Miracle-dz/UniFAR-FTUs huggingface dataset:
A Random Effects Transition Model For Longitudinal Binary Data With Informative Missingness

Understanding the transitions between disease states is often the goal in studying chronic disease. These studies, however, are typically subject to a large amount of missingness either due to patient dropout or intermittent missed visits. The missing data is often informative since missingness and dropout are usually related to either an individual's underlying disease process or the actual value of the missed observation. Our motivating example is a study of opiate addiction that examined the effect of a new treatment on thrice‐weekly binary urine tests to assess opiate use over follow‐up. The interest in this opiate addiction clinical trial was to characterize the transition pattern of opiate use (in each treatment arm) as well as to compare both the marginal probability of a positive urine test over follow‐up and the time until the first positive urine test between the treatment arms. We develop a shared random effects model that links together the propensity of transition between states and the probability of either an intermittent missed observation or dropout. This approach allows for heterogeneous transition and missing data patterns between individuals as well as incorporating informative intermittent missing data and dropout. We compare this new approach with other approaches proposed for the analysis of longitudinal binary data with informative missingness.
HETEAC – the Hybrid End-To-End Aerosol Classification model for EarthCARE

Abstract. The Hybrid End-To-End Aerosol Classification (HETEAC) model for the Earth Clouds, Aerosols and Radiation Explorer (EarthCARE) mission is introduced. The model serves as the common baseline for the development, evaluation, and implementation of EarthCARE algorithms. It guarantees the consistency of different aerosol products from the multi-instrument platform and facilitates the conformity of broad-band optical properties needed for EarthCARE radiative-closure assessments. While the hybrid approach ensures that the theoretical description of aerosol microphysical properties is consistent with the optical properties of the measured aerosol types, the end-to-end model permits the uniform representation of aerosol types in terms of microphysical, optical, and radiative properties. Four basic aerosol components with prescribed microphysical properties are used to compose various natural and anthropogenic aerosols of the troposphere. The components contain weakly and strongly absorbing fine-mode and spherical and non-spherical coarse-mode particles and thus are representative for pollution, smoke, sea salt, and dust, respectively. Their microphysical properties are selected such that good coverage of the observational phase space of intensive, i.e., concentration-independent, optical aerosol properties derived from EarthCARE measurements is obtained. Mixing rules to calculate optical and radiative properties of any aerosol blend composed of the four basic components are provided. Applications of HETEAC in the generation of test scenes, the development of retrieval algorithms for stand-alone and synergistic aerosol products from EarthCARE's atmospheric lidar (ATLID) and multi-spectral imager (MSI), and for radiative-closure assessments are introduced. Finally, the implications of simplifying model assumptions and possible improvements are discussed, and conclusions for future validation and development work are drawn.
On the p-rank of the tame kernel of algebraic number fields.

For quadratic number fields F, several authors investigated the divisibility of order of the tarne kernel K2 OF or of corresponding Bernoulli numbers by odd prime numbers p. In particular this divisibility is related to the divisibility by p of the class number of an appropriate quadratic number field. See e.g. papers of Queen [13], Lu [12], Browkin [4], G. Gras [7], Urbanowicz [16], [17], Boldy [1], [2], Gangl [5], Kolster [10], Geijsberts [6]. There are also known general results concerning the p-rank (K2 OF), for number fields F, see Täte [15], Keune [8], [9], Kolster [10], [11].
Modeling of Combined Thermal and Mechanical Action in Concrete

To describe the response of concrete under combined thermal and mechanical action it is necessary to abandon the usual assumption that thermal strain and mechanical strain can be treated as mutually independent, additive components. A generalized model which accounts for the thermomechanical interaction observed in tests is discussed. The basic feature of the formulation is that the thermal strain rate is considered to be a function of both rate of temperature change and the current state of stress. The problems dealt with in the paper are of great practical interest in the design of concrete structures exposed to severe thermal loading.
Velocity shear and fluctuations in the auroral regions of the ionosphere

The theory of collisional electrostatic modes that are driven unstable by a sheared field-aligned ion flow velocity (i.e., Vi0 = V0(x)ez, B0 = B0ez) is presented. The instability threshold condition is |dV0/dx| > 2(1 + Ti/Te)νin, where νin is the ion-neutral collision frequency, the characteristic longitudinal wavelengths λ∥ > λe, λe being the electron collision mean free path, and the transverse wavelengths λ⊥ > 21/2πρi, ρi being the ion gyroradius. The linearly unstable modes can account for fluctuations with transverse wavelengths ranging from a kilometer to several meters for only a moderate amount of shear (in the parallel velocity). Thus the instability provides a direct means of exciting almost the entire range of the observed (Basu et al., 1988) subkilometer scale irregularities in the auroral F region. The quasi-linear analysis presented here shows that an effective viscosity describing momentum transport in the x direction can be derived in the presence of the shear-driven fluctuations. The spatial profiles of the excited modes are evaluated from the solution of the appropriate dispersion equation. A model is proposed to describe the nonlinear evolution of the instability while ensuring that the characteristics of the turbulent fluctuation spectra resulting from it are consistent with those of the observed spectra.
Numerical prediction of isothermally reacting mixing layer using vortex‐in‐cell and filtered density function

