Model selection with misspecified spatial covariance structure

Spatial data analysis has become more and more important in the studies of ecology and economics during the last decade. One focus of spatial data analysis is how to select predictors, variance functions and correlation functions. However, in general, the true covariance function is unknown and the working covariance structure is often misspecified. In this paper, our target is to find a good strategy to identify the best model from the candidate set using model selection criteria. This paper is to evaluate the ability of some information criteria (corrected Akaike information criterion, Bayesian information criterion (BIC) and residual information criterion (RIC)) for choosing the optimal model when the working correlation function, the working variance function and the working mean function are correct or misspecified. Simulations are carried out for small to moderate sample sizes. Four candidate covariance functions (exponential, Gaussian, Matern and rational quadratic) are used in simulation studies. With the summary in simulation results, we find that the misspecified working correlation structure can still capture some spatial correlation information in model fitting. When the sample size is large enough, BIC and RIC perform well even if the the working covariance is misspecified. Moreover, the performance of these information criteria is related to the average level of model fitting which can be indicated by the average adjusted R square ( [GRAPHICS] ), and overall RIC performs well.

Smooth stabilisation of nonholonomic robots subject to disturbances

In this paper, we address the problem of stabilisation of robots subject to nonholonommic constraints and external disturbances using port-Hamiltonian theory and smooth time-invariant control laws. This should be contrasted with the commonly used switched or time-varying laws. We propose a control design that provides asymptotic stability of an manifold (also called relative equilibria)-due to the Brockett condition this is the only type of stabilisation possible using smooth time-invariant control laws. The equilibrium manifold can be shaped to certain extent to satisfy specific control objectives. The proposed control law also incorporates integral action, and thus the closed-loop system is robust to unknown constant disturbances. A key step in the proposed design is a change of coordinates not only in the momentum, but also in the position vector, which differs from coordinate transformations previously proposed in the literature for the control of nonholonomic systems. The theoretical properties of the control law are verified via numerical simulation based on a robotic ground vehicle model with differential traction wheels and non co-axial centre of mass and point of contact.

Thermal conductivity of a new carbon nanotube analog: The diamond nanothread

Based on the non-equilibrium molecular dynamics simulations, we have studied the thermal conductivities of a novel ultra-thin one-dimensional carbon nanomaterial - diamond nanothread (DNT). Unlike single-wall carbon nanotube (CNT), the existence of the Stone-Wales transformations in DNT endows it with richer thermal transport characteristics. There is a transition from wave-dominated to particle-dominated transport region, which depends on the length of poly-benzene rings. However, independent of the transport region, strong length dependence in thermal conductivity is observed in DNTs with different lengths of poly-benzene ring. The distinctive SW characteristic in DNT provides more degrees of freedom to tune the thermal conductivity not found in the homogeneous structure of CNT. Therefore, DNT is an ideal platform to investigate various thermal transport mechanisms at the nanoscale. Its high tunability raises the potential to design DNTs for different applications, such as thermal connection and temperature management.

Crystallization as a Tool for Controlling and Designing Properties of Pharmaceutical Solids

The ability to deliver the drug to the patient in a safe, efficacious and cost-effective manner depends largely on the physicochemical properties of the active pharmaceutical ingredient (API) in the solid state. In this context, crystallization is of critical importance in pharmaceutical industry, as it defines physical and powder properties of crystalline APIs. An improved knowledge of the various aspects of crystallization process is therefore needed. The overall goal of this thesis was to gain better understanding of the relationships between crystallization, solid-state form and properties of pharmaceutical solids with a focus on a crystal engineering approach to design technological properties of APIs. Specifically, solid-state properties of the crystalline forms of the model APIs, erythromycin A and baclofen, and the influence of solvent on their crystallization behavior were investigated. In addition, the physical phenomena associated with wet granulation and hot-melting processing of the model APIs were examined at the molecular level. Finally, the effect of crystal habit modification of a model API on its tabletting properties was evaluated. The thesis enabled the understanding of the relationship between the crystalline forms of the model APIs, which is of practical importance for solid-state control during processing and storage. Moreover, a new crystalline form, baclofen monohydrate, was discovered and characterized. Upon polymorph screening, erythromycin A demonstrated high solvate-forming propensity thus emphasizing the need for careful control of the solvent effects during formulation. The solvent compositions that yield the desirable crystalline form of erythromycin A were defined. Furthermore, new examples on solvent-mediated phase transformations taking place during wet granulation of baclofen and hot-melt processing of erythromycin A dihydrate with PEG 6000 are reported. Since solvent-mediated phase transformations involve the crystallization of a stable phase and hence affect the dissolution kinetics and possibly absorption of the API these transformations must be well documented. Finally, a controlled-crystallization method utilizing HPMC as a crystal habit modifier was developed for erythromycin A dihydrate. The crystals with modified habit were shown to posses improved compaction properties as compared with those of unmodified crystals. This result supports the idea of morphological crystal engineering as a tool for designing technological properties of APIs and is of utmost practical interest.

