[en] In the present work, we show how the generalized Cramér–Rao inequality for the estimation of a parameter, presented in a recent paper, can be extended to the multidimensional case with general norms on Rⁿ, and to a wider context. As a particular case, we obtain a new multidimensional Cramér–Rao inequality which is saturated by generalized q-Gaussian distributions. We also give another related Cramér–Rao inequality, for a general norm, which is saturated as well by these distributions. Finally, we derive uncertainty relations from these Cramér–Rao inequalities. These uncertainty relations involve moments computed with respect to escort distributions, and we show that some of these relations are saturated by generalized q-Gaussian distributions. These results introduce extended versions of Fisher information, new Cramér–Rao inequalities, and new characterizations of generalized q-Gaussian distributions which are important in several areas of physics and mathematics. (paper)

[en] The level spacing distribution of general, non-normal, Gaussian random 2D matrices is derived. In particular, tridiagonal matrices have no level repulsion and show a halfsided Gaussian distribution. General non-normal matrices show strong level repulsion. The repulsion exponent is 2 - 0_log

No abstract available

[en] This paper was first motivated by the following question: 'A pair of twins, R and S, each gives the same hard push on a block. R's block is on a rougher floor than S's. Who does more work?' It is shown that S will do more work on his block if there is no constraint on the distance over which the force is applied. On the other hand, if the assumption is relaxed to 'the same hard push within some distance', say due to the length of their arms, then it is possible that R does more work than S. To resolve this issue, general formulae for the velocity, displacement and work done are obtained for a Gaussian impulsive force acting on a body moving on a horizontal surface.

No abstract available

[en] Based on the partial-coherence theory and the method of the window function being expanded into a finite sum of complex-valued Gaussian functions, the analytic expressions for second-order moments of general truncated beams propagating through atmospheric turbulence are derived, from which some important characteristic parameters, such as the mean-squared beam width, the angular spread, the beam propagation factor (i.e. M²-factor), the Rayleigh range and the effective radius of curvature are also derived. It is shown that general truncated beams may have the same directionality as a fully coherent Gaussian beam if a certain condition is satisfied. Taking a truncated sinh-Gaussian beam as an example of general truncated beams, some numerical calculations are performed to illustrate the general results obtained in this paper. The analytic results obtained in this paper are general and very useful in studying the propagation property and the beam quality of laser beams. (paper)

[en] A small-angle neutron scattering study of a series of star-branched polyethylenes has been undertaken. The samples were in the molten state, and the aim was to study the effects of branching on the conformation of the molecules. Results are presented showing the high quality of the fits of the experimental data to the scattering curve predicted by the Gaussian model. The relationship between the radius of gyration obtained from these fits and the degree of branching and molecular mass is discussed in terms of possible theoretical models. (author) 5 refs., 3 figs

[en] We study the framework of Bayesian statistics for analyzing the capabilities and results of future experiments looking to solve the issue of the neutrino mass ordering. Starting from the general scenario, we then give examples of the procedure for experiments with Gaussian and non-Gaussian distributions for the indicator. We describe in detail what can and cannot be said about the neutrino mass ordering and a future experiment’s capabilities to determine it. Finally, we briefly comment on the application to other binary measurements, such as the determination of the octant of θ_2_3

[en] In computer-aided detection or diagnosis of clustered microcalcifications (MCs) in mammograms, the performance often suffers from not only the presence of false positives (FPs) among the detected individual MCs but also large variability in detection accuracy among different cases. To address this issue, we investigate a locally adaptive decision scheme in MC detection by exploiting the noise characteristics in a lesion area. Instead of developing a new MC detector, we propose a decision scheme on how to best decide whether a detected object is an MC or not in the detector output. We formulate the individual MCs as statistical outliers compared to the many noisy detections in a lesion area so as to account for the local image characteristics. To identify the MCs, we first consider a parametric method for outlier detection, the Mahalanobis distance detector, which is based on a multi-dimensional Gaussian distribution on the noisy detections. We also consider a non-parametric method which is based on a stochastic neighbor graph model of the detected objects. We demonstrated the proposed decision approach with two existing MC detectors on a set of 188 full-field digital mammograms (95 cases). The results, evaluated using free response operating characteristic (FROC) analysis, showed a significant improvement in detection accuracy by the proposed outlier decision approach over traditional thresholding (the partial area under the FROC curve increased from 3.95 to 4.25, p-value  <10⁻⁴). There was also a reduction in case-to-case variability in detected FPs at a given sensitivity level. The proposed adaptive decision approach could not only reduce the number of FPs in detected MCs but also improve case-to-case consistency in detection. (paper)

[en] We report a theoretical study on the possibility of preparing different types of momentum state distributions by two successive resonant Kapitza – Dirac diffractions. It is shown that tableshaped and Gaussian distributions can be obtained as well as the initial single-momentum state can be almost completely reconstructed by the end of the second phase of scattering. We outline the interferometric purposes for which these distributions can be promising. The advantage of the method proposed is the weak dependence of the scattering patterns of interest on such parameters of the system as the field intensity and interaction time. (atom interferometry)