A large eddy simulation based on the filtered vorticity transport equation and the filtered density function (FDF) transport equation developed in an earlier study is extended to predict a chemically reacting flow with no heat release. The filtered vorticity transport equation is solved using the vortex‐in‐cell scheme in conjunction with the dynamic eddy viscosity subgrid‐scale models. The transport equation for FDF is solved using the Lagrangian Monte‐Carlo method. The methodology is tested on a chemically reacting spatially growing mixing layer with no heat release. The effects of Damköhler number (Da) on the concentration structure of the reacting mixing layer, the mean reactant and product concentrations and on the reactant FDF are investigated. It is shown that mixing has a greater effect on scalar field within the vortex structure as compared with the braid regions. Also for high Da, the reaction zones are mainly limited to the thin reacting interfacial zones, i.e. the contact zone between the reactants, whereas for low Da, the reacting zones are spread as reacting pockets within the vortex structure. The effects of Da on mean reactant and product concentrations, root‐mean‐square concentration fluctuations and probability density are discussed. Copyright © 2010 John Wiley & Sons, Ltd.
Note on linear forms

where the ai are fixed positive integers with gcd = 1 and the xi are non-negative integers. In particular the question of finding the smallest n for which all greater integers have a solution has been investigated to some extent [1; 2]. It seems that the solution for s = 1 has been known for some time but that the problem in general remains unsolved for s> 1. In the paper of A. Brauer cited in the bibliography various upper bounds for the smallest n are given and the actual value of the smallest n is determined for the ai consecutive integers. The main result of this paper is the determination of this smallest n when the ai are in arithmetical progression. 2. Our investigation then is with the linear form
Energy spectrum of electrons trapped in the geomagnetic field

Abstract : A Fokker-Planck equation for the distribution function of electrons trapped in a magnetic field in the presence of a scattering atmosphere is applied to the Van Allen electron belt. Solutions are obtained for the equilibrium flux resulting from an electron source of arbitrary energy for the cases where (a) loss of energy by collisions is neglected and (b) loss by diffusion out of the trapping region is neglected; and an approximate solution is obtained for the actual case where both processes are considered. The assumption that the electron source is supplied by decaying neutrons leads to an equilibrium electron flux whose energy dependence is qualitatively different from the observed spectrum. (Author)
Optimization of four-wave mixing conversion efficiency in the presence of nonlinear loss

We analyze the effect of nonlinear loss on four‐wave mixing (FWM) conversion efficiency. Maximum conversion efficiency is geometry independent and equal to e−2|χ(3)/Im{χ(3)}|2 when nonlinear loss dominates. Optimum device length and operating conditions are obtained and theoretical results are verified with a picosecond pulse FWM experiment.
Shape Preserving Constrained data Visualization using Spline Functions

The main spotlight of this paper is the visual display of constrained data that looks smooth, pleasant and attractive. A C1 piecewise rational cubic function has been constructed to preserve the shape of constrained data. The piecewise rational cubic function has three free parameters in its description. One free parameter is constrained to preserve the shape of data that is lying above a line while the other two are left for the user to refine the shape of curve. Further, the piecewise rational cubic function has been extended to rational bi-cubic function to preserve the shape of surface data arranged over a rectangular grid that is lying above a plane. The developed scheme is simple, local and economical as compared to existing schemes. The curve and surface schemes under discussion is C1.
Suppressing stick-slip oscillations in underactuated multibody drill-strings with parametric uncertainties using sliding-mode control

Stabilisation of multibody drill-strings which exhibit stick-slip oscillations is studied in this paper from the point of view of underactuated system. The model has one control torque input acting on the rotary table from the land surface and multi-degree-of-freedom downhole parts to be controlled. Three motion regimes of the model including bit sticking, stick-slip oscillation and rotating at a constant speed are identified and their equilibria are analysed accordingly. The control objective of the system is to avoid the undesired bit sticking and stick-slip oscillation while tracking a desired angular velocity. Three sliding-mode controllers are studied for the drill-string with estimated physical parameters. The stabilities of the proposed controllers are proved by using the Lyapunov direct method ensuring that any trajectory of the system can reach and stays thereafter on the pre-designed sliding surface where the desired equilibrium is asymptotically stable. Extensive simulation results are given to demonstrate the effectiveness of the proposed controllers and their robustness to parametric uncertainties.
Star distribution around a massive black hole in a globular cluster

