Chaotic analysis of Atangana–Baleanu derivative fractional order Willis aneurysm system

A new Willis aneurysm system is proposed, which contains the Atangana-Baleanu(AB) fractional derivative.we obtain the numerical solution of the Atangana–Baleanu fractional Willis aneurysm system(ABWAS) with the AB fractional integral and the predictor–corrector scheme.Moreover, we research the chaotic properties of ABWAS with phase diagrams and Poincare sections.The different values of pulse pressure and system order are used to evaluate and compare their effects on ABWAS.The simulations verify that the changes of pulse pressure and system order are the significant reason for ABWAS'states varying from chaotic to steady.In addition, compared with Caputo fractional WAS(FWAS),ABWAS shows less state that is chaotic.Furthermore, the results of bifurcation diagrams of blood flow damping coefficient and reciprocal heart rate show that the blood flow velocity tends to stabilize with the increase of blood flow damping coefficient or reciprocal heart rate, which is consistent with embolization therapy and drug therapy for clinical treatment of cerebral aneurysms.Finally, in view of the fact that ABWAS in chaotic state increases the possibility of rupture of cerebral aneurysms, a reasonable controller is designed to control ABWAS based on the stability theory.Compared with the control results of FWAS by the same method, the results show that the blood flow velocity in the ABWAS system varies in a smaller range.Therefore, the control effect of ABWAS is better and more stable.The new Willis aneurysm system with Atangana–Baleanu fractional derivative provides new information for the further study on treatment and control of brain aneurysms.

Iterative and accurate determination of small angle X-ray scattering background

X-ray scattering is widely used in material structural characterizations.The weak scattering nature,however,makes it susceptible to background noise and can consequently render the final results unreliable.In this paper,we report an iterative method to determine X-ray scattering background and demonstrate its feasibility by small angle X-ray scattering on gold nanoparticles.This method solely relies on the correct structural modeling of the sample to separate scattering signal from background in data fitting processes,which allows them to be immune from experimental uncertainties.The importance of accurate determination of the scaling factor for background subtraction is also illustrated.

Well-differentiated systemic mastocytosis with KIT K509I mutation and uterus infiltration in an Asian woman with good response to imatinib

To the Editor: We report a 27-year-old woman with a 2-month history of irregular uterine bleeding between periods. Blistering on the head was noted in the patient at the age of 2 months, and she gradually developed red maculopapular lesions over her neck and back during puberty, which were itchy after exposure to physical friction. On admission, physical examination had revealed diffuse faint maculopapular rash mainly on the neck and back [Figure 1]. Pelvic examination showed a smooth red lump (5 cm) on the cervix. No abnormality was detected in the complete blood count. Afterwards, the cervical lump was resected and confirmed to be the infiltration of mature mast cells (MCs) after careful pathological investigation. Additionally, a skin nodule biopsy also indicated mass aggregation of MCs, and a bone marrow (BM) biopsy showed a mass of round MCs with abundant cytoplasmic granules. The MCs accounted for about 22.5% of all cells in the aspirate smears. Flow cytometry immunophenotypic analysis on BM suggested that an aberrant MC population had represented 10% of the total analyzed cells, which was positive for CD117, CD33, and CD9, partially positive for CD2 and CD68, and negative for CD25. Genetic test through exome-wide sequencing for the receptor tyrosine kinase (KIT) gene had revealed K509I mutation.