From Polymorph Screening to Dissolution Testing - Solid Phase Analysis during Pharmaceutical Development and Manufacturing

Solid materials can exist in different physical structures without a change in chemical composition. This phenomenon, known as polymorphism, has several implications on pharmaceutical development and manufacturing. Various solid forms of a drug can possess different physical and chemical properties, which may affect processing characteristics and stability, as well as the performance of a drug in the human body. Therefore, knowledge and control of the solid forms is fundamental to maintain safety and high quality of pharmaceuticals. During manufacture, harsh conditions can give rise to unexpected solid phase transformations and therefore change the behavior of the drug. Traditionally, pharmaceutical production has relied on time-consuming off-line analysis of production batches and finished products. This has led to poor understanding of processes and drug products. Therefore, new powerful methods that enable real time monitoring of pharmaceuticals during manufacturing processes are greatly needed. The aim of this thesis was to apply spectroscopic techniques to solid phase analysis within different stages of drug development and manufacturing, and thus, provide a molecular level insight into the behavior of active pharmaceutical ingredients (APIs) during processing. Applications to polymorph screening and different unit operations were developed and studied. A new approach to dissolution testing, which involves simultaneous measurement of drug concentration in the dissolution medium and in-situ solid phase analysis of the dissolving sample, was introduced and studied. Solid phase analysis was successfully performed during different stages, enabling a molecular level insight into the occurring phenomena. Near-infrared (NIR) spectroscopy was utilized in screening of polymorphs and processing-induced transformations (PITs). Polymorph screening was also studied with NIR and Raman spectroscopy in tandem. Quantitative solid phase analysis during fluidized bed drying was performed with in-line NIR and Raman spectroscopy and partial least squares (PLS) regression, and different dehydration mechanisms were studied using in-situ spectroscopy and partial least squares discriminant analysis (PLS-DA). In-situ solid phase analysis with Raman spectroscopy during dissolution testing enabled analysis of dissolution as a whole, and provided a scientific explanation for changes in the dissolution rate. It was concluded that the methods applied and studied provide better process understanding and knowledge of the drug products, and therefore, a way to achieve better quality.

Investigating physical properties of solid dosage forms during pharmaceutical processing : Process analytical applications of vibrational spectroscopy