To predict the likely distribution of stars around a massive black hole in the core of a cluster of stars, an equation of the Fokker-Planck type is derived that describes the diffusion of stars in the 1/r gravitational well of the black hole, by star-star gravitational collisions. The main assumptions are: (1) the distribution of stars is described by a single-particle distribution function that is shperically symmetric in coordinate space and approximately isotropic in velocity space; (2) the stars have equal masses; (3) star mass very-much-less-thanblack-hole massvery-much-less-thancluster-core mass; (4) a star is destroyed by star-star collisions or by tidal forces when its binding energy in the well exceeds a specified large value; (5) binaries are unimportant. Numerical solutions for the time-dependent equations indicate that the equilibrium star density, closely approached within a collision time, approximates an r/sup -7///sup 4/ power law throughout most of the well. The same equilibrium power law obtains for nonisotropic distribution functions whose anisotropy is independent of r. Stars in bound orbits about a black hole diffuse slowly into its gravitational well under equilibrium conditions. A black hole of approximately-less-than10/sup 3/ M/sub sun/ may accrete stars primarily by capture from unbound orbits.Theshape of the star distribution more » near the cluster center observed with small diaphragms is predicted. As a function of diaphragm size, the velocity dispersion and line profile that might be measured spectroscopically is calculated. Some calculations are also presented for an open slit configuration. For globular clusters in our Galaxy, one might be able to detect black holes with masses approximately-greater-than5 x 10/sup 3/ M/sub sun/ and, with a large space telescope, masses approximately-greater-than10/sup 3/ M/sub sun/. An approximate formula for the mean distance of a massive black hole from the center of mass of the unbound stars is also presented. (AIP) « less
Estudo sobre a variabilidade do módulo de deformação do concreto associada a fatores intrínsecos à produção do material.

The modulus of elasticity requirements for concrete structures is becoming even more frequent. So, the knowledge of the variables involved in the experimental results became more important in order to make more reliable its assessment and enabling better conditions for specifications requirements attendance in relation to this property. Several studies have shown that the variability of mechanical properties of construction materials is subjected to random processes. Therefore, the security methods in the structural design must be based in the probability theory concept rather than deterministic methods. The randomness of the, compressive strength of concrete is already take in account in the quality control process according to the Brazilian Standard ABNT NBR 12655 (2006). The present work aims to study the experimental control of static modulus of elasticity of concrete, showing the influence of the constituent materials used in a Concrete Ready Mix Plant. It also intends to present a discussion on the applicability of the semi-probabilistic concept of national design standards in the mix design and production control of concrete in order to attend the elastic modulus requirements. The research methodology had two main steps: the first one, developed at a Concrete Ready Mix Plant located in Sao Paulo City, was based on the assessment of two characteristic compressive strength (fck) of 25 MPa and 30 MPa, which are commonly demanded in this market. For each strength class, tests were done to evaluate the variability of static modulus of elasticity of concrete, Ecs, three times per week, during a period of nine months. On the second step, an analysis of elastic modulos of concretes provided at six different sites, where the characteristic strength was 30 MPa, which was made using the same materials used in the first step. It has been used the clip gage instrumentation for measuring deformation to the assessment of static modulus of elasticity of concrete. It was used due to the precision that has been observed in recent research. The evaluation has been done according to the Brazilian Standard ABNT NBR 8522 (2008). It was possible to conclude that the modulus of elasticity of concrete is influenced by the compressive strength, so it follows a probabilistic distribution and cannot be associated to a deterministic model of quality control, due to the risk of noncompliance of the requirement.
The matrix model of vortex-beam quadrefringence in a uniaxial crystal

We consider a matrix model for the tilted oblique propagation of singular beams in optically uniaxial crystals. The model predicts a series of fine effects such as vortex conversion and beam quadrefringence, being in a good agreement with the paraxial theory. Although the model gives overrated magnitudes of the beam parameters in the asymptotic case it enables us to calculate the processes occurring with high-order vortex beams, where the theory encounters computation difficulties.
Formation and propagation of failure in shocked glasses

Under plane shock wave compression, a glass may undergo elastic deformation at the shock wave front, and fail catastrophically at a later time. Since this time delay increases with the distance into the material, the phenomenon has been interpreted as a failure wave. In this article, a new theory of failure formation and propagation in shocked glasses is presented. Stress concentration due to the defects and transient loading conditions on the impact surface is assumed as the origin for initiating heterogeneous microdamage. The progressive percolation of microfissures into the material bulk gives rise to the failure wave phenomenon. Through the failure process, the deviatoric strain energy in the intact material is converted to the volumetric potential energy in the comminuted and dilated material. The state of material damage is measured in terms of the dilated volume of comminuted material at full release. The failure propagation is governed by coupled nonlinear diffusion and time-dependent evolution of.
A new coupling term for dual‐porosity models

