Reduced trabecular bone mineral density and cortical thickness accompanied by increased outer bone circumference in metacarpal bone of rheumatoid arthritis patients: a cross-sectional study

Introduction The objective of this study was to assess three-dimensional bone geometry and density at the epiphysis and shaft of the third meta-carpal bone of rheumatoid arthritis (RA) patients in comparison to healthy controls with the novel method of peripheral quantitative computed tomography (pQCT). Methods PQCT scans were performed in 50 female RA patients and 100 healthy female controls at the distal epiphyses and shafts of the third metacarpal bone, the radius and the tibia. Reproducibility was determined by coefficient of varia-tion. Bone densitometric and geometric parameters were compared between the two groups and correlated to disease characteristics. Results Reproducibility of different pQCT parameters was between 0.7% and 2.5%. RA patients had 12% to 19% lower trabecular bone mineral density (BMD) (P ≤ 0.001) at the distal epiphyses of radius, tibia and metacarpal bone. At the shafts of these bones RA patients had 7% to 16% thinner cortices (P ≤ 0.03). Total cross-sectional area (CSA) at the metacarpal bone shaft of pa-tients was larger (between 5% and 7%, P < 0.02), and relative cortical area was reduced by 13%. Erosiveness by Ratingen score correlated negatively with tra-becular and total BMD at the epiphyses and shaft cortical thickness of all measured bones (P < 0.04). Conclusions Reduced trabecular BMD and thinner cortices at peripheral bones, and a greater bone shaft diameter at the metacarpal bone suggest RA spe-cific bone alterations. The proposed pQCT protocol is reliable and allows measuring juxta-articular trabecular BMD and shaft geometry at the metacarpal bone.

Semiparametric Normal Transformation Models for Spatially Correlated Survival Data

There is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiological studies. In this paper, we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data. This class of models assumes that survival outcomes marginally follow a Cox proportional hazard model with unspecified baseline hazard, and their joint distribution is obtained by transforming survival outcomes to normal random variables, whose joint distribution is assumed to be multivariate normal with a spatial correlation structure. A key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields. We study the relationship of the spatial correlation structure of the transformed normal variables and the dependence measures of the original survival times. Direct nonparametric maximum likelihood estimation in such models is practically prohibited due to the high dimensional intractable integration of the likelihood function and the infinite dimensional nuisance baseline hazard parameter. We hence develop a class of spatial semiparametric estimating equations, which conveniently estimate the population-level regression coefficients and the dependence parameters simultaneously. We study the asymptotic properties of the proposed estimators, and show that they are consistent and asymptotically normal. The proposed method is illustrated with an analysis of data from the East Boston Ashma Study and its performance is evaluated using simulations.

Numerical solutions of elliptic inverse problems via the equation error method

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.

Problems in the classical calculus of variations

This dissertation concerns convergence analysis for nonparametric problems in the calculus of variations and sufficient conditions for weak local minimizer of a functional for both nonparametric and parametric problems. Newton's method in infinite-dimensional space is proved to be well-defined and converges quadratically to a weak local minimizer of a functional subject to certain boundary conditions. Sufficient conditions for global converges are proposed and a well-defined algorithm based on those conditions is presented and proved to converge. Finite element discretization is employed to achieve an implementable line-search-based quasi-Newton algorithm and a proof of convergence of the discretization of the algorithm is included. This work also proposes sufficient conditions for weak local minimizer without using the language of conjugate points. The form of new conditions is consistent with the ones in finite-dimensional case. It is believed that the new form of sufficient conditions will lead to simpler approaches to verify an extremal as local minimizer for well-known problems in calculus of variations.

Horizon shells and BMS-like soldering transformations

We revisit the theory of null shells in general relativity, with a particular emphasis on null shells placed at horizons of black holes. We study in detail the considerable freedom that is available in the case that one solders two metrics together across null hypersurfaces (such as Killing horizons) for which the induced metric is invariant under translations along the null generators. In this case the group of soldering transformations turns out to be infinite dimensional, and these solderings create non-trivial horizon shells containing both massless matter and impulsive gravitational wave components. We also rephrase this result in the language of Carrollian symmetry groups. To illustrate this phenomenon we discuss in detail the example of shells on the horizon of the Schwarzschild black hole (with equal interior and exterior mass), uncovering a rich classical structure at the horizon and deriving an explicit expression for the general horizon shell energy-momentum tensor. In the special case of BMS-like soldering supertranslations we find a conserved shell-energy that is strikingly similar to the standard expression for asymptotic BMS supertranslation charges, suggesting a direct relation between the physical properties of these horizon shells and the recently proposed BMS supertranslation hair of a black hole.

Optimal Test for Parameter Instability When the Unstable Process and the Error Distribution are Unknown

This paper proposes asymptotically optimal tests for unstable parameter process under the feasible circumstance that the researcher has little information about the unstable parameter process and the error distribution, and suggests conditions under which the knowledge of those processes does not provide asymptotic power gains. I first derive a test under known error distribution, which is asymptotically equivalent to LR tests for correctly identified unstable parameter processes under suitable conditions. The conditions are weak enough to cover a wide range of unstable processes such as various types of structural breaks and time varying parameter processes. The test is then extended to semiparametric models in which the underlying distribution in unknown but treated as unknown infinite dimensional nuisance parameter. The semiparametric test is adaptive in the sense that its asymptotic power function is equivalent to the power envelope under known error distribution.

On the Closure of the Tame Automorphism Group of Affine Three-Space

We provide explicit families of tame automorphisms of the complex affine three-space which degenerate to wild automorphisms. This shows that the tame subgroup of the group of polynomial automorphisms of C3 is not closed, when the latter is seen as an infinite-dimensional algebraic group.

