Central limit theorems for Poisson hyperplane tessellations

We derive a central limit theorem for the number of vertices of convex polytopes induced by stationary Poisson hyperplane processes in $\mathbb{R}^d$. This result generalizes an earlier one proved by Paroux [Adv. in Appl. Probab. 30 (1998) 640--656] for intersection points of motion-invariant Poisson line processes in $\mathbb{R}^2$. Our proof is based on Hoeffding's decomposition of $U$-statistics which seems to be more efficient and adequate to tackle the higher-dimensional case than the ``method of moments'' used in [Adv. in Appl. Probab. 30 (1998) 640--656] to treat the case $d=2$. Moreover, we extend our central limit theorem in several directions. First we consider $k$-flat processes induced by Poisson hyperplane processes in $\mathbb{R}^d$ for $0\le k\le d-1$. Second we derive (asymptotic) confidence intervals for the intensities of these $k$-flat processes and, third, we prove multivariate central limit theorems for the $d$-dimensional joint vectors of numbers of $k$-flats and their $k$-volumes, respectively, in an increasing spherical region.Comment: Published at http://dx.doi.org/10.1214/105051606000000033 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Limit theorems for functionals on the facets of stationary random tessellations

We observe stationary random tessellations $X=\{\Xi_n\}_{n\ge1}$ in $\mathbb{R}^d$ through a convex sampling window $W$ that expands unboundedly and we determine the total $(k-1)$-volume of those $(k-1)$-dimensional manifold processes which are induced on the $k$-facets of $X$ ($1\le k\le d-1$) by their intersections with the $(d-1)$-facets of independent and identically distributed motion-invariant tessellations $X_n$ generated within each cell $\Xi_n$ of $X$. The cases of $X$ being either a Poisson hyperplane tessellation or a random tessellation with weak dependences are treated separately. In both cases, however, we obtain that all of the total volumes measured in $W$ are approximately normally distributed when $W$ is sufficiently large. Structural formulae for mean values and asymptotic variances are derived and explicit numerical values are given for planar Poisson--Voronoi tessellations (PVTs) and Poisson line tessellations (PLTs).Comment: Published at http://dx.doi.org/10.3150/07-BEJ6131 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Replica Density Functional Study of One-Dimensional Hard Core Fluids in Porous Media

A binary quenched-annealed hard core mixture is considered in one dimension in order to model fluid adsorbates in narrow channels filled with a random matrix. Two different density functional approaches are employed to calculate adsorbate bulk properties and interface structure at matrix surfaces. The first approach uses Percus' functional for the annealed component and an explicit averaging over matrix configurations; this provides numerically exact results for the bulk partition coefficient and for inhomogeneous density profiles. The second approach is based on a quenched-annealed density functional whose results we find to approximate very well those of the former over the full range of possible densities. Furthermore we give a derivation of the underlying replica density functional theory.Comment: 22 pages, 11 figures, to be published in JS

The legal meaning of state custodianship in the context of the Mineral and Petroleum Resources Development Act 28 of 2002

The Mineral and Petroleum Resources Development Act, 2002 introduces a new mineral and petroleum law dispensation in South Africa. The introduction of the new dispensation follows the first democratic election in 1994 that required a reconsideration of the role of the state in the allocation and exploitation of mineral and petroleum resources. The state's right to sovereignty is realised by introducing the principle of state custodianship. Whilst the MPRDA does not define state custodianship, the courts have been hesitant in providing an interpretation. Historically, the majority of South Africans were excluded from the allocation and exploitation of mineral and petroleum resources caused by racial practices. The notion of state custodianship brings substantive changes to the regulation of mineral and petroleum resources. The state as custodian is responsible for regulating the nation's mineral and petroleum resources in accordance with the objectives determined by the MPRDA. As regulator, the state has been allocated increased control over prospecting and mining activities. This increased control must enhance the transformative goals of the new mineral and petroleum law dispensation whilst simultaneously considering the role of mineral and petroleum resources in the economic development of the country. In accordance with its responsibilities imposed in terms of the Constitution, the state must ensure that everyone benefits from mineral and petroleum exploitation. Such responsibilities must be exercised within the Constitutional imperative to avoid or minimize environmental harm The state as custodian owes a fiduciary duty towards the nation in respect of the minerals and petroleum resources. This fiduciary duty exists between the state and its citizens. The state must exercise its duty to the standard required of a fiduciary with regards to the property entrusted to it to regulate. Due to the nature of the concept of custodianship, the state is not the owner of mineral and petroleum resources. Whilst the landowner, and in certain instances the mineral rights holder, before the adoption of the MPRDA determined access to minerals, the state as custodian is now responsible for determining access to minerals. The joint interests of the South African nation as a whole is to be promoted by the state in its role as custodian. The public interest of access to and use of the mineral and petroleum resources determined by the MPRDA, and the Constitution must be safeguarded. The implementation of the object of equitable access to minerals is dependent on the state as custodian. The transformative role of the state is enhanced by the shifting of the basis of mineral law to public law. The administering of a state controlled mineral law system has led to the responsibilities of state custodianship having to be exercised within a public law environment. The interpretation of the state's duties as custodian is dependent on various considerations, some of them being the provisions of the MPRDA, the application of the principles of administrative law and the fiduciary nature of state custodianship