In order to improve and continuously develop the quality of pharmaceutical products, the process analytical technology (PAT) framework has been adopted by the US Food and Drug Administration. One of the aims of PAT is to identify critical process parameters and their effect on the quality of the final product. Real time analysis of the process data enables better control of the processes to obtain a high quality product. The main purpose of this work was to monitor crucial pharmaceutical unit operations (from blending to coating) and to examine the effect of processing on solid-state transformations and physical properties. The tools used were near-infrared (NIR) and Raman spectroscopy combined with multivariate data analysis, as well as X-ray powder diffraction (XRPD) and terahertz pulsed imaging (TPI). To detect process-induced transformations in active pharmaceutical ingredients (APIs), samples were taken after blending, granulation, extrusion, spheronisation, and drying. These samples were monitored by XRPD, Raman, and NIR spectroscopy showing hydrate formation in the case of theophylline and nitrofurantoin. For erythromycin dihydrate formation of the isomorphic dehydrate was critical. Thus, the main focus was on the drying process. NIR spectroscopy was applied in-line during a fluid-bed drying process. Multivariate data analysis (principal component analysis) enabled detection of the dehydrate formation at temperatures above 45°C. Furthermore, a small-scale rotating plate device was tested to provide an insight into film coating. The process was monitored using NIR spectroscopy. A calibration model, using partial least squares regression, was set up and applied to data obtained by in-line NIR measurements of a coating drum process. The predicted coating thickness agreed with the measured coating thickness. For investigating the quality of film coatings TPI was used to create a 3-D image of a coated tablet. With this technique it was possible to determine coating layer thickness, distribution, reproducibility, and uniformity. In addition, it was possible to localise defects of either the coating or the tablet. It can be concluded from this work that the applied techniques increased the understanding of physico-chemical properties of drugs and drug products during and after processing. They additionally provided useful information to improve and verify the quality of pharmaceutical dosage forms

Paraxial-wave optics and relativistic front description .1. The scalar theory

With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincaré group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincaré group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

La modernización entre cafetales : San José, Costa Rica, 1880-1930

This work examines the urban modernization of San José, Costa Rica, between 1880 and 1930, using a cultural approach to trace the emergence of the bourgeois city in a small Central American capital, within the context of order and progress. As proposed by Henri Lefebvre, Manuel Castells and Edward Soja, space is given its rightful place as protagonist. The city, subject of this study, is explored as a seat of social power and as the embodiment of a cultural transformation that took shape in that space, a transformation spearheaded by the dominant social group, the Liberal elite. An analysis of the product built environment allows us to understand why the city grew in a determined manner: how the urban space became organized and how its infrastructure and services distributed. Although the emphasis is on the Liberal heyday from 1880-1930, this study also examines the history of the city since its origins in the late colonial period through its consolidation as a capital during the independent era, in order to characterize the nineteenth century colonial city that prevailed up to 1890 s. A diverse array of primary sources including official acts, memoirs, newspaper sources, maps and plans, photographs, and travelogues are used to study the initial phase of San Jose s urban growth. The investigation places the first period of modern urban growth at the turn of the nineteenth century within the prevailing ideological and political context of Positivism and Liberalism. The ideas of the city s elite regarding progress were translated into and reflected in the physical transformation of the city and in the social construction of space. Not only the transformations but also the limits and contradictions of the process of urban change are examined. At the same time, the reorganization of the city s physical space and the beginnings of the ensanche are studied. Hygiene as an engine of urban renovation is explored by studying the period s new public infrastructure (including pipelines, sewer systems, and the use of asphalt pavement) as part of the Saneamiento of San José. The modernization of public space is analyzed through a study of the first parks, boulevards and monuments and the emergence of a new urban culture prominently displayed in these green spaces. Parks and boulevards were new public and secular places of power within the modern city, used by the elite to display and educate the urban population into the new civic and secular traditions. The study goes on to explore the idealized image of the modern city through an analysis of European and North American travelogues and photography. The new esthetic of theatrical-spectacular representation of the modern city constructed a visual guide of how to understand and come to know the city. A partial and selective image of generalized urban change presented only the bourgeois facade and excluded everything that challenged the idea of progress. The enduring patterns of spatial and symbolic exclusion built into Costa Rica s capital city at the dawn of the twentieth century shed important light on the long-term political social and cultural processes that have created the troubled urban landscapes of contemporary Latin America.

Two-dimensional phase transitions at electrochemical interfaces

A two-state Ising model has been applied to the two-dimensional condensation of tymine at the mercury-water interface. The model predicts a quadratic dependence of the transition potential on temperature and on the logarithm of the adsorbate concentration. Both predictions have been confirmed experimentally.

