A new statistic has been developed to quantify the amount of regularity in data. This statistic, ApEn (approximate entropy), appears to have potential application throughout medicine, notably in electrocardiogram and related heart rate data analyses and in the analysis of endocrine hormone release pulsatility. The focus of this article is ApEn. We commence with a simple example of what we are trying to discern. We then discuss exact regularity statistics and practical difficulties of using them in data analysis. The mathematic formula development for ApEn concludes the Solution section. We next discuss the two key input requirements, followed by an account of a pilot study successfully applying ApEn to neonatal heart rate analysis. We conclude with the important topic of ApEn as a relative (not absolute) measure, potential applications, and some caveats about appropriate usage of ApEn. Appendix A provides example ApEn and entropy computations to develop intuition about these measures. Appendix B contains a Fortran program for computing ApEn. This article can be read from at least three viewpoints. The practitioner who wishes to use a "black box" to measure regularity should concentrate on the exact formula, choices for the two input variables, potential applications, and caveats about appropriate usage. The physician who wishes to apply ApEn to heart rate analysis should particularly note the pilot study discussion. The more mathematically inclined reader will benefit from discussions of the relative (comparative) property of ApEn and from Appendix A.

A regularity statistic for medical data analysis

Many of the fundamental questions regarding the solid-state chemistry of boron are still unsolved, more than 200 years after its discovery. Recently, theoretical work on the existence and stability of known and new modifications of the element combined with high-pressure and high-temperature experiments have revealed new aspects. A lot has also happened over the last few years in the field of reactions between boron and main group elements. Binary compounds such as B(6)O, MgB(2), LiB(1-x), Na(3)B(20), and CaB(6) have caused much excitement, but the electron-precise, colorless boride carbides Li(2)B(12)C(2), LiB(13)C(2), and MgB(12)C(2) as well as the graphite analogue BeB(2)C(2) also deserve special attention. Physical properties such as hardness, superconductivity, neutron scattering length, and thermoelectricity have also made boron-rich compounds attractive to materials research and for applications. The greatest challenges to boron chemistry, however, are still the synthesis of monophasic products in macroscopic quantities and in the form of single crystals, the unequivocal identification and determination of crystal structures, and a thorough understanding of their electronic situation. Linked polyhedra are the dominating structural elements of the boron-rich compounds of the main group elements. In many cases, their structures can be derived from those that have been assigned to modifications of the element. Again, even these require a critical revision and discussion.

Boron: elementary challenge for experimenters and theoreticians.

Critical fluctuation of the order parameter in type-ii superconductors.

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Dislocations in solids

This paper addresses both old, but "renovated" methods and new methods for diffraction line-profile analysis. Classical and even extremely simple single-line methods for separating "size" and "strain" broadening effects have merit for characterization of the material im- perfectness, but it is generally very difficult to interpret the data obtained in terms of microstructure parameters as used in materials science. Developments of recent years, focusing on distinct anisotropic line-broadening effects, as due to the type, orientation and distribution of dislocations and minute compositional variation, will be touched upon. The most promising development may be the synthesis of line profiles on the basis of a microstructure model and application of the (kinematical) diffraction theory without any further assumption, which contrasts with the other methods. This approach can in principle be applied in sin- gle-line and multiple-line variants and also in analyses of the whole diffraction pattern. The advantage is the direct evaluation of microstructure parameters as used in materi- als science. The challenge is to develop microstructure models which are flexible enough to be applicable in more than one case ...

The “state of the art” of the diffraction analysis of crystallite size and lattice strain.

Deformation characteristics of rolled zirconium alloys: a study by X-ray diffraction line profile analysis

Core level X-ray photoelectron spectroscopy (XPS) studies have been carried out on polycrystalline MgB 2 pellets over the whole binding energy range with a view to having an idea of the charge state of magnesium (Mg). We observe three distinct peaks in Mg 2p spectra at 49.3 eV (trace), 51.3 eV (major) and 54.0 eV (trace), corresponding to metallic Mg, MgB 2 and MgCO 3 or, divalent Mg species, respectively. Similar trend has been noticed in Mg 2s spectra. The binding energy of Mg in MgB 2 is lower than that corresponding to Mg(2+), indicative of the fact that the charge state of Mg in MgB 2 is less than (2+). Lowering of the formal charge of Mg promotes the σ → π electron transfer in boron (B) giving rise to holes on the top of the σ-band which are involved in coupling with B E 2g phonons for superconductivity. Through this charge transfer, Mg plays a positive role in hole superconductivity. B 1s spectra consist of three peaks corresponding to MgB 2 , boron and B 2 O 3 . There is also evidence of MgO due to surface oxidation as seen from O 1s spectra.

X-ray photoelectron spectroscopy studies of MgB2 for valence state of Mg

The diffraction peaks of Zircaloy-2 and Zr–2.5% Nb alloys at various deformations are found to be asymmetric in nature. In order to characterize the microstructure from these asymmetric peaks of these deformed alloys, X-ray diffraction line profile analysis like Williamson–Hall technique, Variance method based on second- and fourth-order restricted moments and Stephens model based on anisotropic strain distribution have been adopted. The domain size and dislocation density have been evaluated as a function of deformation for both these alloys. These techniques are useful where the dislocation structure is highly inhomogeneous inside the matrix causing asymmetry in the line profile, particularly for deformed polycrystalline materials.

X-ray diffraction studies on asymmetrically broadened peaks of heavily deformed zirconium-based alloys

The Portevin-Le Chatelier (PLC) effect has been investigated by deforming Al–2.5%Mg alloy in the strain rate regime where simultaneously two types (type B and type A) of serrations appear in the stress–strain curve. Our analysis of the time series data suggests that in this strain rate regime the entire PLC dynamics is governed by a single band which changes its character during the deformation.

Character of the deformation bands in the (A + B) regime of the Portevin-Le Chatelier effect in Al–2.5%Mg alloy

We report the fluctuation-induced conductivity of Ca doped Y 1 Ba 2 Ca 3 O 7−δ samples. The analysis has been done with partial substitution of Ca(II) in place of Y(III). The Ca contents are 0.02, 0.05, 0.1 and 0.2. In each case excess conductivity has been analysed and we tried to make a fit with the Aslamazov-Larkin and Lawrence-Doniach equations. It is observed that our data fit well with the 3D AL equation and a cross-over from 2D to 3D has been found in our samples. For the first time we have employed this transition to estimate the Josephson coupling strength in the multiperiodic layered defect superconductor. This interlayer coupling strenght J that controls the transition decreases with increase in Ca content. The variation of the Josephson coupling strength and T c with x have been discussed. The Ginzburg-Landau coherence lengths ξ c (0) for all cases have also been calculated and plotted.

P. Barat

Papers

Deformation characteristics of rolled zirconium alloys: a study by X-ray diffraction line profile analysis

X-ray photoelectron spectroscopy studies of MgB2 for valence state of Mg

X-ray diffraction studies on asymmetrically broadened peaks of heavily deformed zirconium-based alloys

Character of the deformation bands in the (A + B) regime of the Portevin-Le Chatelier effect in Al–2.5%Mg alloy

Fluctuation-induced conductivity of polycrystalline Y1−xCaxBa2Cu3O7−δ superconductors