Density functional theory for colloidal mixtures of hard platelets, rods, and spheres

A geometry-based density functional theory is presented for mixtures of hard spheres, hard needles and hard platelets; both the needles and the platelets are taken to be of vanishing thickness. Geometrical weight functions that are characteristic for each species are given and it is shown how convolutions of pairs of weight functions recover each Mayer bond of the ternary mixture and hence ensure the correct second virial expansion of the excess free energy functional. The case of sphere-platelet overlap relies on the same approximation as does Rosenfeld's functional for strictly two-dimensional hard disks. We explicitly control contributions to the excess free energy that are of third order in density. Analytic expressions relevant for the application of the theory to states with planar translational and cylindrical rotational symmetry, e.g. to describe behavior at planar smooth walls, are given. For binary sphere-platelet mixtures, in the appropriate limit of small platelet densities, the theory differs from that used in a recent treatment [L. Harnau and S. Dietrich, Phys. Rev. E 71, 011504 (2004)]. As a test case of our approach we consider the isotropic-nematic bulk transition of pure hard platelets, which we find to be weakly first order, with values for the coexistence densities and the nematic order parameter that compare well with simulation results.Comment: 39 pages, 8 figure

Comorbidities of patients in tiotropium clinical trials : comparison with observational studies of patients with chronic obstructive pulmonary disease

Acknowledgments The authors are fully responsible for all content and editorial decisions made, were involved at all stages of manuscript development, and have approved the final version for publication. Editorial assistance, supported financially by Boehringer Ingelheim and Pfizer, was provided by Godfrey Lisk of PAREXEL International during the preparation of this manuscript. This work is published by Dove Medical Press Limited, and licensed under Creative Commons Attribution - Non Commercial (unported, v3.0) License. The full terms of the License are available at http://creativecommons.org/licenses/by-nc/3.0/. Non-commercial uses of the work are permitted without any further permission from Dove Medical Press Limited, provided the work is properly attributed. Permissions beyond the scope of the License are administered by Dove Medical Press Limited.Peer reviewedPublisher PD

A new comparative approach to macroeconomic modeling and policy analysis

In the aftermath of the global financial crisis, the state of macroeconomic modeling and the use of macroeconomic models in policy analysis has come under heavy criticism. Macroeconomists in academia and policy institutions have been blamed for relying too much on a particular class of macroeconomic models. This paper proposes a comparative approach to macroeconomic policy analysis that is open to competing modeling paradigms. Macroeconomic model comparison projects have helped produce some very influential insights such as the Taylor rule. However, they have been infrequent and costly, because they require the input of many teams of researchers and multiple meetings to obtain a limited set of comparative findings. This paper provides a new approach that enables individual researchers to conduct model comparisons easily, frequently, at low cost and on a large scale. Using this approach a model archive is built that includes many well-known empirically estimated models that may be used for quantitative analysis of monetary and fiscal stabilization policies. A computational platform is created that allows straightforward comparisons of models’ implications. Its application is illustrated by comparing different monetary and fiscal policies across selected models. Researchers can easily include new models in the data base and compare the effects of novel extensions to established benchmarks thereby fostering a comparative instead of insular approach to model development