Some Methods for Summarizing Survivorship Data in Nonstandard Situations

One difficulty in summarising biological survivorship data is that the hazard rates are often neither constant nor increasing with time or decreasing with time in the entire life span. The promising Weibull model does not work here. The paper demonstrates how bath tub shaped quadratic models may be used in such a case. Further, sometimes due to a paucity of data actual lifetimes are not as certainable. It is shown how a concept from queuing theory namely first in first out (FIFO) can be profitably used here. Another nonstandard situation considered is one in which lifespan of the individual entity is too long compared to duration of the experiment. This situation is dealt with, by using ancilliary information. In each case the methodology is illustrated with numerical examples.

Adsorption isotherms for neutral organic compounds-A hierarchy in modelling: Part II

A two-state model allowing for size disparity between the solvent and the adsorbate is analysed to derive the adsorption isotherm for electrosorption of organic compounds. Explicity, the organic adsorbate is assumed to occupy "n" lattice sites at the interface as compared to "one" by the solvent. The model parameters are the respective permanent and induced dipole moments apart from the nearest neighbour distance. The coulombic interactions due to permanent and induced dipole moments, discreteness of charge effects, and short-range and specific substrate interactions have all been incorporated. The adsorption isotherm is then derived using mean field approximation (MFA) and is found to be more general than the earlier multi-site versions of Bockris and Swinkels, Mohilner et al., and Bennes, as far as the entropy contributions are concerned. The role of electrostatic forces is explicity reflected in the adsorption isotherm via the Gibbs energy of adsorption term which itself is a quadratic function of the electrode charge-density. The approximation implicit in the adsorption isotherm of Mohilner et al. or Bennes is indicated briefly.

A unified approach to the gauging of space-time and internal symmetries

The properties of the manifold of a Lie groupG, fibered by the cosets of a sub-groupH, are exploited to obtain a geometrical description of gauge theories in space-timeG/H. Gauge potentials and matter fields are pullbacks of equivariant fields onG. Our concept of a connection is more restricted than that in the similar scheme of Ne'eman and Regge, so that its degrees of freedom are just those of a set of gauge potentials forG, onG/H, with no redundant components. The ldquotranslationalrdquo gauge potentials give rise in a natural way to a nonsingular tetrad onG/H. The underlying groupG to be gauged is the groupG of left translations on the manifoldG and is associated with a ldquotrivialrdquo connection, namely the Maurer-Cartan form. Gauge transformations are all those diffeomorphisms onG that preserve the fiber-bundle structure.

Anisotropic gaussian beams

Anisotropic gaussian beams are obtained as exact solutions to the parabolic wave equation. These beams have a quadratic phase front whose principal radii of curvature are non-degenerate everywhere. It is shown that, for the lowest order beams, there exists a plane normal to the beam axis where the intensity distribution is rotationally symmetric about the beam axis. A possible application of these beams as normal modes of laser cavities with astigmatic mirrors is noted.

Coplanar gas-discharge display

1. The electric field strength between coplanar electrodes is calculated employing "conformal transformations." The electron multiplication factor is then computed in the nonuniform field region. These calculations have been made for different gap lengths, voltages, and also for different gases and gas pressures. The configuration results in a curved discharge path. It is found that the electron multiplication is maximum along a particular flux line and the prebreakdown discharge is expected to follow this flux line. Experimental tubes incorporating several coplanar gaps have been fabricated. Breakdown voltages have been measured for various discharge gaps and also for various gases such as xenon, helium, neon, argon, and neon-argon mixture (99.5:0.5) at different filling pressures. The variation of breakdown voltage with pressure and gap length is discussed. The observed discharge paths are curved and this is in agreement with theoretical results. A few experimental single-digit coplanar gas-discharge displays (CGDD's) with digit height of 5 cm have been fabricated and dependence of their characteristics on various parameters, including spacing between top glass plate and bottom substrate, have been studied.

Fast Iterative Division of p-adic Numbers

A fast iterative scheme based on the Newton method is described for finding the reciprocal of a finite segment p-adic numbers (Hensel code). The rate of generation of the reciprocal digits per step can be made quadratic or higher order by a proper choice of the starting value and the iterating function. The extension of this method to find the inverse transform of the Hensel code of a rational polynomial over a finite field is also indicated.