort laser irradiation. The new model allowed to investigate the effect of laser-induced pressure and temperature of the lattice on the melting kinetics. Two competing melting mechanisms, heterogeneous and homogeneous, were identified in our big-scale simulations. Apart from the classical heterogeneous melting mechanism, the nucleation of the liquid phase homogeneously inside the material significantly contributes to the melting process. The simulations showed, that due to the open diamond structure of the crystal, the laser-generated internal compressive stresses reduce the crystal stability against the homogeneous melting. Consequently, the latter can take a massive character within several picoseconds upon the laser heating. Due to the large negative volume of melting of silicon, the material contracts upon the phase transition, relaxes the compressive stresses, and the subsequent melting proceeds heterogeneously until the excess of thermal energy is consumed. A series of simulations for a range of absorbed fluences allowed us to find the threshold fluence value at which homogeneous liquid nucleation starts contributing to the classical heterogeneous propagation of the solid-liquid interface. A series of simulations for a range of the material thicknesses showed that the sample width we chosen in our simulations (800 nm) corresponds to a thick sample. Additionally, in order to support the main conclusions, the results were verified for a different interatomic potential. Possible improvements of the model to account for nonthermal effects are discussed and certain restrictions on the suitable interatomic potentials are found. As a first step towards the inclusion of these effects into MD-nTTM, we performed nanometer-scale MD simulations with a new interatomic potential, designed to reproduce ab initio calculations at the laser-induced electronic temperature of 18946 K. The simulations demonstrated that, similarly to thermal melting, nonthermal phase transition occurs through nucleation. A series of simulations showed that higher (lower) initial pressure reinforces (hinders) the creation and the growth of nonthermal liquid nuclei. For the example of Si, the laser melting kinetics of semiconductors was found to be noticeably different from that of metals with a face-centered cubic crystal structure. The results of this study, therefore, have important implications for interpretation of experimental data on the kinetics of melting process of semiconductors.

Learning mathematics : issues, theory and classroom practice.

Recurso para profesores de matemáticas de primaria y secundaria. El texto considera las cuestiones relativas a cómo los estudiantes aprenden matemáticas. Cada uno de los once capítulos trata un tema particular que ilustra la interacción entre la teoría y la práctica. Esta edición cuenta con dos nuevos capítulos: uno relacionado con la cognición y la transferencia del aprendizaje, y otro que examina la importancia del modelo de aprendizaje en las matemáticas.

Equivalence of truncated count mixture distributions and mixtures of truncated count distributions

This article is about modeling count data with zero truncation. A parametric count density family is considered. The truncated mixture of densities from this family is different from the mixture of truncated densities from the same family. Whereas the former model is more natural to formulate and to interpret, the latter model is theoretically easier to treat. It is shown that for any mixing distribution leading to a truncated mixture, a (usually different) mixing distribution can be found so. that the associated mixture of truncated densities equals the truncated mixture, and vice versa. This implies that the likelihood surfaces for both situations agree, and in this sense both models are equivalent. Zero-truncated count data models are used frequently in the capture-recapture setting to estimate population size, and it can be shown that the two Horvitz-Thompson estimators, associated with the two models, agree. In particular, it is possible to achieve strong results for mixtures of truncated Poisson densities, including reliable, global construction of the unique NPMLE (nonparametric maximum likelihood estimator) of the mixing distribution, implying a unique estimator for the population size. The benefit of these results lies in the fact that it is valid to work with the mixture of truncated count densities, which is less appealing for the practitioner but theoretically easier. Mixtures of truncated count densities form a convex linear model, for which a developed theory exists, including global maximum likelihood theory as well as algorithmic approaches. Once the problem has been solved in this class, it might readily be transformed back to the original problem by means of an explicitly given mapping. Applications of these ideas are given, particularly in the case of the truncated Poisson family.

