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Physical Sciences and Mathematics Commons™
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University of Massachusetts Amherst
Mathematics and Statistics Department Faculty Publication Series
- Discipline
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Phase Diagram, Stability And Magnetic Properties Of Nonlinear Excitations In Spinor Bose–Einstein Condensates, G. C. Katsimiga, S. I. Mistakidis, P. Schmelcher, P. G. Kevrekidis
Phase Diagram, Stability And Magnetic Properties Of Nonlinear Excitations In Spinor Bose–Einstein Condensates, G. C. Katsimiga, S. I. Mistakidis, P. Schmelcher, P. G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We present the phase diagram, the underlying stability and magnetic properties as well as the dynamics of nonlinear solitary wave excitations arising in the distinct phases of a harmonically confined spinor F = 1 Bose-Einstein condensate. Particularly, it is found that nonlinear excitations in the form of dark-dark-bright solitons exist in the antiferromagnetic and in the easy-axis phase of a spinor gas, being generally unstable in the former while possessing stability intervals in the latter phase. Dark-bright-bright solitons can be realized in the polar and the easy-plane phases as unstable and stable configurations respectively; the latter phase can also feature …
Generalized Catalan Numbers From Hypergraphs, Paul E. Gunnells
Generalized Catalan Numbers From Hypergraphs, Paul E. Gunnells
Mathematics and Statistics Department Faculty Publication Series
The Catalan numbers Cn ∈ {1,1,2,5,14,42,…} form one of the most venerable sequences in combinatorics. They have many combinatorial interpretations, from counting bracketings of products in non-associative algebra to counting plane trees and noncrossing set partitions. They also arise in the GUE matrix model as the leading coefficient of certain polynomials, a connection closely related to the plane trees and noncrossing set partitions interpretations. In this paper we defi ne a generalization of the Catalan numbers. In fact we defi ne an infinite collection of generalizations Cn(m) , m >= 1, with m = 1 giving the …
Immune Classification Of Osteosarcoma, Trang Le, Sumeyye Su, Leili Shahriyari
Immune Classification Of Osteosarcoma, Trang Le, Sumeyye Su, Leili Shahriyari
Mathematics and Statistics Department Faculty Publication Series
Tumor immune microenvironment has been shown to be important in predicting the tumor progression and the outcome of treatments. This work aims to identify different immune patterns in osteosarcoma and their clinical characteristics. We use the latest and best performing deconvolution method, CIBERSORTx, to obtain the relative abundance of 22 immune cells. Then we cluster patients based on their estimated immune abundance and study the characteristics of these clusters, along with the relationship between immune infiltration and outcome of patients. We find that abundance of CD8 T cells, NK cells and M1 Macrophages have a positive association with prognosis, while …