Parameterized monogamy and polygamy relations of multipartite entanglement

Monogamy and polygamy relations are important properties of entanglement,which characterize the entanglement distribution of multipartite systems.We explore monogamy and polygamy relations of entanglement in multipartite systems by using two newly derived parameterized mathematical inequalities,and establish classes of parameterized monogamy and polygamy relations of multiqubit entanglement in terms of concurrence and entanglement of formation.We show that these new parameterized monogamy and poelygamy inequalities are tighter than the existing ones by detailed examples.

Cystatin C and serum creatinine in estimating acute kidney injury of shock patients

BACKGROUND： Serum creatinine （SCr） is the most commonly used parameter to estimate renal function impairement, but there are some shortcomings. Many factors including age, gender, drug, diet, muscle mass and metabolic rate can in？ uence SCr, leading to an inaccurate estimation of kidney impairment. Studies have shown that cystatin C （CysC） is not affected by factors such as muscle mass, age, gender, diet, in？ ammation or tumor. The present study was undertaken to compare the sensitivity of CysC and SCr in evaluating renal function impairment at early stage of shock.METHODS： Seventy-one patients aged 38.3±21.4 years, who had been treated at the Emergency Medicine Department of the First Affiliated Hospital, Sun Yat-sen University between February 2006 and June 2007, were studied. They were divided into groups A, B, C, and D according to the shock time. Serum sample was drawn from each patient at 1, 2, 3, 4 hours after shock to determine SCr and CysC. CysC and SCr were determined again at 72 hours and 7 days after shock.RESULTS： CysC increased earlier than SCr in the 71 patients, and CysC decreased slower than SCr when shock was corrected. CysC increased at 1 hour after shock. There was a negative correlationship between CysC, SCr and glomerular filtration rate （GFR）, especially at early stage of shock.CONCLUSIONS： There is renal injury at early stage of shock. CysC is more sensitive than SCr in assessing renal function at the early stage of shock.

Ultrasound-guided microwave ablation as a palliative treatment for mycosis fungoides eyelid involvement:A case report

BACKGROUND Mycosis fungoides(MF)is a form of lymphoma derived from heterogeneous T cells,and eyelid involvement is extremely rare.The common methods to treat eyelid involvement are radiotherapy and chemotherapy,but their efficacies are limited.Herein,we report a case of advanced-stage MF eyelid involvement,propose ultrasound(US)-guided microwave ablation(MWA)therapy and present a literature review.CASE SUMMARY A male patient was admitted to our hospital in June 2018 and diagnosed with MF via radiological and histopathological examinations.The patient’s condition was not well controlled by various conventional chemotherapies.US-guided MWA was performed to relieve the patient’s symptoms and improve his quality of life,showing satisfactory efficacy.CONCLUSION Eyelid involvement is one of the most troublesome clinical problems for advanced-stage MF patients.This is the first report on the use of US-guided MWA as a palliative therapy for MF eyelid involvement;the treatment successfully relieved the patient’s clinical symptoms and reduced his anxiety behaviours.Our study sheds new light on methods for improving the clinical management of eyelid involvement in MF.

Multigraphic Degree Sequences and Hamiltonian-connected Line Graphs

Let G be a multigraph.Suppose that e=u1v1 and e′=u2v2 are two edges of G.If e≠e′,then G(e,e′)is the graph obtained from G by replacing e=u1v1 with a path u1vev1 and by replacing e′=u2v2 with a path u2ve′v2,where ve,ve′are two new vertices not in V(G).If e=e′,then G(e,e′),also denoted by G(e),is obtained from G by replacing e=u1v1 with a path u1vev1.A graph G is strongly spanning trailable if for any e,e′∈E(G),G(e,e′)has a spanning(ve,ve′)-trail.The design of n processor network with given number of connections from each processor and with a desirable strength of the network can be modelled as a degree sequence realization problem with certain desirable graphical properties.A sequence d=(d1,d2,⋯,dn)is multigraphic if there is a multigraph G with degree sequence d,and such a graph G is called a realization of d.A multigraphic degree sequence d is strongly spanning trailable if d has a realization G which is a strongly spanning trailable graph,and d is line-hamiltonian-connected if d has a realization G such that the line graph of G is hamiltonian-connected.In this paper,we prove that a nonincreasing multigraphic sequence d=(d1,d2)⋯,dn)is strongly spanning trailable if and only if either n=1 and d1=0 or n≥2 and dn≥3.Applying this result,we prove that for a nonincreasing multigraphic sequence d=(d1,d2,⋯,dn),if n≥2 and dn≥3,then d is line-hamiltonian-connected.