Book reviews

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48161/1/267_2005_Article_BF01866106.pd

Asymptotic iteration method for eigenvalue problems

An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y'' = lambda(x) y' + s(x) y is introduced, where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to Schroedinger type problems, including some with highly singular potentials, are presented.Comment: 14 page

Construction of exact solutions to eigenvalue problems by the asymptotic iteration method

We apply the asymptotic iteration method (AIM) [J. Phys. A: Math. Gen. 36, 11807 (2003)] to solve new classes of second-order homogeneous linear differential equation. In particular, solutions are found for a general class of eigenvalue problems which includes Schroedinger problems with Coulomb, harmonic oscillator, or Poeschl-Teller potentials, as well as the special eigenproblems studied recently by Bender et al [J. Phys. A: Math. Gen. 34 9835 (2001)] and generalized in the present paper to higher dimensions.Comment: 10 page

Semiclassical energy formulas for power-law and log potentials in quantum mechanics

We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be represented exactly by the semiclassical expression E_{n\ell}(q) = min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) = ln(r). By writing one power as a smooth transformation of another, and using envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are monotone increasing. Recent refinements to the comparison theorem of QM in which comparison potentials can cross over, allow us to prove for n = 1 that Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q} is monotone decreasing. Thus P(q) cannot increase too slowly. This result yields some sharper estimates for power-potential eigenvlaues at the bottom of each angular-momentum subspace.Comment: 20 pages, 5 figure

Reduction and Emergence in Bose-Einstein Condensates

A closer look at some proposed Gedanken-experiments on BECs promises to shed light on several aspects of reduction and emergence in physics. These include the relations between classical descriptions and different quantum treatments of macroscopic systems, and the emergence of new properties and even new objects as a result of spontaneous symmetry breaking

Nuclear factor I-C overexpression promotes monocytic development and cell survival in acute myeloid leukemia

Nuclear factor I-C (NFIC) belongs to a family of NFI transcription factors that binds to DNA through CAATT-boxes and are involved in cellular differentiation and stem cell maintenance. Here we show NFIC protein is significantly overexpressed in 69% of acute myeloid leukemia patients. Examination of the functional consequences of NFIC overexpression in HSPCs showed that this protein promoted monocytic differentiation. Single-cell RNA sequencing analysis further demonstrated that NFIC overexpressing monocytes had increased expression of growth and survival genes. In contrast, depletion of NFIC through shRNA decreased cell growth, increased cell cycle arrest and apoptosis in AML cell lines and AML patient blasts. Further, in AML cell lines (THP-1), bulk RNA sequencing of NFIC knockdown led to downregulation of genes involved in cell survival and oncogenic signaling pathways including mixed lineage leukemia-1 (MLL-1). Lastly, we show that NFIC knockdown in an ex vivo mouse MLL::AF9 pre-leukemic stem cell model, decreased their growth and colony formation and increased expression of myeloid differentiation markers Gr1 and Mac1. Collectively, our results suggest that NFIC is an important transcription factor in myeloid differentiation as well as AML cell survival and is a potential therapeutic target in AML