Numerous models are available for simulating dual-porosity flow of groundwater, heat, or solute in a fractured porous medium. Each approach includes various approximations and results in models of varying complexity. One of the simplest models has been proposed by both Barenblatt et al. (1960) and Warren and Root (1963). It assumes that the flow exchange (of fluid, heat, or solute) between the two porosity systems can be written as a linear function of the difference between averaged driving potentials (pressure, temperature, or concentration). This has been called a quasi-static formulation because it can be shown to be correct only for long dimensionless time. A new formulation of this model is proposed here which retains the original simplicity but is not restricted to very slow transient flows. The integral method is used to derive the coupling term for the early parts of the transient regime.
Bayes Hilbert Spaces

A Bayes linear space is a linear space of equivalence classes of proportional σ‐finite measures, including probability measures. Measures are identified with their density functions. Addition is given by Bayes' rule and substraction by Radon–Nikodym derivatives. The present contribution shows the subspace of square‐log‐integrable densities to be a Hilbert space, which can include probability and infinite measures, measures on the whole real line or discrete measures. It extends the ideas from the Hilbert space of densities on a finite support towards Hilbert spaces on general measure spaces. It is also a generalisation of the Euclidean structure of the simplex, the sample space of random compositions. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. A key tool is the centred‐log‐ratio transformation, a generalization of that used in compositional data analysis, which maps the Hilbert space of measures into a subspace of square‐integrable functions. As a consequence of this structure, distances between densities, orthonormal bases, and Fourier series representing measures become available. As an application, Fourier series of normal distributions and distances between them are derived, and an example related to grain size distributions is presented. The geometry of the sample space of random compositions, known as Aitchison geometry of the simplex, is obtained as a particular case of the Hilbert space when the measures have discrete and finite support.
On phase kinks, negative frequencies, and other third-order peculiarities of modulated surface waves

Numerous laboratory and field experiments on nonlinear surface wave trains propagating in deep water (Lake & Yuen 1978; Ramamonjiarisoa & Mollo-Christensen 1979; Mollo-Christensen & Ramamonjiarisoa 1982; Melville 1983) have showed a specific wave modulation that so far has not been explained by nonlinear theories. Typical effects were the so-called wave phase reversals, negative frequencies, and crest pairing, experimentally observed in some portions of the modulated wave train. In the present paper, in order to explain these modulation manifestations, the equations for wavenumber, frequency, and velocity potential amplitude are derived consistently in the third-order approximation related to the wave steepness. The resulting model generalizes, for instance, the well-known nonlinear Schrödinger equation theory, to which it transforms at certain values of the governing parameters. The stationary solutions to the derived set of equations are found in quadrature and then analysed. Within well-defined ranges of the model parameters, these solutions explicitly manifest the above-mentioned wave modulation effects. In particular, they show the wave phase kinks to arise on areas of relatively small free-surface displacement in complete accordance with the experiments. The model with deeply modulated wavenumber and frequency permits one also to analyse the appropriately short surface wavepackets and modulation periods. In this case, a variety of new interesting wave solutions arises revealing complicated alteration of smooth and rough portions of the free surface. Of special importance are solitary waves, naturally generalizing envelope solitons of the nonlinear Schrödinger equation, but having a varying frequency (as a principle of the proposed theory) and a non-zero wave ‘pedestal’ at infinity. These new types of modulated surface waves should be also observable in laboratory tanks and under field conditions, because the relevant free parameters of theory are not extreme.
Convergence of pinching deformations and matings of geometrically finite polynomials

We give a thorough study of Cui’s control of distortion technique in the analysis of convergence of simple pinching deformations, and extend his result from geometrically finite rational maps to some subset of geometrically infinite maps. We then combine this with mating techniques for pairs of polynomials to establish existence and continuity results for matings of polynomials with parabolic points. Consequently, if two hyperbolic quadratic polynomials tend to their respective root polynomials radially, and do not belong to conjugate limbs of the Mandelbrot set, their mating exists and deforms continuously to the mating of the two root polynomials.
BOUNDING SURFACE PLASTICITY, I: MATHEMATICAL FOUNDATION AND HYPOPLASTICITY

The mathematical foundation of the general bounding surface constitutive formulation in plasticity is presented. Along these lines the concept of hypoplasticity is formally introduced, and it is shown that a particular class of hypoplastic formulations arises naturally from certain bounding surface models, with the distinguishing feature being the dependence of the elastoplastic moduli and/or the plastic strain rate direction on the stress rate direction. The general analytical perspective allows the better understanding and improvement of existing bounding surface plasticity and hypoplasticity models, which are briefly discussed, and suggests the proper way to construct new ones for future applications.