Jensen-Renyi’s-Tsallis Fuzzy Divergence Information Measure with its Applications

In this paper,we have characterized the sum of two general measures associated with two distributions with discrete random variables.One of these measures is logarithmic,while others contains the power of variables,named as joint representation of Renyi’s-Tsallis divergence measure.Then,we propose a divergence measure based on Jensen-Renyi’s-Tsallis entropy which is known as a Jensen-Renyi’s-Tsallis divergence measure.It is a generalization of J-divergence information measure.One of the silent features of this measure is that we can allot the equal weight to each probability distribution.This makes it specifically reasonable for the study of decision problems,where the weights could be the prior probabilities.Further,the idea has been generalized from probabilistic to fuzzy similarity/dissimilarity measure.Besides the validation of the proposed measure,some of its key properties are also studied.Further,the performance of the proposed measure is contrasted with some existing measures.At last,some illustrative examples are solved in the context of clustering analysis,financial diagnosis and pattern recognition which demonstrate the practicality and adequacy of the proposed measure between two fuzzy sets(FSs).

GEOMETRY ON THE WASSERSTEIN SPACE OVER A COMPACT RIEMANNIAN MANIFOLD

We revisit the intrinsic differential geometry of the Wasserstein space over a Riemannian manifold,due to a series of papers by Otto,Otto-Villani,Lott,Ambrosio-Gigli-Savaré,etc.

Study on direct point spread function measurement of capillary plate collimators with divergent X-ray beams

Purpose The Filed of View(FOV)of eXTP/LAD is limited by lead-glass capillary plate collimators placed in front of the Silicon Drift Detectors(SDDs)for reducing the background contamination caused by the photons of Cosmic X-ray Background(CXB)leaking from outside the FOV.The core quality parameters of lead-glass capillary plate collimators are Open Area Ratio(OAR)and FOV.The performance of lead-glass capillary plate collimators is determined by its design specification such as pore-to-pore misalignment,pore perpendicularity with collimator surface and pore diameter.Since the design specification is the result of a large number of micropores,we use the full width at half maximum(FWHM)and peak value of point spread function(PSF)to characterize the capillary plate collimator performance.In order to quickly evaluate the performances of collimators,we developed a direct PSF measurement method using divergent beams.Methods In this paper,the simulation package of the divergent beamsmeasurement setup is developed based on Geant4.The simulation parameters of scintillator absorption length are corrected by experimental data.We simulate the PSF of collimators with different distribution of pore diameter and misalignment by parallel beams and divergent beams.By comparing the peak value and FWHM of collimators PSF,the feasibility in replacing parallel beams measurement with divergent beams measurement is studied.Results It is verified that the influence of the geometric size of 33μm radius of the micro-focus of X-ray tube can be ignored.The results show that the FWHM of collimators is increased with error root mean square error(RMS)of the distribution of collimators pore diameter and pore inclination angle.The peak value of PSF is mainly influenced by pore non-parallelism of the pores,and it decreases with an increase in pore inclination angle.Comparison of parallel beams PSF and divergent beams PSF shows well consistency of peak value and FWHM of collimator.But,the peak value of the divergent beams PSF is mainly affected by the defects of the pores close to the optical axis and result in difference from the parallel beams results consequently.We have developed capillary plate collimators response function based on the projected area function of a cylindrical pore and the fluorescence broadening of the scintillator and fitted PSF by response function.The capillary plate collimator open area ratio is calculated by using the micropores radius and collimator frame thickness obtained by fitting parameter,and the result is close to the parallel beams PSF.Conclusion The feasibility divergent beams measurement is verified.