Modeling of the Division Point of Different Propagation Mechanisms in the Near-Region Within Arched Tunnels

An accurate characterization of the near-region propagation of radio waves inside tunnels is of practical importance for the design and planning of advanced communication systems. However, there has been no consensus yet on the propagation mechanism in this region. Some authors claim that the propagation mechanism follows the free space model, others intend to interpret it by the multi-mode waveguide model. This paper clarifies the situation in the near-region of arched tunnels by analytical modeling of the division point between the two propagation mechanisms. The procedure is based on the combination of the propagation theory and the three-dimensional solid geometry. Three groups of measurements are employed to verify the model in different tunnels at different frequencies. Furthermore, simplified models for the division point in five specific application situations are derived to facilitate the use of the model. The results in this paper could help to deepen the insight into the propagation mechanism within tunnel environments.

Propagation Mechanism Analysis Before the Break Point Inside Tunnels

There is no unanimous consensus yet on the propagation mechanism before the break point inside tunnels. Some deem that the propagation mechanism follows the free space model, others argue that it should be described by the multimode waveguide model. Firstly, this paper analyzes the propagation loss in two mechanisms. Then, by conjunctively using the propagation theory and the three-dimensional solid geometry, a generic analytical model for the boundary between the free space mechanism and the multi-mode waveguide mechanism inside tunnels has been presented. Three measurement campaigns validate the model in different tunnels at different frequencies. Furthermore, the condition of the validity of the free space model used in tunnel environment has been discussed in some specific situations. Finally, through mathematical derivation, the seemingly conflicting viewpoints on the free space mechanism and the multi-mode waveguide mechanism have been unified in some specific situations by the presented generic model. The results in this paper can be helpful to gain deeper insight and better understanding of the propagation mechanism inside tunnels

Propagation mechanism modelling in the near region of circular tunnels

Artículo sobre comunicaciones ferroviarias. Abstract: Along with the increase in operating frequencies in advanced radio communication systems utilised inside tunnels, the location of the break point is further and further away from the transmitter. This means that the near region lengthens considerably and even occupies the whole propagation cell or the entire length of some short tunnels. To begin with, this study analyses the propagation loss resulting from the free-space mechanism and the multi-mode waveguide mechanism in the near region of circular tunnels, respectively. Then, by conjunctive employing the propagation theory and the three-dimensional solid geometry, a general analytical model of the dividing point between two propagation mechanisms is presented for the first time. Moreover, the model is validated by a wide range of measurement campaigns in different tunnels at different frequencies. Finally, discussions on the simplified formulae of the dividing point in some application situations are made. The results in this study can be helpful to grasp the essence of the propagation mechanism inside tunnels.

Propagation Mechanism modeling in the Near-Region of Arbitrary Cross-Sectional Tunnels.

Along with the increase of the use of working frequencies in advanced radio communication systems, the near-region inside tunnels lengthens considerably and even occupies the whole propagation cell or the entire length of some short tunnels. This paper analytically models the propagation mechanisms and their dividing point in the near-region of arbitrary cross-sectional tunnels for the first time. To begin with, the propagation losses owing to the free space mechanism and the multimode waveguide mechanism are modeled, respectively. Then, by conjunctively employing the propagation theory and the three-dimensional solid geometry, the paper presents a general model for the dividing point between two propagation mechanisms. It is worthy to mention that this model can be applied in arbitrary cross-sectional tunnels. Furthermore, the general dividing point model is specified in rectangular, circular, and arched tunnels, respectively. Five groups of measurements are used to justify the model in different tunnels at different frequencies. Finally, in order to facilitate the use of the model, simplified analytical solutions for the dividing point in five specific application situations are derived. The results in this paper could help deepen the insight into the propagation mechanisms in tunnels.

Vector spaces of entire functions of unbounded type

Let E be an infinite dimensional complex Banach space. We prove the existence of an infinitely generated algebra, an infinite dimensional closed subspace and a dense subspace of entire functions on E whose non-zero elements are functions of unbounded type. We also show that the τδ topology on the space of all holomorphic functions cannot be obtained as a countable inductive limit of Fr´echet spaces. RESUMEN. Sea E un espacio de Banach complejo de dimensión infinita y sea H(E) el espacio de funciones holomorfas definidas en E. En el artículo se demuestra la existencia de un álgebra infinitamente generada en H(E), un subespacio vectorial en H(E) cerrado de dimensión infinita y un subespacio denso en H(E) cuyos elementos no nulos son funciones de tipo no acotado. También se demuestra que el espacio de funciones holomorfas con la topología ? no es un límite inductivo numberable de espacios de Fréchet.

On real analytic functions of unbounded type

In this paper we prove several results on the existence of analytic functions on an infinite dimensional real Banach space which are bounded on some given collection of open sets and unbounded on others. In addition, we also obtain results on the density of some subsets of the space of all analytic functions for natural locally convex topologies on this space. RESUMEN. Los autores demuestran varios resultados de existencia de funciones analíticas en espacios de Banach reales de dimensión infinita que están acotadas en un colección de subconjuntos abiertos y no acotadas en los conjuntos de otra colección. Además, se demuestra la densidad de ciertos subconjuntos de funciones analíticas para varias topologías localmente convexas.

A characterization of conserved quantities in non-equilibrium thermodynamics

The well-known Noether theorem in Lagrangian and Hamiltonian mechanics associates symmetries in the evolution equations of a mechanical system with conserved quantities. In this work, we extend this classical idea to problems of non-equilibrium thermodynamics formulated within the GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling) framework. The geometric meaning of symmetry is reviewed in this formal setting and then utilized to identify possible conserved quantities and the conditions that guarantee their strict conservation. Examples are provided that demonstrate the validity of the proposed definition in the context of finite and infinite dimensional thermoelastic problems.