Whither tube theory: From believing to measuring

This short contribution examines the difficulties that have not yet been fully overcome in the many developments made from the simplest (and original) tube model for entangled polymers. It is concluded that many more length scales have to be considered sequentially when deriving a continuum rheological model from molecular considerations than have been considered in the past. In particular, most unresolved issues of the tube theory are related to the length scales of tube diameter, and molecular dynamics simulations is the perfect route to resolve them. The power of molecular simulations is illustrated by two examples: stress contributions from bonded and non-bonded interaction, and the inter-chain coupling, which is usually neglected in the tube theory.

Neurofuzzy mixture of experts network parallel learning and model construction algorithms

A connection between a fuzzy neural network model with the mixture of experts network (MEN) modelling approach is established. Based on this linkage, two new neuro-fuzzy MEN construction algorithms are proposed to overcome the curse of dimensionality that is inherent in the majority of associative memory networks and/or other rule based systems. The first construction algorithm employs a function selection manager module in an MEN system. The second construction algorithm is based on a new parallel learning algorithm in which each model rule is trained independently, for which the parameter convergence property of the new learning method is established. As with the first approach, an expert selection criterion is utilised in this algorithm. These two construction methods are equivalent in their effectiveness in overcoming the curse of dimensionality by reducing the dimensionality of the regression vector, but the latter has the additional computational advantage of parallel processing. The proposed algorithms are analysed for effectiveness followed by numerical examples to illustrate their efficacy for some difficult data based modelling problems.

Ideological dominance in recreation provision: towards a theory of Local Authority response to Compulsory Competitive Tendering in Britain

This paper considers how the delivery of public leisure services in Britain has been affected by the imposition of Compulsory Competitive Tendering (CCT) on the management of facilities. In particular, it focuses on the changing relationship between the central and local levels of government, theorising a tripartite local response to CCT, incorporating local statism, post-Fordist rejection of CCT and post- Fordist compliance with the aims of the central administration. The paper then discusses the actual implementation of CCT, relating the theorised responses to those witnessed in practice. This results in the delineation of a continuum of stances, ranging from pragmatic forms of local statism, such as the protection of the former direct labour force, to centrist attempts to combine the ethics of socialism with the mechanics of the market, to an outright rejection of state organisation and control. The paper concludes that although legitimate attempts have been made to protect local services, the outcome of the CCT process has undoubtedly been the regeneration of public leisure provision away from its service roots towards a market model of provision.

A simple analysis of thermodynamic properties for classical plasmas: I. theory

By eliminating the short range negative divergence of the Debye–Hückel pair distribution function, but retaining the exponential charge screening known to operate at large interparticle separation, the thermodynamic properties of one-component plasmas of point ions or charged hard spheres can be well represented even in the strong coupling regime. Predicted electrostatic free energies agree within 5% of simulation data for typical Coulomb interactions up to a factor of 10 times the average kinetic energy. Here, this idea is extended to the general case of a uniform ionic mixture, comprising an arbitrary number of components, embedded in a rigid neutralizing background. The new theory is implemented in two ways: (i) by an unambiguous iterative algorithm that requires numerical methods and breaks the symmetry of cross correlation functions; and (ii) by invoking generalized matrix inverses that maintain symmetry and yield completely analytic solutions, but which are not uniquely determined. The extreme computational simplicity of the theory is attractive when considering applications to complex inhomogeneous fluids of charged particles.

A continuum model of melt pond evolution on Arctic sea ice

[1] During the Northern Hemisphere summer, absorbed solar radiation melts snow and the upper surface of Arctic sea ice to generate meltwater that accumulates in ponds. The melt ponds reduce the albedo of the sea ice cover during the melting season, with a significant impact on the heat and mass budget of the sea ice and the upper ocean. We have developed a model, designed to be suitable for inclusion into a global circulation model (GCM), which simulates the formation and evolution of the melt pond cover. In order to be compatible with existing GCM sea ice models, our melt pond model builds upon the existing theory of the evolution of the sea ice thickness distribution. Since this theory does not describe the topography of the ice cover, which is crucial to determining the location, extent, and depth of individual ponds, we have needed to introduce some assumptions. We describe our model, present calculations and a sensitivity analysis, and discuss our results.